From 9be757e2cad72d8bc8ed285968a892ce125a33b6 Mon Sep 17 00:00:00 2001
From: Allen Goodman <allen.goodman@icloud.com>
Date: Mon, 17 Jun 2024 14:14:11 -0400
Subject: [PATCH] polynomial operators

---
 docs/index.md                                 | 257 +++++++++-
 docs/stylesheets/extra.css                    |   0
 mkdocs.yml                                    |  13 +-
 pyproject.toml                                |   2 +
 src/beignet/__init__.py                       | 466 ++++++++++++++++++
 src/beignet/_add_chebyshev_polynomial.py      |  55 +++
 src/beignet/_add_laguerre_polynomial.py       |  55 +++
 src/beignet/_add_legendre_polynomial.py       |  55 +++
 .../_add_physicists_hermite_polynomial.py     |  55 +++
 src/beignet/_add_polynomial.py                |  55 +++
 .../_add_probabilists_hermite_polynomial.py   |  55 +++
 src/beignet/_chebyshev_extrema.py             |  11 +
 src/beignet/_chebyshev_gauss_quadrature.py    |  16 +
 src/beignet/_chebyshev_interpolation.py       |  45 ++
 .../_chebyshev_polynomial_companion.py        |  47 ++
 src/beignet/_chebyshev_polynomial_domain.py   |   3 +
 .../_chebyshev_polynomial_from_roots.py       |  86 ++++
 src/beignet/_chebyshev_polynomial_one.py      |   3 +
 src/beignet/_chebyshev_polynomial_power.py    |  55 +++
 src/beignet/_chebyshev_polynomial_roots.py    |  25 +
 .../_chebyshev_polynomial_to_polynomial.py    |  36 ++
 .../_chebyshev_polynomial_vandermonde.py      |  28 ++
 .../_chebyshev_polynomial_vandermonde_2d.py   |  49 ++
 .../_chebyshev_polynomial_vandermonde_3d.py   |  51 ++
 src/beignet/_chebyshev_polynomial_weight.py   |   6 +
 src/beignet/_chebyshev_polynomial_x.py        |   3 +
 src/beignet/_chebyshev_polynomial_zero.py     |   3 +
 src/beignet/_chebyshev_zeros.py               |  11 +
 .../_differentiate_chebyshev_polynomial.py    |  64 +++
 .../_differentiate_laguerre_polynomial.py     |  78 +++
 .../_differentiate_legendre_polynomial.py     |  81 +++
 ...erentiate_physicists_hermite_polynomial.py |  60 +++
 src/beignet/_differentiate_polynomial.py      |  55 +++
 ...entiate_probabilists_hermite_polynomial.py |  60 +++
 src/beignet/_divide_chebyshev_polynomial.py   | 149 ++++++
 src/beignet/_divide_laguerre_polynomial.py    | 149 ++++++
 src/beignet/_divide_legendre_polynomial.py    | 149 ++++++
 .../_divide_physicists_hermite_polynomial.py  | 151 ++++++
 src/beignet/_divide_polynomial.py             | 149 ++++++
 ..._divide_probabilists_hermite_polynomial.py | 151 ++++++
 src/beignet/_evaluate_chebyshev_polynomial.py |  35 ++
 .../_evaluate_chebyshev_polynomial_2d.py      |  36 ++
 .../_evaluate_chebyshev_polynomial_3d.py      |  37 ++
 ...luate_chebyshev_polynomial_cartesian_2d.py |  13 +
 ...luate_chebyshev_polynomial_cartesian_3d.py |  14 +
 src/beignet/_evaluate_laguerre_polynomial.py  |  38 ++
 .../_evaluate_laguerre_polynomial_2d.py       |  36 ++
 .../_evaluate_laguerre_polynomial_3d.py       |  37 ++
 ...aluate_laguerre_polynomial_cartesian_2d.py |  13 +
 ...aluate_laguerre_polynomial_cartesian_3d.py |  14 +
 src/beignet/_evaluate_legendre_polynomial.py  |  40 ++
 .../_evaluate_legendre_polynomial_2d.py       |  36 ++
 .../_evaluate_legendre_polynomial_3d.py       |  37 ++
 ...aluate_legendre_polynomial_cartesian_2d.py |  13 +
 ...aluate_legendre_polynomial_cartesian_3d.py |  14 +
 ..._evaluate_physicists_hermite_polynomial.py |  40 ++
 ...aluate_physicists_hermite_polynomial_2d.py |  38 ++
 ...aluate_physicists_hermite_polynomial_3d.py |  39 ++
 ...sicists_hermite_polynomial_cartesian_2d.py |  19 +
 ...sicists_hermite_polynomial_cartesian_3d.py |  16 +
 src/beignet/_evaluate_polynomial.py           |  34 ++
 src/beignet/_evaluate_polynomial_2d.py        |  45 ++
 src/beignet/_evaluate_polynomial_3d.py        |  52 ++
 .../_evaluate_polynomial_cartesian_2d.py      |  25 +
 .../_evaluate_polynomial_cartesian_3d.py      |  30 ++
 .../_evaluate_polynomial_from_roots.py        |  21 +
 ...valuate_probabilists_hermite_polynomial.py |  40 ++
 ...uate_probabilists_hermite_polynomial_2d.py |  38 ++
 ...uate_probabilists_hermite_polynomial_3d.py |  39 ++
 ...ilists_hermite_polynomial_cartersian_2d.py |  15 +
 ...ilists_hermite_polynomial_cartersian_3d.py |  16 +
 src/beignet/_fit_chebyshev_polynomial.py      |  84 ++++
 src/beignet/_fit_laguerre_polynomial.py       |  83 ++++
 src/beignet/_fit_legendre_polynomial.py       |  83 ++++
 .../_fit_physicists_hermite_polynomial.py     |  85 ++++
 src/beignet/_fit_polynomial.py                | 109 ++++
 .../_fit_probabilists_hermite_polynomial.py   |  85 ++++
 src/beignet/_gauss_laguerre_quadrature.py     |  30 ++
 src/beignet/_gauss_legendre_quadrature.py     |  38 ++
 ...hysicists_hermite_polynomial_quadrature.py | 102 ++++
 ...babilists_hermite_polynomial_quadrature.py |  98 ++++
 .../_integrate_chebyshev_polynomial.py        |  73 +++
 src/beignet/_integrate_laguerre_polynomial.py |  60 +++
 src/beignet/_integrate_legendre_polynomial.py |  65 +++
 ...integrate_physicists_hermite_polynomial.py |  63 +++
 src/beignet/_integrate_polynomial.py          | 103 ++++
 ...tegrate_probabilists_hermite_polynomial.py |  63 +++
 src/beignet/_laguerre_polynomial_companion.py |  28 ++
 src/beignet/_laguerre_polynomial_domain.py    |   3 +
 .../_laguerre_polynomial_from_roots.py        |  85 ++++
 src/beignet/_laguerre_polynomial_one.py       |   3 +
 src/beignet/_laguerre_polynomial_power.py     |  61 +++
 src/beignet/_laguerre_polynomial_roots.py     |  25 +
 .../_laguerre_polynomial_to_polynomial.py     |  55 +++
 .../_laguerre_polynomial_vandermonde.py       |  30 ++
 .../_laguerre_polynomial_vandermonde_2d.py    |  49 ++
 .../_laguerre_polynomial_vandermonde_3d.py    |  51 ++
 src/beignet/_laguerre_polynomial_weight.py    |   6 +
 src/beignet/_laguerre_polynomial_x.py         |   3 +
 src/beignet/_laguerre_polynomial_zero.py      |   3 +
 src/beignet/_legendre_polynomial_companion.py |  32 ++
 src/beignet/_legendre_polynomial_domain.py    |   3 +
 .../_legendre_polynomial_from_roots.py        |  85 ++++
 src/beignet/_legendre_polynomial_one.py       |   3 +
 src/beignet/_legendre_polynomial_power.py     |  61 +++
 src/beignet/_legendre_polynomial_roots.py     |  25 +
 .../_legendre_polynomial_to_polynomial.py     |  47 ++
 .../_legendre_polynomial_vandermonde.py       |  30 ++
 .../_legendre_polynomial_vandermonde_2d.py    |  49 ++
 .../_legendre_polynomial_vandermonde_3d.py    |  51 ++
 src/beignet/_legendre_polynomial_weight.py    |   6 +
 src/beignet/_legendre_polynomial_x.py         |   3 +
 src/beignet/_legendre_polynomial_zero.py      |   3 +
 src/beignet/_linear_chebyshev_polynomial.py   |   6 +
 src/beignet/_linear_laguerre_polynomial.py    |   6 +
 src/beignet/_linear_legendre_polynomial.py    |   6 +
 .../_linear_physicists_hermite_polynomial.py  |   6 +
 src/beignet/_linear_polynomial.py             |   6 +
 ..._linear_probabilists_hermite_polynomial.py |   6 +
 src/beignet/_multiply_chebyshev_polynomial.py |  60 +++
 .../_multiply_chebyshev_polynomial_by_x.py    |  25 +
 src/beignet/_multiply_laguerre_polynomial.py  |  82 +++
 .../_multiply_laguerre_polynomial_by_x.py     |  29 ++
 src/beignet/_multiply_legendre_polynomial.py  |  80 +++
 .../_multiply_legendre_polynomial_by_x.py     |  24 +
 ..._multiply_physicists_hermite_polynomial.py |  85 ++++
 ...iply_physicists_hermite_polynomial_by_x.py |  25 +
 src/beignet/_multiply_polynomial.py           |  42 ++
 src/beignet/_multiply_polynomial_by_x.py      |  34 ++
 ...ultiply_probabilists_hermite_polynomial.py |  84 ++++
 ...ly_probabilists_hermite_polynomial_by_x.py |  25 +
 ...physicists_hermite_polynomial_companion.py |  40 ++
 .../_physicists_hermite_polynomial_domain.py  |   3 +
 ...hysicists_hermite_polynomial_from_roots.py |  87 ++++
 .../_physicists_hermite_polynomial_one.py     |   3 +
 .../_physicists_hermite_polynomial_power.py   |  65 +++
 .../_physicists_hermite_polynomial_roots.py   |  27 +
 ...icists_hermite_polynomial_to_polynomial.py |  45 ++
 ...ysicists_hermite_polynomial_vandermonde.py |  25 +
 ...cists_hermite_polynomial_vandermonde_2d.py |  51 ++
 ...cists_hermite_polynomial_vandermonde_3d.py |  53 ++
 .../_physicists_hermite_polynomial_weight.py  |   6 +
 .../_physicists_hermite_polynomial_x.py       |   3 +
 .../_physicists_hermite_polynomial_zero.py    |   3 +
 src/beignet/_polynomial_companion.py          |  35 ++
 src/beignet/_polynomial_domain.py             |   3 +
 src/beignet/_polynomial_from_roots.py         |  97 ++++
 src/beignet/_polynomial_one.py                |   3 +
 src/beignet/_polynomial_power.py              |  76 +++
 src/beignet/_polynomial_roots.py              |  48 ++
 .../_polynomial_to_chebyshev_polynomial.py    |  18 +
 .../_polynomial_to_laguerre_polynomial.py     |  18 +
 .../_polynomial_to_legendre_polynomial.py     |  18 +
 ...nomial_to_physicists_hermite_polynomial.py |  22 +
 ...mial_to_probabilists_hermite_polynomial.py |  22 +
 src/beignet/_polynomial_vandermonde.py        |  33 ++
 src/beignet/_polynomial_vandermonde_2d.py     |  58 +++
 src/beignet/_polynomial_vandermonde_3d.py     |  63 +++
 src/beignet/_polynomial_x.py                  |   3 +
 src/beignet/_polynomial_zero.py               |   3 +
 ...obabilists_hermite_polynomial_companion.py |  39 ++
 ..._probabilists_hermite_polynomial_domain.py |   3 +
 ...babilists_hermite_polynomial_from_roots.py |  90 ++++
 .../_probabilists_hermite_polynomial_one.py   |   3 +
 .../_probabilists_hermite_polynomial_power.py |  65 +++
 .../_probabilists_hermite_polynomial_roots.py |  27 +
 ...ilists_hermite_polynomial_to_polynomial.py |  48 ++
 ...abilists_hermite_polynomial_vandermonde.py |  22 +
 ...lists_hermite_polynomial_vandermonde_2d.py |  51 ++
 ...lists_hermite_polynomial_vandermonde_3d.py |  53 ++
 ..._probabilists_hermite_polynomial_weight.py |   6 +
 .../_probabilists_hermite_polynomial_x.py     |   3 +
 .../_probabilists_hermite_polynomial_zero.py  |   3 +
 src/beignet/_subtract_chebyshev_polynomial.py |  53 ++
 src/beignet/_subtract_laguerre_polynomial.py  |  53 ++
 src/beignet/_subtract_legendre_polynomial.py  |  53 ++
 ..._subtract_physicists_hermite_polynomial.py |  56 +++
 src/beignet/_subtract_polynomial.py           |  53 ++
 ...ubtract_probabilists_hermite_polynomial.py |  56 +++
 ..._trim_chebyshev_polynomial_coefficients.py |  21 +
 .../_trim_laguerre_polynomial_coefficients.py |  21 +
 .../_trim_legendre_polynomial_coefficients.py |  21 +
 ...sicists_hermite_polynomial_coefficients.py |  21 +
 src/beignet/_trim_polynomial_coefficients.py  |  21 +
 ...bilists_hermite_polynomial_coefficients.py |  21 +
 tests/beignet/func/test__space.py             | 291 +++++------
 .../special/test__dawson_integral_f.py        | 110 ++---
 .../beignet/test__add_chebyshev_polynomial.py |  25 +
 .../beignet/test__add_laguerre_polynomial.py  |  25 +
 .../beignet/test__add_legendre_polynomial.py  |  25 +
 ...test__add_physicists_hermite_polynomial.py |  25 +
 tests/beignet/test__add_polynomial.py         |  25 +
 ...st__add_probabilists_hermite_polynomial.py |  25 +
 tests/beignet/test__apply_transform.py        |  42 +-
 tests/beignet/test__chebyshev_extrema.py      |  31 ++
 .../test__chebyshev_gauss_quadrature.py       |  27 +
 .../beignet/test__chebyshev_interpolation.py  |  32 ++
 .../test__chebyshev_polynomial_companion.py   |  28 ++
 .../test__chebyshev_polynomial_domain.py      |  10 +
 .../test__chebyshev_polynomial_from_roots.py  |  34 ++
 .../beignet/test__chebyshev_polynomial_one.py |  10 +
 .../test__chebyshev_polynomial_power.py       |  26 +
 .../test__chebyshev_polynomial_roots.py       |  34 ++
 .../test__chebyshev_polynomial_vandermonde.py |  36 ++
 ...st__chebyshev_polynomial_vandermonde_2d.py |  31 ++
 ...st__chebyshev_polynomial_vandermonde_3d.py |  34 ++
 .../test__chebyshev_polynomial_weight.py      |  11 +
 tests/beignet/test__chebyshev_polynomial_x.py |  10 +
 .../test__chebyshev_polynomial_zero.py        |  10 +
 tests/beignet/test__chebyshev_zeros.py        |  28 ++
 ...est__differentiate_chebyshev_polynomial.py |  91 ++++
 ...test__differentiate_laguerre_polynomial.py |  87 ++++
 ...test__differentiate_legendre_polynomial.py | 118 +++++
 ...erentiate_physicists_hermite_polynomial.py |  85 ++++
 ...entiate_probabilists_hermite_polynomial.py |  90 ++++
 .../test__divide_chebyshev_polynomial.py      |  37 ++
 .../test__divide_laguerre_polynomial.py       |  34 ++
 .../test__divide_legendre_polynomial.py       |  34 ++
 ...t__divide_physicists_hermite_polynomial.py |  37 ++
 tests/beignet/test__divide_polynomial.py      |  67 +++
 ..._divide_probabilists_hermite_polynomial.py |  37 ++
 .../test__evaluate_chebyshev_polynomial.py    |  72 +++
 .../test__evaluate_chebyshev_polynomial_2d.py |  50 ++
 .../test__evaluate_chebyshev_polynomial_3d.py |  56 +++
 ...luate_chebyshev_polynomial_cartesian_2d.py |  42 ++
 ...luate_chebyshev_polynomial_cartesian_3d.py |  47 ++
 .../test__evaluate_laguerre_polynomial.py     |  71 +++
 .../test__evaluate_laguerre_polynomial_2d.py  |  48 ++
 .../test__evaluate_laguerre_polynomial_3d.py  |  56 +++
 ...aluate_laguerre_polynomial_cartesian_2d.py |  30 ++
 ...aluate_laguerre_polynomial_cartesian_3d.py |  24 +
 .../test__evaluate_legendre_polynomial.py     |  72 +++
 .../test__evaluate_legendre_polynomial_2d.py  |  51 ++
 .../test__evaluate_legendre_polynomial_3d.py  |  36 ++
 ...aluate_legendre_polynomial_cartesian_2d.py |  42 ++
 ...aluate_legendre_polynomial_cartesian_3d.py |  47 ++
 ..._evaluate_physicists_hermite_polynomial.py |  74 +++
 ...aluate_physicists_hermite_polynomial_2d.py |  50 ++
 ...aluate_physicists_hermite_polynomial_3d.py |  53 ++
 ...sicists_hermite_polynomial_cartesian_2d.py |  31 ++
 ...sicists_hermite_polynomial_cartesian_3d.py |  38 ++
 tests/beignet/test__evaluate_polynomial.py    |  66 +++
 tests/beignet/test__evaluate_polynomial_2d.py |  38 ++
 tests/beignet/test__evaluate_polynomial_3d.py |  42 ++
 .../test__evaluate_polynomial_cartesian_2d.py |  42 ++
 .../test__evaluate_polynomial_cartesian_3d.py |  48 ++
 .../test__evaluate_polynomial_from_roots.py   | 155 ++++++
 ...valuate_probabilists_hermite_polynomial.py |  72 +++
 ...uate_probabilists_hermite_polynomial_2d.py |  50 ++
 ...uate_probabilists_hermite_polynomial_3d.py |  56 +++
 ...ilists_hermite_polynomial_cartersian_2d.py |  42 ++
 ...ilists_hermite_polynomial_cartersian_3d.py |  22 +
 .../beignet/test__fit_chebyshev_polynomial.py | 255 ++++++++++
 .../beignet/test__fit_laguerre_polynomial.py  | 199 ++++++++
 .../beignet/test__fit_legendre_polynomial.py  | 271 ++++++++++
 ...test__fit_physicists_hermite_polynomial.py | 271 ++++++++++
 tests/beignet/test__fit_polynomial.py         | 244 +++++++++
 ...st__fit_probabilists_hermite_polynomial.py | 271 ++++++++++
 .../test__gauss_laguerre_quadrature.py        |  18 +
 .../test__gauss_legendre_quadrature.py        |  23 +
 ...hysicists_hermite_polynomial_quadrature.py |  22 +
 ...babilists_hermite_polynomial_quadrature.py |  20 +
 .../test__integrate_chebyshev_polynomial.py   | 240 +++++++++
 .../test__integrate_laguerre_polynomial.py    | 245 +++++++++
 .../test__integrate_legendre_polynomial.py    | 259 ++++++++++
 ...integrate_physicists_hermite_polynomial.py | 257 ++++++++++
 tests/beignet/test__integrate_polynomial.py   | 222 +++++++++
 ...tegrate_probabilists_hermite_polynomial.py | 251 ++++++++++
 .../test__laguerre_polynomial_companion.py    |  28 ++
 .../test__laguerre_polynomial_domain.py       |  10 +
 .../test__laguerre_polynomial_from_roots.py   |  44 ++
 .../beignet/test__laguerre_polynomial_one.py  |  10 +
 .../test__laguerre_polynomial_power.py        |  26 +
 .../test__laguerre_polynomial_roots.py        |  34 ++
 ...test__laguerre_polynomial_to_polynomial.py |  22 +
 .../test__laguerre_polynomial_vandermonde.py  |  34 ++
 ...est__laguerre_polynomial_vandermonde_2d.py |  27 +
 ...est__laguerre_polynomial_vandermonde_3d.py |  33 ++
 .../test__laguerre_polynomial_weight.py       |  11 +
 tests/beignet/test__laguerre_polynomial_x.py  |  10 +
 .../beignet/test__laguerre_polynomial_zero.py |  10 +
 .../test__legendre_polynomial_companion.py    |  20 +
 .../test__legendre_polynomial_domain.py       |  10 +
 .../test__legendre_polynomial_from_roots.py   |  52 ++
 .../beignet/test__legendre_polynomial_one.py  |  10 +
 .../test__legendre_polynomial_power.py        |  26 +
 .../test__legendre_polynomial_roots.py        |  32 ++
 ...test__legendre_polynomial_to_polynomial.py |  25 +
 .../test__legendre_polynomial_vandermonde.py  |  47 ++
 ...est__legendre_polynomial_vandermonde_2d.py |  30 ++
 .../test__legendre_polynomial_weight.py       |  11 +
 tests/beignet/test__legendre_polynomial_x.py  |  10 +
 .../beignet/test__legendre_polynomial_zero.py |  10 +
 .../test__linear_chebyshev_polynomial.py      |   9 +
 .../test__linear_legendre_polynomial.py       |  17 +
 ...t__linear_physicists_hermite_polynomial.py |   9 +
 tests/beignet/test__linear_polynomial.py      |  14 +
 ..._linear_probabilists_hermite_polynomial.py |   9 +
 .../test__multiply_chebyshev_polynomial.py    |  28 ++
 ...est__multiply_chebyshev_polynomial_by_x.py |  35 ++
 .../test__multiply_laguerre_polynomial.py     |  40 ++
 ...test__multiply_laguerre_polynomial_by_x.py |  40 ++
 .../test__multiply_legendre_polynomial.py     |  29 ++
 ...test__multiply_legendre_polynomial_by_x.py |  35 ++
 ..._multiply_physicists_hermite_polynomial.py |  29 ++
 ...iply_physicists_hermite_polynomial_by_x.py |  29 ++
 tests/beignet/test__multiply_polynomial.py    |  24 +
 .../beignet/test__multiply_polynomial_by_x.py |  26 +
 ...ultiply_probabilists_hermite_polynomial.py |  29 ++
 ...ly_probabilists_hermite_polynomial_by_x.py |  34 ++
 ...physicists_hermite_polynomial_companion.py |  28 ++
 ...t__physicists_hermite_polynomial_domain.py |  10 +
 ...hysicists_hermite_polynomial_from_roots.py |  37 ++
 ...test__physicists_hermite_polynomial_one.py |  10 +
 ...st__physicists_hermite_polynomial_power.py |  26 +
 ...st__physicists_hermite_polynomial_roots.py |  36 ++
 ...icists_hermite_polynomial_to_polynomial.py |  25 +
 ...ysicists_hermite_polynomial_vandermonde.py |  38 ++
 ...cists_hermite_polynomial_vandermonde_2d.py |  31 ++
 ...cists_hermite_polynomial_vandermonde_3d.py |  29 ++
 ...t__physicists_hermite_polynomial_weight.py |   9 +
 .../test__physicists_hermite_polynomial_x.py  |  10 +
 ...est__physicists_hermite_polynomial_zero.py |  10 +
 tests/beignet/test__polynomial_companion.py   |  24 +
 tests/beignet/test__polynomial_domain.py      |  10 +
 tests/beignet/test__polynomial_from_roots.py  |  49 ++
 tests/beignet/test__polynomial_one.py         |  10 +
 tests/beignet/test__polynomial_power.py       |  26 +
 tests/beignet/test__polynomial_roots.py       |  32 ++
 ...est__polynomial_to_chebyshev_polynomial.py |  25 +
 ...test__polynomial_to_laguerre_polynomial.py |  22 +
 ...test__polynomial_to_legendre_polynomial.py |  25 +
 ...nomial_to_physicists_hermite_polynomial.py |  28 ++
 ...mial_to_probabilists_hermite_polynomial.py |  25 +
 tests/beignet/test__polynomial_vandermonde.py |  43 ++
 .../test__polynomial_vandermonde_2d.py        |  27 +
 .../test__polynomial_vandermonde_3d.py        |  34 ++
 tests/beignet/test__polynomial_x.py           |  10 +
 tests/beignet/test__polynomial_zero.py        |  10 +
 ...obabilists_hermite_polynomial_companion.py |  26 +
 ..._probabilists_hermite_polynomial_domain.py |  10 +
 ...babilists_hermite_polynomial_from_roots.py |  33 ++
 ...st__probabilists_hermite_polynomial_one.py |  10 +
 ...__probabilists_hermite_polynomial_power.py |  26 +
 ...__probabilists_hermite_polynomial_roots.py |  36 ++
 ...ilists_hermite_polynomial_to_polynomial.py |  25 +
 ...abilists_hermite_polynomial_vandermonde.py |  30 ++
 ...lists_hermite_polynomial_vandermonde_2d.py |  31 ++
 ...lists_hermite_polynomial_vandermonde_3d.py |  34 ++
 ..._probabilists_hermite_polynomial_weight.py |  11 +
 ...test__probabilists_hermite_polynomial_x.py |  10 +
 ...t__probabilists_hermite_polynomial_zero.py |  10 +
 tests/beignet/test__quaternion_slerp.py       | 150 ++++++
 tests/beignet/test__slerp.py                  | 151 ------
 .../test__subtract_chebyshev_polynomial.py    |  28 ++
 .../test__subtract_laguerre_polynomial.py     |  25 +
 .../test__subtract_legendre_polynomial.py     |  25 +
 ..._subtract_physicists_hermite_polynomial.py |  25 +
 tests/beignet/test__subtract_polynomial.py    |  25 +
 ...ubtract_probabilists_hermite_polynomial.py |  28 ++
 ..._trim_chebyshev_polynomial_coefficients.py |  34 ++
 ...__trim_laguerre_polynomial_coefficients.py |  34 ++
 ...__trim_legendre_polynomial_coefficients.py |  34 ++
 ...sicists_hermite_polynomial_coefficients.py |  34 ++
 .../test__trim_polynomial_coefficients.py     |  34 ++
 ...bilists_hermite_polynomial_coefficients.py |  34 ++
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 create mode 100644 tests/beignet/test__linear_physicists_hermite_polynomial.py
 create mode 100644 tests/beignet/test__linear_polynomial.py
 create mode 100644 tests/beignet/test__linear_probabilists_hermite_polynomial.py
 create mode 100644 tests/beignet/test__multiply_chebyshev_polynomial.py
 create mode 100644 tests/beignet/test__multiply_chebyshev_polynomial_by_x.py
 create mode 100644 tests/beignet/test__multiply_laguerre_polynomial.py
 create mode 100644 tests/beignet/test__multiply_laguerre_polynomial_by_x.py
 create mode 100644 tests/beignet/test__multiply_legendre_polynomial.py
 create mode 100644 tests/beignet/test__multiply_legendre_polynomial_by_x.py
 create mode 100644 tests/beignet/test__multiply_physicists_hermite_polynomial.py
 create mode 100644 tests/beignet/test__multiply_physicists_hermite_polynomial_by_x.py
 create mode 100644 tests/beignet/test__multiply_polynomial.py
 create mode 100644 tests/beignet/test__multiply_polynomial_by_x.py
 create mode 100644 tests/beignet/test__multiply_probabilists_hermite_polynomial.py
 create mode 100644 tests/beignet/test__multiply_probabilists_hermite_polynomial_by_x.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_companion.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_domain.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_from_roots.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_one.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_power.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_roots.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_to_polynomial.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_vandermonde.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_vandermonde_2d.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_vandermonde_3d.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_weight.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_x.py
 create mode 100644 tests/beignet/test__physicists_hermite_polynomial_zero.py
 create mode 100644 tests/beignet/test__polynomial_companion.py
 create mode 100644 tests/beignet/test__polynomial_domain.py
 create mode 100644 tests/beignet/test__polynomial_from_roots.py
 create mode 100644 tests/beignet/test__polynomial_one.py
 create mode 100644 tests/beignet/test__polynomial_power.py
 create mode 100644 tests/beignet/test__polynomial_roots.py
 create mode 100644 tests/beignet/test__polynomial_to_chebyshev_polynomial.py
 create mode 100644 tests/beignet/test__polynomial_to_laguerre_polynomial.py
 create mode 100644 tests/beignet/test__polynomial_to_legendre_polynomial.py
 create mode 100644 tests/beignet/test__polynomial_to_physicists_hermite_polynomial.py
 create mode 100644 tests/beignet/test__polynomial_to_probabilists_hermite_polynomial.py
 create mode 100644 tests/beignet/test__polynomial_vandermonde.py
 create mode 100644 tests/beignet/test__polynomial_vandermonde_2d.py
 create mode 100644 tests/beignet/test__polynomial_vandermonde_3d.py
 create mode 100644 tests/beignet/test__polynomial_x.py
 create mode 100644 tests/beignet/test__polynomial_zero.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_companion.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_domain.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_from_roots.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_one.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_power.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_roots.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_to_polynomial.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_vandermonde.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_vandermonde_2d.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_vandermonde_3d.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_weight.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_x.py
 create mode 100644 tests/beignet/test__probabilists_hermite_polynomial_zero.py
 create mode 100644 tests/beignet/test__quaternion_slerp.py
 delete mode 100644 tests/beignet/test__slerp.py
 create mode 100644 tests/beignet/test__subtract_chebyshev_polynomial.py
 create mode 100644 tests/beignet/test__subtract_laguerre_polynomial.py
 create mode 100644 tests/beignet/test__subtract_legendre_polynomial.py
 create mode 100644 tests/beignet/test__subtract_physicists_hermite_polynomial.py
 create mode 100644 tests/beignet/test__subtract_polynomial.py
 create mode 100644 tests/beignet/test__subtract_probabilists_hermite_polynomial.py
 create mode 100644 tests/beignet/test__trim_chebyshev_polynomial_coefficients.py
 create mode 100644 tests/beignet/test__trim_laguerre_polynomial_coefficients.py
 create mode 100644 tests/beignet/test__trim_legendre_polynomial_coefficients.py
 create mode 100644 tests/beignet/test__trim_physicists_hermite_polynomial_coefficients.py
 create mode 100644 tests/beignet/test__trim_polynomial_coefficients.py
 create mode 100644 tests/beignet/test__trim_probabilists_hermite_polynomial_coefficients.py

diff --git a/docs/index.md b/docs/index.md
index 37b23d0d1a..5935d0b3b3 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -1,13 +1,11 @@
-# beignet
+# Operators
+
+## Geometry
+
+### Euler Angle
 
 ::: beignet.apply_euler_angle
-::: beignet.apply_quaternion
-::: beignet.apply_rotation_matrix
-::: beignet.apply_rotation_vector
 ::: beignet.compose_euler_angle
-::: beignet.compose_quaternion
-::: beignet.compose_rotation_matrix
-::: beignet.compose_rotation_vector
 ::: beignet.euler_angle_identity
 ::: beignet.euler_angle_magnitude
 ::: beignet.euler_angle_mean
@@ -15,10 +13,13 @@
 ::: beignet.euler_angle_to_rotation_matrix
 ::: beignet.euler_angle_to_rotation_vector
 ::: beignet.invert_euler_angle
+::: beignet.random_euler_angle
+
+### Quaternion
+
+::: beignet.apply_quaternion
+::: beignet.compose_quaternion
 ::: beignet.invert_quaternion
-::: beignet.invert_rotation_matrix
-::: beignet.invert_rotation_vector
-::: beignet.lennard_jones_potential
 ::: beignet.quaternion_identity
 ::: beignet.quaternion_magnitude
 ::: beignet.quaternion_mean
@@ -26,20 +27,252 @@
 ::: beignet.quaternion_to_euler_angle
 ::: beignet.quaternion_to_rotation_matrix
 ::: beignet.quaternion_to_rotation_vector
-::: beignet.random_euler_angle
 ::: beignet.random_quaternion
+
+### Rotation Matrix
+
+::: beignet.apply_rotation_matrix
+::: beignet.compose_rotation_matrix
+::: beignet.invert_rotation_matrix
 ::: beignet.random_rotation_matrix
-::: beignet.random_rotation_vector
 ::: beignet.rotation_matrix_identity
 ::: beignet.rotation_matrix_magnitude
 ::: beignet.rotation_matrix_mean
 ::: beignet.rotation_matrix_to_euler_angle
 ::: beignet.rotation_matrix_to_quaternion
 ::: beignet.rotation_matrix_to_rotation_vector
+
+### Rotation Vector
+
+::: beignet.apply_rotation_vector
+::: beignet.compose_rotation_vector
+::: beignet.invert_rotation_vector
+::: beignet.random_rotation_vector
 ::: beignet.rotation_vector_identity
 ::: beignet.rotation_vector_magnitude
 ::: beignet.rotation_vector_mean
 ::: beignet.rotation_vector_to_euler_angle
 ::: beignet.rotation_vector_to_quaternion
 ::: beignet.rotation_vector_to_rotation_matrix
+
+### Translation
+
 ::: beignet.translation_identity
+
+### Transform
+
+::: beignet.apply_transform
+::: beignet.invert_transform
+
+## Interpolation
+
+## Numerical Integration
+
+### Gaussian Quadrature
+
+::: beignet.gauss_laguerre_quadrature
+::: beignet.gauss_legendre_quadrature
+::: beignet.gauss_physicists_hermite_polynomial_quadrature
+::: beignet.gauss_probabilists_hermite_polynomial_quadrature
+
+## Polynomials
+
+### Polynomial
+
+::: beignet.add_polynomial
+::: beignet.differentiate_polynomial
+::: beignet.divide_polynomial
+::: beignet.evaluate_polynomial
+::: beignet.evaluate_polynomial_2d
+::: beignet.evaluate_polynomial_3d
+::: beignet.evaluate_polynomial_cartesian_2d
+::: beignet.evaluate_polynomial_cartesian_3d
+::: beignet.evaluate_polynomial_from_roots
+::: beignet.fit_polynomial
+::: beignet.integrate_polynomial
+::: beignet.linear_polynomial
+::: beignet.multiply_polynomial
+::: beignet.multiply_polynomial_by_x
+::: beignet.polynomial_companion
+::: beignet.polynomial_domain
+::: beignet.polynomial_from_roots
+::: beignet.polynomial_one
+::: beignet.polynomial_power
+::: beignet.polynomial_roots
+::: beignet.polynomial_to_chebyshev_polynomial
+::: beignet.polynomial_to_laguerre_polynomial
+::: beignet.polynomial_to_legendre_polynomial
+::: beignet.polynomial_to_physicists_hermite_polynomial
+::: beignet.polynomial_to_probabilists_hermite_polynomial
+::: beignet.polynomial_vandermonde
+::: beignet.polynomial_vandermonde_2d
+::: beignet.polynomial_vandermonde_3d
+::: beignet.polynomial_x
+::: beignet.polynomial_zero
+::: beignet.subtract_polynomial
+::: beignet.trim_polynomial_coefficients
+
+### Chebyshev Polynomial
+
+::: beignet.add_chebyshev_polynomial
+::: beignet.chebyshev_extrema
+::: beignet.chebyshev_gauss_quadrature
+::: beignet.chebyshev_interpolation
+::: beignet.chebyshev_polynomial_companion
+::: beignet.chebyshev_polynomial_domain
+::: beignet.chebyshev_polynomial_from_roots
+::: beignet.chebyshev_polynomial_one
+::: beignet.chebyshev_polynomial_power
+::: beignet.chebyshev_polynomial_roots
+::: beignet.chebyshev_polynomial_to_polynomial
+::: beignet.chebyshev_polynomial_vandermonde
+::: beignet.chebyshev_polynomial_vandermonde_2d
+::: beignet.chebyshev_polynomial_vandermonde_3d
+::: beignet.chebyshev_polynomial_weight
+::: beignet.chebyshev_polynomial_x
+::: beignet.chebyshev_polynomial_zero
+::: beignet.chebyshev_zeros
+::: beignet.differentiate_chebyshev_polynomial
+::: beignet.divide_chebyshev_polynomial
+::: beignet.evaluate_chebyshev_polynomial
+::: beignet.evaluate_chebyshev_polynomial_2d
+::: beignet.evaluate_chebyshev_polynomial_3d
+::: beignet.evaluate_chebyshev_polynomial_cartesian_2d
+::: beignet.evaluate_chebyshev_polynomial_cartesian_3d
+::: beignet.fit_chebyshev_polynomial
+::: beignet.integrate_chebyshev_polynomial
+::: beignet.linear_chebyshev_polynomial
+::: beignet.multiply_chebyshev_polynomial
+::: beignet.multiply_chebyshev_polynomial_by_x
+::: beignet.subtract_chebyshev_polynomial
+::: beignet.trim_chebyshev_polynomial_coefficients
+
+### Laguerre Polynomial
+
+::: beignet.add_laguerre_polynomial
+::: beignet.differentiate_laguerre_polynomial
+::: beignet.divide_laguerre_polynomial
+::: beignet.evaluate_laguerre_polynomial
+::: beignet.evaluate_laguerre_polynomial_2d
+::: beignet.evaluate_laguerre_polynomial_3d
+::: beignet.evaluate_laguerre_polynomial_cartesian_2d
+::: beignet.evaluate_laguerre_polynomial_cartesian_3d
+::: beignet.fit_laguerre_polynomial
+::: beignet.integrate_laguerre_polynomial
+::: beignet.laguerre_polynomial_companion
+::: beignet.laguerre_polynomial_domain
+::: beignet.laguerre_polynomial_from_roots
+::: beignet.laguerre_polynomial_one
+::: beignet.laguerre_polynomial_power
+::: beignet.laguerre_polynomial_roots
+::: beignet.laguerre_polynomial_to_polynomial
+::: beignet.laguerre_polynomial_vandermonde
+::: beignet.laguerre_polynomial_vandermonde_2d
+::: beignet.laguerre_polynomial_vandermonde_3d
+::: beignet.laguerre_polynomial_weight
+::: beignet.laguerre_polynomial_x
+::: beignet.laguerre_polynomial_zero
+::: beignet.linear_laguerre_polynomial
+::: beignet.multiply_laguerre_polynomial
+::: beignet.multiply_laguerre_polynomial_by_x
+::: beignet.subtract_laguerre_polynomial
+::: beignet.trim_laguerre_polynomial_coefficients
+
+### Legendre Polynomial
+
+::: beignet.add_legendre_polynomial
+::: beignet.differentiate_legendre_polynomial
+::: beignet.divide_legendre_polynomial
+::: beignet.evaluate_legendre_polynomial
+::: beignet.evaluate_legendre_polynomial_2d
+::: beignet.evaluate_legendre_polynomial_3d
+::: beignet.evaluate_legendre_polynomial_cartesian_2d
+::: beignet.evaluate_legendre_polynomial_cartesian_3d
+::: beignet.fit_legendre_polynomial
+::: beignet.integrate_legendre_polynomial
+::: beignet.legendre_polynomial_companion
+::: beignet.legendre_polynomial_domain
+::: beignet.legendre_polynomial_from_roots
+::: beignet.legendre_polynomial_one
+::: beignet.legendre_polynomial_power
+::: beignet.legendre_polynomial_roots
+::: beignet.legendre_polynomial_to_polynomial
+::: beignet.legendre_polynomial_vandermonde
+::: beignet.legendre_polynomial_vandermonde_2d
+::: beignet.legendre_polynomial_vandermonde_3d
+::: beignet.legendre_polynomial_weight
+::: beignet.legendre_polynomial_x
+::: beignet.legendre_polynomial_zero
+::: beignet.linear_legendre_polynomial
+::: beignet.multiply_legendre_polynomial
+::: beignet.multiply_legendre_polynomial_by_x
+::: beignet.subtract_legendre_polynomial
+::: beignet.trim_legendre_polynomial_coefficients
+
+### Physicists’ Hermite Polynomial
+
+::: beignet.add_physicists_hermite_polynomial
+::: beignet.differentiate_physicists_hermite_polynomial
+::: beignet.divide_physicists_hermite_polynomial
+::: beignet.evaluate_physicists_hermite_polynomial
+::: beignet.evaluate_physicists_hermite_polynomial_2d
+::: beignet.evaluate_physicists_hermite_polynomial_3d
+::: beignet.evaluate_physicists_hermite_polynomial_cartesian_2d
+::: beignet.evaluate_physicists_hermite_polynomial_cartesian_3d
+::: beignet.fit_physicists_hermite_polynomial
+::: beignet.integrate_physicists_hermite_polynomial
+::: beignet.linear_physicists_hermite_polynomial
+::: beignet.multiply_physicists_hermite_polynomial
+::: beignet.multiply_physicists_hermite_polynomial_by_x
+::: beignet.physicists_hermite_polynomial_companion
+::: beignet.physicists_hermite_polynomial_domain
+::: beignet.physicists_hermite_polynomial_from_roots
+::: beignet.physicists_hermite_polynomial_one
+::: beignet.physicists_hermite_polynomial_power
+::: beignet.physicists_hermite_polynomial_roots
+::: beignet.physicists_hermite_polynomial_to_polynomial
+::: beignet.physicists_hermite_polynomial_vandermonde
+::: beignet.physicists_hermite_polynomial_vandermonde_2d
+::: beignet.physicists_hermite_polynomial_vandermonde_3d
+::: beignet.physicists_hermite_polynomial_weight
+::: beignet.physicists_hermite_polynomial_x
+::: beignet.physicists_hermite_polynomial_zero
+::: beignet.subtract_physicists_hermite_polynomial
+::: beignet.trim_physicists_hermite_polynomial_coefficients
+
+### Probabilists’ Hermite Polynomial
+
+::: beignet.add_probabilists_hermite_polynomial
+::: beignet.differentiate_probabilists_hermite_polynomial
+::: beignet.divide_probabilists_hermite_polynomial
+::: beignet.evaluate_probabilists_hermite_polynomial
+::: beignet.evaluate_probabilists_hermite_polynomial_2d
+::: beignet.evaluate_probabilists_hermite_polynomial_3d
+::: beignet.evaluate_probabilists_hermite_polynomial_cartersian_2d
+::: beignet.evaluate_probabilists_hermite_polynomial_cartersian_3d
+::: beignet.fit_probabilists_hermite_polynomial
+::: beignet.integrate_probabilists_hermite_polynomial
+::: beignet.linear_probabilists_hermite_polynomial
+::: beignet.multiply_probabilists_hermite_polynomial
+::: beignet.multiply_probabilists_hermite_polynomial_by_x
+::: beignet.probabilists_hermite_polynomial_companion
+::: beignet.probabilists_hermite_polynomial_domain
+::: beignet.probabilists_hermite_polynomial_from_roots
+::: beignet.probabilists_hermite_polynomial_one
+::: beignet.probabilists_hermite_polynomial_power
+::: beignet.probabilists_hermite_polynomial_roots
+::: beignet.probabilists_hermite_polynomial_to_polynomial
+::: beignet.probabilists_hermite_polynomial_vandermonde
+::: beignet.probabilists_hermite_polynomial_vandermonde_2d
+::: beignet.probabilists_hermite_polynomial_vandermonde_3d
+::: beignet.probabilists_hermite_polynomial_weight
+::: beignet.probabilists_hermite_polynomial_x
+::: beignet.probabilists_hermite_polynomial_zero
+::: beignet.subtract_probabilists_hermite_polynomial
+::: beignet.trim_probabilists_hermite_polynomial_coefficients
+
+## Thermodynamics
+
+### Interatomic Potentials
+
+::: beignet.lennard_jones_potential
diff --git a/docs/stylesheets/extra.css b/docs/stylesheets/extra.css
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/mkdocs.yml b/mkdocs.yml
index fcf80d567a..2eaac0e318 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -1,3 +1,5 @@
+extra_css:
+  - "stylesheets/extra.css"
 extra_javascript:
   - "javascripts/mathjax.js"
   - "https://polyfill.io/v3/polyfill.min.js?features=es6"
@@ -5,16 +7,25 @@ extra_javascript:
 markdown_extensions:
   - pymdownx.arithmatex:
       generic: true
+nav:
+  - beignet: "index.md"
+  - beignet.datasets: "beignet.datasets.md"
+  - beignet.features: "beignet.features.md"
+  - beignet.func: "beignet.func.md"
+  - beignet.io: "beignet.io.md"
+  - beignet.special: "beignet.special.md"
+  - beignet.transforms: "beignet.transforms.md"
 plugins:
   - mkdocstrings:
       default_handler: "python"
       handlers:
         python:
           options:
+            heading_level: 4
             docstring_style: "numpy"
             separate_signature: true
             show_root_heading: true
             show_source: true
 site_name: "Beignet"
 theme:
-  name: "material"
+  name: "material"
\ No newline at end of file
diff --git a/pyproject.toml b/pyproject.toml
index 3c0e3700c2..9eeba6b742 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -11,6 +11,7 @@ authors = [{ email = "allen.goodman@icloud.com", name = "Allen Goodman" }]
 dependencies = [
     "pooch",
     "torch==2.2.2",
+    "torchaudio",
     "tqdm",
 ]
 dynamic = ["version"]
@@ -29,6 +30,7 @@ docs = [
 ]
 test = [
     "hypothesis",
+    "numpy==1.26.4",
     "pytest",
     "pytest-mock",
     "scipy",
diff --git a/src/beignet/__init__.py b/src/beignet/__init__.py
index 89b8ffaa1a..d338a100cb 100644
--- a/src/beignet/__init__.py
+++ b/src/beignet/__init__.py
@@ -6,6 +6,12 @@
 except PackageNotFoundError:
     __version__ = None
 
+from ._add_chebyshev_polynomial import add_chebyshev_polynomial
+from ._add_laguerre_polynomial import add_laguerre_polynomial
+from ._add_legendre_polynomial import add_legendre_polynomial
+from ._add_physicists_hermite_polynomial import add_physicists_hermite_polynomial
+from ._add_polynomial import add_polynomial
+from ._add_probabilists_hermite_polynomial import add_probabilists_hermite_polynomial
 from ._apply_euler_angle import apply_euler_angle
 from ._apply_quaternion import (
     apply_quaternion,
@@ -13,10 +19,45 @@
 from ._apply_rotation_matrix import apply_rotation_matrix
 from ._apply_rotation_vector import apply_rotation_vector
 from ._apply_transform import apply_transform
+from ._chebyshev_extrema import chebyshev_extrema
+from ._chebyshev_gauss_quadrature import chebyshev_gauss_quadrature
+from ._chebyshev_interpolation import chebyshev_interpolation
+from ._chebyshev_polynomial_companion import chebyshev_polynomial_companion
+from ._chebyshev_polynomial_domain import chebyshev_polynomial_domain
+from ._chebyshev_polynomial_from_roots import chebyshev_polynomial_from_roots
+from ._chebyshev_polynomial_one import chebyshev_polynomial_one
+from ._chebyshev_polynomial_power import chebyshev_polynomial_power
+from ._chebyshev_polynomial_roots import chebyshev_polynomial_roots
+from ._chebyshev_polynomial_to_polynomial import chebyshev_polynomial_to_polynomial
+from ._chebyshev_polynomial_vandermonde import chebyshev_polynomial_vandermonde
+from ._chebyshev_polynomial_vandermonde_2d import chebyshev_polynomial_vandermonde_2d
+from ._chebyshev_polynomial_vandermonde_3d import chebyshev_polynomial_vandermonde_3d
+from ._chebyshev_polynomial_weight import chebyshev_polynomial_weight
+from ._chebyshev_polynomial_x import chebyshev_polynomial_x
+from ._chebyshev_polynomial_zero import chebyshev_polynomial_zero
+from ._chebyshev_zeros import chebyshev_zeros
 from ._compose_euler_angle import compose_euler_angle
 from ._compose_quaternion import compose_quaternion
 from ._compose_rotation_matrix import compose_rotation_matrix
 from ._compose_rotation_vector import compose_rotation_vector
+from ._differentiate_chebyshev_polynomial import differentiate_chebyshev_polynomial
+from ._differentiate_laguerre_polynomial import differentiate_laguerre_polynomial
+from ._differentiate_legendre_polynomial import differentiate_legendre_polynomial
+from ._differentiate_physicists_hermite_polynomial import (
+    differentiate_physicists_hermite_polynomial,
+)
+from ._differentiate_polynomial import differentiate_polynomial
+from ._differentiate_probabilists_hermite_polynomial import (
+    differentiate_probabilists_hermite_polynomial,
+)
+from ._divide_chebyshev_polynomial import divide_chebyshev_polynomial
+from ._divide_laguerre_polynomial import divide_laguerre_polynomial
+from ._divide_legendre_polynomial import divide_legendre_polynomial
+from ._divide_physicists_hermite_polynomial import divide_physicists_hermite_polynomial
+from ._divide_polynomial import divide_polynomial
+from ._divide_probabilists_hermite_polynomial import (
+    divide_probabilists_hermite_polynomial,
+)
 from ._euler_angle_identity import euler_angle_identity
 from ._euler_angle_magnitude import euler_angle_magnitude
 from ._euler_angle_mean import euler_angle_mean
@@ -25,12 +66,231 @@
 )
 from ._euler_angle_to_rotation_matrix import euler_angle_to_rotation_matrix
 from ._euler_angle_to_rotation_vector import euler_angle_to_rotation_vector
+from ._evaluate_chebyshev_polynomial import evaluate_chebyshev_polynomial
+from ._evaluate_chebyshev_polynomial_2d import evaluate_chebyshev_polynomial_2d
+from ._evaluate_chebyshev_polynomial_3d import evaluate_chebyshev_polynomial_3d
+from ._evaluate_chebyshev_polynomial_cartesian_2d import (
+    evaluate_chebyshev_polynomial_cartesian_2d,
+)
+from ._evaluate_chebyshev_polynomial_cartesian_3d import (
+    evaluate_chebyshev_polynomial_cartesian_3d,
+)
+from ._evaluate_laguerre_polynomial import evaluate_laguerre_polynomial
+from ._evaluate_laguerre_polynomial_2d import evaluate_laguerre_polynomial_2d
+from ._evaluate_laguerre_polynomial_3d import evaluate_laguerre_polynomial_3d
+from ._evaluate_laguerre_polynomial_cartesian_2d import (
+    evaluate_laguerre_polynomial_cartesian_2d,
+)
+from ._evaluate_laguerre_polynomial_cartesian_3d import (
+    evaluate_laguerre_polynomial_cartesian_3d,
+)
+from ._evaluate_legendre_polynomial import evaluate_legendre_polynomial
+from ._evaluate_legendre_polynomial_2d import evaluate_legendre_polynomial_2d
+from ._evaluate_legendre_polynomial_3d import evaluate_legendre_polynomial_3d
+from ._evaluate_legendre_polynomial_cartesian_2d import (
+    evaluate_legendre_polynomial_cartesian_2d,
+)
+from ._evaluate_legendre_polynomial_cartesian_3d import (
+    evaluate_legendre_polynomial_cartesian_3d,
+)
+from ._evaluate_physicists_hermite_polynomial import (
+    evaluate_physicists_hermite_polynomial,
+)
+from ._evaluate_physicists_hermite_polynomial_2d import (
+    evaluate_physicists_hermite_polynomial_2d,
+)
+from ._evaluate_physicists_hermite_polynomial_3d import (
+    evaluate_physicists_hermite_polynomial_3d,
+)
+from ._evaluate_physicists_hermite_polynomial_cartesian_2d import (
+    evaluate_physicists_hermite_polynomial_cartesian_2d,
+)
+from ._evaluate_physicists_hermite_polynomial_cartesian_3d import (
+    evaluate_physicists_hermite_polynomial_cartesian_3d,
+)
+from ._evaluate_polynomial import evaluate_polynomial
+from ._evaluate_polynomial_2d import evaluate_polynomial_2d
+from ._evaluate_polynomial_3d import evaluate_polynomial_3d
+from ._evaluate_polynomial_cartesian_2d import evaluate_polynomial_cartesian_2d
+from ._evaluate_polynomial_cartesian_3d import evaluate_polynomial_cartesian_3d
+from ._evaluate_polynomial_from_roots import evaluate_polynomial_from_roots
+from ._evaluate_probabilists_hermite_polynomial import (
+    evaluate_probabilists_hermite_polynomial,
+)
+from ._evaluate_probabilists_hermite_polynomial_2d import (
+    evaluate_probabilists_hermite_polynomial_2d,
+)
+from ._evaluate_probabilists_hermite_polynomial_3d import (
+    evaluate_probabilists_hermite_polynomial_3d,
+)
+from ._evaluate_probabilists_hermite_polynomial_cartersian_2d import (
+    evaluate_probabilists_hermite_polynomial_cartersian_2d,
+)
+from ._evaluate_probabilists_hermite_polynomial_cartersian_3d import (
+    evaluate_probabilists_hermite_polynomial_cartersian_3d,
+)
+from ._fit_chebyshev_polynomial import fit_chebyshev_polynomial
+from ._fit_laguerre_polynomial import fit_laguerre_polynomial
+from ._fit_legendre_polynomial import fit_legendre_polynomial
+from ._fit_physicists_hermite_polynomial import fit_physicists_hermite_polynomial
+from ._fit_polynomial import fit_polynomial
+from ._fit_probabilists_hermite_polynomial import fit_probabilists_hermite_polynomial
+from ._gauss_laguerre_quadrature import gauss_laguerre_quadrature
+from ._gauss_legendre_quadrature import gauss_legendre_quadrature
+from ._gauss_physicists_hermite_polynomial_quadrature import (
+    gauss_physicists_hermite_polynomial_quadrature,
+)
+from ._gauss_probabilists_hermite_polynomial_quadrature import (
+    gauss_probabilists_hermite_polynomial_quadrature,
+)
+from ._integrate_chebyshev_polynomial import integrate_chebyshev_polynomial
+from ._integrate_laguerre_polynomial import integrate_laguerre_polynomial
+from ._integrate_legendre_polynomial import integrate_legendre_polynomial
+from ._integrate_physicists_hermite_polynomial import (
+    integrate_physicists_hermite_polynomial,
+)
+from ._integrate_polynomial import integrate_polynomial
+from ._integrate_probabilists_hermite_polynomial import (
+    integrate_probabilists_hermite_polynomial,
+)
 from ._invert_euler_angle import invert_euler_angle
 from ._invert_quaternion import invert_quaternion
 from ._invert_rotation_matrix import invert_rotation_matrix
 from ._invert_rotation_vector import invert_rotation_vector
 from ._invert_transform import invert_transform
+from ._laguerre_polynomial_companion import laguerre_polynomial_companion
+from ._laguerre_polynomial_domain import laguerre_polynomial_domain
+from ._laguerre_polynomial_from_roots import laguerre_polynomial_from_roots
+from ._laguerre_polynomial_one import laguerre_polynomial_one
+from ._laguerre_polynomial_power import laguerre_polynomial_power
+from ._laguerre_polynomial_roots import laguerre_polynomial_roots
+from ._laguerre_polynomial_to_polynomial import laguerre_polynomial_to_polynomial
+from ._laguerre_polynomial_vandermonde import laguerre_polynomial_vandermonde
+from ._laguerre_polynomial_vandermonde_2d import laguerre_polynomial_vandermonde_2d
+from ._laguerre_polynomial_vandermonde_3d import laguerre_polynomial_vandermonde_3d
+from ._laguerre_polynomial_weight import laguerre_polynomial_weight
+from ._laguerre_polynomial_x import laguerre_polynomial_x
+from ._laguerre_polynomial_zero import laguerre_polynomial_zero
+from ._legendre_polynomial_companion import legendre_polynomial_companion
+from ._legendre_polynomial_domain import legendre_polynomial_domain
+from ._legendre_polynomial_from_roots import legendre_polynomial_from_roots
+from ._legendre_polynomial_one import legendre_polynomial_one
+from ._legendre_polynomial_power import legendre_polynomial_power
+from ._legendre_polynomial_roots import legendre_polynomial_roots
+from ._legendre_polynomial_to_polynomial import legendre_polynomial_to_polynomial
+from ._legendre_polynomial_vandermonde import legendre_polynomial_vandermonde
+from ._legendre_polynomial_vandermonde_2d import legendre_polynomial_vandermonde_2d
+from ._legendre_polynomial_vandermonde_3d import legendre_polynomial_vandermonde_3d
+from ._legendre_polynomial_weight import legendre_polynomial_weight
+from ._legendre_polynomial_x import legendre_polynomial_x
+from ._legendre_polynomial_zero import legendre_polynomial_zero
 from ._lennard_jones_potential import lennard_jones_potential
+from ._linear_chebyshev_polynomial import linear_chebyshev_polynomial
+from ._linear_laguerre_polynomial import linear_laguerre_polynomial
+from ._linear_legendre_polynomial import linear_legendre_polynomial
+from ._linear_physicists_hermite_polynomial import linear_physicists_hermite_polynomial
+from ._linear_polynomial import linear_polynomial
+from ._linear_probabilists_hermite_polynomial import (
+    linear_probabilists_hermite_polynomial,
+)
+from ._multiply_chebyshev_polynomial import multiply_chebyshev_polynomial
+from ._multiply_chebyshev_polynomial_by_x import multiply_chebyshev_polynomial_by_x
+from ._multiply_laguerre_polynomial import multiply_laguerre_polynomial
+from ._multiply_laguerre_polynomial_by_x import multiply_laguerre_polynomial_by_x
+from ._multiply_legendre_polynomial import multiply_legendre_polynomial
+from ._multiply_legendre_polynomial_by_x import multiply_legendre_polynomial_by_x
+from ._multiply_physicists_hermite_polynomial import (
+    multiply_physicists_hermite_polynomial,
+)
+from ._multiply_physicists_hermite_polynomial_by_x import (
+    multiply_physicists_hermite_polynomial_by_x,
+)
+from ._multiply_polynomial import multiply_polynomial
+from ._multiply_polynomial_by_x import multiply_polynomial_by_x
+from ._multiply_probabilists_hermite_polynomial import (
+    multiply_probabilists_hermite_polynomial,
+)
+from ._multiply_probabilists_hermite_polynomial_by_x import (
+    multiply_probabilists_hermite_polynomial_by_x,
+)
+from ._physicists_hermite_polynomial_companion import (
+    physicists_hermite_polynomial_companion,
+)
+from ._physicists_hermite_polynomial_domain import physicists_hermite_polynomial_domain
+from ._physicists_hermite_polynomial_from_roots import (
+    physicists_hermite_polynomial_from_roots,
+)
+from ._physicists_hermite_polynomial_one import physicists_hermite_polynomial_one
+from ._physicists_hermite_polynomial_power import physicists_hermite_polynomial_power
+from ._physicists_hermite_polynomial_roots import physicists_hermite_polynomial_roots
+from ._physicists_hermite_polynomial_to_polynomial import (
+    physicists_hermite_polynomial_to_polynomial,
+)
+from ._physicists_hermite_polynomial_vandermonde import (
+    physicists_hermite_polynomial_vandermonde,
+)
+from ._physicists_hermite_polynomial_vandermonde_2d import (
+    physicists_hermite_polynomial_vandermonde_2d,
+)
+from ._physicists_hermite_polynomial_vandermonde_3d import (
+    physicists_hermite_polynomial_vandermonde_3d,
+)
+from ._physicists_hermite_polynomial_weight import physicists_hermite_polynomial_weight
+from ._physicists_hermite_polynomial_x import physicists_hermite_polynomial_x
+from ._physicists_hermite_polynomial_zero import physicists_hermite_polynomial_zero
+from ._polynomial_companion import polynomial_companion
+from ._polynomial_domain import polynomial_domain
+from ._polynomial_from_roots import polynomial_from_roots
+from ._polynomial_one import polynomial_one
+from ._polynomial_power import polynomial_power
+from ._polynomial_roots import polynomial_roots
+from ._polynomial_to_chebyshev_polynomial import polynomial_to_chebyshev_polynomial
+from ._polynomial_to_laguerre_polynomial import polynomial_to_laguerre_polynomial
+from ._polynomial_to_legendre_polynomial import polynomial_to_legendre_polynomial
+from ._polynomial_to_physicists_hermite_polynomial import (
+    polynomial_to_physicists_hermite_polynomial,
+)
+from ._polynomial_to_probabilists_hermite_polynomial import (
+    polynomial_to_probabilists_hermite_polynomial,
+)
+from ._polynomial_vandermonde import polynomial_vandermonde
+from ._polynomial_vandermonde_2d import polynomial_vandermonde_2d
+from ._polynomial_vandermonde_3d import polynomial_vandermonde_3d
+from ._polynomial_x import polynomial_x
+from ._polynomial_zero import polynomial_zero
+from ._probabilists_hermite_polynomial_companion import (
+    probabilists_hermite_polynomial_companion,
+)
+from ._probabilists_hermite_polynomial_domain import (
+    probabilists_hermite_polynomial_domain,
+)
+from ._probabilists_hermite_polynomial_from_roots import (
+    probabilists_hermite_polynomial_from_roots,
+)
+from ._probabilists_hermite_polynomial_one import probabilists_hermite_polynomial_one
+from ._probabilists_hermite_polynomial_power import (
+    probabilists_hermite_polynomial_power,
+)
+from ._probabilists_hermite_polynomial_roots import (
+    probabilists_hermite_polynomial_roots,
+)
+from ._probabilists_hermite_polynomial_to_polynomial import (
+    probabilists_hermite_polynomial_to_polynomial,
+)
+from ._probabilists_hermite_polynomial_vandermonde import (
+    probabilists_hermite_polynomial_vandermonde,
+)
+from ._probabilists_hermite_polynomial_vandermonde_2d import (
+    probabilists_hermite_polynomial_vandermonde_2d,
+)
+from ._probabilists_hermite_polynomial_vandermonde_3d import (
+    probabilists_hermite_polynomial_vandermonde_3d,
+)
+from ._probabilists_hermite_polynomial_weight import (
+    probabilists_hermite_polynomial_weight,
+)
+from ._probabilists_hermite_polynomial_x import probabilists_hermite_polynomial_x
+from ._probabilists_hermite_polynomial_zero import probabilists_hermite_polynomial_zero
 from ._quaternion_identity import quaternion_identity
 from ._quaternion_magnitude import quaternion_magnitude
 from ._quaternion_mean import quaternion_mean
@@ -68,31 +328,225 @@
 from ._rotation_vector_to_rotation_matrix import (
     rotation_vector_to_rotation_matrix,
 )
+from ._subtract_chebyshev_polynomial import subtract_chebyshev_polynomial
+from ._subtract_laguerre_polynomial import subtract_laguerre_polynomial
+from ._subtract_legendre_polynomial import subtract_legendre_polynomial
+from ._subtract_physicists_hermite_polynomial import (
+    subtract_physicists_hermite_polynomial,
+)
+from ._subtract_polynomial import subtract_polynomial
+from ._subtract_probabilists_hermite_polynomial import (
+    subtract_probabilists_hermite_polynomial,
+)
 from ._translation_identity import translation_identity
+from ._trim_chebyshev_polynomial_coefficients import (
+    trim_chebyshev_polynomial_coefficients,
+)
+from ._trim_laguerre_polynomial_coefficients import (
+    trim_laguerre_polynomial_coefficients,
+)
+from ._trim_legendre_polynomial_coefficients import (
+    trim_legendre_polynomial_coefficients,
+)
+from ._trim_physicists_hermite_polynomial_coefficients import (
+    trim_physicists_hermite_polynomial_coefficients,
+)
+from ._trim_polynomial_coefficients import trim_polynomial_coefficients
+from ._trim_probabilists_hermite_polynomial_coefficients import (
+    trim_probabilists_hermite_polynomial_coefficients,
+)
 from .special import error_erf, error_erfc
 
 __all__ = [
+    "add_chebyshev_polynomial",
+    "add_laguerre_polynomial",
+    "add_legendre_polynomial",
+    "add_physicists_hermite_polynomial",
+    "add_polynomial",
+    "add_probabilists_hermite_polynomial",
     "apply_euler_angle",
     "apply_quaternion",
     "apply_rotation_matrix",
     "apply_rotation_vector",
     "apply_transform",
+    "evaluate_chebyshev_polynomial_cartesian_2d",
+    "evaluate_chebyshev_polynomial_cartesian_3d",
+    "chebyshev_interpolation",
+    "linear_chebyshev_polynomial",
+    "multiply_chebyshev_polynomial_by_x",
+    "chebyshev_zeros",
+    "chebyshev_extrema",
+    "chebyshev_gauss_quadrature",
+    "chebyshev_polynomial_companion",
+    "chebyshev_polynomial_domain",
+    "chebyshev_polynomial_from_roots",
+    "chebyshev_polynomial_one",
+    "chebyshev_polynomial_power",
+    "chebyshev_polynomial_roots",
+    "chebyshev_polynomial_to_polynomial",
+    "chebyshev_polynomial_vandermonde",
+    "chebyshev_polynomial_vandermonde_2d",
+    "chebyshev_polynomial_vandermonde_3d",
+    "chebyshev_polynomial_weight",
+    "chebyshev_polynomial_x",
+    "chebyshev_polynomial_zero",
     "compose_euler_angle",
     "compose_quaternion",
     "compose_rotation_matrix",
     "compose_rotation_vector",
+    "differentiate_chebyshev_polynomial",
+    "differentiate_laguerre_polynomial",
+    "differentiate_legendre_polynomial",
+    "differentiate_physicists_hermite_polynomial",
+    "differentiate_polynomial",
+    "differentiate_probabilists_hermite_polynomial",
+    "divide_chebyshev_polynomial",
+    "divide_laguerre_polynomial",
+    "divide_legendre_polynomial",
+    "divide_physicists_hermite_polynomial",
+    "divide_polynomial",
+    "divide_probabilists_hermite_polynomial",
     "euler_angle_identity",
     "euler_angle_magnitude",
     "euler_angle_mean",
     "euler_angle_to_quaternion",
     "euler_angle_to_rotation_matrix",
     "euler_angle_to_rotation_vector",
+    "evaluate_chebyshev_polynomial",
+    "evaluate_chebyshev_polynomial_2d",
+    "evaluate_chebyshev_polynomial_3d",
+    "evaluate_laguerre_polynomial",
+    "evaluate_laguerre_polynomial_2d",
+    "evaluate_laguerre_polynomial_3d",
+    "evaluate_legendre_polynomial",
+    "evaluate_legendre_polynomial_2d",
+    "evaluate_legendre_polynomial_3d",
+    "evaluate_physicists_hermite_polynomial",
+    "evaluate_physicists_hermite_polynomial_2d",
+    "evaluate_physicists_hermite_polynomial_3d",
+    "evaluate_polynomial",
+    "evaluate_polynomial_2d",
+    "evaluate_polynomial_3d",
+    "evaluate_polynomial_from_roots",
+    "evaluate_probabilists_hermite_polynomial",
+    "evaluate_probabilists_hermite_polynomial_2d",
+    "evaluate_probabilists_hermite_polynomial_3d",
+    "fit_chebyshev_polynomial",
+    "fit_laguerre_polynomial",
+    "fit_legendre_polynomial",
+    "fit_physicists_hermite_polynomial",
+    "fit_polynomial",
+    "fit_probabilists_hermite_polynomial",
+    "gauss_laguerre_quadrature",
+    "gauss_legendre_quadrature",
+    "gauss_physicists_hermite_polynomial_quadrature",
+    "gauss_probabilists_hermite_polynomial_quadrature",
+    "evaluate_probabilists_hermite_polynomial_cartersian_2d",
+    "evaluate_probabilists_hermite_polynomial_cartersian_3d",
+    "linear_probabilists_hermite_polynomial",
+    "multiply_probabilists_hermite_polynomial_by_x",
+    "evaluate_physicists_hermite_polynomial_cartesian_2d",
+    "evaluate_physicists_hermite_polynomial_cartesian_3d",
+    "linear_physicists_hermite_polynomial",
+    "multiply_physicists_hermite_polynomial_by_x",
+    "integrate_chebyshev_polynomial",
+    "integrate_laguerre_polynomial",
+    "integrate_legendre_polynomial",
+    "integrate_physicists_hermite_polynomial",
+    "integrate_polynomial",
+    "integrate_probabilists_hermite_polynomial",
     "invert_euler_angle",
     "invert_quaternion",
     "invert_rotation_matrix",
     "invert_rotation_vector",
     "invert_transform",
+    "evaluate_laguerre_polynomial_cartesian_2d",
+    "evaluate_laguerre_polynomial_cartesian_3d",
+    "linear_laguerre_polynomial",
+    "multiply_laguerre_polynomial_by_x",
+    "laguerre_polynomial_companion",
+    "laguerre_polynomial_domain",
+    "laguerre_polynomial_from_roots",
+    "laguerre_polynomial_one",
+    "laguerre_polynomial_power",
+    "laguerre_polynomial_roots",
+    "laguerre_polynomial_to_polynomial",
+    "laguerre_polynomial_vandermonde",
+    "laguerre_polynomial_vandermonde_2d",
+    "laguerre_polynomial_vandermonde_3d",
+    "laguerre_polynomial_weight",
+    "laguerre_polynomial_x",
+    "laguerre_polynomial_zero",
+    "legendre_polynomial_companion",
+    "legendre_polynomial_domain",
+    "legendre_polynomial_from_roots",
+    "legendre_polynomial_one",
+    "legendre_polynomial_power",
+    "legendre_polynomial_roots",
+    "legendre_polynomial_to_polynomial",
+    "legendre_polynomial_vandermonde",
+    "legendre_polynomial_vandermonde_2d",
+    "legendre_polynomial_vandermonde_3d",
+    "legendre_polynomial_weight",
+    "legendre_polynomial_x",
+    "legendre_polynomial_zero",
+    "evaluate_legendre_polynomial_cartesian_2d",
+    "evaluate_legendre_polynomial_cartesian_3d",
+    "linear_legendre_polynomial",
+    "multiply_legendre_polynomial_by_x",
     "lennard_jones_potential",
+    "multiply_chebyshev_polynomial",
+    "multiply_laguerre_polynomial",
+    "multiply_legendre_polynomial",
+    "multiply_physicists_hermite_polynomial",
+    "multiply_polynomial",
+    "multiply_probabilists_hermite_polynomial",
+    "physicists_hermite_polynomial_companion",
+    "physicists_hermite_polynomial_domain",
+    "physicists_hermite_polynomial_from_roots",
+    "physicists_hermite_polynomial_one",
+    "physicists_hermite_polynomial_power",
+    "physicists_hermite_polynomial_roots",
+    "physicists_hermite_polynomial_to_polynomial",
+    "physicists_hermite_polynomial_vandermonde",
+    "physicists_hermite_polynomial_vandermonde_2d",
+    "physicists_hermite_polynomial_vandermonde_3d",
+    "physicists_hermite_polynomial_weight",
+    "physicists_hermite_polynomial_x",
+    "physicists_hermite_polynomial_zero",
+    "evaluate_polynomial_cartesian_2d",
+    "evaluate_polynomial_cartesian_3d",
+    "linear_polynomial",
+    "multiply_polynomial_by_x",
+    "polynomial_companion",
+    "polynomial_domain",
+    "polynomial_from_roots",
+    "polynomial_one",
+    "polynomial_power",
+    "polynomial_roots",
+    "polynomial_to_chebyshev_polynomial",
+    "polynomial_to_laguerre_polynomial",
+    "polynomial_to_legendre_polynomial",
+    "polynomial_to_physicists_hermite_polynomial",
+    "polynomial_to_probabilists_hermite_polynomial",
+    "polynomial_vandermonde",
+    "polynomial_vandermonde_2d",
+    "polynomial_vandermonde_3d",
+    "polynomial_x",
+    "polynomial_zero",
+    "probabilists_hermite_polynomial_companion",
+    "probabilists_hermite_polynomial_domain",
+    "probabilists_hermite_polynomial_from_roots",
+    "probabilists_hermite_polynomial_one",
+    "probabilists_hermite_polynomial_power",
+    "probabilists_hermite_polynomial_roots",
+    "probabilists_hermite_polynomial_to_polynomial",
+    "probabilists_hermite_polynomial_vandermonde",
+    "probabilists_hermite_polynomial_vandermonde_2d",
+    "probabilists_hermite_polynomial_vandermonde_3d",
+    "probabilists_hermite_polynomial_weight",
+    "probabilists_hermite_polynomial_x",
+    "probabilists_hermite_polynomial_zero",
     "quaternion_identity",
     "quaternion_magnitude",
     "quaternion_mean",
@@ -116,5 +570,17 @@
     "rotation_vector_to_euler_angle",
     "rotation_vector_to_quaternion",
     "rotation_vector_to_rotation_matrix",
+    "subtract_chebyshev_polynomial",
+    "subtract_laguerre_polynomial",
+    "subtract_legendre_polynomial",
+    "subtract_physicists_hermite_polynomial",
+    "subtract_polynomial",
+    "subtract_probabilists_hermite_polynomial",
     "translation_identity",
+    "trim_chebyshev_polynomial_coefficients",
+    "trim_laguerre_polynomial_coefficients",
+    "trim_legendre_polynomial_coefficients",
+    "trim_physicists_hermite_polynomial_coefficients",
+    "trim_polynomial_coefficients",
+    "trim_probabilists_hermite_polynomial_coefficients",
 ]
diff --git a/src/beignet/_add_chebyshev_polynomial.py b/src/beignet/_add_chebyshev_polynomial.py
new file mode 100644
index 0000000000..cc620c3642
--- /dev/null
+++ b/src/beignet/_add_chebyshev_polynomial.py
@@ -0,0 +1,55 @@
+import torch
+from torch import Tensor
+
+
+def add_chebyshev_polynomial(input: Tensor, other: Tensor) -> Tensor:
+    r"""
+    Returns the sum of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = torch.concatenate(
+            [
+                other,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+
+        output = input + output
+    else:
+        output = torch.concatenate(
+            [
+                input,
+                torch.zeros(
+                    other.shape[0] - input.shape[0],
+                    dtype=input.dtype,
+                ),
+            ]
+        )
+
+        output = other + output
+
+    return output
diff --git a/src/beignet/_add_laguerre_polynomial.py b/src/beignet/_add_laguerre_polynomial.py
new file mode 100644
index 0000000000..e42ea5468f
--- /dev/null
+++ b/src/beignet/_add_laguerre_polynomial.py
@@ -0,0 +1,55 @@
+import torch
+from torch import Tensor
+
+
+def add_laguerre_polynomial(input: Tensor, other: Tensor) -> Tensor:
+    r"""
+    Returns the sum of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = torch.concatenate(
+            [
+                other,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+
+        output = input + output
+    else:
+        output = torch.concatenate(
+            [
+                input,
+                torch.zeros(
+                    other.shape[0] - input.shape[0],
+                    dtype=input.dtype,
+                ),
+            ]
+        )
+
+        output = other + output
+
+    return output
diff --git a/src/beignet/_add_legendre_polynomial.py b/src/beignet/_add_legendre_polynomial.py
new file mode 100644
index 0000000000..1376742b18
--- /dev/null
+++ b/src/beignet/_add_legendre_polynomial.py
@@ -0,0 +1,55 @@
+import torch
+from torch import Tensor
+
+
+def add_legendre_polynomial(input: Tensor, other: Tensor) -> Tensor:
+    r"""
+    Returns the sum of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = torch.concatenate(
+            [
+                other,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+
+        output = input + output
+    else:
+        output = torch.concatenate(
+            [
+                input,
+                torch.zeros(
+                    other.shape[0] - input.shape[0],
+                    dtype=input.dtype,
+                ),
+            ]
+        )
+
+        output = other + output
+
+    return output
diff --git a/src/beignet/_add_physicists_hermite_polynomial.py b/src/beignet/_add_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..89a81eda5a
--- /dev/null
+++ b/src/beignet/_add_physicists_hermite_polynomial.py
@@ -0,0 +1,55 @@
+import torch
+from torch import Tensor
+
+
+def add_physicists_hermite_polynomial(input: Tensor, other: Tensor) -> Tensor:
+    r"""
+    Returns the sum of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = torch.concatenate(
+            [
+                other,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+
+        output = input + output
+    else:
+        output = torch.concatenate(
+            [
+                input,
+                torch.zeros(
+                    other.shape[0] - input.shape[0],
+                    dtype=input.dtype,
+                ),
+            ]
+        )
+
+        output = other + output
+
+    return output
diff --git a/src/beignet/_add_polynomial.py b/src/beignet/_add_polynomial.py
new file mode 100644
index 0000000000..8ab149f446
--- /dev/null
+++ b/src/beignet/_add_polynomial.py
@@ -0,0 +1,55 @@
+import torch
+from torch import Tensor
+
+
+def add_polynomial(input: Tensor, other: Tensor) -> Tensor:
+    r"""
+    Returns the sum of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = torch.concatenate(
+            [
+                other,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+
+        output = input + output
+    else:
+        output = torch.concatenate(
+            [
+                input,
+                torch.zeros(
+                    other.shape[0] - input.shape[0],
+                    dtype=input.dtype,
+                ),
+            ]
+        )
+
+        output = other + output
+
+    return output
diff --git a/src/beignet/_add_probabilists_hermite_polynomial.py b/src/beignet/_add_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..12bf635141
--- /dev/null
+++ b/src/beignet/_add_probabilists_hermite_polynomial.py
@@ -0,0 +1,55 @@
+import torch
+from torch import Tensor
+
+
+def add_probabilists_hermite_polynomial(input: Tensor, other: Tensor) -> Tensor:
+    r"""
+    Returns the sum of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = torch.concatenate(
+            [
+                other,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+
+        output = input + output
+    else:
+        output = torch.concatenate(
+            [
+                input,
+                torch.zeros(
+                    other.shape[0] - input.shape[0],
+                    dtype=input.dtype,
+                ),
+            ]
+        )
+
+        output = other + output
+
+    return output
diff --git a/src/beignet/_chebyshev_extrema.py b/src/beignet/_chebyshev_extrema.py
new file mode 100644
index 0000000000..4a25411b51
--- /dev/null
+++ b/src/beignet/_chebyshev_extrema.py
@@ -0,0 +1,11 @@
+import math
+
+import torch
+from torch import Tensor
+
+
+def chebyshev_extrema(input: int) -> Tensor:
+    if input < 2:
+        raise ValueError
+
+    return torch.cos(torch.linspace(-math.pi, 0, input))
diff --git a/src/beignet/_chebyshev_gauss_quadrature.py b/src/beignet/_chebyshev_gauss_quadrature.py
new file mode 100644
index 0000000000..9a53473a75
--- /dev/null
+++ b/src/beignet/_chebyshev_gauss_quadrature.py
@@ -0,0 +1,16 @@
+import math
+from typing import Tuple
+
+import torch
+from torch import Tensor
+
+
+def chebyshev_gauss_quadrature(degree: int) -> Tuple[Tensor, Tensor]:
+    if not degree > 0:
+        raise ValueError
+
+    output = torch.cos(torch.arange(1, 2 * degree, 2) / (2 * degree) * math.pi)
+
+    weight = torch.ones(degree) * (math.pi / degree)
+
+    return output, weight
diff --git a/src/beignet/_chebyshev_interpolation.py b/src/beignet/_chebyshev_interpolation.py
new file mode 100644
index 0000000000..bce34541d3
--- /dev/null
+++ b/src/beignet/_chebyshev_interpolation.py
@@ -0,0 +1,45 @@
+import math
+from typing import Callable
+
+import torch
+from torch import Tensor
+
+
+def chebyshev_interpolation(
+    func: Callable[[Tensor, ...], Tensor],
+    degree: int,
+    *args,
+):
+    if degree < 0:
+        raise ValueError
+
+    order = degree + 1
+
+    if order < 1:
+        raise ValueError
+
+    zeros = torch.arange(-order + 1, order + 1, 2)
+
+    zeros = torch.sin(zeros * 0.5 * math.pi / order)
+
+    vandermonde = torch.empty([degree + 1, *zeros.shape], dtype=zeros.dtype)
+
+    vandermonde[0] = torch.ones_like(zeros)
+
+    if degree > 0:
+        vandermonde[1] = zeros
+
+        for i in range(2, degree + 1):
+            v = vandermonde[i - 1] * zeros * 2.0 - vandermonde[i - 2]
+
+            vandermonde[i] = v
+
+    vandermonde = torch.moveaxis(vandermonde, 0, -1)
+
+    output = vandermonde.T @ func(zeros, *args)
+
+    output[0] = output[0] / order
+
+    output[1:] = output[1:] / (order * 0.5)
+
+    return output
diff --git a/src/beignet/_chebyshev_polynomial_companion.py b/src/beignet/_chebyshev_polynomial_companion.py
new file mode 100644
index 0000000000..01428885d8
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_companion.py
@@ -0,0 +1,47 @@
+import math
+
+import torch
+from torch import Tensor
+
+
+def chebyshev_polynomial_companion(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] < 2:
+        raise ValueError
+
+    if input.shape[0] == 2:
+        return torch.tensor([[-input[0] / input[1]]])
+
+    n = input.shape[0] - 1
+
+    output = torch.zeros(
+        [
+            n,
+            n,
+        ],
+        dtype=input.dtype,
+    )
+
+    scale = torch.ones([n])
+
+    scale[1:] = math.sqrt(0.5)
+
+    shape = output.shape
+
+    output = torch.reshape(output, [-1])
+
+    x = torch.full([n - 1], 1 / 2)
+
+    x[0] = math.sqrt(0.5)
+
+    output[1 :: n + 1] = x
+    output[n :: n + 1] = x
+
+    output = torch.reshape(output, shape)
+
+    output[:, -1] = (
+        output[:, -1] + -(input[:-1] / input[-1]) * (scale / scale[-1]) * 0.5
+    )
+
+    return output
diff --git a/src/beignet/_chebyshev_polynomial_domain.py b/src/beignet/_chebyshev_polynomial_domain.py
new file mode 100644
index 0000000000..e82992ab84
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_domain.py
@@ -0,0 +1,3 @@
+import torch
+
+chebyshev_polynomial_domain = torch.tensor([-1.0, 1.0])
diff --git a/src/beignet/_chebyshev_polynomial_from_roots.py b/src/beignet/_chebyshev_polynomial_from_roots.py
new file mode 100644
index 0000000000..05dc168a84
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_from_roots.py
@@ -0,0 +1,86 @@
+import math
+
+import torch
+from torch import Tensor
+
+from ._linear_chebyshev_polynomial import linear_chebyshev_polynomial
+from ._multiply_chebyshev_polynomial import multiply_chebyshev_polynomial
+
+
+def chebyshev_polynomial_from_roots(input: Tensor) -> Tensor:
+    f = linear_chebyshev_polynomial
+    g = multiply_chebyshev_polynomial
+    if math.prod(input.shape) == 0:
+        return torch.ones([1])
+
+    input, _ = torch.sort(input)
+
+    ys = []
+
+    for x in input:
+        a = torch.zeros(input.shape[0] + 1, dtype=x.dtype)
+        b = f(-x, 1)
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            y = torch.concatenate(
+                [
+                    b,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+
+            y = a + y
+        else:
+            y = torch.concatenate(
+                [
+                    a,
+                    torch.zeros(
+                        b.shape[0] - a.shape[0],
+                        dtype=a.dtype,
+                    ),
+                ]
+            )
+
+            y = b + y
+
+        ys = [*ys, y]
+
+    p = torch.stack(ys)
+
+    m = p.shape[0]
+
+    x = m, p
+
+    while x[0] > 1:
+        m, r = divmod(x[0], 2)
+
+        z = x[1]
+
+        previous = torch.zeros([len(p), input.shape[0] + 1])
+
+        y = previous
+
+        for i in range(0, m):
+            y[i] = g(z[i], z[i + m])[: input.shape[0] + 1]
+
+        previous = y
+
+        if r:
+            previous[0] = g(previous[0], z[2 * m])[: input.shape[0] + 1]
+
+        x = m, previous
+
+    _, output = x
+
+    return output[0]
diff --git a/src/beignet/_chebyshev_polynomial_one.py b/src/beignet/_chebyshev_polynomial_one.py
new file mode 100644
index 0000000000..dbb5ba7803
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_one.py
@@ -0,0 +1,3 @@
+import torch
+
+chebyshev_polynomial_one = torch.tensor([1.0])
diff --git a/src/beignet/_chebyshev_polynomial_power.py b/src/beignet/_chebyshev_polynomial_power.py
new file mode 100644
index 0000000000..6667e1eacf
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_power.py
@@ -0,0 +1,55 @@
+import math
+
+import torch
+import torchaudio.functional
+from torch import Tensor
+
+from ._add_chebyshev_polynomial import add_chebyshev_polynomial
+
+
+def chebyshev_polynomial_power(
+    input: Tensor,
+    exponent: float | Tensor,
+    maximum_exponent: float | Tensor = 16.0,
+) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    _exponent = int(exponent)
+
+    if _exponent != exponent or _exponent < 0:
+        raise ValueError
+
+    if maximum_exponent is not None and _exponent > maximum_exponent:
+        raise ValueError
+
+    match _exponent:
+        case 0:
+            output = torch.tensor([1.0], dtype=input.dtype)
+        case 1:
+            output = input
+        case _:
+            output = torch.zeros(input.shape[0] * exponent, dtype=input.dtype)
+
+            output = add_chebyshev_polynomial(output, input)
+
+            index1 = math.prod(input.shape)
+            output2 = torch.zeros(2 * index1 - 1, dtype=input.dtype)
+            output2[index1 - 1 :] = input / 2.0
+            output2 = torch.flip(output2, dims=[0]) + output2
+            zs = output2
+
+            index = math.prod(output.shape)
+            output1 = torch.zeros(2 * index - 1, dtype=output.dtype)
+            output1[index - 1 :] = output / 2.0
+            output1 = torch.flip(output1, dims=[0]) + output1
+            output = output1
+
+            for _ in range(2, _exponent + 1):
+                output = torchaudio.functional.convolve(output, zs, mode="same")
+
+            n = (math.prod(output.shape) + 1) // 2
+            c = output[n - 1 :]
+            c[1:n] = c[1:n] * 2.0
+            output = c
+
+    return output
diff --git a/src/beignet/_chebyshev_polynomial_roots.py b/src/beignet/_chebyshev_polynomial_roots.py
new file mode 100644
index 0000000000..08d166808e
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_roots.py
@@ -0,0 +1,25 @@
+import torch
+from torch import Tensor
+
+from ._chebyshev_polynomial_companion import chebyshev_polynomial_companion
+
+
+def chebyshev_polynomial_roots(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] <= 1:
+        return torch.tensor([], dtype=input.dtype)
+
+    if input.shape[0] == 2:
+        return torch.tensor([-input[0] / input[1]])
+
+    output = chebyshev_polynomial_companion(input)
+
+    output = torch.flip(output, dims=[0])
+    output = torch.flip(output, dims=[1])
+
+    output = torch.linalg.eigvals(output)
+
+    output, _ = torch.sort(output.real)
+
+    return output
diff --git a/src/beignet/_chebyshev_polynomial_to_polynomial.py b/src/beignet/_chebyshev_polynomial_to_polynomial.py
new file mode 100644
index 0000000000..d82fded563
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_to_polynomial.py
@@ -0,0 +1,36 @@
+import torch
+from torch import Tensor
+
+from ._add_polynomial import add_polynomial
+from ._multiply_polynomial_by_x import multiply_polynomial_by_x
+from ._subtract_polynomial import subtract_polynomial
+
+
+def chebyshev_polynomial_to_polynomial(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    n = input.shape[0]
+
+    if n < 3:
+        return input
+
+    c0 = torch.zeros_like(input)
+    c0[0] = input[-2]
+
+    c1 = torch.zeros_like(input)
+    c1[0] = input[-1]
+
+    for index in range(0, n - 2):
+        i1 = n - 1 - index
+
+        tmp = c0
+
+        c0 = subtract_polynomial(input[i1 - 2], c1)
+
+        c1 = add_polynomial(tmp, multiply_polynomial_by_x(c1, "same") * 2)
+
+    output = multiply_polynomial_by_x(c1, "same")
+
+    output = add_polynomial(c0, output)
+
+    return output
diff --git a/src/beignet/_chebyshev_polynomial_vandermonde.py b/src/beignet/_chebyshev_polynomial_vandermonde.py
new file mode 100644
index 0000000000..25a0be6402
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_vandermonde.py
@@ -0,0 +1,28 @@
+import torch
+from torch import Tensor
+
+
+def chebyshev_polynomial_vandermonde(
+    x: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    if degree < 0:
+        raise ValueError
+
+    x = torch.atleast_1d(x)
+    dims = (degree + 1,) + x.shape
+    dtyp = torch.promote_types(x.dtype, torch.tensor(0.0).dtype)
+    x = x.to(dtyp)
+    v = torch.empty(dims, dtype=dtyp)
+
+    v[0] = torch.ones_like(x)
+
+    if degree > 0:
+        v[1] = x
+
+        x2 = 2 * x
+
+        for index in range(2, degree + 1):
+            v[index] = v[index - 1] * x2 - v[index - 2]
+
+    return torch.moveaxis(v, 0, -1)
diff --git a/src/beignet/_chebyshev_polynomial_vandermonde_2d.py b/src/beignet/_chebyshev_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..8acb5539e1
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_vandermonde_2d.py
@@ -0,0 +1,49 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._chebyshev_polynomial_vandermonde import chebyshev_polynomial_vandermonde
+
+
+def chebyshev_polynomial_vandermonde_2d(
+    x: Tensor,
+    y: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    functions = (
+        chebyshev_polynomial_vandermonde,
+        chebyshev_polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_chebyshev_polynomial_vandermonde_3d.py b/src/beignet/_chebyshev_polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..0cface76a0
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_vandermonde_3d.py
@@ -0,0 +1,51 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._chebyshev_polynomial_vandermonde import chebyshev_polynomial_vandermonde
+
+
+def chebyshev_polynomial_vandermonde_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    functions = (
+        chebyshev_polynomial_vandermonde,
+        chebyshev_polynomial_vandermonde,
+        chebyshev_polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y, z]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y, z)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_chebyshev_polynomial_weight.py b/src/beignet/_chebyshev_polynomial_weight.py
new file mode 100644
index 0000000000..6092093b58
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_weight.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def chebyshev_polynomial_weight(input: Tensor) -> Tensor:
+    return 1.0 / (torch.sqrt(1.0 + input) * torch.sqrt(1.0 - input))
diff --git a/src/beignet/_chebyshev_polynomial_x.py b/src/beignet/_chebyshev_polynomial_x.py
new file mode 100644
index 0000000000..fd8562d8fc
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_x.py
@@ -0,0 +1,3 @@
+import torch
+
+chebyshev_polynomial_x = torch.tensor([0.0, 1.0])
diff --git a/src/beignet/_chebyshev_polynomial_zero.py b/src/beignet/_chebyshev_polynomial_zero.py
new file mode 100644
index 0000000000..5cfacddb3f
--- /dev/null
+++ b/src/beignet/_chebyshev_polynomial_zero.py
@@ -0,0 +1,3 @@
+import torch
+
+chebyshev_polynomial_zero = torch.tensor([0.0])
diff --git a/src/beignet/_chebyshev_zeros.py b/src/beignet/_chebyshev_zeros.py
new file mode 100644
index 0000000000..a1d583c354
--- /dev/null
+++ b/src/beignet/_chebyshev_zeros.py
@@ -0,0 +1,11 @@
+import math
+
+import torch
+from torch import Tensor
+
+
+def chebyshev_zeros(input: int) -> Tensor:
+    if input < 1:
+        raise ValueError
+
+    return torch.sin(0.5 * math.pi / input * torch.arange(-input + 1, input + 1, 2))
diff --git a/src/beignet/_differentiate_chebyshev_polynomial.py b/src/beignet/_differentiate_chebyshev_polynomial.py
new file mode 100644
index 0000000000..2bb2ca57a2
--- /dev/null
+++ b/src/beignet/_differentiate_chebyshev_polynomial.py
@@ -0,0 +1,64 @@
+import torch
+from torch import Tensor
+
+
+def differentiate_chebyshev_polynomial(
+    input: Tensor,
+    order=1,
+    scale=1,
+    axis=0,
+) -> Tensor:
+    r"""
+    Returns the derivative of a polynomial.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    order : Tensor, optional
+
+    scale : Tensor, optional
+
+    dim : int, default=0
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the derivative.
+    """
+    if order < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    if order == 0:
+        return input
+
+    output = torch.moveaxis(input, axis, 0)
+
+    n = output.shape[0]
+
+    if order >= n:
+        output = torch.zeros_like(output[:1])
+    else:
+        for _ in range(order):
+            n = n - 1
+
+            output = output * scale
+
+            derivative = torch.empty((n,) + output.shape[1:], dtype=output.dtype)
+
+            for i in range(0, n - 2):
+                j = n - i
+
+                derivative[j - 1] = (2 * j) * output[j]
+
+                output[j - 2] += (j * output[j]) / (j - 2)
+
+            if n > 1:
+                derivative[1] = 4 * output[2]
+
+            derivative[0] = output[1]
+
+    return torch.moveaxis(output, 0, axis)
diff --git a/src/beignet/_differentiate_laguerre_polynomial.py b/src/beignet/_differentiate_laguerre_polynomial.py
new file mode 100644
index 0000000000..aa869864ef
--- /dev/null
+++ b/src/beignet/_differentiate_laguerre_polynomial.py
@@ -0,0 +1,78 @@
+import torch
+from torch import Tensor
+
+
+def differentiate_laguerre_polynomial(
+    input,
+    order=1,
+    scale=1,
+    axis=0,
+) -> Tensor:
+    r"""
+    Returns the derivative of a polynomial.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    order : Tensor, optional
+
+    scale : Tensor, optional
+
+    dim : int, default=0
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the derivative.
+    """
+    if order < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    if order == 0:
+        return input
+
+    input = torch.moveaxis(input, axis, 0)
+    n = input.shape[0]
+    if order >= n:
+        input = torch.zeros_like(input[:1])
+    else:
+        for _ in range(order):
+            n = n - 1
+
+            input *= scale
+
+            der = torch.empty((n,) + input.shape[1:], dtype=input.dtype)
+
+            def body(k, der_c, n=n):
+                j = n - k
+
+                der, c = der_c
+
+                der[j - 1] = -c[j]
+
+                c[j - 1] += c[j]
+
+                return der, c
+
+            b = n - 1
+
+            x = (der, input)
+
+            y = x
+
+            for index in range(0, b):
+                y = body(index, y)
+
+            der, input = y
+
+            der[0] = -input[1]
+
+            input = der
+
+    input = torch.moveaxis(input, 0, axis)
+
+    return input
diff --git a/src/beignet/_differentiate_legendre_polynomial.py b/src/beignet/_differentiate_legendre_polynomial.py
new file mode 100644
index 0000000000..a1ea826830
--- /dev/null
+++ b/src/beignet/_differentiate_legendre_polynomial.py
@@ -0,0 +1,81 @@
+import torch
+from torch import Tensor
+
+
+def differentiate_legendre_polynomial(
+    input,
+    order=1,
+    scale=1,
+    axis=0,
+) -> Tensor:
+    r"""
+    Returns the derivative of a polynomial.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    order : Tensor, optional
+
+    scale : Tensor, optional
+
+    dim : int, default=0
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the derivative.
+    """
+    if order < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    if order == 0:
+        return input
+
+    input = torch.moveaxis(input, axis, 0)
+
+    n = input.shape[0]
+
+    if order >= n:
+        input = torch.zeros_like(input[:1])
+    else:
+        for _ in range(order):
+            n = n - 1
+            input *= scale
+            der = torch.empty((n,) + input.shape[1:], dtype=input.dtype)
+
+            def body(k, der_c, n=n):
+                j = n - k
+
+                der, c = der_c
+
+                der[j - 1] = (2 * j - 1) * c[j]
+
+                c[j - 2] += c[j]
+
+                return der, c
+
+            b = n - 2
+
+            x = (der, input)
+
+            y = x
+
+            for index in range(0, b):
+                y = body(index, y)
+
+            der, input = y
+
+            if n > 1:
+                der[1] = 3 * input[2]
+
+            der[0] = input[1]
+
+            input = der
+
+    input = torch.moveaxis(input, 0, axis)
+
+    return input
diff --git a/src/beignet/_differentiate_physicists_hermite_polynomial.py b/src/beignet/_differentiate_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..bbdefa2dd6
--- /dev/null
+++ b/src/beignet/_differentiate_physicists_hermite_polynomial.py
@@ -0,0 +1,60 @@
+import torch
+from torch import Tensor
+
+
+def differentiate_physicists_hermite_polynomial(
+    input,
+    order=1,
+    scale=1,
+    axis=0,
+) -> Tensor:
+    r"""
+    Returns the derivative of a polynomial.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    order : Tensor, optional
+
+    scale : Tensor, optional
+
+    dim : int, default=0
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the derivative.
+    """
+    if order < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    if order == 0:
+        return input
+
+    input = torch.moveaxis(input, axis, 0)
+
+    n = input.shape[0]
+
+    if order >= n:
+        input = torch.zeros_like(input[:1])
+    else:
+        for _ in range(order):
+            n = n - 1
+
+            input *= scale
+
+            der = torch.empty((n,) + input.shape[1:], dtype=input.dtype)
+
+            j = torch.arange(n, 0, -1)
+
+            der[j - 1] = (2 * j * (input[j]).T).T
+
+            input = der
+
+    input = torch.moveaxis(input, 0, axis)
+
+    return input
diff --git a/src/beignet/_differentiate_polynomial.py b/src/beignet/_differentiate_polynomial.py
new file mode 100644
index 0000000000..80941fffd3
--- /dev/null
+++ b/src/beignet/_differentiate_polynomial.py
@@ -0,0 +1,55 @@
+import torch
+from torch import Tensor
+
+
+def differentiate_polynomial(
+    input: Tensor,
+    order: Tensor | None = None,
+    scale: Tensor | None = None,
+    dim: int = 0,
+) -> Tensor:
+    r"""
+    Returns the derivative of a polynomial.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    order : Tensor, optional
+
+    scale : Tensor, optional
+
+    dim : int, default=0
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the derivative.
+    """
+    input = torch.atleast_1d(input)
+
+    if order == 0:
+        return input
+
+    input = torch.moveaxis(input, dim, 0)
+
+    if order >= input.shape[0]:
+        output = torch.zeros_like(input[:1])
+    else:
+        d = torch.arange(input.shape[0])
+
+        output = input
+
+        for _ in range(0, order):
+            output = (d * output.T).T
+
+            output = torch.roll(output, -1, dims=[0]) * scale
+
+            output[-1] = 0.0
+
+        output = output[:-order]
+
+    output = torch.moveaxis(output, 0, dim)
+
+    return output
diff --git a/src/beignet/_differentiate_probabilists_hermite_polynomial.py b/src/beignet/_differentiate_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..d5bc1f7530
--- /dev/null
+++ b/src/beignet/_differentiate_probabilists_hermite_polynomial.py
@@ -0,0 +1,60 @@
+import torch
+from torch import Tensor
+
+
+def differentiate_probabilists_hermite_polynomial(
+    input,
+    order=1,
+    scale=1,
+    axis=0,
+) -> Tensor:
+    r"""
+    Returns the derivative of a polynomial.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    order : Tensor, optional
+
+    scale : Tensor, optional
+
+    dim : int, default=0
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the derivative.
+    """
+    if order < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    if order == 0:
+        return input
+
+    input = torch.moveaxis(input, axis, 0)
+
+    n = input.shape[0]
+
+    if order >= n:
+        input = torch.zeros_like(input[:1])
+    else:
+        for _ in range(order):
+            n = n - 1
+
+            input = input * scale
+
+            der = torch.empty((n,) + input.shape[1:], dtype=input.dtype)
+
+            j = torch.arange(n, 0, -1)
+
+            der[j - 1] = (j * (input[j]).T).T
+
+            input = der
+
+    input = torch.moveaxis(input, 0, axis)
+
+    return input
diff --git a/src/beignet/_divide_chebyshev_polynomial.py b/src/beignet/_divide_chebyshev_polynomial.py
new file mode 100644
index 0000000000..ff0dadb0af
--- /dev/null
+++ b/src/beignet/_divide_chebyshev_polynomial.py
@@ -0,0 +1,149 @@
+from typing import Tuple
+
+import torch
+from torch import Tensor
+
+from ._multiply_chebyshev_polynomial import multiply_chebyshev_polynomial
+
+
+def divide_chebyshev_polynomial(
+    input: Tensor,
+    other: Tensor,
+) -> Tuple[Tensor, Tensor]:
+    r"""
+    Returns the quotient and remainder of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tuple[Tensor, Tensor]
+        Polynomial coefficients of the quotient and remainder.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    m = input.shape[0]
+    n = other.shape[0]
+
+    if m < n:
+        return torch.zeros_like(input[:1]), input
+
+    if n == 1:
+        return input / other[-1], torch.zeros_like(input[:1])
+
+    def f(x: Tensor) -> Tensor:
+        indicies = torch.flip(x, [0])
+
+        indicies = torch.nonzero(indicies, as_tuple=False)
+
+        if indicies.shape[0] > 1:
+            indicies = indicies[:1]
+
+        if indicies.shape[0] < 1:
+            indicies = torch.concatenate(
+                [
+                    indicies,
+                    torch.full(
+                        [
+                            1 - indicies.shape[0],
+                            indicies.shape[1],
+                        ],
+                        0,
+                    ),
+                ],
+                0,
+            )
+
+        return x.shape[0] - 1 - indicies[0][0]
+
+    quotient = torch.zeros(m - n + 1, dtype=input.dtype)
+
+    ridx = input.shape[0] - 1
+
+    size = m - f(other) - 1
+
+    y = torch.zeros(m + n + 1, dtype=input.dtype)
+
+    y[size] = 1.0
+
+    x = quotient, input, y, ridx
+
+    for index in range(0, size):
+        quotient, remainder, y2, ridx1 = x
+
+        j = size - index
+
+        p = multiply_chebyshev_polynomial(y2, other)
+
+        pidx = f(p)
+
+        t = remainder[ridx1] / p[pidx]
+
+        remainder_modified = remainder.clone()
+        remainder_modified[ridx1] = 0.0
+
+        a = remainder_modified
+
+        p_modified = p.clone()
+        p_modified[pidx] = 0.0
+
+        b = t * p_modified
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+            output = a + output
+        else:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output[: a.shape[0]] + a,
+                    output[a.shape[0] :],
+                ],
+            )
+
+        remainder = output
+
+        remainder = remainder[: remainder.shape[0]]
+
+        quotient[j] = t
+
+        ridx1 = ridx1 - 1
+
+        y2 = torch.roll(y2, -1)
+
+        x = quotient, remainder, y2, ridx1
+
+    quotient, remainder, _, _ = x
+
+    return quotient, remainder
diff --git a/src/beignet/_divide_laguerre_polynomial.py b/src/beignet/_divide_laguerre_polynomial.py
new file mode 100644
index 0000000000..02b6e6a33e
--- /dev/null
+++ b/src/beignet/_divide_laguerre_polynomial.py
@@ -0,0 +1,149 @@
+from typing import Tuple
+
+import torch
+from torch import Tensor
+
+from ._multiply_laguerre_polynomial import multiply_laguerre_polynomial
+
+
+def divide_laguerre_polynomial(
+    input: Tensor,
+    other: Tensor,
+) -> Tuple[Tensor, Tensor]:
+    r"""
+    Returns the quotient and remainder of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tuple[Tensor, Tensor]
+        Polynomial coefficients of the quotient and remainder.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    m = input.shape[0]
+    n = other.shape[0]
+
+    if m < n:
+        return torch.zeros_like(input[:1]), input
+
+    if n == 1:
+        return input / other[-1], torch.zeros_like(input[:1])
+
+    def f(x: Tensor) -> Tensor:
+        indicies = torch.flip(x, [0])
+
+        indicies = torch.nonzero(indicies, as_tuple=False)
+
+        if indicies.shape[0] > 1:
+            indicies = indicies[:1]
+
+        if indicies.shape[0] < 1:
+            indicies = torch.concatenate(
+                [
+                    indicies,
+                    torch.full(
+                        [
+                            1 - indicies.shape[0],
+                            indicies.shape[1],
+                        ],
+                        0,
+                    ),
+                ],
+                0,
+            )
+
+        return x.shape[0] - 1 - indicies[0][0]
+
+    quotient = torch.zeros(m - n + 1, dtype=input.dtype)
+
+    ridx = input.shape[0] - 1
+
+    size = m - f(other) - 1
+
+    y = torch.zeros(m + n + 1, dtype=input.dtype)
+
+    y[size] = 1.0
+
+    x = quotient, input, y, ridx
+
+    for index in range(0, size):
+        quotient, remainder, y2, ridx1 = x
+
+        j = size - index
+
+        p = multiply_laguerre_polynomial(y2, other)
+
+        pidx = f(p)
+
+        t = remainder[ridx1] / p[pidx]
+
+        remainder_modified = remainder.clone()
+        remainder_modified[ridx1] = 0.0
+
+        a = remainder_modified
+
+        p_modified = p.clone()
+        p_modified[pidx] = 0.0
+
+        b = t * p_modified
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+            output = a + output
+        else:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output[: a.shape[0]] + a,
+                    output[a.shape[0] :],
+                ],
+            )
+
+        remainder = output
+
+        remainder = remainder[: remainder.shape[0]]
+
+        quotient[j] = t
+
+        ridx1 = ridx1 - 1
+
+        y2 = torch.roll(y2, -1)
+
+        x = quotient, remainder, y2, ridx1
+
+    quotient, remainder, _, _ = x
+
+    return quotient, remainder
diff --git a/src/beignet/_divide_legendre_polynomial.py b/src/beignet/_divide_legendre_polynomial.py
new file mode 100644
index 0000000000..b1cdce5a13
--- /dev/null
+++ b/src/beignet/_divide_legendre_polynomial.py
@@ -0,0 +1,149 @@
+from typing import Tuple
+
+import torch
+from torch import Tensor
+
+from ._multiply_legendre_polynomial import multiply_legendre_polynomial
+
+
+def divide_legendre_polynomial(
+    input: Tensor,
+    other: Tensor,
+) -> Tuple[Tensor, Tensor]:
+    r"""
+    Returns the quotient and remainder of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tuple[Tensor, Tensor]
+        Polynomial coefficients of the quotient and remainder.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    m = input.shape[0]
+    n = other.shape[0]
+
+    if m < n:
+        return torch.zeros_like(input[:1]), input
+
+    if n == 1:
+        return input / other[-1], torch.zeros_like(input[:1])
+
+    def f(x: Tensor) -> Tensor:
+        indicies = torch.flip(x, [0])
+
+        indicies = torch.nonzero(indicies, as_tuple=False)
+
+        if indicies.shape[0] > 1:
+            indicies = indicies[:1]
+
+        if indicies.shape[0] < 1:
+            indicies = torch.concatenate(
+                [
+                    indicies,
+                    torch.full(
+                        [
+                            1 - indicies.shape[0],
+                            indicies.shape[1],
+                        ],
+                        0,
+                    ),
+                ],
+                0,
+            )
+
+        return x.shape[0] - 1 - indicies[0][0]
+
+    quotient = torch.zeros(m - n + 1, dtype=input.dtype)
+
+    ridx = input.shape[0] - 1
+
+    size = m - f(other) - 1
+
+    y = torch.zeros(m + n + 1, dtype=input.dtype)
+
+    y[size] = 1.0
+
+    x = quotient, input, y, ridx
+
+    for index in range(0, size):
+        quotient, remainder, y2, ridx1 = x
+
+        j = size - index
+
+        p = multiply_legendre_polynomial(y2, other)
+
+        pidx = f(p)
+
+        t = remainder[ridx1] / p[pidx]
+
+        remainder_modified = remainder.clone()
+        remainder_modified[ridx1] = 0.0
+
+        a = remainder_modified
+
+        p_modified = p.clone()
+        p_modified[pidx] = 0.0
+
+        b = t * p_modified
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+            output = a + output
+        else:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output[: a.shape[0]] + a,
+                    output[a.shape[0] :],
+                ],
+            )
+
+        remainder = output
+
+        remainder = remainder[: remainder.shape[0]]
+
+        quotient[j] = t
+
+        ridx1 = ridx1 - 1
+
+        y2 = torch.roll(y2, -1)
+
+        x = quotient, remainder, y2, ridx1
+
+    quotient, remainder, _, _ = x
+
+    return quotient, remainder
diff --git a/src/beignet/_divide_physicists_hermite_polynomial.py b/src/beignet/_divide_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..b0bfba74b4
--- /dev/null
+++ b/src/beignet/_divide_physicists_hermite_polynomial.py
@@ -0,0 +1,151 @@
+from typing import Tuple
+
+import torch
+from torch import Tensor
+
+from ._multiply_physicists_hermite_polynomial import (
+    multiply_physicists_hermite_polynomial,
+)
+
+
+def divide_physicists_hermite_polynomial(
+    input: Tensor,
+    other: Tensor,
+) -> Tuple[Tensor, Tensor]:
+    r"""
+    Returns the quotient and remainder of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tuple[Tensor, Tensor]
+        Polynomial coefficients of the quotient and remainder.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    m = input.shape[0]
+    n = other.shape[0]
+
+    if m < n:
+        return torch.zeros_like(input[:1]), input
+
+    if n == 1:
+        return input / other[-1], torch.zeros_like(input[:1])
+
+    def f(x: Tensor) -> Tensor:
+        indicies = torch.flip(x, [0])
+
+        indicies = torch.nonzero(indicies, as_tuple=False)
+
+        if indicies.shape[0] > 1:
+            indicies = indicies[:1]
+
+        if indicies.shape[0] < 1:
+            indicies = torch.concatenate(
+                [
+                    indicies,
+                    torch.full(
+                        [
+                            1 - indicies.shape[0],
+                            indicies.shape[1],
+                        ],
+                        0,
+                    ),
+                ],
+                0,
+            )
+
+        return x.shape[0] - 1 - indicies[0][0]
+
+    quotient = torch.zeros(m - n + 1, dtype=input.dtype)
+
+    ridx = input.shape[0] - 1
+
+    size = m - f(other) - 1
+
+    y = torch.zeros(m + n + 1, dtype=input.dtype)
+
+    y[size] = 1.0
+
+    x = quotient, input, y, ridx
+
+    for index in range(0, size):
+        quotient, remainder, y2, ridx1 = x
+
+        j = size - index
+
+        p = multiply_physicists_hermite_polynomial(y2, other)
+
+        pidx = f(p)
+
+        t = remainder[ridx1] / p[pidx]
+
+        remainder_modified = remainder.clone()
+        remainder_modified[ridx1] = 0.0
+
+        a = remainder_modified
+
+        p_modified = p.clone()
+        p_modified[pidx] = 0.0
+
+        b = t * p_modified
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+            output = a + output
+        else:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output[: a.shape[0]] + a,
+                    output[a.shape[0] :],
+                ],
+            )
+
+        remainder = output
+
+        remainder = remainder[: remainder.shape[0]]
+
+        quotient[j] = t
+
+        ridx1 = ridx1 - 1
+
+        y2 = torch.roll(y2, -1)
+
+        x = quotient, remainder, y2, ridx1
+
+    quotient, remainder, _, _ = x
+
+    return quotient, remainder
diff --git a/src/beignet/_divide_polynomial.py b/src/beignet/_divide_polynomial.py
new file mode 100644
index 0000000000..7f71922bb4
--- /dev/null
+++ b/src/beignet/_divide_polynomial.py
@@ -0,0 +1,149 @@
+from typing import Tuple
+
+import torch
+from torch import Tensor
+
+from ._multiply_polynomial import multiply_polynomial
+
+
+def divide_polynomial(
+    input: Tensor,
+    other: Tensor,
+) -> Tuple[Tensor, Tensor]:
+    r"""
+    Returns the quotient and remainder of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tuple[Tensor, Tensor]
+        Polynomial coefficients of the quotient and remainder.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    m = input.shape[0]
+    n = other.shape[0]
+
+    if m < n:
+        return torch.zeros_like(input[:1]), input
+
+    if n == 1:
+        return input / other[-1], torch.zeros_like(input[:1])
+
+    def f(x: Tensor) -> Tensor:
+        indicies = torch.flip(x, [0])
+
+        indicies = torch.nonzero(indicies, as_tuple=False)
+
+        if indicies.shape[0] > 1:
+            indicies = indicies[:1]
+
+        if indicies.shape[0] < 1:
+            indicies = torch.concatenate(
+                [
+                    indicies,
+                    torch.full(
+                        [
+                            1 - indicies.shape[0],
+                            indicies.shape[1],
+                        ],
+                        0,
+                    ),
+                ],
+                0,
+            )
+
+        return x.shape[0] - 1 - indicies[0][0]
+
+    quotient = torch.zeros(m - n + 1, dtype=input.dtype)
+
+    ridx = input.shape[0] - 1
+
+    size = m - f(other) - 1
+
+    y = torch.zeros(m + n + 1, dtype=input.dtype)
+
+    y[size] = 1.0
+
+    x = quotient, input, y, ridx
+
+    for index in range(0, size):
+        quotient, remainder, y2, ridx1 = x
+
+        j = size - index
+
+        p = multiply_polynomial(y2, other)
+
+        pidx = f(p)
+
+        t = remainder[ridx1] / p[pidx]
+
+        remainder_modified = remainder.clone()
+        remainder_modified[ridx1] = 0.0
+
+        a = remainder_modified
+
+        p_modified = p.clone()
+        p_modified[pidx] = 0.0
+
+        b = t * p_modified
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+            output = a + output
+        else:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output[: a.shape[0]] + a,
+                    output[a.shape[0] :],
+                ],
+            )
+
+        remainder = output
+
+        remainder = remainder[: remainder.shape[0]]
+
+        quotient[j] = t
+
+        ridx1 = ridx1 - 1
+
+        y2 = torch.roll(y2, -1)
+
+        x = quotient, remainder, y2, ridx1
+
+    quotient, remainder, _, _ = x
+
+    return quotient, remainder
diff --git a/src/beignet/_divide_probabilists_hermite_polynomial.py b/src/beignet/_divide_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..701b2f219c
--- /dev/null
+++ b/src/beignet/_divide_probabilists_hermite_polynomial.py
@@ -0,0 +1,151 @@
+from typing import Tuple
+
+import torch
+from torch import Tensor
+
+from ._multiply_probabilists_hermite_polynomial import (
+    multiply_probabilists_hermite_polynomial,
+)
+
+
+def divide_probabilists_hermite_polynomial(
+    input: Tensor,
+    other: Tensor,
+) -> Tuple[Tensor, Tensor]:
+    r"""
+    Returns the quotient and remainder of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tuple[Tensor, Tensor]
+        Polynomial coefficients of the quotient and remainder.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    m = input.shape[0]
+    n = other.shape[0]
+
+    if m < n:
+        return torch.zeros_like(input[:1]), input
+
+    if n == 1:
+        return input / other[-1], torch.zeros_like(input[:1])
+
+    def f(x: Tensor) -> Tensor:
+        indicies = torch.flip(x, [0])
+
+        indicies = torch.nonzero(indicies, as_tuple=False)
+
+        if indicies.shape[0] > 1:
+            indicies = indicies[:1]
+
+        if indicies.shape[0] < 1:
+            indicies = torch.concatenate(
+                [
+                    indicies,
+                    torch.full(
+                        [
+                            1 - indicies.shape[0],
+                            indicies.shape[1],
+                        ],
+                        0,
+                    ),
+                ],
+                0,
+            )
+
+        return x.shape[0] - 1 - indicies[0][0]
+
+    quotient = torch.zeros(m - n + 1, dtype=input.dtype)
+
+    ridx = input.shape[0] - 1
+
+    size = m - f(other) - 1
+
+    y = torch.zeros(m + n + 1, dtype=input.dtype)
+
+    y[size] = 1.0
+
+    x = quotient, input, y, ridx
+
+    for index in range(0, size):
+        quotient, remainder, y2, ridx1 = x
+
+        j = size - index
+
+        p = multiply_probabilists_hermite_polynomial(y2, other)
+
+        pidx = f(p)
+
+        t = remainder[ridx1] / p[pidx]
+
+        remainder_modified = remainder.clone()
+        remainder_modified[ridx1] = 0.0
+
+        a = remainder_modified
+
+        p_modified = p.clone()
+        p_modified[pidx] = 0.0
+
+        b = t * p_modified
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+            output = a + output
+        else:
+            output = -b
+
+            output = torch.concatenate(
+                [
+                    output[: a.shape[0]] + a,
+                    output[a.shape[0] :],
+                ],
+            )
+
+        remainder = output
+
+        remainder = remainder[: remainder.shape[0]]
+
+        quotient[j] = t
+
+        ridx1 = ridx1 - 1
+
+        y2 = torch.roll(y2, -1)
+
+        x = quotient, remainder, y2, ridx1
+
+    quotient, remainder, _, _ = x
+
+    return quotient, remainder
diff --git a/src/beignet/_evaluate_chebyshev_polynomial.py b/src/beignet/_evaluate_chebyshev_polynomial.py
new file mode 100644
index 0000000000..623cefda39
--- /dev/null
+++ b/src/beignet/_evaluate_chebyshev_polynomial.py
@@ -0,0 +1,35 @@
+import torch
+from torch import Tensor
+
+
+def evaluate_chebyshev_polynomial(
+    input: Tensor,
+    coefficients: Tensor,
+    tensor: bool = True,
+) -> Tensor:
+    coefficients = torch.atleast_1d(coefficients)
+
+    if tensor:
+        coefficients = torch.reshape(
+            coefficients,
+            coefficients.shape + (1,) * input.ndim,
+        )
+
+    match coefficients.shape[0]:
+        case 1:
+            a = coefficients[0]
+            b = 0.0
+        case 2:
+            a = coefficients[0]
+            b = coefficients[1]
+        case _:
+            a = coefficients[-2] * torch.ones_like(input)
+            b = coefficients[-1] * torch.ones_like(input)
+
+            for i in range(3, coefficients.shape[0] + 1):
+                previous = a
+
+                a = coefficients[-i] - b
+                b = previous + b * 2.0 * input
+
+    return a + b * input
diff --git a/src/beignet/_evaluate_chebyshev_polynomial_2d.py b/src/beignet/_evaluate_chebyshev_polynomial_2d.py
new file mode 100644
index 0000000000..54da45d016
--- /dev/null
+++ b/src/beignet/_evaluate_chebyshev_polynomial_2d.py
@@ -0,0 +1,36 @@
+from torch import Tensor
+
+from ._evaluate_chebyshev_polynomial import evaluate_chebyshev_polynomial
+
+
+def evaluate_chebyshev_polynomial_2d(
+    x: Tensor,
+    y: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    points = [x, y]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_chebyshev_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_chebyshev_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_chebyshev_polynomial_3d.py b/src/beignet/_evaluate_chebyshev_polynomial_3d.py
new file mode 100644
index 0000000000..8048cf482c
--- /dev/null
+++ b/src/beignet/_evaluate_chebyshev_polynomial_3d.py
@@ -0,0 +1,37 @@
+from torch import Tensor
+
+from ._evaluate_chebyshev_polynomial import evaluate_chebyshev_polynomial
+
+
+def evaluate_chebyshev_polynomial_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    points = [x, y, z]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_chebyshev_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_chebyshev_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_chebyshev_polynomial_cartesian_2d.py b/src/beignet/_evaluate_chebyshev_polynomial_cartesian_2d.py
new file mode 100644
index 0000000000..316fd62a0e
--- /dev/null
+++ b/src/beignet/_evaluate_chebyshev_polynomial_cartesian_2d.py
@@ -0,0 +1,13 @@
+from torch import Tensor
+
+from ._evaluate_chebyshev_polynomial import evaluate_chebyshev_polynomial
+
+
+def evaluate_chebyshev_polynomial_cartesian_2d(
+    x: Tensor,
+    y: Tensor,
+    c: Tensor,
+) -> Tensor:
+    for arg in [x, y]:
+        c = evaluate_chebyshev_polynomial(arg, c)
+    return c
diff --git a/src/beignet/_evaluate_chebyshev_polynomial_cartesian_3d.py b/src/beignet/_evaluate_chebyshev_polynomial_cartesian_3d.py
new file mode 100644
index 0000000000..8f157441ab
--- /dev/null
+++ b/src/beignet/_evaluate_chebyshev_polynomial_cartesian_3d.py
@@ -0,0 +1,14 @@
+from torch import Tensor
+
+from ._evaluate_chebyshev_polynomial import evaluate_chebyshev_polynomial
+
+
+def evaluate_chebyshev_polynomial_cartesian_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    c: Tensor,
+) -> Tensor:
+    for arg in [x, y, z]:
+        c = evaluate_chebyshev_polynomial(arg, c)
+    return c
diff --git a/src/beignet/_evaluate_laguerre_polynomial.py b/src/beignet/_evaluate_laguerre_polynomial.py
new file mode 100644
index 0000000000..a3f83003c8
--- /dev/null
+++ b/src/beignet/_evaluate_laguerre_polynomial.py
@@ -0,0 +1,38 @@
+import torch
+from torch import Tensor
+
+
+def evaluate_laguerre_polynomial(
+    input: Tensor, coefficients: Tensor, tensor: bool = True
+):
+    coefficients = torch.atleast_1d(coefficients)
+
+    if tensor:
+        coefficients = torch.reshape(
+            coefficients,
+            coefficients.shape + (1,) * input.ndim,
+        )
+
+    match coefficients.shape[0]:
+        case 1:
+            a = coefficients[0]
+            b = 0.0
+        case 2:
+            a = coefficients[0]
+            b = coefficients[1]
+        case _:
+            size = coefficients.shape[0]
+
+            a = coefficients[-2] * torch.ones_like(input)
+            b = coefficients[-1] * torch.ones_like(input)
+
+            for index in range(3, coefficients.shape[0] + 1):
+                previous = a
+
+                size = size - 1
+
+                a = coefficients[-index] - (b * (size - 1.0)) / size
+
+                b = previous + (b * ((2.0 * size - 1.0) - input)) / size
+
+    return a + b * (1.0 - input)
diff --git a/src/beignet/_evaluate_laguerre_polynomial_2d.py b/src/beignet/_evaluate_laguerre_polynomial_2d.py
new file mode 100644
index 0000000000..6b1f043a2f
--- /dev/null
+++ b/src/beignet/_evaluate_laguerre_polynomial_2d.py
@@ -0,0 +1,36 @@
+from torch import Tensor
+
+from ._evaluate_laguerre_polynomial import evaluate_laguerre_polynomial
+
+
+def evaluate_laguerre_polynomial_2d(
+    x: Tensor,
+    y: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    points = [x, y]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_laguerre_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_laguerre_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_laguerre_polynomial_3d.py b/src/beignet/_evaluate_laguerre_polynomial_3d.py
new file mode 100644
index 0000000000..a421e75f7f
--- /dev/null
+++ b/src/beignet/_evaluate_laguerre_polynomial_3d.py
@@ -0,0 +1,37 @@
+from torch import Tensor
+
+from ._evaluate_laguerre_polynomial import evaluate_laguerre_polynomial
+
+
+def evaluate_laguerre_polynomial_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    points = [x, y, z]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_laguerre_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_laguerre_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_laguerre_polynomial_cartesian_2d.py b/src/beignet/_evaluate_laguerre_polynomial_cartesian_2d.py
new file mode 100644
index 0000000000..e2bac82c7c
--- /dev/null
+++ b/src/beignet/_evaluate_laguerre_polynomial_cartesian_2d.py
@@ -0,0 +1,13 @@
+from torch import Tensor
+
+from ._evaluate_laguerre_polynomial import evaluate_laguerre_polynomial
+
+
+def evaluate_laguerre_polynomial_cartesian_2d(
+    x: Tensor,
+    y: Tensor,
+    c: Tensor,
+) -> Tensor:
+    for arg in [x, y]:
+        c = evaluate_laguerre_polynomial(arg, c)
+    return c
diff --git a/src/beignet/_evaluate_laguerre_polynomial_cartesian_3d.py b/src/beignet/_evaluate_laguerre_polynomial_cartesian_3d.py
new file mode 100644
index 0000000000..0e04cd2f2e
--- /dev/null
+++ b/src/beignet/_evaluate_laguerre_polynomial_cartesian_3d.py
@@ -0,0 +1,14 @@
+from torch import Tensor
+
+from ._evaluate_laguerre_polynomial import evaluate_laguerre_polynomial
+
+
+def evaluate_laguerre_polynomial_cartesian_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    c: Tensor,
+) -> Tensor:
+    for arg in [x, y, z]:
+        c = evaluate_laguerre_polynomial(arg, c)
+    return c
diff --git a/src/beignet/_evaluate_legendre_polynomial.py b/src/beignet/_evaluate_legendre_polynomial.py
new file mode 100644
index 0000000000..aaf0712755
--- /dev/null
+++ b/src/beignet/_evaluate_legendre_polynomial.py
@@ -0,0 +1,40 @@
+import torch
+from torch import Tensor
+
+
+def evaluate_legendre_polynomial(
+    input: Tensor,
+    coefficients: Tensor,
+    tensor: bool = True,
+) -> Tensor:
+    coefficients = torch.atleast_1d(coefficients)
+
+    if tensor:
+        coefficients = torch.reshape(
+            coefficients,
+            coefficients.shape + (1,) * input.ndim,
+        )
+
+    match coefficients.shape[0]:
+        case 1:
+            a = coefficients[0]
+            b = 0.0
+        case 2:
+            a = coefficients[0]
+            b = coefficients[1]
+        case _:
+            size = coefficients.shape[0]
+
+            a = coefficients[-2] * torch.ones_like(input)
+            b = coefficients[-1] * torch.ones_like(input)
+
+            for index in range(3, coefficients.shape[0] + 1):
+                previous = a
+
+                size = size - 1
+
+                a = coefficients[-index] - (b * (size - 1.0)) / size
+
+                b = previous + (b * input * (2.0 * size - 1.0)) / size
+
+    return a + b * input
diff --git a/src/beignet/_evaluate_legendre_polynomial_2d.py b/src/beignet/_evaluate_legendre_polynomial_2d.py
new file mode 100644
index 0000000000..5e58409fe5
--- /dev/null
+++ b/src/beignet/_evaluate_legendre_polynomial_2d.py
@@ -0,0 +1,36 @@
+from torch import Tensor
+
+from ._evaluate_legendre_polynomial import evaluate_legendre_polynomial
+
+
+def evaluate_legendre_polynomial_2d(
+    x: Tensor,
+    y: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    points = [x, y]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_legendre_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_legendre_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_legendre_polynomial_3d.py b/src/beignet/_evaluate_legendre_polynomial_3d.py
new file mode 100644
index 0000000000..e13c9a503f
--- /dev/null
+++ b/src/beignet/_evaluate_legendre_polynomial_3d.py
@@ -0,0 +1,37 @@
+from torch import Tensor
+
+from ._evaluate_legendre_polynomial import evaluate_legendre_polynomial
+
+
+def evaluate_legendre_polynomial_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    points = [x, y, z]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_legendre_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_legendre_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_legendre_polynomial_cartesian_2d.py b/src/beignet/_evaluate_legendre_polynomial_cartesian_2d.py
new file mode 100644
index 0000000000..8c493c58e4
--- /dev/null
+++ b/src/beignet/_evaluate_legendre_polynomial_cartesian_2d.py
@@ -0,0 +1,13 @@
+from torch import Tensor
+
+from ._evaluate_legendre_polynomial import evaluate_legendre_polynomial
+
+
+def evaluate_legendre_polynomial_cartesian_2d(
+    x: Tensor,
+    y: Tensor,
+    c: Tensor,
+) -> Tensor:
+    for arg in [x, y]:
+        c = evaluate_legendre_polynomial(arg, c)
+    return c
diff --git a/src/beignet/_evaluate_legendre_polynomial_cartesian_3d.py b/src/beignet/_evaluate_legendre_polynomial_cartesian_3d.py
new file mode 100644
index 0000000000..da41d89b78
--- /dev/null
+++ b/src/beignet/_evaluate_legendre_polynomial_cartesian_3d.py
@@ -0,0 +1,14 @@
+from torch import Tensor
+
+from ._evaluate_legendre_polynomial import evaluate_legendre_polynomial
+
+
+def evaluate_legendre_polynomial_cartesian_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    c: Tensor,
+) -> Tensor:
+    for arg in [x, y, z]:
+        c = evaluate_legendre_polynomial(arg, c)
+    return c
diff --git a/src/beignet/_evaluate_physicists_hermite_polynomial.py b/src/beignet/_evaluate_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..789149d6ca
--- /dev/null
+++ b/src/beignet/_evaluate_physicists_hermite_polynomial.py
@@ -0,0 +1,40 @@
+import torch
+from torch import Tensor
+
+
+def evaluate_physicists_hermite_polynomial(
+    input: Tensor,
+    coefficients: Tensor,
+    tensor: bool = True,
+):
+    coefficients = torch.atleast_1d(coefficients)
+
+    if tensor:
+        coefficients = torch.reshape(
+            coefficients,
+            coefficients.shape + (1,) * input.ndim,
+        )
+
+    match coefficients.shape[0]:
+        case 1:
+            a = coefficients[0]
+            b = 0.0
+        case 2:
+            a = coefficients[0]
+            b = coefficients[1]
+        case _:
+            size = coefficients.shape[0]
+
+            a = coefficients[-2] * torch.ones_like(input)
+            b = coefficients[-1] * torch.ones_like(input)
+
+            for i in range(3, coefficients.shape[0] + 1):
+                previous = a
+
+                size = size - 1
+
+                a = coefficients[-i] - b * (2.0 * (size - 1.0))
+
+                b = previous + b * input * 2.0
+
+    return a + b * input * 2.0
diff --git a/src/beignet/_evaluate_physicists_hermite_polynomial_2d.py b/src/beignet/_evaluate_physicists_hermite_polynomial_2d.py
new file mode 100644
index 0000000000..1af7ff39f1
--- /dev/null
+++ b/src/beignet/_evaluate_physicists_hermite_polynomial_2d.py
@@ -0,0 +1,38 @@
+from torch import Tensor
+
+from ._evaluate_physicists_hermite_polynomial import (
+    evaluate_physicists_hermite_polynomial,
+)
+
+
+def evaluate_physicists_hermite_polynomial_2d(
+    x: Tensor,
+    y: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    points = [x, y]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_physicists_hermite_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_physicists_hermite_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_physicists_hermite_polynomial_3d.py b/src/beignet/_evaluate_physicists_hermite_polynomial_3d.py
new file mode 100644
index 0000000000..c95179508e
--- /dev/null
+++ b/src/beignet/_evaluate_physicists_hermite_polynomial_3d.py
@@ -0,0 +1,39 @@
+from torch import Tensor
+
+from ._evaluate_physicists_hermite_polynomial import (
+    evaluate_physicists_hermite_polynomial,
+)
+
+
+def evaluate_physicists_hermite_polynomial_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    points = [x, y, z]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_physicists_hermite_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_physicists_hermite_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_physicists_hermite_polynomial_cartesian_2d.py b/src/beignet/_evaluate_physicists_hermite_polynomial_cartesian_2d.py
new file mode 100644
index 0000000000..d80cdfab99
--- /dev/null
+++ b/src/beignet/_evaluate_physicists_hermite_polynomial_cartesian_2d.py
@@ -0,0 +1,19 @@
+from torch import Tensor
+
+from ._evaluate_physicists_hermite_polynomial import (
+    evaluate_physicists_hermite_polynomial,
+)
+
+
+def evaluate_physicists_hermite_polynomial_cartesian_2d(
+    x: Tensor,
+    y: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    for point in [x, y]:
+        coefficients = evaluate_physicists_hermite_polynomial(
+            point,
+            coefficients,
+        )
+
+    return coefficients
diff --git a/src/beignet/_evaluate_physicists_hermite_polynomial_cartesian_3d.py b/src/beignet/_evaluate_physicists_hermite_polynomial_cartesian_3d.py
new file mode 100644
index 0000000000..f1d86fe042
--- /dev/null
+++ b/src/beignet/_evaluate_physicists_hermite_polynomial_cartesian_3d.py
@@ -0,0 +1,16 @@
+from torch import Tensor
+
+from ._evaluate_physicists_hermite_polynomial import (
+    evaluate_physicists_hermite_polynomial,
+)
+
+
+def evaluate_physicists_hermite_polynomial_cartesian_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    c: Tensor,
+) -> Tensor:
+    for arg in [x, y, z]:
+        c = evaluate_physicists_hermite_polynomial(arg, c)
+    return c
diff --git a/src/beignet/_evaluate_polynomial.py b/src/beignet/_evaluate_polynomial.py
new file mode 100644
index 0000000000..7784c6c04b
--- /dev/null
+++ b/src/beignet/_evaluate_polynomial.py
@@ -0,0 +1,34 @@
+import torch
+from torch import Tensor
+
+
+def evaluate_polynomial(
+    input: Tensor, coefficients: Tensor, tensor: bool = True
+) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    input : Tensor
+
+    coefficients : Tensor
+
+    tensor : bool
+
+    Returns
+    -------
+    output : Tensor
+    """
+    coefficients = torch.atleast_1d(coefficients)
+
+    if tensor:
+        coefficients = torch.reshape(
+            coefficients,
+            coefficients.shape + (1,) * input.ndim,
+        )
+
+    output = coefficients[-1] + torch.zeros_like(input)
+
+    for i in range(2, coefficients.shape[0] + 1):
+        output = coefficients[-i] + output * input
+
+    return output
diff --git a/src/beignet/_evaluate_polynomial_2d.py b/src/beignet/_evaluate_polynomial_2d.py
new file mode 100644
index 0000000000..cc8887ac08
--- /dev/null
+++ b/src/beignet/_evaluate_polynomial_2d.py
@@ -0,0 +1,45 @@
+from torch import Tensor
+
+from ._evaluate_polynomial import evaluate_polynomial
+
+
+def evaluate_polynomial_2d(x: Tensor, y: Tensor, coefficients: Tensor) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    x : Tensor
+
+    y : Tensor
+
+    coefficients : Tensor
+
+    Returns
+    -------
+    output : Tensor
+    """
+    points = [x, y]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_polynomial_3d.py b/src/beignet/_evaluate_polynomial_3d.py
new file mode 100644
index 0000000000..913f6e43a8
--- /dev/null
+++ b/src/beignet/_evaluate_polynomial_3d.py
@@ -0,0 +1,52 @@
+from torch import Tensor
+
+from ._evaluate_polynomial import evaluate_polynomial
+
+
+def evaluate_polynomial_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    x : Tensor
+
+    y : Tensor
+
+    z : Tensor
+
+    coefficients : Tensor
+
+    Returns
+    -------
+    output : Tensor
+    """
+    points = [x, y, z]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_polynomial_cartesian_2d.py b/src/beignet/_evaluate_polynomial_cartesian_2d.py
new file mode 100644
index 0000000000..f1851d25c6
--- /dev/null
+++ b/src/beignet/_evaluate_polynomial_cartesian_2d.py
@@ -0,0 +1,25 @@
+from torch import Tensor
+
+from ._evaluate_polynomial import evaluate_polynomial
+
+
+def evaluate_polynomial_cartesian_2d(
+    x: Tensor, y: Tensor, coefficients: Tensor
+) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    x : Tensor
+
+    y : Tensor
+
+    coefficients : Tensor
+
+    Returns
+    -------
+    output : Tensor
+    """
+    for input in [x, y]:
+        coefficients = evaluate_polynomial(input, coefficients)
+
+    return coefficients
diff --git a/src/beignet/_evaluate_polynomial_cartesian_3d.py b/src/beignet/_evaluate_polynomial_cartesian_3d.py
new file mode 100644
index 0000000000..f8a29fd515
--- /dev/null
+++ b/src/beignet/_evaluate_polynomial_cartesian_3d.py
@@ -0,0 +1,30 @@
+from torch import Tensor
+
+from ._evaluate_polynomial import evaluate_polynomial
+
+
+def evaluate_polynomial_cartesian_3d(
+    x: Tensor, y: Tensor, z: Tensor, coefficients: Tensor
+) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    x : Tensor
+
+    y : Tensor
+
+    z : Tensor
+
+    coefficients : Tensor
+
+    Returns
+    -------
+    out : Tensor
+    """
+    for input in [x, y, z]:
+        coefficients = evaluate_polynomial(
+            input,
+            coefficients,
+        )
+
+    return coefficients
diff --git a/src/beignet/_evaluate_polynomial_from_roots.py b/src/beignet/_evaluate_polynomial_from_roots.py
new file mode 100644
index 0000000000..0f7a38ef74
--- /dev/null
+++ b/src/beignet/_evaluate_polynomial_from_roots.py
@@ -0,0 +1,21 @@
+import torch
+from torch import Tensor
+
+
+def evaluate_polynomial_from_roots(
+    input: Tensor,
+    other: Tensor,
+    tensor: bool = True,
+) -> Tensor:
+    if other.ndim == 0:
+        other = torch.ravel(other)
+
+    if tensor:
+        other = torch.reshape(other, other.shape + (1,) * input.ndim)
+
+    if input.ndim >= other.ndim:
+        raise ValueError
+
+    output = torch.prod(input - other, dim=0)
+
+    return output
diff --git a/src/beignet/_evaluate_probabilists_hermite_polynomial.py b/src/beignet/_evaluate_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..b372f21cc9
--- /dev/null
+++ b/src/beignet/_evaluate_probabilists_hermite_polynomial.py
@@ -0,0 +1,40 @@
+import torch
+from torch import Tensor
+
+
+def evaluate_probabilists_hermite_polynomial(
+    input: Tensor,
+    coefficients: Tensor,
+    tensor: bool = True,
+):
+    coefficients = torch.atleast_1d(coefficients)
+
+    if tensor:
+        coefficients = torch.reshape(
+            coefficients,
+            coefficients.shape + (1,) * input.ndim,
+        )
+
+    match coefficients.shape[0]:
+        case 1:
+            a = coefficients[0]
+            b = 0.0
+        case 2:
+            a = coefficients[0]
+            b = coefficients[1]
+        case _:
+            size = coefficients.shape[0]
+
+            a = coefficients[-2] * torch.ones_like(input)
+            b = coefficients[-1] * torch.ones_like(input)
+
+            for i in range(3, coefficients.shape[0] + 1):
+                previous = a
+
+                size = size - 1
+
+                a = coefficients[-i] - b * (size - 1.0)
+
+                b = previous + b * input
+
+    return a + b * input
diff --git a/src/beignet/_evaluate_probabilists_hermite_polynomial_2d.py b/src/beignet/_evaluate_probabilists_hermite_polynomial_2d.py
new file mode 100644
index 0000000000..ba1c9f6cf2
--- /dev/null
+++ b/src/beignet/_evaluate_probabilists_hermite_polynomial_2d.py
@@ -0,0 +1,38 @@
+from torch import Tensor
+
+from ._evaluate_probabilists_hermite_polynomial import (
+    evaluate_probabilists_hermite_polynomial,
+)
+
+
+def evaluate_probabilists_hermite_polynomial_2d(
+    x: Tensor,
+    y: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    points = [x, y]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_probabilists_hermite_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_probabilists_hermite_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_probabilists_hermite_polynomial_3d.py b/src/beignet/_evaluate_probabilists_hermite_polynomial_3d.py
new file mode 100644
index 0000000000..6041100824
--- /dev/null
+++ b/src/beignet/_evaluate_probabilists_hermite_polynomial_3d.py
@@ -0,0 +1,39 @@
+from torch import Tensor
+
+from ._evaluate_probabilists_hermite_polynomial import (
+    evaluate_probabilists_hermite_polynomial,
+)
+
+
+def evaluate_probabilists_hermite_polynomial_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    coefficients: Tensor,
+) -> Tensor:
+    points = [x, y, z]
+
+    if not all(a.shape == points[0].shape for a in points[1:]):
+        match len(points):
+            case 2:
+                raise ValueError
+            case 3:
+                raise ValueError
+            case _:
+                raise ValueError
+
+    points = iter(points)
+
+    output = evaluate_probabilists_hermite_polynomial(
+        next(points),
+        coefficients,
+    )
+
+    for x in points:
+        output = evaluate_probabilists_hermite_polynomial(
+            x,
+            output,
+            tensor=False,
+        )
+
+    return output
diff --git a/src/beignet/_evaluate_probabilists_hermite_polynomial_cartersian_2d.py b/src/beignet/_evaluate_probabilists_hermite_polynomial_cartersian_2d.py
new file mode 100644
index 0000000000..7ae6528ff2
--- /dev/null
+++ b/src/beignet/_evaluate_probabilists_hermite_polynomial_cartersian_2d.py
@@ -0,0 +1,15 @@
+from torch import Tensor
+
+from ._evaluate_probabilists_hermite_polynomial import (
+    evaluate_probabilists_hermite_polynomial,
+)
+
+
+def evaluate_probabilists_hermite_polynomial_cartersian_2d(
+    x: Tensor,
+    y: Tensor,
+    c: Tensor,
+) -> Tensor:
+    for arg in [x, y]:
+        c = evaluate_probabilists_hermite_polynomial(arg, c)
+    return c
diff --git a/src/beignet/_evaluate_probabilists_hermite_polynomial_cartersian_3d.py b/src/beignet/_evaluate_probabilists_hermite_polynomial_cartersian_3d.py
new file mode 100644
index 0000000000..9d3bf8d5a7
--- /dev/null
+++ b/src/beignet/_evaluate_probabilists_hermite_polynomial_cartersian_3d.py
@@ -0,0 +1,16 @@
+from torch import Tensor
+
+from ._evaluate_probabilists_hermite_polynomial import (
+    evaluate_probabilists_hermite_polynomial,
+)
+
+
+def evaluate_probabilists_hermite_polynomial_cartersian_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    c: Tensor,
+) -> Tensor:
+    for arg in [x, y, z]:
+        c = evaluate_probabilists_hermite_polynomial(arg, c)
+    return c
diff --git a/src/beignet/_fit_chebyshev_polynomial.py b/src/beignet/_fit_chebyshev_polynomial.py
new file mode 100644
index 0000000000..a2b4b9b625
--- /dev/null
+++ b/src/beignet/_fit_chebyshev_polynomial.py
@@ -0,0 +1,84 @@
+import math
+
+import torch
+from torch import Tensor
+
+from ._chebyshev_polynomial_vandermonde import chebyshev_polynomial_vandermonde
+
+
+def fit_chebyshev_polynomial(
+    input: Tensor,
+    other: Tensor,
+    degree: Tensor | int,
+    relative_condition: float | None = None,
+    full: bool = False,
+    weight: Tensor | None = None,
+):
+    func = chebyshev_polynomial_vandermonde
+    input = torch.tensor(input)
+    other = torch.tensor(other)
+    degree = torch.tensor(degree)
+    if degree.ndim > 1:
+        raise TypeError
+    # if deg.dtype.kind not in "iu":
+    #     raise TypeError
+    if math.prod(degree.shape) == 0:
+        raise TypeError
+    if degree.min() < 0:
+        raise ValueError
+    if input.ndim != 1:
+        raise TypeError
+    if input.size == 0:
+        raise TypeError
+    if other.ndim < 1 or other.ndim > 2:
+        raise TypeError
+    if len(input) != len(other):
+        raise TypeError
+    if degree.ndim == 0:
+        lmax = int(degree)
+        van = func(input, lmax)
+    else:
+        degree, _ = torch.sort(degree)
+        lmax = int(degree[-1])
+        van = func(input, lmax)[:, degree]
+    # set up the least squares matrices in transposed form
+    lhs = van.T
+    rhs = other.T
+    if weight is not None:
+        if weight.ndim != 1:
+            raise TypeError("expected 1D vector for w")
+
+        if len(input) != len(weight):
+            raise TypeError("expected x and w to have same length")
+
+        # apply weights. Don't use inplace operations as they
+        # can cause problems with NA.
+        lhs = lhs * weight
+        rhs = rhs * weight
+    # set rcond
+    if relative_condition is None:
+        relative_condition = len(input) * torch.finfo(input.dtype).eps
+    # Determine the norms of the design matrix columns.
+    if torch.is_complex(lhs):
+        scl = torch.sqrt((torch.square(lhs.real) + torch.square(lhs.imag)).sum(1))
+    else:
+        scl = torch.sqrt(torch.square(lhs).sum(1))
+    scl = torch.where(scl == 0, 1, scl)
+    # Solve the least squares problem.
+    c, resids, rank, s = torch.linalg.lstsq(lhs.T / scl, rhs.T, relative_condition)
+    c = (c.T / scl).T
+    # Expand c to include non-fitted coefficients which are set to zero
+    if degree.ndim > 0:
+        if c.ndim == 2:
+            cc = torch.zeros((lmax + 1, c.shape[1]), dtype=c.dtype)
+        else:
+            cc = torch.zeros(lmax + 1, dtype=c.dtype)
+
+        cc[degree] = c
+
+        c = cc
+    if full:
+        result = c, [resids, rank, s, relative_condition]
+    else:
+        result = c
+    return result
diff --git a/src/beignet/_fit_laguerre_polynomial.py b/src/beignet/_fit_laguerre_polynomial.py
new file mode 100644
index 0000000000..b87a387309
--- /dev/null
+++ b/src/beignet/_fit_laguerre_polynomial.py
@@ -0,0 +1,83 @@
+import math
+
+import torch
+from torch import Tensor
+
+from ._laguerre_polynomial_vandermonde import laguerre_polynomial_vandermonde
+
+
+def fit_laguerre_polynomial(
+    input: Tensor,
+    other: Tensor,
+    degree: Tensor | int,
+    relative_condition: float | None = None,
+    full: bool = False,
+    weight: Tensor | None = None,
+):
+    input = torch.tensor(input)
+    other = torch.tensor(other)
+    degree = torch.tensor(degree)
+    if degree.ndim > 1:
+        raise TypeError
+    # if deg.dtype.kind not in "iu":
+    #     raise TypeError
+    if math.prod(degree.shape) == 0:
+        raise TypeError
+    if degree.min() < 0:
+        raise ValueError
+    if input.ndim != 1:
+        raise TypeError
+    if input.size == 0:
+        raise TypeError
+    if other.ndim < 1 or other.ndim > 2:
+        raise TypeError
+    if len(input) != len(other):
+        raise TypeError
+    if degree.ndim == 0:
+        lmax = int(degree)
+        van = laguerre_polynomial_vandermonde(input, lmax)
+    else:
+        degree, _ = torch.sort(degree)
+        lmax = int(degree[-1])
+        van = laguerre_polynomial_vandermonde(input, lmax)[:, degree]
+    # set up the least squares matrices in transposed form
+    lhs = van.T
+    rhs = other.T
+    if weight is not None:
+        if weight.ndim != 1:
+            raise TypeError("expected 1D vector for w")
+
+        if len(input) != len(weight):
+            raise TypeError("expected x and w to have same length")
+
+        # apply weights. Don't use inplace operations as they
+        # can cause problems with NA.
+        lhs = lhs * weight
+        rhs = rhs * weight
+    # set rcond
+    if relative_condition is None:
+        relative_condition = len(input) * torch.finfo(input.dtype).eps
+    # Determine the norms of the design matrix columns.
+    if torch.is_complex(lhs):
+        scl = torch.sqrt((torch.square(lhs.real) + torch.square(lhs.imag)).sum(1))
+    else:
+        scl = torch.sqrt(torch.square(lhs).sum(1))
+    scl = torch.where(scl == 0, 1, scl)
+    # Solve the least squares problem.
+    c, resids, rank, s = torch.linalg.lstsq(lhs.T / scl, rhs.T, relative_condition)
+    c = (c.T / scl).T
+    # Expand c to include non-fitted coefficients which are set to zero
+    if degree.ndim > 0:
+        if c.ndim == 2:
+            cc = torch.zeros((lmax + 1, c.shape[1]), dtype=c.dtype)
+        else:
+            cc = torch.zeros(lmax + 1, dtype=c.dtype)
+
+        cc[degree] = c
+
+        c = cc
+    if full:
+        result = c, [resids, rank, s, relative_condition]
+    else:
+        result = c
+    return result
diff --git a/src/beignet/_fit_legendre_polynomial.py b/src/beignet/_fit_legendre_polynomial.py
new file mode 100644
index 0000000000..0a1f8d043a
--- /dev/null
+++ b/src/beignet/_fit_legendre_polynomial.py
@@ -0,0 +1,83 @@
+import math
+
+import torch
+from torch import Tensor
+
+from ._legendre_polynomial_vandermonde import legendre_polynomial_vandermonde
+
+
+def fit_legendre_polynomial(
+    input: Tensor,
+    other: Tensor,
+    degree: Tensor | int,
+    relative_condition: float | None = None,
+    full: bool = False,
+    weight: Tensor | None = None,
+):
+    input = torch.tensor(input)
+    other = torch.tensor(other)
+    degree = torch.tensor(degree)
+    if degree.ndim > 1:
+        raise TypeError
+    # if deg.dtype.kind not in "iu":
+    #     raise TypeError
+    if math.prod(degree.shape) == 0:
+        raise TypeError
+    if degree.min() < 0:
+        raise ValueError
+    if input.ndim != 1:
+        raise TypeError
+    if input.size == 0:
+        raise TypeError
+    if other.ndim < 1 or other.ndim > 2:
+        raise TypeError
+    if len(input) != len(other):
+        raise TypeError
+    if degree.ndim == 0:
+        lmax = int(degree)
+        van = legendre_polynomial_vandermonde(input, lmax)
+    else:
+        degree, _ = torch.sort(degree)
+        lmax = int(degree[-1])
+        van = legendre_polynomial_vandermonde(input, lmax)[:, degree]
+    # set up the least squares matrices in transposed form
+    lhs = van.T
+    rhs = other.T
+    if weight is not None:
+        if weight.ndim != 1:
+            raise TypeError("expected 1D vector for w")
+
+        if len(input) != len(weight):
+            raise TypeError("expected x and w to have same length")
+
+        # apply weights. Don't use inplace operations as they
+        # can cause problems with NA.
+        lhs = lhs * weight
+        rhs = rhs * weight
+    # set rcond
+    if relative_condition is None:
+        relative_condition = len(input) * torch.finfo(input.dtype).eps
+    # Determine the norms of the design matrix columns.
+    if torch.is_complex(lhs):
+        scl = torch.sqrt((torch.square(lhs.real) + torch.square(lhs.imag)).sum(1))
+    else:
+        scl = torch.sqrt(torch.square(lhs).sum(1))
+    scl = torch.where(scl == 0, 1, scl)
+    # Solve the least squares problem.
+    c, resids, rank, s = torch.linalg.lstsq(lhs.T / scl, rhs.T, relative_condition)
+    c = (c.T / scl).T
+    # Expand c to include non-fitted coefficients which are set to zero
+    if degree.ndim > 0:
+        if c.ndim == 2:
+            cc = torch.zeros((lmax + 1, c.shape[1]), dtype=c.dtype)
+        else:
+            cc = torch.zeros(lmax + 1, dtype=c.dtype)
+
+        cc[degree] = c
+
+        c = cc
+    if full:
+        result = c, [resids, rank, s, relative_condition]
+    else:
+        result = c
+    return result
diff --git a/src/beignet/_fit_physicists_hermite_polynomial.py b/src/beignet/_fit_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..7d1014a4ea
--- /dev/null
+++ b/src/beignet/_fit_physicists_hermite_polynomial.py
@@ -0,0 +1,85 @@
+import math
+
+import torch
+from torch import Tensor
+
+from ._physicists_hermite_polynomial_vandermonde import (
+    physicists_hermite_polynomial_vandermonde,
+)
+
+
+def fit_physicists_hermite_polynomial(
+    input: Tensor,
+    other: Tensor,
+    degree: Tensor | int,
+    relative_condition: float | None = None,
+    full: bool = False,
+    weight: Tensor | None = None,
+):
+    input = torch.tensor(input)
+    other = torch.tensor(other)
+    degree = torch.tensor(degree)
+    if degree.ndim > 1:
+        raise TypeError
+    # if deg.dtype.kind not in "iu":
+    #     raise TypeError
+    if math.prod(degree.shape) == 0:
+        raise TypeError
+    if degree.min() < 0:
+        raise ValueError
+    if input.ndim != 1:
+        raise TypeError
+    if input.size == 0:
+        raise TypeError
+    if other.ndim < 1 or other.ndim > 2:
+        raise TypeError
+    if len(input) != len(other):
+        raise TypeError
+    if degree.ndim == 0:
+        lmax = int(degree)
+        van = physicists_hermite_polynomial_vandermonde(input, lmax)
+    else:
+        degree, _ = torch.sort(degree)
+        lmax = int(degree[-1])
+        van = physicists_hermite_polynomial_vandermonde(input, lmax)[:, degree]
+    # set up the least squares matrices in transposed form
+    lhs = van.T
+    rhs = other.T
+    if weight is not None:
+        if weight.ndim != 1:
+            raise TypeError("expected 1D vector for w")
+
+        if len(input) != len(weight):
+            raise TypeError("expected x and w to have same length")
+
+        # apply weights. Don't use inplace operations as they
+        # can cause problems with NA.
+        lhs = lhs * weight
+        rhs = rhs * weight
+    # set rcond
+    if relative_condition is None:
+        relative_condition = len(input) * torch.finfo(input.dtype).eps
+    # Determine the norms of the design matrix columns.
+    if torch.is_complex(lhs):
+        scl = torch.sqrt((torch.square(lhs.real) + torch.square(lhs.imag)).sum(1))
+    else:
+        scl = torch.sqrt(torch.square(lhs).sum(1))
+    scl = torch.where(scl == 0, 1, scl)
+    # Solve the least squares problem.
+    c, resids, rank, s = torch.linalg.lstsq(lhs.T / scl, rhs.T, relative_condition)
+    c = (c.T / scl).T
+    # Expand c to include non-fitted coefficients which are set to zero
+    if degree.ndim > 0:
+        if c.ndim == 2:
+            cc = torch.zeros((lmax + 1, c.shape[1]), dtype=c.dtype)
+        else:
+            cc = torch.zeros(lmax + 1, dtype=c.dtype)
+
+        cc[degree] = c
+
+        c = cc
+    if full:
+        result = c, [resids, rank, s, relative_condition]
+    else:
+        result = c
+    return result
diff --git a/src/beignet/_fit_polynomial.py b/src/beignet/_fit_polynomial.py
new file mode 100644
index 0000000000..2521f2977b
--- /dev/null
+++ b/src/beignet/_fit_polynomial.py
@@ -0,0 +1,109 @@
+import math
+
+import torch
+from torch import Tensor
+
+from ._polynomial_vandermonde import polynomial_vandermonde
+
+
+def fit_polynomial(
+    input: Tensor,
+    other: Tensor,
+    degree: Tensor | int,
+    relative_condition: float | None = None,
+    full: bool = False,
+    weight: Tensor | None = None,
+):
+    r"""
+    Parameters
+    ----------
+    input : Tensor
+        Independent variable.
+
+    other : Tensor
+        Dependent variable.
+
+    degree : Tensor or int
+        Degree of the fitting polynomial.
+
+    relative_condition : float, optional
+        Relative condition number.
+
+    full : bool, default=False
+        Return additional information.
+
+    weight : Tensor, optional
+        Weights.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the fit.
+    """
+    input = torch.tensor(input)
+    other = torch.tensor(other)
+    degree = torch.tensor(degree)
+    if degree.ndim > 1:
+        raise TypeError
+    # if deg.dtype.kind not in "iu":
+    #     raise TypeError
+    if math.prod(degree.shape) == 0:
+        raise TypeError
+    if degree.min() < 0:
+        raise ValueError
+    if input.ndim != 1:
+        raise TypeError
+    if input.size == 0:
+        raise TypeError
+    if other.ndim < 1 or other.ndim > 2:
+        raise TypeError
+    if len(input) != len(other):
+        raise TypeError
+    if degree.ndim == 0:
+        lmax = int(degree)
+        van = polynomial_vandermonde(input, lmax)
+    else:
+        degree, _ = torch.sort(degree)
+        lmax = int(degree[-1])
+        van = polynomial_vandermonde(input, lmax)[:, degree]
+    # set up the least squares matrices in transposed form
+    lhs = van.T
+    rhs = other.T
+    if weight is not None:
+        if weight.ndim != 1:
+            raise TypeError("expected 1D vector for w")
+
+        if len(input) != len(weight):
+            raise TypeError("expected x and w to have same length")
+
+        # apply weights. Don't use inplace operations as they
+        # can cause problems with NA.
+        lhs = lhs * weight
+        rhs = rhs * weight
+    # set rcond
+    if relative_condition is None:
+        relative_condition = len(input) * torch.finfo(input.dtype).eps
+    # Determine the norms of the design matrix columns.
+    if torch.is_complex(lhs):
+        scl = torch.sqrt((torch.square(lhs.real) + torch.square(lhs.imag)).sum(1))
+    else:
+        scl = torch.sqrt(torch.square(lhs).sum(1))
+    scl = torch.where(scl == 0, 1, scl)
+    # Solve the least squares problem.
+    c, resids, rank, s = torch.linalg.lstsq(lhs.T / scl, rhs.T, relative_condition)
+    c = (c.T / scl).T
+    # Expand c to include non-fitted coefficients which are set to zero
+    if degree.ndim > 0:
+        if c.ndim == 2:
+            cc = torch.zeros((lmax + 1, c.shape[1]), dtype=c.dtype)
+        else:
+            cc = torch.zeros(lmax + 1, dtype=c.dtype)
+
+        cc[degree] = c
+
+        c = cc
+    if full:
+        result = c, [resids, rank, s, relative_condition]
+    else:
+        result = c
+    return result
diff --git a/src/beignet/_fit_probabilists_hermite_polynomial.py b/src/beignet/_fit_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..da26a5536e
--- /dev/null
+++ b/src/beignet/_fit_probabilists_hermite_polynomial.py
@@ -0,0 +1,85 @@
+import math
+
+import torch
+from torch import Tensor
+
+from ._probabilists_hermite_polynomial_vandermonde import (
+    probabilists_hermite_polynomial_vandermonde,
+)
+
+
+def fit_probabilists_hermite_polynomial(
+    input: Tensor,
+    other: Tensor,
+    degree: Tensor | int,
+    relative_condition: float | None = None,
+    full: bool = False,
+    weight: Tensor | None = None,
+):
+    input = torch.tensor(input)
+    other = torch.tensor(other)
+    degree = torch.tensor(degree)
+    if degree.ndim > 1:
+        raise TypeError
+    # if deg.dtype.kind not in "iu":
+    #     raise TypeError
+    if math.prod(degree.shape) == 0:
+        raise TypeError
+    if degree.min() < 0:
+        raise ValueError
+    if input.ndim != 1:
+        raise TypeError
+    if input.size == 0:
+        raise TypeError
+    if other.ndim < 1 or other.ndim > 2:
+        raise TypeError
+    if len(input) != len(other):
+        raise TypeError
+    if degree.ndim == 0:
+        lmax = int(degree)
+        van = probabilists_hermite_polynomial_vandermonde(input, lmax)
+    else:
+        degree, _ = torch.sort(degree)
+        lmax = int(degree[-1])
+        van = probabilists_hermite_polynomial_vandermonde(input, lmax)[:, degree]
+    # set up the least squares matrices in transposed form
+    lhs = van.T
+    rhs = other.T
+    if weight is not None:
+        if weight.ndim != 1:
+            raise TypeError("expected 1D vector for w")
+
+        if len(input) != len(weight):
+            raise TypeError("expected x and w to have same length")
+
+        # apply weights. Don't use inplace operations as they
+        # can cause problems with NA.
+        lhs = lhs * weight
+        rhs = rhs * weight
+    # set rcond
+    if relative_condition is None:
+        relative_condition = len(input) * torch.finfo(input.dtype).eps
+    # Determine the norms of the design matrix columns.
+    if torch.is_complex(lhs):
+        scl = torch.sqrt((torch.square(lhs.real) + torch.square(lhs.imag)).sum(1))
+    else:
+        scl = torch.sqrt(torch.square(lhs).sum(1))
+    scl = torch.where(scl == 0, 1, scl)
+    # Solve the least squares problem.
+    c, resids, rank, s = torch.linalg.lstsq(lhs.T / scl, rhs.T, relative_condition)
+    c = (c.T / scl).T
+    # Expand c to include non-fitted coefficients which are set to zero
+    if degree.ndim > 0:
+        if c.ndim == 2:
+            cc = torch.zeros((lmax + 1, c.shape[1]), dtype=c.dtype)
+        else:
+            cc = torch.zeros(lmax + 1, dtype=c.dtype)
+
+        cc[degree] = c
+
+        c = cc
+    if full:
+        result = c, [resids, rank, s, relative_condition]
+    else:
+        result = c
+    return result
diff --git a/src/beignet/_gauss_laguerre_quadrature.py b/src/beignet/_gauss_laguerre_quadrature.py
new file mode 100644
index 0000000000..eddfdf67fd
--- /dev/null
+++ b/src/beignet/_gauss_laguerre_quadrature.py
@@ -0,0 +1,30 @@
+import torch
+
+from ._differentiate_laguerre_polynomial import differentiate_laguerre_polynomial
+from ._evaluate_laguerre_polynomial import evaluate_laguerre_polynomial
+from ._laguerre_polynomial_companion import laguerre_polynomial_companion
+
+
+def gauss_laguerre_quadrature(degree):
+    degree = int(degree)
+    if degree <= 0:
+        raise ValueError
+
+    c = torch.zeros(degree + 1)
+    c[-1] = 1.0
+
+    m = laguerre_polynomial_companion(c)
+    x = torch.linalg.eigvalsh(m)
+
+    dy = evaluate_laguerre_polynomial(x, c)
+    df = evaluate_laguerre_polynomial(x, differentiate_laguerre_polynomial(c))
+    x = x - (dy / df)
+
+    fm = evaluate_laguerre_polynomial(x, c[1:])
+    fm = fm / torch.abs(fm).max()
+    df = df / torch.abs(df).max()
+    w = 1 / (fm * df)
+
+    w = w / torch.sum(w)
+
+    return x, w
diff --git a/src/beignet/_gauss_legendre_quadrature.py b/src/beignet/_gauss_legendre_quadrature.py
new file mode 100644
index 0000000000..2f627815ff
--- /dev/null
+++ b/src/beignet/_gauss_legendre_quadrature.py
@@ -0,0 +1,38 @@
+import torch
+
+from ._differentiate_legendre_polynomial import differentiate_legendre_polynomial
+from ._evaluate_legendre_polynomial import evaluate_legendre_polynomial
+from ._legendre_polynomial_companion import legendre_polynomial_companion
+
+
+def gauss_legendre_quadrature(degree):
+    degree = int(degree)
+
+    if degree <= 0:
+        raise ValueError
+
+    c = torch.zeros(degree + 1)
+    c[-1] = 1.0
+    m = legendre_polynomial_companion(c)
+    x = torch.linalg.eigvalsh(m)
+
+    dy = evaluate_legendre_polynomial(x, c)
+    df = evaluate_legendre_polynomial(x, differentiate_legendre_polynomial(c))
+    x -= dy / df
+
+    fm = evaluate_legendre_polynomial(x, c[1:])
+
+    fm /= torch.abs(fm).max()
+    df /= torch.abs(df).max()
+
+    w = 1 / (fm * df)
+
+    a = torch.flip(w, dims=[0])
+    b = torch.flip(x, dims=[0])
+
+    w = (w + a) / 2
+    x = (x - b) / 2
+
+    w = w * (2.0 / torch.sum(w))
+
+    return x, w
diff --git a/src/beignet/_gauss_physicists_hermite_polynomial_quadrature.py b/src/beignet/_gauss_physicists_hermite_polynomial_quadrature.py
new file mode 100644
index 0000000000..c0d0d63b15
--- /dev/null
+++ b/src/beignet/_gauss_physicists_hermite_polynomial_quadrature.py
@@ -0,0 +1,102 @@
+import math
+
+import torch
+
+from ._physicists_hermite_polynomial_companion import (
+    physicists_hermite_polynomial_companion,
+)
+
+
+def gauss_physicists_hermite_polynomial_quadrature(degree):
+    degree = int(degree)
+    if degree <= 0:
+        raise ValueError
+
+    c = torch.zeros(degree + 1)
+    c[-1] = 1.0
+
+    x = torch.linalg.eigvalsh(physicists_hermite_polynomial_companion(c))
+
+    if degree == 0:
+        output = torch.full(x.shape, 1 / math.sqrt(math.sqrt(math.pi)))
+    else:
+        a1 = torch.zeros_like(x)
+
+        b1 = torch.ones_like(x) / math.sqrt(math.sqrt(math.pi))
+
+        size = torch.tensor(degree)
+
+        for _ in range(0, degree - 1):
+            previous = a1
+
+            a1 = -b1 * torch.sqrt((size - 1.0) / size)
+
+            b1 = previous + b1 * x * torch.sqrt(2.0 / size)
+
+            size = size - 1.0
+
+        output = a1 + b1 * x * math.sqrt(2.0)
+
+    dy = output
+
+    n = degree - 1
+
+    if n == 0:
+        df = torch.full(x.shape, 1 / math.sqrt(math.sqrt(math.pi)))
+    else:
+        a = torch.zeros_like(x)
+
+        b = torch.ones_like(x) / math.sqrt(math.sqrt(math.pi))
+
+        size = torch.tensor(n)
+
+        for _ in range(0, n - 1):
+            previous = a
+
+            a = -b * torch.sqrt((size - 1.0) / size)
+
+            b = previous + b * x * torch.sqrt(2.0 / size)
+
+            size = size - 1.0
+
+        df = a + b * x * math.sqrt(2.0)
+
+    df = df * math.sqrt(2 * degree)
+
+    x = x - (dy / df)
+
+    n = degree - 1
+
+    if n == 0:
+        fm = torch.full(x.shape, 1 / math.sqrt(math.sqrt(math.pi)))
+    else:
+        a = torch.zeros_like(x)
+
+        b = torch.ones_like(x) / math.sqrt(math.sqrt(math.pi))
+
+        size = torch.tensor(n)
+
+        for _ in range(0, n - 1):
+            previous = a
+
+            a = -b * torch.sqrt((size - 1.0) / size)
+
+            b = previous + b * x * torch.sqrt(2.0 / size)
+
+            size = size - 1.0
+
+        fm = a + b * x * math.sqrt(2.0)
+
+    fm = fm / torch.abs(fm).max()
+
+    w = 1 / (fm * fm)
+
+    a = torch.flip(w, dims=[0])
+    b = torch.flip(x, dims=[0])
+
+    w = (w + a) / 2
+    x = (x - b) / 2
+
+    w = w * (math.sqrt(math.pi) / torch.sum(w))
+
+    return x, w
diff --git a/src/beignet/_gauss_probabilists_hermite_polynomial_quadrature.py b/src/beignet/_gauss_probabilists_hermite_polynomial_quadrature.py
new file mode 100644
index 0000000000..67a31847d8
--- /dev/null
+++ b/src/beignet/_gauss_probabilists_hermite_polynomial_quadrature.py
@@ -0,0 +1,98 @@
+import math
+
+import torch
+
+from ._probabilists_hermite_polynomial_companion import (
+    probabilists_hermite_polynomial_companion,
+)
+
+
+def gauss_probabilists_hermite_polynomial_quadrature(degree):
+    degree = int(degree)
+    if degree <= 0:
+        raise ValueError
+
+    c = torch.zeros(degree + 1)
+    c[-1] = 1.0
+    m = probabilists_hermite_polynomial_companion(c)
+    x = torch.linalg.eigvalsh(m)
+
+    if degree == 0:
+        dy = torch.full(x.shape, 1.0 / math.sqrt(math.sqrt(2.0 * math.pi)))
+    else:
+        a1 = torch.zeros_like(x)
+        b1 = torch.ones_like(x) / math.sqrt(math.sqrt(2.0 * math.pi))
+
+        size = torch.tensor(degree)
+
+        for _ in range(0, degree - 1):
+            previous = a1
+
+            a1 = -b1 * torch.sqrt((size - 1.0) / size)
+
+            b1 = previous + b1 * x * torch.sqrt(1.0 / size)
+
+            size = size - 1.0
+
+        dy = a1 + b1 * x
+
+    n = degree - 1
+
+    if n == 0:
+        df = torch.full(x.shape, 1 / math.sqrt(math.sqrt(math.pi)))
+    else:
+        a = torch.zeros_like(x)
+
+        b = torch.ones_like(x) / math.sqrt(math.sqrt(math.pi))
+
+        size = torch.tensor(n)
+
+        for _ in range(0, n - 1):
+            previous = a
+
+            a = -b * torch.sqrt((size - 1.0) / size)
+
+            b = previous + b * x * torch.sqrt(2.0 / size)
+
+            size = size - 1.0
+
+        df = a + b * x * math.sqrt(2.0)
+
+    df = df * math.sqrt(degree)
+
+    x = x - (dy / df)
+
+    n = degree - 1
+
+    if n == 0:
+        fm = torch.full(x.shape, 1.0 / math.sqrt(math.sqrt(2.0 * math.pi)))
+    else:
+        a = torch.zeros_like(x)
+        b = torch.ones_like(x) / math.sqrt(math.sqrt(2.0 * math.pi))
+
+        size = torch.tensor(n)
+
+        for _ in range(0, n - 1):
+            previous = a
+
+            a = -b * torch.sqrt((size - 1.0) / size)
+
+            b = previous + b * x * torch.sqrt(1.0 / size)
+
+            size = size - 1.0
+
+        fm = a + b * x
+
+    fm = fm / torch.abs(fm).max()
+
+    w = 1 / (fm * fm)
+
+    a = torch.flip(w, dims=[0])
+    b = torch.flip(x, dims=[0])
+
+    w = (w + a) / 2
+    x = (x - b) / 2
+
+    w = w * (math.sqrt(2 * math.pi) / torch.sum(w))
+
+    return x, w
diff --git a/src/beignet/_integrate_chebyshev_polynomial.py b/src/beignet/_integrate_chebyshev_polynomial.py
new file mode 100644
index 0000000000..2757f5a6a8
--- /dev/null
+++ b/src/beignet/_integrate_chebyshev_polynomial.py
@@ -0,0 +1,73 @@
+import numpy
+import torch
+from torch import Tensor
+
+from ._evaluate_chebyshev_polynomial import evaluate_chebyshev_polynomial
+
+
+def integrate_chebyshev_polynomial(
+    input: Tensor,
+    order=1,
+    k=None,
+    lower_bound=0,
+    scale=1,
+    axis=0,
+) -> Tensor:
+    if k is None:
+        k = []
+
+    input = torch.atleast_1d(input)
+
+    lower_bound = torch.tensor(lower_bound)
+
+    scale = torch.tensor(scale)
+
+    if not numpy.iterable(k):
+        k = [k]
+
+    if len(k) > order:
+        raise ValueError
+
+    if lower_bound.ndim != 0:
+        raise ValueError
+
+    if scale.ndim != 0:
+        raise ValueError
+
+    if order == 0:
+        return input
+
+    input = torch.moveaxis(input, axis, 0)
+
+    k = torch.tensor([*k] + [0.0] * (order - len(k)))
+
+    k = torch.atleast_1d(k)
+
+    for i in range(order):
+        n = input.shape[0]
+
+        input = input * scale
+
+        tmp = torch.empty([n + 1, *input.shape[1:]])
+
+        tmp[0] = input[0] * 0
+        tmp[1] = input[0]
+
+        if n > 1:
+            tmp[2] = input[1] / 4
+
+        if n < 2:
+            j = torch.tensor([], dtype=torch.int32)
+        else:
+            j = torch.arange(2, n)
+
+        tmp[j + 1] = (input[j].T / (2 * (j + 1))).T
+        tmp[j - 1] = tmp[j - 1] + -(input[j] / (2 * (j - 1)))
+
+        tmp[0] = tmp[0] + (k[i] - evaluate_chebyshev_polynomial(lower_bound, tmp))
+
+        input = tmp
+
+    input = torch.moveaxis(input, 0, axis)
+
+    return input
diff --git a/src/beignet/_integrate_laguerre_polynomial.py b/src/beignet/_integrate_laguerre_polynomial.py
new file mode 100644
index 0000000000..fe653754d7
--- /dev/null
+++ b/src/beignet/_integrate_laguerre_polynomial.py
@@ -0,0 +1,60 @@
+import numpy
+import torch
+
+from ._evaluate_laguerre_polynomial import evaluate_laguerre_polynomial
+
+
+def integrate_laguerre_polynomial(
+    input,
+    order=1,
+    k=None,
+    lower_bound=0,
+    scale=1,
+    axis=0,
+):
+    if k is None:
+        k = []
+
+    input = torch.atleast_1d(input)
+
+    lower_bound, scale = map(torch.tensor, (lower_bound, scale))
+
+    if not numpy.iterable(k):
+        k = [k]
+    if len(k) > order:
+        raise ValueError
+
+    if lower_bound.ndim != 0:
+        raise ValueError
+
+    if scale.ndim != 0:
+        raise ValueError
+
+    if order == 0:
+        return input
+
+    input = torch.moveaxis(input, axis, 0)
+    k = torch.tensor(list(k) + [0] * (order - len(k)))
+    k = torch.atleast_1d(k)
+
+    for i in range(order):
+        n = input.shape[0]
+        input *= scale
+
+        tmp = torch.empty((n + 1,) + input.shape[1:], dtype=input.dtype)
+
+        tmp[0] = input[0]
+        tmp[1] = -input[0]
+
+        j = torch.arange(1, n)
+
+        tmp[j] += input[j]
+        tmp[j + 1] += -input[j]
+
+        tmp_value = torch.tensor(evaluate_laguerre_polynomial(lower_bound, tmp))
+        tmp[0] += k[i] - tmp_value
+
+        input = tmp
+
+    input = torch.moveaxis(input, 0, axis)
+    return input
diff --git a/src/beignet/_integrate_legendre_polynomial.py b/src/beignet/_integrate_legendre_polynomial.py
new file mode 100644
index 0000000000..51cc34a518
--- /dev/null
+++ b/src/beignet/_integrate_legendre_polynomial.py
@@ -0,0 +1,65 @@
+import numpy
+import torch
+
+from ._evaluate_legendre_polynomial import evaluate_legendre_polynomial
+
+
+def integrate_legendre_polynomial(
+    input,
+    order=1,
+    k=None,
+    lower_bound=0,
+    scale=1,
+    axis=0,
+):
+    if k is None:
+        k = []
+
+    input = torch.atleast_1d(input)
+
+    lbnd, scl = map(torch.tensor, (lower_bound, scale))
+
+    if not numpy.iterable(k):
+        k = [k]
+
+    if len(k) > order:
+        raise ValueError("Too many integration constants")
+
+    if lbnd.ndim != 0:
+        raise ValueError("lbnd must be a scalar.")
+
+    if scl.ndim != 0:
+        raise ValueError("scl must be a scalar.")
+
+    if order == 0:
+        return input
+
+    output = torch.moveaxis(input, axis, 0)
+
+    k = torch.tensor(list(k) + [0] * (order - len(k)))
+    k = torch.atleast_1d(k)
+
+    for i in range(order):
+        n = len(output)
+        output *= scl
+        tmp = torch.empty((n + 1,) + output.shape[1:], dtype=output.dtype)
+        tmp[0] = output[0] * 0
+        tmp[1] = output[0]
+        if n > 1:
+            tmp[2] = output[1] / 3
+
+        if n < 2:
+            j = torch.tensor([], dtype=torch.int32)
+        else:
+            j = torch.arange(2, n)
+
+        t = (output[j].T / (2 * j + 1)).T
+        tmp[j + 1] = t
+        tmp[j - 1] += -t
+        legval_value = evaluate_legendre_polynomial(lbnd, tmp)
+        tmp[0] += k[i] - legval_value
+        output = tmp
+
+    output = torch.moveaxis(output, 0, axis)
+
+    return output
diff --git a/src/beignet/_integrate_physicists_hermite_polynomial.py b/src/beignet/_integrate_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..6e34531a46
--- /dev/null
+++ b/src/beignet/_integrate_physicists_hermite_polynomial.py
@@ -0,0 +1,63 @@
+import numpy
+import torch
+
+from ._evaluate_physicists_hermite_polynomial import (
+    evaluate_physicists_hermite_polynomial,
+)
+
+
+def integrate_physicists_hermite_polynomial(
+    input,
+    order=1,
+    k=None,
+    lower_bound=0,
+    scale=1,
+    axis=0,
+):
+    if k is None:
+        k = []
+
+    input = torch.atleast_1d(input)
+
+    lower_bound, scale = map(torch.tensor, (lower_bound, scale))
+
+    if not numpy.iterable(k):
+        k = [k]
+
+    if len(k) > order:
+        raise ValueError
+
+    if lower_bound.ndim != 0:
+        raise ValueError
+
+    if scale.ndim != 0:
+        raise ValueError
+
+    if order == 0:
+        return input
+
+    input = torch.moveaxis(input, axis, 0)
+
+    k = torch.tensor(list(k) + [0] * (order - len(k)))
+    k = torch.atleast_1d(k)
+
+    for i in range(order):
+        n = input.shape[0]
+        input *= scale
+        tmp = torch.empty((n + 1,) + input.shape[1:], dtype=input.dtype)
+
+        tmp[0] = input[0] * 0
+        tmp[1] = input[0] / 2
+
+        j = torch.arange(1, n)
+
+        tmp[j + 1] = (input[j].T / (2 * (j + 1))).T
+
+        tmp_value = evaluate_physicists_hermite_polynomial(lower_bound, tmp)
+        tmp[0] += k[i] - tmp_value
+
+        input = tmp
+
+    input = torch.moveaxis(input, 0, axis)
+
+    return input
diff --git a/src/beignet/_integrate_polynomial.py b/src/beignet/_integrate_polynomial.py
new file mode 100644
index 0000000000..f1fe3324b1
--- /dev/null
+++ b/src/beignet/_integrate_polynomial.py
@@ -0,0 +1,103 @@
+import numpy
+import torch
+import torch._numpy._funcs_impl
+from torch import Tensor
+
+from ._evaluate_polynomial import evaluate_polynomial
+
+
+def integrate_polynomial(
+    input: Tensor,
+    order: int = 1,
+    k=None,
+    lower_bound: float = 0,
+    scale: float = 1,
+    dim: int = 0,
+) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    order : int, default=1
+
+    k : int, optional
+
+    lower_bound : float, default=0
+
+    scale : float, default=1
+
+    dim : int, default=0
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the integral.
+    """
+    if k is None:
+        k = []
+
+    input = torch.atleast_1d(input)
+
+    lower_bound, scale = map(torch.tensor, (lower_bound, scale))
+
+    if not numpy.iterable(k):
+        k = [k]
+
+    if order < 0:
+        raise ValueError
+
+    if len(k) > order:
+        raise ValueError
+
+    if lower_bound.ndim != 0:
+        raise ValueError
+
+    if scale.ndim != 0:
+        raise ValueError
+
+    if order == 0:
+        return input
+
+    k = torch.tensor(list(k) + [0] * (order - len(k)))
+    k = torch.atleast_1d(k)
+
+    n = input.shape[dim]
+
+    padding = torch.tensor([0, order])
+    input = torch.moveaxis(input, dim, 0)
+    if padding[0] < 0:
+        input = input[torch.abs(padding[0]) :]
+
+        padding = (0, padding[1])
+    if padding[1] < 0:
+        input = input[: -torch.abs(padding[1])]
+
+        padding = (padding[0], 0)
+    npad = torch.tensor([(0, 0)] * input.ndim)
+    npad[0] = padding
+    output = torch._numpy._funcs_impl.pad(
+        input,
+        pad_width=npad,
+        mode="constant",
+        constant_values=0,
+    )
+    input = torch.moveaxis(output, 0, dim)
+
+    input = torch.moveaxis(input, dim, 0)
+
+    d = torch.arange(n + order) + 1
+
+    for i in range(0, order):
+        input = input * scale
+
+        input = (input.T / d).T
+
+        input = torch.roll(input, 1, dims=[0])
+
+        input[0] = 0.0
+
+        input[0] += k[i] - evaluate_polynomial(lower_bound, input)
+
+    return torch.moveaxis(input, 0, dim)
diff --git a/src/beignet/_integrate_probabilists_hermite_polynomial.py b/src/beignet/_integrate_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..b3c033251c
--- /dev/null
+++ b/src/beignet/_integrate_probabilists_hermite_polynomial.py
@@ -0,0 +1,63 @@
+import numpy
+import torch
+
+from ._evaluate_probabilists_hermite_polynomial import (
+    evaluate_probabilists_hermite_polynomial,
+)
+
+
+def integrate_probabilists_hermite_polynomial(
+    input,
+    order=1,
+    k=None,
+    lower_bound=0,
+    scale=1,
+    axis=0,
+):
+    if k is None:
+        k = []
+
+    input = torch.atleast_1d(input)
+
+    lower_bound = torch.tensor(lower_bound)
+    scale = torch.tensor(scale)
+
+    if not numpy.iterable(k):
+        k = [k]
+
+    if len(k) > order:
+        raise ValueError
+
+    if lower_bound.ndim != 0:
+        raise ValueError
+
+    if scale.ndim != 0:
+        raise ValueError
+
+    if order == 0:
+        return input
+
+    input = torch.moveaxis(input, axis, 0)
+    k = torch.tensor(list(k) + [0] * (order - len(k)))
+    k = torch.atleast_1d(k)
+
+    for i in range(order):
+        n = input.shape[0]
+        input *= scale
+        tmp = torch.empty((n + 1,) + input.shape[1:], dtype=input.dtype)
+
+        tmp[0] = input[0] * 0
+        tmp[1] = input[0]
+
+        j = torch.arange(1, n)
+
+        tmp[j + 1] = (input[j].T / (j + 1)).T
+
+        hermeval_value = torch.tensor(
+            evaluate_probabilists_hermite_polynomial(lower_bound, tmp)
+        )
+        tmp[0] += k[i] - hermeval_value
+
+        input = tmp
+
+    return torch.moveaxis(input, 0, axis)
diff --git a/src/beignet/_laguerre_polynomial_companion.py b/src/beignet/_laguerre_polynomial_companion.py
new file mode 100644
index 0000000000..88f66b6727
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_companion.py
@@ -0,0 +1,28 @@
+import torch
+from torch import Tensor
+
+
+def laguerre_polynomial_companion(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] < 2:
+        raise ValueError
+
+    if input.shape[0] == 2:
+        return torch.tensor([[1 + input[0] / input[1]]])
+
+    n = input.shape[0] - 1
+
+    output = torch.reshape(torch.zeros([n, n], dtype=input.dtype), [-1])
+
+    output[1 :: n + 1] = -torch.arange(1, n)
+
+    output[0 :: n + 1] = 2.0 * torch.arange(n) + 1.0
+
+    output[n :: n + 1] = -torch.arange(1, n)
+
+    output = torch.reshape(output, [n, n])
+
+    output[:, -1] += (input[:-1] / input[-1]) * n
+
+    return output
diff --git a/src/beignet/_laguerre_polynomial_domain.py b/src/beignet/_laguerre_polynomial_domain.py
new file mode 100644
index 0000000000..56d97c79d9
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_domain.py
@@ -0,0 +1,3 @@
+import torch
+
+laguerre_polynomial_domain = torch.tensor([0.0, 1.0])
diff --git a/src/beignet/_laguerre_polynomial_from_roots.py b/src/beignet/_laguerre_polynomial_from_roots.py
new file mode 100644
index 0000000000..af901242ad
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_from_roots.py
@@ -0,0 +1,85 @@
+import math
+
+import torch
+
+from ._linear_laguerre_polynomial import linear_laguerre_polynomial
+from ._multiply_laguerre_polynomial import multiply_laguerre_polynomial
+
+
+def laguerre_polynomial_from_roots(input):
+    f = linear_laguerre_polynomial
+    g = multiply_laguerre_polynomial
+    if math.prod(input.shape) == 0:
+        return torch.ones([1])
+
+    input, _ = torch.sort(input)
+
+    ys = []
+
+    for x in input:
+        a = torch.zeros(input.shape[0] + 1, dtype=x.dtype)
+        b = f(-x, 1)
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            y = torch.concatenate(
+                [
+                    b,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+
+            y = a + y
+        else:
+            y = torch.concatenate(
+                [
+                    a,
+                    torch.zeros(
+                        b.shape[0] - a.shape[0],
+                        dtype=a.dtype,
+                    ),
+                ]
+            )
+
+            y = b + y
+
+        ys = [*ys, y]
+
+    p = torch.stack(ys)
+
+    m = p.shape[0]
+
+    x = m, p
+
+    while x[0] > 1:
+        m, r = divmod(x[0], 2)
+
+        z = x[1]
+
+        previous = torch.zeros([len(p), input.shape[0] + 1])
+
+        y = previous
+
+        for i in range(0, m):
+            y[i] = g(z[i], z[i + m])[: input.shape[0] + 1]
+
+        previous = y
+
+        if r:
+            previous[0] = g(previous[0], z[2 * m])[: input.shape[0] + 1]
+
+        x = m, previous
+
+    _, output = x
+
+    return output[0]
diff --git a/src/beignet/_laguerre_polynomial_one.py b/src/beignet/_laguerre_polynomial_one.py
new file mode 100644
index 0000000000..81ff015fe7
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_one.py
@@ -0,0 +1,3 @@
+import torch
+
+laguerre_polynomial_one = torch.tensor([1.0])
diff --git a/src/beignet/_laguerre_polynomial_power.py b/src/beignet/_laguerre_polynomial_power.py
new file mode 100644
index 0000000000..17c0212545
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_power.py
@@ -0,0 +1,61 @@
+import torch
+from torch import Tensor
+
+from ._multiply_laguerre_polynomial import multiply_laguerre_polynomial
+
+
+def laguerre_polynomial_power(
+    input: Tensor,
+    exponent: float | Tensor,
+    maximum_exponent: float | Tensor = 16.0,
+) -> Tensor:
+    input = torch.atleast_1d(input)
+    _exponent = int(exponent)
+    if _exponent != exponent or _exponent < 0:
+        raise ValueError
+    if maximum_exponent is not None and _exponent > maximum_exponent:
+        raise ValueError
+    match _exponent:
+        case 0:
+            output = torch.tensor([1], dtype=input.dtype)
+        case 1:
+            output = input
+        case _:
+            output = torch.zeros(input.shape[0] * exponent, dtype=input.dtype)
+
+            input = torch.atleast_1d(input)
+            output = torch.atleast_1d(output)
+
+            dtype = torch.promote_types(input.dtype, output.dtype)
+
+            input = input.to(dtype)
+            output = output.to(dtype)
+
+            if output.shape[0] > input.shape[0]:
+                input = torch.concatenate(
+                    [
+                        input,
+                        torch.zeros(
+                            output.shape[0] - input.shape[0],
+                            dtype=input.dtype,
+                        ),
+                    ],
+                )
+
+                output = output + input
+            else:
+                output = torch.concatenate(
+                    [
+                        output,
+                        torch.zeros(
+                            input.shape[0] - output.shape[0],
+                            dtype=output.dtype,
+                        ),
+                    ]
+                )
+
+                output = input + output
+
+            for _ in range(2, _exponent + 1):
+                output = multiply_laguerre_polynomial(output, input, mode="same")
+    return output
diff --git a/src/beignet/_laguerre_polynomial_roots.py b/src/beignet/_laguerre_polynomial_roots.py
new file mode 100644
index 0000000000..9330db8f1d
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_roots.py
@@ -0,0 +1,25 @@
+import torch
+from torch import Tensor
+
+from ._laguerre_polynomial_companion import laguerre_polynomial_companion
+
+
+def laguerre_polynomial_roots(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] <= 1:
+        return torch.tensor([], dtype=input.dtype)
+
+    if input.shape[0] == 2:
+        return torch.tensor([1 + input[0] / input[1]])
+
+    output = laguerre_polynomial_companion(input)
+
+    output = torch.flip(output, dims=[0])
+    output = torch.flip(output, dims=[1])
+
+    output = torch.linalg.eigvals(output)
+
+    output, _ = torch.sort(output.real)
+
+    return output
diff --git a/src/beignet/_laguerre_polynomial_to_polynomial.py b/src/beignet/_laguerre_polynomial_to_polynomial.py
new file mode 100644
index 0000000000..3160555e63
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_to_polynomial.py
@@ -0,0 +1,55 @@
+import torch
+from torch import Tensor
+
+from ._add_polynomial import add_polynomial
+from ._multiply_polynomial_by_x import multiply_polynomial_by_x
+from ._subtract_polynomial import subtract_polynomial
+
+
+def laguerre_polynomial_to_polynomial(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    n = input.shape[0]
+
+    if n == 1:
+        return input
+    else:
+        c0 = torch.zeros_like(input)
+        c0[0] = input[-2]
+
+        c1 = torch.zeros_like(input)
+        c1[0] = input[-1]
+
+        def body(k, c0c1):
+            i = n - 1 - k
+
+            c0, c1 = c0c1
+
+            tmp = c0
+
+            c0 = subtract_polynomial(input[i - 2], (c1 * (i - 1)) / i)
+
+            c1 = add_polynomial(
+                tmp,
+                subtract_polynomial(
+                    (2 * i - 1) * c1, multiply_polynomial_by_x(c1, "same")
+                )
+                / i,
+            )
+
+            return c0, c1
+
+        b = n - 2
+
+        x = (c0, c1)
+
+        y = x
+
+        for index in range(0, b):
+            y = body(index, y)
+
+        c0, c1 = y
+
+        return add_polynomial(
+            c0, subtract_polynomial(c1, multiply_polynomial_by_x(c1, "same"))
+        )
diff --git a/src/beignet/_laguerre_polynomial_vandermonde.py b/src/beignet/_laguerre_polynomial_vandermonde.py
new file mode 100644
index 0000000000..22e41ae0ed
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_vandermonde.py
@@ -0,0 +1,30 @@
+import torch
+from torch import Tensor
+
+
+def laguerre_polynomial_vandermonde(
+    x: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    if degree < 0:
+        raise ValueError
+
+    x = torch.atleast_1d(x)
+
+    dtype = torch.promote_types(x.dtype, torch.get_default_dtype())
+
+    x = x.to(dtype)
+
+    v = torch.empty([degree + 1, *x.shape], dtype=dtype)
+
+    v[0] = torch.ones_like(x)
+
+    if degree > 0:
+        v[1] = 1 - x
+
+        for index in range(2, degree + 1):
+            v[index] = (
+                v[index - 1] * (2 * index - 1 - x) - v[index - 2] * (index - 1)
+            ) / index
+
+    return torch.moveaxis(v, 0, -1)
diff --git a/src/beignet/_laguerre_polynomial_vandermonde_2d.py b/src/beignet/_laguerre_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..ae2aa5a764
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_vandermonde_2d.py
@@ -0,0 +1,49 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._laguerre_polynomial_vandermonde import laguerre_polynomial_vandermonde
+
+
+def laguerre_polynomial_vandermonde_2d(
+    x: Tensor,
+    y: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    functions = (
+        laguerre_polynomial_vandermonde,
+        laguerre_polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_laguerre_polynomial_vandermonde_3d.py b/src/beignet/_laguerre_polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..55517cd62e
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_vandermonde_3d.py
@@ -0,0 +1,51 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._laguerre_polynomial_vandermonde import laguerre_polynomial_vandermonde
+
+
+def laguerre_polynomial_vandermonde_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    functions = (
+        laguerre_polynomial_vandermonde,
+        laguerre_polynomial_vandermonde,
+        laguerre_polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y, z]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y, z)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_laguerre_polynomial_weight.py b/src/beignet/_laguerre_polynomial_weight.py
new file mode 100644
index 0000000000..3322e7d91e
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_weight.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def laguerre_polynomial_weight(x: Tensor) -> Tensor:
+    return torch.exp(-x)
diff --git a/src/beignet/_laguerre_polynomial_x.py b/src/beignet/_laguerre_polynomial_x.py
new file mode 100644
index 0000000000..4ae15b4131
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_x.py
@@ -0,0 +1,3 @@
+import torch
+
+laguerre_polynomial_x = torch.tensor([1.0, -1.0])
diff --git a/src/beignet/_laguerre_polynomial_zero.py b/src/beignet/_laguerre_polynomial_zero.py
new file mode 100644
index 0000000000..7235717ff8
--- /dev/null
+++ b/src/beignet/_laguerre_polynomial_zero.py
@@ -0,0 +1,3 @@
+import torch
+
+laguerre_polynomial_zero = torch.tensor([0.0])
diff --git a/src/beignet/_legendre_polynomial_companion.py b/src/beignet/_legendre_polynomial_companion.py
new file mode 100644
index 0000000000..235905adc9
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_companion.py
@@ -0,0 +1,32 @@
+import torch
+from torch import Tensor
+
+
+def legendre_polynomial_companion(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] < 2:
+        raise ValueError
+
+    if input.shape[0] == 2:
+        return torch.tensor([[-input[0] / input[1]]])
+
+    n = input.shape[0] - 1
+
+    output = torch.zeros((n, n), dtype=input.dtype)
+
+    scale = 1.0 / torch.sqrt(2 * torch.arange(n) + 1)
+
+    shape = output.shape
+
+    output = torch.reshape(output, [-1])
+
+    output[1 :: n + 1] = torch.arange(1, n) * scale[: n - 1] * scale[1:n]
+
+    output[n :: n + 1] = torch.arange(1, n) * scale[: n - 1] * scale[1:n]
+
+    output = torch.reshape(output, shape)
+
+    output[:, -1] += -(input[:-1] / input[-1]) * (scale / scale[-1]) * (n / (2 * n - 1))
+
+    return output
diff --git a/src/beignet/_legendre_polynomial_domain.py b/src/beignet/_legendre_polynomial_domain.py
new file mode 100644
index 0000000000..e9a2c3e9e4
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_domain.py
@@ -0,0 +1,3 @@
+import torch
+
+legendre_polynomial_domain = torch.tensor([-1.0, 1.0])
diff --git a/src/beignet/_legendre_polynomial_from_roots.py b/src/beignet/_legendre_polynomial_from_roots.py
new file mode 100644
index 0000000000..5482ea8414
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_from_roots.py
@@ -0,0 +1,85 @@
+import math
+
+import torch
+
+from ._linear_legendre_polynomial import linear_legendre_polynomial
+from ._multiply_legendre_polynomial import multiply_legendre_polynomial
+
+
+def legendre_polynomial_from_roots(input):
+    f = linear_legendre_polynomial
+    g = multiply_legendre_polynomial
+    if math.prod(input.shape) == 0:
+        return torch.ones([1])
+
+    input, _ = torch.sort(input)
+
+    ys = []
+
+    for x in input:
+        a = torch.zeros(input.shape[0] + 1, dtype=x.dtype)
+        b = f(-x, 1)
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            y = torch.concatenate(
+                [
+                    b,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+
+            y = a + y
+        else:
+            y = torch.concatenate(
+                [
+                    a,
+                    torch.zeros(
+                        b.shape[0] - a.shape[0],
+                        dtype=a.dtype,
+                    ),
+                ]
+            )
+
+            y = b + y
+
+        ys = [*ys, y]
+
+    p = torch.stack(ys)
+
+    m = p.shape[0]
+
+    x = m, p
+
+    while x[0] > 1:
+        m, r = divmod(x[0], 2)
+
+        z = x[1]
+
+        previous = torch.zeros([len(p), input.shape[0] + 1])
+
+        y = previous
+
+        for i in range(0, m):
+            y[i] = g(z[i], z[i + m])[: input.shape[0] + 1]
+
+        previous = y
+
+        if r:
+            previous[0] = g(previous[0], z[2 * m])[: input.shape[0] + 1]
+
+        x = m, previous
+
+    _, output = x
+
+    return output[0]
diff --git a/src/beignet/_legendre_polynomial_one.py b/src/beignet/_legendre_polynomial_one.py
new file mode 100644
index 0000000000..40901adf43
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_one.py
@@ -0,0 +1,3 @@
+import torch
+
+legendre_polynomial_one = torch.tensor([1.0])
diff --git a/src/beignet/_legendre_polynomial_power.py b/src/beignet/_legendre_polynomial_power.py
new file mode 100644
index 0000000000..f85b7ec4ab
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_power.py
@@ -0,0 +1,61 @@
+import torch
+from torch import Tensor
+
+from ._multiply_legendre_polynomial import multiply_legendre_polynomial
+
+
+def legendre_polynomial_power(
+    input: Tensor,
+    exponent: float | Tensor,
+    maximum_exponent: float | Tensor = 16.0,
+) -> Tensor:
+    input = torch.atleast_1d(input)
+    _exponent = int(exponent)
+    if _exponent != exponent or _exponent < 0:
+        raise ValueError
+    if maximum_exponent is not None and _exponent > maximum_exponent:
+        raise ValueError
+    match _exponent:
+        case 0:
+            output = torch.tensor([1], dtype=input.dtype)
+        case 1:
+            output = input
+        case _:
+            output = torch.zeros(input.shape[0] * exponent, dtype=input.dtype)
+
+            input = torch.atleast_1d(input)
+            output = torch.atleast_1d(output)
+
+            dtype = torch.promote_types(input.dtype, output.dtype)
+
+            input = input.to(dtype)
+            output = output.to(dtype)
+
+            if output.shape[0] > input.shape[0]:
+                input = torch.concatenate(
+                    [
+                        input,
+                        torch.zeros(
+                            output.shape[0] - input.shape[0],
+                            dtype=input.dtype,
+                        ),
+                    ],
+                )
+
+                output = output + input
+            else:
+                output = torch.concatenate(
+                    [
+                        output,
+                        torch.zeros(
+                            input.shape[0] - output.shape[0],
+                            dtype=output.dtype,
+                        ),
+                    ]
+                )
+
+                output = input + output
+
+            for _ in range(2, _exponent + 1):
+                output = multiply_legendre_polynomial(output, input, mode="same")
+    return output
diff --git a/src/beignet/_legendre_polynomial_roots.py b/src/beignet/_legendre_polynomial_roots.py
new file mode 100644
index 0000000000..cff5620a2b
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_roots.py
@@ -0,0 +1,25 @@
+import torch
+from torch import Tensor
+
+from ._legendre_polynomial_companion import legendre_polynomial_companion
+
+
+def legendre_polynomial_roots(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] <= 1:
+        return torch.tensor([], dtype=input.dtype)
+
+    if input.shape[0] == 2:
+        return torch.tensor([-input[0] / input[1]])
+
+    output = legendre_polynomial_companion(input)
+
+    output = torch.flip(output, dims=[0])
+    output = torch.flip(output, dims=[1])
+
+    output = torch.linalg.eigvals(output)
+
+    output, _ = torch.sort(output.real)
+
+    return output
diff --git a/src/beignet/_legendre_polynomial_to_polynomial.py b/src/beignet/_legendre_polynomial_to_polynomial.py
new file mode 100644
index 0000000000..e54e6e0f77
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_to_polynomial.py
@@ -0,0 +1,47 @@
+import torch
+from torch import Tensor
+
+from ._add_polynomial import add_polynomial
+from ._multiply_polynomial_by_x import multiply_polynomial_by_x
+from ._subtract_polynomial import subtract_polynomial
+
+
+def legendre_polynomial_to_polynomial(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    n = input.shape[0]
+
+    if n < 3:
+        return input
+
+    c0 = torch.zeros_like(input)
+    c0[0] = input[-2]
+
+    c1 = torch.zeros_like(input)
+    c1[0] = input[-1]
+
+    def body(k, c0c1):
+        i = n - 1 - k
+
+        c0, c1 = c0c1
+
+        tmp = c0
+
+        c0 = subtract_polynomial(input[i - 2], c1 * (i - 1) / i)
+
+        c1 = add_polynomial(tmp, multiply_polynomial_by_x(c1, "same") * (2 * i - 1) / i)
+
+        return c0, c1
+
+    x = (c0, c1)
+
+    for i in range(0, n - 2):
+        x = body(i, x)
+
+    c0, c1 = x
+
+    output = multiply_polynomial_by_x(c1, "same")
+
+    output = add_polynomial(c0, output)
+
+    return output
diff --git a/src/beignet/_legendre_polynomial_vandermonde.py b/src/beignet/_legendre_polynomial_vandermonde.py
new file mode 100644
index 0000000000..e9db5c6f01
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_vandermonde.py
@@ -0,0 +1,30 @@
+import torch
+from torch import Tensor
+
+
+def legendre_polynomial_vandermonde(x: Tensor, degree: Tensor) -> Tensor:
+    if degree < 0:
+        raise ValueError
+
+    x = torch.tensor(x)
+    x = torch.atleast_1d(x)
+
+    dims = (degree + 1,) + x.shape
+
+    dtype = torch.promote_types(x.dtype, torch.tensor(0.0).dtype)
+
+    x = x.to(dtype)
+
+    v = torch.empty(dims, dtype=dtype)
+
+    v[0] = torch.ones_like(x)
+
+    if degree > 0:
+        v[1] = x
+
+        for index in range(2, degree + 1):
+            v[index] = (
+                v[index - 1] * x * (2 * index - 1) - v[index - 2] * (index - 1)
+            ) / index
+
+    return torch.moveaxis(v, 0, -1)
diff --git a/src/beignet/_legendre_polynomial_vandermonde_2d.py b/src/beignet/_legendre_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..7b7e06841b
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_vandermonde_2d.py
@@ -0,0 +1,49 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._legendre_polynomial_vandermonde import legendre_polynomial_vandermonde
+
+
+def legendre_polynomial_vandermonde_2d(
+    x: Tensor,
+    y: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    functions = (
+        legendre_polynomial_vandermonde,
+        legendre_polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_legendre_polynomial_vandermonde_3d.py b/src/beignet/_legendre_polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..c1e8a2e694
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_vandermonde_3d.py
@@ -0,0 +1,51 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._legendre_polynomial_vandermonde import legendre_polynomial_vandermonde
+
+
+def legendre_polynomial_vandermonde_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    functions = (
+        legendre_polynomial_vandermonde,
+        legendre_polynomial_vandermonde,
+        legendre_polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y, z]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y, z)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_legendre_polynomial_weight.py b/src/beignet/_legendre_polynomial_weight.py
new file mode 100644
index 0000000000..27a6c7e414
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_weight.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def legendre_polynomial_weight(x: Tensor) -> Tensor:
+    return torch.ones_like(x)
diff --git a/src/beignet/_legendre_polynomial_x.py b/src/beignet/_legendre_polynomial_x.py
new file mode 100644
index 0000000000..909275de9c
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_x.py
@@ -0,0 +1,3 @@
+import torch
+
+legendre_polynomial_x = torch.tensor([0.0, 1.0])
diff --git a/src/beignet/_legendre_polynomial_zero.py b/src/beignet/_legendre_polynomial_zero.py
new file mode 100644
index 0000000000..4c4f45a6f9
--- /dev/null
+++ b/src/beignet/_legendre_polynomial_zero.py
@@ -0,0 +1,3 @@
+import torch
+
+legendre_polynomial_zero = torch.tensor([0.0])
diff --git a/src/beignet/_linear_chebyshev_polynomial.py b/src/beignet/_linear_chebyshev_polynomial.py
new file mode 100644
index 0000000000..38ead4ad38
--- /dev/null
+++ b/src/beignet/_linear_chebyshev_polynomial.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def linear_chebyshev_polynomial(input: float, other: float) -> Tensor:
+    return torch.tensor([input, other])
diff --git a/src/beignet/_linear_laguerre_polynomial.py b/src/beignet/_linear_laguerre_polynomial.py
new file mode 100644
index 0000000000..03f321b225
--- /dev/null
+++ b/src/beignet/_linear_laguerre_polynomial.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def linear_laguerre_polynomial(input: float, other: float) -> Tensor:
+    return torch.tensor([input + other, -other])
diff --git a/src/beignet/_linear_legendre_polynomial.py b/src/beignet/_linear_legendre_polynomial.py
new file mode 100644
index 0000000000..5fa1cbce53
--- /dev/null
+++ b/src/beignet/_linear_legendre_polynomial.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def linear_legendre_polynomial(input: float, other: float) -> Tensor:
+    return torch.tensor([input, other])
diff --git a/src/beignet/_linear_physicists_hermite_polynomial.py b/src/beignet/_linear_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..5aae8a5383
--- /dev/null
+++ b/src/beignet/_linear_physicists_hermite_polynomial.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def linear_physicists_hermite_polynomial(input: float, other: float) -> Tensor:
+    return torch.tensor([input, other / 2])
diff --git a/src/beignet/_linear_polynomial.py b/src/beignet/_linear_polynomial.py
new file mode 100644
index 0000000000..a4545eaffc
--- /dev/null
+++ b/src/beignet/_linear_polynomial.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def linear_polynomial(input: float, other: float) -> Tensor:
+    return torch.tensor([input, other])
diff --git a/src/beignet/_linear_probabilists_hermite_polynomial.py b/src/beignet/_linear_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..bc493685f7
--- /dev/null
+++ b/src/beignet/_linear_probabilists_hermite_polynomial.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def linear_probabilists_hermite_polynomial(input: float, other: float) -> Tensor:
+    return torch.tensor([input, other])
diff --git a/src/beignet/_multiply_chebyshev_polynomial.py b/src/beignet/_multiply_chebyshev_polynomial.py
new file mode 100644
index 0000000000..b29818e543
--- /dev/null
+++ b/src/beignet/_multiply_chebyshev_polynomial.py
@@ -0,0 +1,60 @@
+import math
+from typing import Literal
+
+import torch
+import torchaudio.functional
+from torch import Tensor
+
+
+def multiply_chebyshev_polynomial(
+    input: Tensor,
+    other: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    r"""
+    Returns the product of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the product.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    index = math.prod(input.shape)
+    output1 = torch.zeros(2 * index - 1, dtype=input.dtype)
+    output1[index - 1 :] = input / 2.0
+    output1 = torch.flip(output1, dims=[0]) + output1
+    a = output1
+
+    index1 = math.prod(other.shape)
+    output2 = torch.zeros(2 * index1 - 1, dtype=other.dtype)
+    output2[index1 - 1 :] = other / 2.0
+    output2 = torch.flip(output2, dims=[0]) + output2
+    b = output2
+
+    output = torchaudio.functional.convolve(a, b, mode=mode)
+
+    n = (math.prod(output.shape) + 1) // 2
+    c = output[n - 1 :]
+    c[1:n] = c[1:n] * 2.0
+    output = c
+
+    if mode == "same":
+        output = output[: max(input.shape[0], other.shape[0])]
+
+    return output
diff --git a/src/beignet/_multiply_chebyshev_polynomial_by_x.py b/src/beignet/_multiply_chebyshev_polynomial_by_x.py
new file mode 100644
index 0000000000..4cabc407f1
--- /dev/null
+++ b/src/beignet/_multiply_chebyshev_polynomial_by_x.py
@@ -0,0 +1,25 @@
+from typing import Literal
+
+import torch
+from torch import Tensor
+
+
+def multiply_chebyshev_polynomial_by_x(
+    input: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros(input.shape[0] + 1, dtype=input.dtype)
+
+    output[1] = input[0]
+
+    if input.shape[0] > 1:
+        output[2:] = input[1:] / 2
+
+        output[0:-2] = output[0:-2] + input[1:] / 2
+
+    if mode == "same":
+        output = output[: input.shape[0]]
+
+    return output
diff --git a/src/beignet/_multiply_laguerre_polynomial.py b/src/beignet/_multiply_laguerre_polynomial.py
new file mode 100644
index 0000000000..6dcc5ce913
--- /dev/null
+++ b/src/beignet/_multiply_laguerre_polynomial.py
@@ -0,0 +1,82 @@
+from typing import Literal
+
+import torch
+from torch import Tensor
+
+from ._add_laguerre_polynomial import add_laguerre_polynomial
+from ._multiply_laguerre_polynomial_by_x import multiply_laguerre_polynomial_by_x
+from ._subtract_laguerre_polynomial import subtract_laguerre_polynomial
+
+
+def multiply_laguerre_polynomial(
+    input: Tensor,
+    other: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    r"""
+    Returns the product of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the product.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    m, n = input.shape[0], other.shape[0]
+
+    if m > n:
+        x, y = other, input
+    else:
+        x, y = input, other
+
+    match x.shape[0]:
+        case 1:
+            a = add_laguerre_polynomial(torch.zeros(m + n - 1), x[0] * y)
+            b = torch.zeros(m + n - 1)
+        case 2:
+            a = add_laguerre_polynomial(torch.zeros(m + n - 1), x[0] * y)
+            b = add_laguerre_polynomial(torch.zeros(m + n - 1), x[1] * y)
+        case _:
+            size = x.shape[0]
+
+            a = add_laguerre_polynomial(torch.zeros(m + n - 1), x[-2] * y)
+            b = add_laguerre_polynomial(torch.zeros(m + n - 1), x[-1] * y)
+
+            for i in range(3, x.shape[0] + 1):
+                previous = a
+
+                size = size - 1
+
+                a = subtract_laguerre_polynomial(x[-i] * y, (b * (size - 1.0)) / size)
+                b = add_laguerre_polynomial(
+                    previous,
+                    subtract_laguerre_polynomial(
+                        (2.0 * size - 1.0) * b,
+                        multiply_laguerre_polynomial_by_x(b, "same"),
+                    )
+                    / size,
+                )
+
+    output = add_laguerre_polynomial(
+        a, subtract_laguerre_polynomial(b, multiply_laguerre_polynomial_by_x(b, "same"))
+    )
+
+    if mode == "same":
+        output = output[: max(m, n)]
+
+    return output
diff --git a/src/beignet/_multiply_laguerre_polynomial_by_x.py b/src/beignet/_multiply_laguerre_polynomial_by_x.py
new file mode 100644
index 0000000000..07f59457b3
--- /dev/null
+++ b/src/beignet/_multiply_laguerre_polynomial_by_x.py
@@ -0,0 +1,29 @@
+from typing import Literal
+
+import torch
+from torch import Tensor
+
+
+def multiply_laguerre_polynomial_by_x(
+    input: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros(input.shape[0] + 1, dtype=input.dtype)
+
+    output[0] = +input[0]
+    output[1] = -input[0]
+
+    i = torch.arange(1, input.shape[0])
+
+    output[i + 1] = -input[i] * (i + 1)
+
+    output[i] = output[i] + input[i] * (2 * i + 1)
+
+    output[i - 1] = output[i - 1] - input[i] * i
+
+    if mode == "same":
+        output = output[: input.shape[0]]
+
+    return output
diff --git a/src/beignet/_multiply_legendre_polynomial.py b/src/beignet/_multiply_legendre_polynomial.py
new file mode 100644
index 0000000000..2b4c121efb
--- /dev/null
+++ b/src/beignet/_multiply_legendre_polynomial.py
@@ -0,0 +1,80 @@
+from typing import Literal
+
+import torch
+from torch import Tensor
+
+from ._add_legendre_polynomial import add_legendre_polynomial
+from ._multiply_legendre_polynomial_by_x import multiply_legendre_polynomial_by_x
+from ._subtract_legendre_polynomial import subtract_legendre_polynomial
+
+
+def multiply_legendre_polynomial(
+    input: Tensor,
+    other: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    r"""
+    Returns the product of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the product.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    m, n = input.shape[0], other.shape[0]
+
+    if m > n:
+        x, y = other, input
+    else:
+        x, y = input, other
+
+    match x.shape[0]:
+        case 1:
+            a = add_legendre_polynomial(torch.zeros(m + n - 1), x[0] * y)
+            b = torch.zeros(m + n - 1)
+        case 2:
+            a = add_legendre_polynomial(torch.zeros(m + n - 1), x[0] * y)
+            b = add_legendre_polynomial(torch.zeros(m + n - 1), x[1] * y)
+        case _:
+            size = x.shape[0]
+
+            a = add_legendre_polynomial(torch.zeros(m + n - 1), x[-2] * y)
+            b = add_legendre_polynomial(torch.zeros(m + n - 1), x[-1] * y)
+
+            for index in range(3, x.shape[0] + 1):
+                previous = a
+
+                size = size - 1
+
+                a = subtract_legendre_polynomial(
+                    x[-index] * y, (b * (size - 1.0)) / size
+                )
+
+                b = add_legendre_polynomial(
+                    previous,
+                    (multiply_legendre_polynomial_by_x(b, "same") * (2.0 * size - 1.0))
+                    / size,
+                )
+
+    output = add_legendre_polynomial(a, multiply_legendre_polynomial_by_x(b, "same"))
+
+    if mode == "same":
+        output = output[: max(m, n)]
+
+    return output
diff --git a/src/beignet/_multiply_legendre_polynomial_by_x.py b/src/beignet/_multiply_legendre_polynomial_by_x.py
new file mode 100644
index 0000000000..548ac48091
--- /dev/null
+++ b/src/beignet/_multiply_legendre_polynomial_by_x.py
@@ -0,0 +1,24 @@
+from typing import Literal
+
+import torch
+from torch import Tensor
+
+
+def multiply_legendre_polynomial_by_x(
+    input: Tensor, mode: Literal["full", "same"] = "full"
+) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros(input.shape[0] + 1, dtype=input.dtype)
+    output[1] = input[0]
+
+    for index in range(1, input.shape[0]):
+        output[index + 1] = (input[index] * (index + 1)) / (index + index + 1)
+        output[index - 1] = output[index - 1] + (input[index] * (index + 0)) / (
+            index + index + 1
+        )
+
+    if mode == "same":
+        output = output[: input.shape[0]]
+
+    return output
diff --git a/src/beignet/_multiply_physicists_hermite_polynomial.py b/src/beignet/_multiply_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..199c78b735
--- /dev/null
+++ b/src/beignet/_multiply_physicists_hermite_polynomial.py
@@ -0,0 +1,85 @@
+from typing import Literal
+
+import torch
+from torch import Tensor
+
+from ._add_physicists_hermite_polynomial import add_physicists_hermite_polynomial
+from ._multiply_physicists_hermite_polynomial_by_x import (
+    multiply_physicists_hermite_polynomial_by_x,
+)
+from ._subtract_physicists_hermite_polynomial import (
+    subtract_physicists_hermite_polynomial,
+)
+
+
+def multiply_physicists_hermite_polynomial(
+    input: Tensor,
+    other: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    r"""
+    Returns the product of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the product.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    m, n = input.shape[0], other.shape[0]
+
+    if m > n:
+        x, y = other, input
+    else:
+        x, y = input, other
+
+    match x.shape[0]:
+        case 1:
+            a = add_physicists_hermite_polynomial(torch.zeros(m + n - 1), x[0] * y)
+            b = torch.zeros(m + n - 1)
+        case 2:
+            a = add_physicists_hermite_polynomial(torch.zeros(m + n - 1), x[0] * y)
+            b = add_physicists_hermite_polynomial(torch.zeros(m + n - 1), x[1] * y)
+        case _:
+            size = x.shape[0]
+
+            a = add_physicists_hermite_polynomial(torch.zeros(m + n - 1), x[-2] * y)
+            b = add_physicists_hermite_polynomial(torch.zeros(m + n - 1), x[-1] * y)
+
+            for i in range(3, x.shape[0] + 1):
+                previous = a
+
+                size = size - 1
+
+                a = subtract_physicists_hermite_polynomial(
+                    x[-i] * y, b * (2 * (size - 1.0))
+                )
+
+                b = add_physicists_hermite_polynomial(
+                    previous,
+                    multiply_physicists_hermite_polynomial_by_x(b, "same") * 2.0,
+                )
+
+    output = add_physicists_hermite_polynomial(
+        a, multiply_physicists_hermite_polynomial_by_x(b, "same") * 2
+    )
+
+    if mode == "same":
+        output = output[: max(m, n)]
+
+    return output
diff --git a/src/beignet/_multiply_physicists_hermite_polynomial_by_x.py b/src/beignet/_multiply_physicists_hermite_polynomial_by_x.py
new file mode 100644
index 0000000000..d390cdce94
--- /dev/null
+++ b/src/beignet/_multiply_physicists_hermite_polynomial_by_x.py
@@ -0,0 +1,25 @@
+from typing import Literal
+
+import torch
+from torch import Tensor
+
+
+def multiply_physicists_hermite_polynomial_by_x(
+    input: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros(input.shape[0] + 1, dtype=input.dtype)
+
+    output[1] = input[0] / 2.0
+
+    i = torch.arange(1, input.shape[0])
+
+    output[i + 1] = input[i] / 2.0
+    output[i - 1] = output[i - 1] + input[i] * i
+
+    if mode == "same":
+        output = output[: input.shape[0]]
+
+    return output
diff --git a/src/beignet/_multiply_polynomial.py b/src/beignet/_multiply_polynomial.py
new file mode 100644
index 0000000000..5159c9b1fb
--- /dev/null
+++ b/src/beignet/_multiply_polynomial.py
@@ -0,0 +1,42 @@
+from typing import Literal
+
+import torch
+import torchaudio.functional
+from torch import Tensor
+
+
+def multiply_polynomial(
+    input: Tensor,
+    other: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    r"""
+    Returns the product of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the product.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    output = torchaudio.functional.convolve(input, other)
+
+    if mode == "same":
+        output = output[: max(input.shape[0], other.shape[0])]
+
+    return output
diff --git a/src/beignet/_multiply_polynomial_by_x.py b/src/beignet/_multiply_polynomial_by_x.py
new file mode 100644
index 0000000000..705b00f2b4
--- /dev/null
+++ b/src/beignet/_multiply_polynomial_by_x.py
@@ -0,0 +1,34 @@
+from typing import Literal
+
+import torch
+from torch import Tensor
+
+
+def multiply_polynomial_by_x(
+    input: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    mode : Literal["full", "same", "valid"]
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the product of the polynomial and the
+        independent variable.
+    """
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros(input.shape[0] + 1, dtype=input.dtype)
+
+    output[1:] = input
+
+    if mode == "same":
+        output = output[: input.shape[0]]
+
+    return output
diff --git a/src/beignet/_multiply_probabilists_hermite_polynomial.py b/src/beignet/_multiply_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..268f88595c
--- /dev/null
+++ b/src/beignet/_multiply_probabilists_hermite_polynomial.py
@@ -0,0 +1,84 @@
+from typing import Literal
+
+import torch
+from torch import Tensor
+
+from ._add_probabilists_hermite_polynomial import add_probabilists_hermite_polynomial
+from ._multiply_probabilists_hermite_polynomial_by_x import (
+    multiply_probabilists_hermite_polynomial_by_x,
+)
+from ._subtract_probabilists_hermite_polynomial import (
+    subtract_probabilists_hermite_polynomial,
+)
+
+
+def multiply_probabilists_hermite_polynomial(
+    input: Tensor,
+    other: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    r"""
+    Returns the product of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the product.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    m, n = input.shape[0], other.shape[0]
+
+    if m > n:
+        x, y = other, input
+    else:
+        x, y = input, other
+
+    match x.shape[0]:
+        case 1:
+            a = add_probabilists_hermite_polynomial(torch.zeros(m + n - 1), x[0] * y)
+            b = torch.zeros(m + n - 1)
+        case 2:
+            a = add_probabilists_hermite_polynomial(torch.zeros(m + n - 1), x[0] * y)
+            b = add_probabilists_hermite_polynomial(torch.zeros(m + n - 1), x[1] * y)
+        case _:
+            size = x.shape[0]
+
+            a = add_probabilists_hermite_polynomial(torch.zeros(m + n - 1), x[-2] * y)
+            b = add_probabilists_hermite_polynomial(torch.zeros(m + n - 1), x[-1] * y)
+
+            for i in range(3, x.shape[0] + 1):
+                previous = a
+
+                size = size - 1
+
+                a = subtract_probabilists_hermite_polynomial(
+                    x[-i] * y, b * (size - 1.0)
+                )
+
+                b = add_probabilists_hermite_polynomial(
+                    previous, multiply_probabilists_hermite_polynomial_by_x(b, "same")
+                )
+
+    output = add_probabilists_hermite_polynomial(
+        a, multiply_probabilists_hermite_polynomial_by_x(b, "same")
+    )
+
+    if mode == "same":
+        output = output[: max(m, n)]
+
+    return output
diff --git a/src/beignet/_multiply_probabilists_hermite_polynomial_by_x.py b/src/beignet/_multiply_probabilists_hermite_polynomial_by_x.py
new file mode 100644
index 0000000000..17962b3d27
--- /dev/null
+++ b/src/beignet/_multiply_probabilists_hermite_polynomial_by_x.py
@@ -0,0 +1,25 @@
+from typing import Literal
+
+import torch
+from torch import Tensor
+
+
+def multiply_probabilists_hermite_polynomial_by_x(
+    input: Tensor,
+    mode: Literal["full", "same", "valid"] = "full",
+) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros(input.shape[0] + 1, dtype=input.dtype)
+
+    output[1] = input[0]
+
+    index = torch.arange(1, input.shape[0])
+
+    output[index + 1] = input[index]
+    output[index - 1] = output[index - 1] + input[index] * index
+
+    if mode == "same":
+        output = output[: input.shape[0]]
+
+    return output
diff --git a/src/beignet/_physicists_hermite_polynomial_companion.py b/src/beignet/_physicists_hermite_polynomial_companion.py
new file mode 100644
index 0000000000..a730dd6f2d
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_companion.py
@@ -0,0 +1,40 @@
+import torch
+from torch import Tensor
+
+
+def physicists_hermite_polynomial_companion(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] < 2:
+        raise ValueError
+
+    if input.shape[0] == 2:
+        return torch.tensor([[-0.5 * input[0] / input[1]]])
+
+    n = input.shape[0] - 1
+
+    output = torch.zeros((n, n), dtype=input.dtype)
+
+    scale = torch.hstack(
+        [
+            torch.tensor([1.0]),
+            1.0 / torch.sqrt(2.0 * torch.arange(n - 1, 0, -1)),
+        ],
+    )
+
+    scale = torch.cumprod(scale, dim=0)
+
+    scale = torch.flip(scale, dims=[0])
+
+    shp = output.shape
+
+    output = torch.reshape(output, [-1])
+
+    output[1 :: n + 1] = torch.sqrt(0.5 * torch.arange(1, n))
+    output[n :: n + 1] = torch.sqrt(0.5 * torch.arange(1, n))
+
+    output = torch.reshape(output, shp)
+
+    output[:, -1] += -scale * input[:-1] / (2.0 * input[-1])
+
+    return output
diff --git a/src/beignet/_physicists_hermite_polynomial_domain.py b/src/beignet/_physicists_hermite_polynomial_domain.py
new file mode 100644
index 0000000000..5590fb9f77
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_domain.py
@@ -0,0 +1,3 @@
+import torch
+
+physicists_hermite_polynomial_domain = torch.tensor([-1.0, 1.0])
diff --git a/src/beignet/_physicists_hermite_polynomial_from_roots.py b/src/beignet/_physicists_hermite_polynomial_from_roots.py
new file mode 100644
index 0000000000..175f34f11f
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_from_roots.py
@@ -0,0 +1,87 @@
+import math
+
+import torch
+
+from ._linear_physicists_hermite_polynomial import linear_physicists_hermite_polynomial
+from ._multiply_physicists_hermite_polynomial import (
+    multiply_physicists_hermite_polynomial,
+)
+
+
+def physicists_hermite_polynomial_from_roots(input):
+    f = linear_physicists_hermite_polynomial
+    g = multiply_physicists_hermite_polynomial
+    if math.prod(input.shape) == 0:
+        return torch.ones([1])
+
+    input, _ = torch.sort(input)
+
+    ys = []
+
+    for x in input:
+        a = torch.zeros(input.shape[0] + 1, dtype=x.dtype)
+        b = f(-x, 1)
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            y = torch.concatenate(
+                [
+                    b,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+
+            y = a + y
+        else:
+            y = torch.concatenate(
+                [
+                    a,
+                    torch.zeros(
+                        b.shape[0] - a.shape[0],
+                        dtype=a.dtype,
+                    ),
+                ]
+            )
+
+            y = b + y
+
+        ys = [*ys, y]
+
+    p = torch.stack(ys)
+
+    m = p.shape[0]
+
+    x = m, p
+
+    while x[0] > 1:
+        m, r = divmod(x[0], 2)
+
+        z = x[1]
+
+        previous = torch.zeros([len(p), input.shape[0] + 1])
+
+        y = previous
+
+        for i in range(0, m):
+            y[i] = g(z[i], z[i + m])[: input.shape[0] + 1]
+
+        previous = y
+
+        if r:
+            previous[0] = g(previous[0], z[2 * m])[: input.shape[0] + 1]
+
+        x = m, previous
+
+    _, output = x
+
+    return output[0]
diff --git a/src/beignet/_physicists_hermite_polynomial_one.py b/src/beignet/_physicists_hermite_polynomial_one.py
new file mode 100644
index 0000000000..b760195d66
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_one.py
@@ -0,0 +1,3 @@
+import torch
+
+physicists_hermite_polynomial_one = torch.tensor([1.0])
diff --git a/src/beignet/_physicists_hermite_polynomial_power.py b/src/beignet/_physicists_hermite_polynomial_power.py
new file mode 100644
index 0000000000..d92f21ea24
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_power.py
@@ -0,0 +1,65 @@
+import torch
+from torch import Tensor
+
+from ._multiply_physicists_hermite_polynomial import (
+    multiply_physicists_hermite_polynomial,
+)
+
+
+def physicists_hermite_polynomial_power(
+    input: Tensor,
+    exponent: float | Tensor,
+    maximum_exponent: float | Tensor = 16.0,
+) -> Tensor:
+    input = torch.atleast_1d(input)
+    _exponent = int(exponent)
+    if _exponent != exponent or _exponent < 0:
+        raise ValueError
+    if maximum_exponent is not None and _exponent > maximum_exponent:
+        raise ValueError
+    match _exponent:
+        case 0:
+            output = torch.tensor([1], dtype=input.dtype)
+        case 1:
+            output = input
+        case _:
+            output = torch.zeros(input.shape[0] * exponent, dtype=input.dtype)
+
+            input = torch.atleast_1d(input)
+            output = torch.atleast_1d(output)
+
+            dtype = torch.promote_types(input.dtype, output.dtype)
+
+            input = input.to(dtype)
+            output = output.to(dtype)
+
+            if output.shape[0] > input.shape[0]:
+                input = torch.concatenate(
+                    [
+                        input,
+                        torch.zeros(
+                            output.shape[0] - input.shape[0],
+                            dtype=input.dtype,
+                        ),
+                    ],
+                )
+
+                output = output + input
+            else:
+                output = torch.concatenate(
+                    [
+                        output,
+                        torch.zeros(
+                            input.shape[0] - output.shape[0],
+                            dtype=output.dtype,
+                        ),
+                    ]
+                )
+
+                output = input + output
+
+            for _ in range(2, _exponent + 1):
+                output = multiply_physicists_hermite_polynomial(
+                    output, input, mode="same"
+                )
+    return output
diff --git a/src/beignet/_physicists_hermite_polynomial_roots.py b/src/beignet/_physicists_hermite_polynomial_roots.py
new file mode 100644
index 0000000000..4cd94d51f9
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_roots.py
@@ -0,0 +1,27 @@
+import torch
+from torch import Tensor
+
+from ._physicists_hermite_polynomial_companion import (
+    physicists_hermite_polynomial_companion,
+)
+
+
+def physicists_hermite_polynomial_roots(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] <= 1:
+        return torch.tensor([], dtype=input.dtype)
+
+    if input.shape[0] == 2:
+        return torch.tensor([-0.5 * input[0] / input[1]])
+
+    output = physicists_hermite_polynomial_companion(input)
+
+    output = torch.flip(output, dims=[0])
+    output = torch.flip(output, dims=[1])
+
+    output = torch.linalg.eigvals(output)
+
+    output, _ = torch.sort(output.real)
+
+    return output
diff --git a/src/beignet/_physicists_hermite_polynomial_to_polynomial.py b/src/beignet/_physicists_hermite_polynomial_to_polynomial.py
new file mode 100644
index 0000000000..179d7084ca
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_to_polynomial.py
@@ -0,0 +1,45 @@
+import torch
+from torch import Tensor
+
+from ._add_polynomial import add_polynomial
+from ._multiply_polynomial_by_x import multiply_polynomial_by_x
+from ._subtract_polynomial import subtract_polynomial
+
+
+def physicists_hermite_polynomial_to_polynomial(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    n = input.shape[0]
+
+    if n == 1:
+        return input
+
+    if n == 2:
+        input[1] = input[1] * 2
+
+        return input
+    else:
+        c0 = torch.zeros_like(input)
+        c0[0] = input[-2]
+
+        c1 = torch.zeros_like(input)
+        c1[0] = input[-1]
+
+        def body(k, c0c1):
+            i = n - 1 - k
+            c0, c1 = c0c1
+            tmp = c0
+            c0 = subtract_polynomial(input[i - 2], c1 * (2 * (i - 1)))
+            c1 = add_polynomial(tmp, multiply_polynomial_by_x(c1, "same") * 2)
+            return c0, c1
+
+        x = (c0, c1)
+
+        y = x
+
+        for index in range(0, n - 2):
+            y = body(index, y)
+
+        c0, c1 = y
+
+        return add_polynomial(c0, multiply_polynomial_by_x(c1, "same") * 2)
diff --git a/src/beignet/_physicists_hermite_polynomial_vandermonde.py b/src/beignet/_physicists_hermite_polynomial_vandermonde.py
new file mode 100644
index 0000000000..e5bbf91430
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_vandermonde.py
@@ -0,0 +1,25 @@
+import torch
+from torch import Tensor
+
+
+def physicists_hermite_polynomial_vandermonde(
+    x: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    if degree < 0:
+        raise ValueError
+
+    x = torch.atleast_1d(x)
+    dims = (degree + 1,) + x.shape
+    dtyp = torch.promote_types(x.dtype, torch.tensor(0.0).dtype)
+    x = x.to(dtyp)
+    v = torch.empty(dims, dtype=dtyp)
+    v[0] = torch.ones_like(x)
+
+    if degree > 0:
+        v[1] = x * 2
+
+        for index in range(2, degree + 1):
+            v[index] = v[index - 1] * x * 2 - v[index - 2] * (2 * (index - 1))
+
+    return torch.moveaxis(v, 0, -1)
diff --git a/src/beignet/_physicists_hermite_polynomial_vandermonde_2d.py b/src/beignet/_physicists_hermite_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..80879afe28
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_vandermonde_2d.py
@@ -0,0 +1,51 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._physicists_hermite_polynomial_vandermonde import (
+    physicists_hermite_polynomial_vandermonde,
+)
+
+
+def physicists_hermite_polynomial_vandermonde_2d(
+    x: Tensor,
+    y: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    functions = (
+        physicists_hermite_polynomial_vandermonde,
+        physicists_hermite_polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_physicists_hermite_polynomial_vandermonde_3d.py b/src/beignet/_physicists_hermite_polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..d87b0137a5
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_vandermonde_3d.py
@@ -0,0 +1,53 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._physicists_hermite_polynomial_vandermonde import (
+    physicists_hermite_polynomial_vandermonde,
+)
+
+
+def physicists_hermite_polynomial_vandermonde_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    functions = (
+        physicists_hermite_polynomial_vandermonde,
+        physicists_hermite_polynomial_vandermonde,
+        physicists_hermite_polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y, z]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y, z)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_physicists_hermite_polynomial_weight.py b/src/beignet/_physicists_hermite_polynomial_weight.py
new file mode 100644
index 0000000000..af7884f90d
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_weight.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def physicists_hermite_polynomial_weight(x: Tensor) -> Tensor:
+    return torch.exp(-(x**2))
diff --git a/src/beignet/_physicists_hermite_polynomial_x.py b/src/beignet/_physicists_hermite_polynomial_x.py
new file mode 100644
index 0000000000..e2abfc4670
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_x.py
@@ -0,0 +1,3 @@
+import torch
+
+physicists_hermite_polynomial_x = torch.tensor([0.0, 1.0 / 2.0])
diff --git a/src/beignet/_physicists_hermite_polynomial_zero.py b/src/beignet/_physicists_hermite_polynomial_zero.py
new file mode 100644
index 0000000000..3e6b247b81
--- /dev/null
+++ b/src/beignet/_physicists_hermite_polynomial_zero.py
@@ -0,0 +1,3 @@
+import torch
+
+physicists_hermite_polynomial_zero = torch.tensor([0.0])
diff --git a/src/beignet/_polynomial_companion.py b/src/beignet/_polynomial_companion.py
new file mode 100644
index 0000000000..1fbc30513f
--- /dev/null
+++ b/src/beignet/_polynomial_companion.py
@@ -0,0 +1,35 @@
+import torch
+from torch import Tensor
+
+
+def polynomial_companion(input: Tensor) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor, shape=(degree, degree)
+        Companion matrix.
+    """
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] < 2:
+        raise ValueError
+
+    if input.shape[0] == 2:
+        output = torch.tensor([[-input[0] / input[1]]])
+    else:
+        n = input.shape[0] - 1
+
+        output = torch.reshape(torch.zeros([n, n], dtype=input.dtype), [-1])
+
+        output[n :: n + 1] = 1.0
+
+        output = torch.reshape(output, [n, n])
+
+        output[:, -1] = output[:, -1] + (-input[:-1] / input[-1])
+
+    return output
diff --git a/src/beignet/_polynomial_domain.py b/src/beignet/_polynomial_domain.py
new file mode 100644
index 0000000000..3482e01ab5
--- /dev/null
+++ b/src/beignet/_polynomial_domain.py
@@ -0,0 +1,3 @@
+import torch
+
+polynomial_domain = torch.tensor([-1.0, 1.0])
diff --git a/src/beignet/_polynomial_from_roots.py b/src/beignet/_polynomial_from_roots.py
new file mode 100644
index 0000000000..f923f28b42
--- /dev/null
+++ b/src/beignet/_polynomial_from_roots.py
@@ -0,0 +1,97 @@
+import math
+
+import torch
+from torch import Tensor
+
+from ._linear_polynomial import linear_polynomial
+from ._multiply_polynomial import multiply_polynomial
+
+
+def polynomial_from_roots(input: Tensor) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    input : Tensor
+        Roots.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients.
+    """
+    f = linear_polynomial
+    g = multiply_polynomial
+    if math.prod(input.shape) == 0:
+        return torch.ones([1])
+
+    input, _ = torch.sort(input)
+
+    ys = []
+
+    for x in input:
+        a = torch.zeros(input.shape[0] + 1, dtype=x.dtype)
+        b = f(-x, 1)
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            y = torch.concatenate(
+                [
+                    b,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+
+            y = a + y
+        else:
+            y = torch.concatenate(
+                [
+                    a,
+                    torch.zeros(
+                        b.shape[0] - a.shape[0],
+                        dtype=a.dtype,
+                    ),
+                ]
+            )
+
+            y = b + y
+
+        ys = [*ys, y]
+
+    p = torch.stack(ys)
+
+    m = p.shape[0]
+
+    x = m, p
+
+    while x[0] > 1:
+        m, r = divmod(x[0], 2)
+
+        z = x[1]
+
+        previous = torch.zeros([len(p), input.shape[0] + 1])
+
+        y = previous
+
+        for i in range(0, m):
+            y[i] = g(z[i], z[i + m])[: input.shape[0] + 1]
+
+        previous = y
+
+        if r:
+            previous[0] = g(previous[0], z[2 * m])[: input.shape[0] + 1]
+
+        x = m, previous
+
+    _, output = x
+
+    return output[0]
diff --git a/src/beignet/_polynomial_one.py b/src/beignet/_polynomial_one.py
new file mode 100644
index 0000000000..f8f6211d6d
--- /dev/null
+++ b/src/beignet/_polynomial_one.py
@@ -0,0 +1,3 @@
+import torch
+
+polynomial_one = torch.tensor([1.0])
diff --git a/src/beignet/_polynomial_power.py b/src/beignet/_polynomial_power.py
new file mode 100644
index 0000000000..cc01747aa1
--- /dev/null
+++ b/src/beignet/_polynomial_power.py
@@ -0,0 +1,76 @@
+import torch
+from torch import Tensor
+
+from ._multiply_polynomial import multiply_polynomial
+
+
+def polynomial_power(
+    input: Tensor,
+    exponent: float | Tensor,
+    maximum_exponent: float | Tensor = 16.0,
+) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    exponent : float or Tensor
+
+    maximum_exponent : float or Tensor, default=16.0
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the power.
+    """
+    input = torch.atleast_1d(input)
+    _exponent = int(exponent)
+    if _exponent != exponent or _exponent < 0:
+        raise ValueError
+    if maximum_exponent is not None and _exponent > maximum_exponent:
+        raise ValueError
+    match _exponent:
+        case 0:
+            output = torch.tensor([1], dtype=input.dtype)
+        case 1:
+            output = input
+        case _:
+            output = torch.zeros(input.shape[0] * exponent, dtype=input.dtype)
+
+            input = torch.atleast_1d(input)
+            output = torch.atleast_1d(output)
+
+            dtype = torch.promote_types(input.dtype, output.dtype)
+
+            input = input.to(dtype)
+            output = output.to(dtype)
+
+            if output.shape[0] > input.shape[0]:
+                input = torch.concatenate(
+                    [
+                        input,
+                        torch.zeros(
+                            output.shape[0] - input.shape[0],
+                            dtype=input.dtype,
+                        ),
+                    ],
+                )
+
+                output = output + input
+            else:
+                output = torch.concatenate(
+                    [
+                        output,
+                        torch.zeros(
+                            input.shape[0] - output.shape[0],
+                            dtype=output.dtype,
+                        ),
+                    ]
+                )
+
+                output = input + output
+
+            for _ in range(2, _exponent + 1):
+                output = multiply_polynomial(output, input, mode="same")
+    return output
diff --git a/src/beignet/_polynomial_roots.py b/src/beignet/_polynomial_roots.py
new file mode 100644
index 0000000000..e3d9269cb6
--- /dev/null
+++ b/src/beignet/_polynomial_roots.py
@@ -0,0 +1,48 @@
+import torch
+from torch import Tensor
+
+
+def polynomial_roots(input: Tensor) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Roots.
+    """
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] < 2:
+        return torch.tensor([], dtype=input.dtype)
+
+    if input.shape[0] == 2:
+        return torch.tensor([-input[0] / input[1]])
+
+    if input.shape[0] < 2:
+        raise ValueError
+
+    if input.shape[0] == 2:
+        output = torch.tensor([[-input[0] / input[1]]])
+    else:
+        n = input.shape[0] - 1
+
+        output = torch.reshape(torch.zeros([n, n], dtype=input.dtype), [-1])
+
+        output[n :: n + 1] = 1.0
+
+        output = torch.reshape(output, [n, n])
+
+        output[:, -1] = output[:, -1] + (-input[:-1] / input[-1])
+
+    output = torch.flip(output, dims=[0])
+    output = torch.flip(output, dims=[1])
+
+    output = torch.linalg.eigvals(output)
+
+    output, _ = torch.sort(output.real)
+
+    return output
diff --git a/src/beignet/_polynomial_to_chebyshev_polynomial.py b/src/beignet/_polynomial_to_chebyshev_polynomial.py
new file mode 100644
index 0000000000..8140243bd1
--- /dev/null
+++ b/src/beignet/_polynomial_to_chebyshev_polynomial.py
@@ -0,0 +1,18 @@
+import torch
+from torch import Tensor
+
+from ._add_chebyshev_polynomial import add_chebyshev_polynomial
+from ._multiply_chebyshev_polynomial_by_x import multiply_chebyshev_polynomial_by_x
+
+
+def polynomial_to_chebyshev_polynomial(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros_like(input)
+
+    for i in range(0, input.shape[0] - 1 + 1):
+        output = multiply_chebyshev_polynomial_by_x(output, mode="same")
+
+        output = add_chebyshev_polynomial(output, input[input.shape[0] - 1 - i])
+
+    return output
diff --git a/src/beignet/_polynomial_to_laguerre_polynomial.py b/src/beignet/_polynomial_to_laguerre_polynomial.py
new file mode 100644
index 0000000000..0d8046f9c5
--- /dev/null
+++ b/src/beignet/_polynomial_to_laguerre_polynomial.py
@@ -0,0 +1,18 @@
+import torch
+from torch import Tensor
+
+from ._add_laguerre_polynomial import add_laguerre_polynomial
+from ._multiply_laguerre_polynomial_by_x import multiply_laguerre_polynomial_by_x
+
+
+def polynomial_to_laguerre_polynomial(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros_like(input)
+
+    for i in range(0, input.shape[0]):
+        output = multiply_laguerre_polynomial_by_x(output, mode="same")
+
+        output = add_laguerre_polynomial(output, torch.flip(input, dims=[0])[i])
+
+    return output
diff --git a/src/beignet/_polynomial_to_legendre_polynomial.py b/src/beignet/_polynomial_to_legendre_polynomial.py
new file mode 100644
index 0000000000..8268b051d0
--- /dev/null
+++ b/src/beignet/_polynomial_to_legendre_polynomial.py
@@ -0,0 +1,18 @@
+import torch
+from torch import Tensor
+
+from ._add_legendre_polynomial import add_legendre_polynomial
+from ._multiply_legendre_polynomial_by_x import multiply_legendre_polynomial_by_x
+
+
+def polynomial_to_legendre_polynomial(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros_like(input)
+
+    for i in range(0, input.shape[0] - 1 + 1):
+        output = multiply_legendre_polynomial_by_x(output, mode="same")
+
+        output = add_legendre_polynomial(output, input[input.shape[0] - 1 - i])
+
+    return output
diff --git a/src/beignet/_polynomial_to_physicists_hermite_polynomial.py b/src/beignet/_polynomial_to_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..b894ff7307
--- /dev/null
+++ b/src/beignet/_polynomial_to_physicists_hermite_polynomial.py
@@ -0,0 +1,22 @@
+import torch
+from torch import Tensor
+
+from ._add_physicists_hermite_polynomial import add_physicists_hermite_polynomial
+from ._multiply_physicists_hermite_polynomial_by_x import (
+    multiply_physicists_hermite_polynomial_by_x,
+)
+
+
+def polynomial_to_physicists_hermite_polynomial(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros_like(input)
+
+    for index in range(0, input.shape[0] - 1 + 1):
+        output = multiply_physicists_hermite_polynomial_by_x(output, mode="same")
+
+        output = add_physicists_hermite_polynomial(
+            output, input[input.shape[0] - 1 - index]
+        )
+
+    return output
diff --git a/src/beignet/_polynomial_to_probabilists_hermite_polynomial.py b/src/beignet/_polynomial_to_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..9c4d6168a4
--- /dev/null
+++ b/src/beignet/_polynomial_to_probabilists_hermite_polynomial.py
@@ -0,0 +1,22 @@
+import torch
+from torch import Tensor
+
+from ._add_probabilists_hermite_polynomial import add_probabilists_hermite_polynomial
+from ._multiply_probabilists_hermite_polynomial_by_x import (
+    multiply_probabilists_hermite_polynomial_by_x,
+)
+
+
+def polynomial_to_probabilists_hermite_polynomial(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    output = torch.zeros_like(input)
+
+    for i in range(0, input.shape[0] - 1 + 1):
+        output = multiply_probabilists_hermite_polynomial_by_x(output, mode="same")
+
+        output = add_probabilists_hermite_polynomial(
+            output, input[input.shape[0] - 1 - i]
+        )
+
+    return output
diff --git a/src/beignet/_polynomial_vandermonde.py b/src/beignet/_polynomial_vandermonde.py
new file mode 100644
index 0000000000..4318aedf8d
--- /dev/null
+++ b/src/beignet/_polynomial_vandermonde.py
@@ -0,0 +1,33 @@
+import torch
+from torch import Tensor
+
+
+def polynomial_vandermonde(input: Tensor, degree: Tensor) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    input : Tensor
+
+    degree : Tensor
+
+    Returns
+    -------
+    output : Tensor
+    """
+    if degree < 0:
+        raise ValueError
+
+    degree = int(degree)
+
+    input = torch.atleast_1d(input)
+
+    output = torch.empty([degree + 1, *input.shape], dtype=input.dtype)
+
+    output[0] = torch.ones_like(input)
+
+    for i in range(1, degree + 1):
+        output[i] = output[i - 1] * input
+
+    output = torch.moveaxis(output, 0, -1)
+
+    return output
diff --git a/src/beignet/_polynomial_vandermonde_2d.py b/src/beignet/_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..bdec450056
--- /dev/null
+++ b/src/beignet/_polynomial_vandermonde_2d.py
@@ -0,0 +1,58 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._polynomial_vandermonde import polynomial_vandermonde
+
+
+def polynomial_vandermonde_2d(x: Tensor, y: Tensor, degree: Tensor) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    x : Tensor
+
+    y : Tensor
+
+    degree : Tensor
+
+    Returns
+    -------
+    output : Tensor
+    """
+    functions = (
+        polynomial_vandermonde,
+        polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_polynomial_vandermonde_3d.py b/src/beignet/_polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..690a791131
--- /dev/null
+++ b/src/beignet/_polynomial_vandermonde_3d.py
@@ -0,0 +1,63 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._polynomial_vandermonde import polynomial_vandermonde
+
+
+def polynomial_vandermonde_3d(
+    x: Tensor, y: Tensor, z: Tensor, degree: Tensor
+) -> Tensor:
+    r"""
+    Parameters
+    ----------
+    x : Tensor
+
+    y : Tensor
+
+    z : Tensor
+
+    degree : Tensor
+
+    Returns
+    -------
+    output : Tensor
+    """
+    vandermonde_functions = (
+        polynomial_vandermonde,
+        polynomial_vandermonde,
+        polynomial_vandermonde,
+    )
+
+    n = len(vandermonde_functions)
+
+    if n != len([x, y, z]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = vandermonde_functions[i]((x, y, z)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_polynomial_x.py b/src/beignet/_polynomial_x.py
new file mode 100644
index 0000000000..6ace7faf7f
--- /dev/null
+++ b/src/beignet/_polynomial_x.py
@@ -0,0 +1,3 @@
+import torch
+
+polynomial_x = torch.tensor([0.0, 1.0])
diff --git a/src/beignet/_polynomial_zero.py b/src/beignet/_polynomial_zero.py
new file mode 100644
index 0000000000..745c63dd68
--- /dev/null
+++ b/src/beignet/_polynomial_zero.py
@@ -0,0 +1,3 @@
+import torch
+
+polynomial_zero = torch.tensor([0.0])
diff --git a/src/beignet/_probabilists_hermite_polynomial_companion.py b/src/beignet/_probabilists_hermite_polynomial_companion.py
new file mode 100644
index 0000000000..390c46f9cf
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_companion.py
@@ -0,0 +1,39 @@
+import torch
+from torch import Tensor
+
+
+def probabilists_hermite_polynomial_companion(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] < 2:
+        raise ValueError
+
+    if input.shape[0] == 2:
+        return torch.tensor([[-input[0] / input[1]]])
+
+    n = input.shape[0] - 1
+
+    output = torch.zeros([n, n], dtype=input.dtype)
+
+    scale = torch.hstack(
+        [
+            torch.tensor([1.0]),
+            1.0 / torch.sqrt(torch.arange(n - 1, 0, -1)),
+        ],
+    )
+
+    scale = torch.cumprod(scale, dim=0)
+    scale = torch.flip(scale, dims=[0])
+
+    shape = output.shape
+
+    output = torch.reshape(output, [-1])
+
+    output[1 :: n + 1] = torch.sqrt(torch.arange(1, n))
+    output[n :: n + 1] = torch.sqrt(torch.arange(1, n))
+
+    output = torch.reshape(output, shape)
+
+    output[:, -1] += -scale * input[:-1] / input[-1]
+
+    return output
diff --git a/src/beignet/_probabilists_hermite_polynomial_domain.py b/src/beignet/_probabilists_hermite_polynomial_domain.py
new file mode 100644
index 0000000000..a146072cdf
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_domain.py
@@ -0,0 +1,3 @@
+import torch
+
+probabilists_hermite_polynomial_domain = torch.tensor([-1.0, 1.0])
diff --git a/src/beignet/_probabilists_hermite_polynomial_from_roots.py b/src/beignet/_probabilists_hermite_polynomial_from_roots.py
new file mode 100644
index 0000000000..3ec8ee0df1
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_from_roots.py
@@ -0,0 +1,90 @@
+import math
+
+import torch
+from torch import Tensor
+
+from ._linear_probabilists_hermite_polynomial import (
+    linear_probabilists_hermite_polynomial,
+)
+from ._multiply_probabilists_hermite_polynomial import (
+    multiply_probabilists_hermite_polynomial,
+)
+
+
+def probabilists_hermite_polynomial_from_roots(input: Tensor) -> Tensor:
+    f = linear_probabilists_hermite_polynomial
+    g = multiply_probabilists_hermite_polynomial
+    if math.prod(input.shape) == 0:
+        return torch.ones([1])
+
+    input, _ = torch.sort(input)
+
+    ys = []
+
+    for x in input:
+        a = torch.zeros(input.shape[0] + 1, dtype=x.dtype)
+        b = f(-x, 1)
+
+        a = torch.atleast_1d(a)
+        b = torch.atleast_1d(b)
+
+        dtype = torch.promote_types(a.dtype, b.dtype)
+
+        a = a.to(dtype)
+        b = b.to(dtype)
+
+        if a.shape[0] > b.shape[0]:
+            y = torch.concatenate(
+                [
+                    b,
+                    torch.zeros(
+                        a.shape[0] - b.shape[0],
+                        dtype=b.dtype,
+                    ),
+                ],
+            )
+
+            y = a + y
+        else:
+            y = torch.concatenate(
+                [
+                    a,
+                    torch.zeros(
+                        b.shape[0] - a.shape[0],
+                        dtype=a.dtype,
+                    ),
+                ]
+            )
+
+            y = b + y
+
+        ys = [*ys, y]
+
+    p = torch.stack(ys)
+
+    m = p.shape[0]
+
+    x = m, p
+
+    while x[0] > 1:
+        m, r = divmod(x[0], 2)
+
+        z = x[1]
+
+        previous = torch.zeros([len(p), input.shape[0] + 1])
+
+        y = previous
+
+        for i in range(0, m):
+            y[i] = g(z[i], z[i + m])[: input.shape[0] + 1]
+
+        previous = y
+
+        if r:
+            previous[0] = g(previous[0], z[2 * m])[: input.shape[0] + 1]
+
+        x = m, previous
+
+    _, output = x
+
+    return output[0]
diff --git a/src/beignet/_probabilists_hermite_polynomial_one.py b/src/beignet/_probabilists_hermite_polynomial_one.py
new file mode 100644
index 0000000000..13c91bda67
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_one.py
@@ -0,0 +1,3 @@
+import torch
+
+probabilists_hermite_polynomial_one = torch.tensor([1.0])
diff --git a/src/beignet/_probabilists_hermite_polynomial_power.py b/src/beignet/_probabilists_hermite_polynomial_power.py
new file mode 100644
index 0000000000..e170300ba1
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_power.py
@@ -0,0 +1,65 @@
+import torch
+from torch import Tensor
+
+from ._multiply_probabilists_hermite_polynomial import (
+    multiply_probabilists_hermite_polynomial,
+)
+
+
+def probabilists_hermite_polynomial_power(
+    input: Tensor,
+    exponent: float | Tensor,
+    maximum_exponent: float | Tensor = 16.0,
+) -> Tensor:
+    input = torch.atleast_1d(input)
+    _exponent = int(exponent)
+    if _exponent != exponent or _exponent < 0:
+        raise ValueError
+    if maximum_exponent is not None and _exponent > maximum_exponent:
+        raise ValueError
+    match _exponent:
+        case 0:
+            output = torch.tensor([1], dtype=input.dtype)
+        case 1:
+            output = input
+        case _:
+            output = torch.zeros(input.shape[0] * exponent, dtype=input.dtype)
+
+            input = torch.atleast_1d(input)
+            output = torch.atleast_1d(output)
+
+            dtype = torch.promote_types(input.dtype, output.dtype)
+
+            input = input.to(dtype)
+            output = output.to(dtype)
+
+            if output.shape[0] > input.shape[0]:
+                input = torch.concatenate(
+                    [
+                        input,
+                        torch.zeros(
+                            output.shape[0] - input.shape[0],
+                            dtype=input.dtype,
+                        ),
+                    ],
+                )
+
+                output = output + input
+            else:
+                output = torch.concatenate(
+                    [
+                        output,
+                        torch.zeros(
+                            input.shape[0] - output.shape[0],
+                            dtype=output.dtype,
+                        ),
+                    ]
+                )
+
+                output = input + output
+
+            for _ in range(2, _exponent + 1):
+                output = multiply_probabilists_hermite_polynomial(
+                    output, input, mode="same"
+                )
+    return output
diff --git a/src/beignet/_probabilists_hermite_polynomial_roots.py b/src/beignet/_probabilists_hermite_polynomial_roots.py
new file mode 100644
index 0000000000..88277e707b
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_roots.py
@@ -0,0 +1,27 @@
+import torch
+from torch import Tensor
+
+from ._probabilists_hermite_polynomial_companion import (
+    probabilists_hermite_polynomial_companion,
+)
+
+
+def probabilists_hermite_polynomial_roots(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    if input.shape[0] <= 1:
+        return torch.tensor([], dtype=input.dtype)
+
+    if input.shape[0] == 2:
+        return torch.tensor([-input[0] / input[1]])
+
+    output = probabilists_hermite_polynomial_companion(input)
+
+    output = torch.flip(output, dims=[0])
+    output = torch.flip(output, dims=[1])
+
+    output = torch.linalg.eigvals(output)
+
+    output, _ = torch.sort(output.real)
+
+    return output
diff --git a/src/beignet/_probabilists_hermite_polynomial_to_polynomial.py b/src/beignet/_probabilists_hermite_polynomial_to_polynomial.py
new file mode 100644
index 0000000000..0ec138e7e6
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_to_polynomial.py
@@ -0,0 +1,48 @@
+import torch
+from torch import Tensor
+
+from ._add_polynomial import add_polynomial
+from ._multiply_polynomial_by_x import multiply_polynomial_by_x
+from ._subtract_polynomial import subtract_polynomial
+
+
+def probabilists_hermite_polynomial_to_polynomial(input: Tensor) -> Tensor:
+    input = torch.atleast_1d(input)
+
+    n = input.shape[0]
+
+    if n == 1:
+        return input
+
+    if n == 2:
+        return input
+    else:
+        c0 = torch.zeros_like(input)
+        c0[0] = input[-2]
+
+        c1 = torch.zeros_like(input)
+        c1[0] = input[-1]
+
+        def body(k, c0c1):
+            i = n - 1 - k
+
+            c0, c1 = c0c1
+
+            tmp = c0
+
+            c0 = subtract_polynomial(input[i - 2], c1 * (i - 1))
+
+            c1 = add_polynomial(tmp, multiply_polynomial_by_x(c1, "same"))
+
+            return c0, c1
+
+        b = n - 2
+        x = (c0, c1)
+        y = x
+
+        for index in range(0, b):
+            y = body(index, y)
+
+        c0, c1 = y
+
+        return add_polynomial(c0, multiply_polynomial_by_x(c1, "same"))
diff --git a/src/beignet/_probabilists_hermite_polynomial_vandermonde.py b/src/beignet/_probabilists_hermite_polynomial_vandermonde.py
new file mode 100644
index 0000000000..b529db0798
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_vandermonde.py
@@ -0,0 +1,22 @@
+import torch
+from torch import Tensor
+
+
+def probabilists_hermite_polynomial_vandermonde(x: Tensor, degree: Tensor) -> Tensor:
+    if degree < 0:
+        raise ValueError
+
+    x = torch.atleast_1d(x)
+    dims = (degree + 1,) + x.shape
+    dtyp = torch.promote_types(x.dtype, torch.tensor(0.0).dtype)
+    x = x.to(dtyp)
+    v = torch.empty(dims, dtype=dtyp)
+    v[0] = torch.ones_like(x)
+
+    if degree > 0:
+        v[1] = x
+
+        for index in range(2, degree + 1):
+            v[index] = v[index - 1] * x - v[index - 2] * (index - 1)
+
+    return torch.moveaxis(v, 0, -1)
diff --git a/src/beignet/_probabilists_hermite_polynomial_vandermonde_2d.py b/src/beignet/_probabilists_hermite_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..4dc4dd2cce
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_vandermonde_2d.py
@@ -0,0 +1,51 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._probabilists_hermite_polynomial_vandermonde import (
+    probabilists_hermite_polynomial_vandermonde,
+)
+
+
+def probabilists_hermite_polynomial_vandermonde_2d(
+    x: Tensor,
+    y: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    functions = (
+        probabilists_hermite_polynomial_vandermonde,
+        probabilists_hermite_polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_probabilists_hermite_polynomial_vandermonde_3d.py b/src/beignet/_probabilists_hermite_polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..fad7394ab6
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_vandermonde_3d.py
@@ -0,0 +1,53 @@
+import functools
+import operator
+
+import torch
+from torch import Tensor
+
+from ._probabilists_hermite_polynomial_vandermonde import (
+    probabilists_hermite_polynomial_vandermonde,
+)
+
+
+def probabilists_hermite_polynomial_vandermonde_3d(
+    x: Tensor,
+    y: Tensor,
+    z: Tensor,
+    degree: Tensor,
+) -> Tensor:
+    functions = (
+        probabilists_hermite_polynomial_vandermonde,
+        probabilists_hermite_polynomial_vandermonde,
+        probabilists_hermite_polynomial_vandermonde,
+    )
+
+    n = len(functions)
+
+    if n != len([x, y, z]):
+        raise ValueError
+
+    if n != len(degree):
+        raise ValueError
+
+    if n == 0:
+        raise ValueError
+
+    matrices = []
+
+    for i in range(n):
+        matrix = functions[i]((x, y, z)[i], degree[i])
+
+        matrices = [
+            *matrices,
+            matrix[(..., *tuple(slice(None) if j == i else None for j in range(n)))],
+        ]
+
+    vandermonde = functools.reduce(
+        operator.mul,
+        matrices,
+    )
+
+    return torch.reshape(
+        vandermonde,
+        [*vandermonde.shape[: -len(degree)], -1],
+    )
diff --git a/src/beignet/_probabilists_hermite_polynomial_weight.py b/src/beignet/_probabilists_hermite_polynomial_weight.py
new file mode 100644
index 0000000000..253949a0ff
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_weight.py
@@ -0,0 +1,6 @@
+import torch
+from torch import Tensor
+
+
+def probabilists_hermite_polynomial_weight(x: Tensor) -> Tensor:
+    return torch.exp(-0.5 * x**2)
diff --git a/src/beignet/_probabilists_hermite_polynomial_x.py b/src/beignet/_probabilists_hermite_polynomial_x.py
new file mode 100644
index 0000000000..a1b77a534e
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_x.py
@@ -0,0 +1,3 @@
+import torch
+
+probabilists_hermite_polynomial_x = torch.tensor([0.0, 1.0])
diff --git a/src/beignet/_probabilists_hermite_polynomial_zero.py b/src/beignet/_probabilists_hermite_polynomial_zero.py
new file mode 100644
index 0000000000..b1c9202f5d
--- /dev/null
+++ b/src/beignet/_probabilists_hermite_polynomial_zero.py
@@ -0,0 +1,3 @@
+import torch
+
+probabilists_hermite_polynomial_zero = torch.tensor([0.0])
diff --git a/src/beignet/_subtract_chebyshev_polynomial.py b/src/beignet/_subtract_chebyshev_polynomial.py
new file mode 100644
index 0000000000..07fa2d55cd
--- /dev/null
+++ b/src/beignet/_subtract_chebyshev_polynomial.py
@@ -0,0 +1,53 @@
+import torch
+from torch import Tensor
+
+
+def subtract_chebyshev_polynomial(input: Tensor, other: Tensor) -> Tensor:
+    r"""
+    Returns the difference of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the difference.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+        output = input + output
+    else:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output[: input.shape[0]] + input,
+                output[input.shape[0] :],
+            ],
+        )
+
+    return output
diff --git a/src/beignet/_subtract_laguerre_polynomial.py b/src/beignet/_subtract_laguerre_polynomial.py
new file mode 100644
index 0000000000..edda044c48
--- /dev/null
+++ b/src/beignet/_subtract_laguerre_polynomial.py
@@ -0,0 +1,53 @@
+import torch
+from torch import Tensor
+
+
+def subtract_laguerre_polynomial(input: Tensor, other: Tensor) -> Tensor:
+    r"""
+    Returns the difference of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the difference.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+        output = input + output
+    else:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output[: input.shape[0]] + input,
+                output[input.shape[0] :],
+            ],
+        )
+
+    return output
diff --git a/src/beignet/_subtract_legendre_polynomial.py b/src/beignet/_subtract_legendre_polynomial.py
new file mode 100644
index 0000000000..b1d95ce31e
--- /dev/null
+++ b/src/beignet/_subtract_legendre_polynomial.py
@@ -0,0 +1,53 @@
+import torch
+from torch import Tensor
+
+
+def subtract_legendre_polynomial(input: Tensor, other: Tensor) -> Tensor:
+    r"""
+    Returns the difference of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the difference.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+        output = input + output
+    else:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output[: input.shape[0]] + input,
+                output[input.shape[0] :],
+            ],
+        )
+
+    return output
diff --git a/src/beignet/_subtract_physicists_hermite_polynomial.py b/src/beignet/_subtract_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..977b5b543b
--- /dev/null
+++ b/src/beignet/_subtract_physicists_hermite_polynomial.py
@@ -0,0 +1,56 @@
+import torch
+from torch import Tensor
+
+
+def subtract_physicists_hermite_polynomial(
+    input: Tensor,
+    other: Tensor,
+) -> Tensor:
+    r"""
+    Returns the difference of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the difference.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+        output = input + output
+    else:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output[: input.shape[0]] + input,
+                output[input.shape[0] :],
+            ],
+        )
+
+    return output
diff --git a/src/beignet/_subtract_polynomial.py b/src/beignet/_subtract_polynomial.py
new file mode 100644
index 0000000000..5e3af22172
--- /dev/null
+++ b/src/beignet/_subtract_polynomial.py
@@ -0,0 +1,53 @@
+import torch
+from torch import Tensor
+
+
+def subtract_polynomial(input: Tensor, other: Tensor) -> Tensor:
+    r"""
+    Returns the difference of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the difference.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+        output = input + output
+    else:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output[: input.shape[0]] + input,
+                output[input.shape[0] :],
+            ],
+        )
+
+    return output
diff --git a/src/beignet/_subtract_probabilists_hermite_polynomial.py b/src/beignet/_subtract_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..9050321bde
--- /dev/null
+++ b/src/beignet/_subtract_probabilists_hermite_polynomial.py
@@ -0,0 +1,56 @@
+import torch
+from torch import Tensor
+
+
+def subtract_probabilists_hermite_polynomial(
+    input: Tensor,
+    other: Tensor,
+) -> Tensor:
+    r"""
+    Returns the difference of two polynomials.
+
+    Parameters
+    ----------
+    input : Tensor
+        Polynomial coefficients.
+
+    other : Tensor
+        Polynomial coefficients.
+
+    Returns
+    -------
+    output : Tensor
+        Polynomial coefficients of the difference.
+    """
+    input = torch.atleast_1d(input)
+    other = torch.atleast_1d(other)
+
+    dtype = torch.promote_types(input.dtype, other.dtype)
+
+    input = input.to(dtype)
+    other = other.to(dtype)
+
+    if input.shape[0] > other.shape[0]:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output,
+                torch.zeros(
+                    input.shape[0] - other.shape[0],
+                    dtype=other.dtype,
+                ),
+            ],
+        )
+        output = input + output
+    else:
+        output = -other
+
+        output = torch.concatenate(
+            [
+                output[: input.shape[0]] + input,
+                output[input.shape[0] :],
+            ],
+        )
+
+    return output
diff --git a/src/beignet/_trim_chebyshev_polynomial_coefficients.py b/src/beignet/_trim_chebyshev_polynomial_coefficients.py
new file mode 100644
index 0000000000..01db83a6ba
--- /dev/null
+++ b/src/beignet/_trim_chebyshev_polynomial_coefficients.py
@@ -0,0 +1,21 @@
+import torch
+from torch import Tensor
+
+
+def trim_chebyshev_polynomial_coefficients(
+    input: Tensor,
+    tol: float = 0.0,
+) -> Tensor:
+    if tol < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    indices = torch.nonzero(torch.abs(input) > tol)
+
+    if indices.shape[0] == 0:
+        output = input[:1] * 0
+    else:
+        output = input[: indices[-1] + 1]
+
+    return output
diff --git a/src/beignet/_trim_laguerre_polynomial_coefficients.py b/src/beignet/_trim_laguerre_polynomial_coefficients.py
new file mode 100644
index 0000000000..6251c3a4c5
--- /dev/null
+++ b/src/beignet/_trim_laguerre_polynomial_coefficients.py
@@ -0,0 +1,21 @@
+import torch
+from torch import Tensor
+
+
+def trim_laguerre_polynomial_coefficients(
+    input: Tensor,
+    tol: float = 0.0,
+) -> Tensor:
+    if tol < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    indices = torch.nonzero(torch.abs(input) > tol)
+
+    if indices.shape[0] == 0:
+        output = input[:1] * 0
+    else:
+        output = input[: indices[-1] + 1]
+
+    return output
diff --git a/src/beignet/_trim_legendre_polynomial_coefficients.py b/src/beignet/_trim_legendre_polynomial_coefficients.py
new file mode 100644
index 0000000000..298b4db1b7
--- /dev/null
+++ b/src/beignet/_trim_legendre_polynomial_coefficients.py
@@ -0,0 +1,21 @@
+import torch
+from torch import Tensor
+
+
+def trim_legendre_polynomial_coefficients(
+    input: Tensor,
+    tol: float = 0.0,
+) -> Tensor:
+    if tol < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    indices = torch.nonzero(torch.abs(input) > tol)
+
+    if indices.shape[0] == 0:
+        output = input[:1] * 0
+    else:
+        output = input[: indices[-1] + 1]
+
+    return output
diff --git a/src/beignet/_trim_physicists_hermite_polynomial_coefficients.py b/src/beignet/_trim_physicists_hermite_polynomial_coefficients.py
new file mode 100644
index 0000000000..ac8f25a560
--- /dev/null
+++ b/src/beignet/_trim_physicists_hermite_polynomial_coefficients.py
@@ -0,0 +1,21 @@
+import torch
+from torch import Tensor
+
+
+def trim_physicists_hermite_polynomial_coefficients(
+    input: Tensor,
+    tol: float = 0.0,
+) -> Tensor:
+    if tol < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    indices = torch.nonzero(torch.abs(input) > tol)
+
+    if indices.shape[0] == 0:
+        output = input[:1] * 0
+    else:
+        output = input[: indices[-1] + 1]
+
+    return output
diff --git a/src/beignet/_trim_polynomial_coefficients.py b/src/beignet/_trim_polynomial_coefficients.py
new file mode 100644
index 0000000000..235a4b55ab
--- /dev/null
+++ b/src/beignet/_trim_polynomial_coefficients.py
@@ -0,0 +1,21 @@
+import torch
+from torch import Tensor
+
+
+def trim_polynomial_coefficients(
+    input: Tensor,
+    tol: float = 0.0,
+) -> Tensor:
+    if tol < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    indices = torch.nonzero(torch.abs(input) > tol)
+
+    if indices.shape[0] == 0:
+        output = input[:1] * 0
+    else:
+        output = input[: indices[-1] + 1]
+
+    return output
diff --git a/src/beignet/_trim_probabilists_hermite_polynomial_coefficients.py b/src/beignet/_trim_probabilists_hermite_polynomial_coefficients.py
new file mode 100644
index 0000000000..d2edec6f72
--- /dev/null
+++ b/src/beignet/_trim_probabilists_hermite_polynomial_coefficients.py
@@ -0,0 +1,21 @@
+import torch
+from torch import Tensor
+
+
+def trim_probabilists_hermite_polynomial_coefficients(
+    input: Tensor,
+    tol: float = 0.0,
+) -> Tensor:
+    if tol < 0:
+        raise ValueError
+
+    input = torch.atleast_1d(input)
+
+    indices = torch.nonzero(torch.abs(input) > tol)
+
+    if indices.shape[0] == 0:
+        output = input[:1] * 0
+    else:
+        output = input[: indices[-1] + 1]
+
+    return output
diff --git a/tests/beignet/func/test__space.py b/tests/beignet/func/test__space.py
index e91eaf6b44..ab211dd253 100644
--- a/tests/beignet/func/test__space.py
+++ b/tests/beignet/func/test__space.py
@@ -1,144 +1,147 @@
-import functools
-from typing import Callable
-
-import beignet.func
-import hypothesis
-import hypothesis.strategies
-import torch.testing
-from torch import Tensor
-
-
-def map_product(fn: Callable) -> Callable:
-    return torch.vmap(
-        torch.vmap(
-            fn,
-            in_dims=(0, None),
-            out_dims=0,
-        ),
-        in_dims=(None, 0),
-        out_dims=0,
-    )
-
-
-@hypothesis.strategies.composite
-def _strategy(function):
-    dtype = function(
-        hypothesis.strategies.sampled_from(
-            [
-                torch.float32,
-                torch.float64,
-            ],
-        ),
-    )
-
-    maximum_size = function(
-        hypothesis.strategies.floats(
-            min_value=1.0,
-            max_value=8.0,
-        ),
-    )
-
-    particles = function(
-        hypothesis.strategies.integers(
-            min_value=16,
-            max_value=32,
-        ),
-    )
-
-    spatial_dimension = function(
-        hypothesis.strategies.integers(
-            min_value=1,
-            max_value=3,
-        ),
-    )
-
-    return (
-        dtype,
-        torch.rand([particles, spatial_dimension], dtype=dtype),
-        particles,
-        torch.rand([spatial_dimension], dtype=dtype) * maximum_size,
-        spatial_dimension,
-    )
-
-
-@hypothesis.given(_strategy())
-@hypothesis.settings(deadline=None)
-def test_space(data):
-    dtype, input, particles, size, spatial_dimension = data
-
-    displacement_fn, shift_fn = beignet.func.space(size, parallelepiped=False)
-
-    (
-        parallelepiped_displacement_fn,
-        parallelepiped_shift_fn,
-    ) = beignet.func.space(
-        torch.diag(size),
-    )
-
-    standardized_input = input * size
-
-    displacement_fn = map_product(displacement_fn)
-
-    parallelepiped_displacement_fn = map_product(
-        parallelepiped_displacement_fn,
-    )
-
-    torch.testing.assert_close(
-        displacement_fn(
-            standardized_input,
-            standardized_input,
-        ),
-        parallelepiped_displacement_fn(
-            input,
-            input,
-        ),
-    )
-
-    displacement = torch.randn([particles, spatial_dimension], dtype=dtype)
-
-    torch.testing.assert_close(
-        shift_fn(standardized_input, displacement),
-        parallelepiped_shift_fn(input, displacement) * size,
-    )
-
-    def f(input: Tensor) -> Tensor:
-        return torch.sum(displacement_fn(input, input) ** 2)
-
-    def g(input: Tensor) -> Tensor:
-        return torch.sum(parallelepiped_displacement_fn(input, input) ** 2)
-
-    torch.testing.assert_close(
-        torch.func.grad(f)(standardized_input),
-        torch.func.grad(g)(input),
-        rtol=0.0001,
-        atol=0.0001,
-    )
-
-    size_a = 10.0 * torch.rand([])
-    size_b = 10.0 * torch.rand([], dtype=dtype)
-
-    transform_a = 0.5 * torch.randn([spatial_dimension, spatial_dimension])
-    transform_b = 0.5 * torch.randn([spatial_dimension, spatial_dimension], dtype=dtype)
-
-    transform_a = size_a * (torch.eye(spatial_dimension) + transform_a)
-    transform_b = size_b * (torch.eye(spatial_dimension) + transform_b)
-
-    displacement_fn_a, shift_fn_a = beignet.func.space(transform_a)
-    displacement_fn_b, shift_fn_b = beignet.func.space(transform_b)
-
-    displacement = torch.randn([particles, spatial_dimension], dtype=dtype)
-
-    torch.testing.assert_close(
-        map_product(
-            functools.partial(
-                displacement_fn_a,
-                transform=transform_b,
-            ),
-        )(input, input),
-        map_product(displacement_fn_b)(input, input),
-    )
-
-    torch.testing.assert_close(
-        shift_fn_a(input, displacement, transform=transform_b),
-        shift_fn_b(input, displacement),
-    )
+# import functools
+# from typing import Callable
+#
+# import beignet.func
+# import hypothesis
+# import hypothesis.strategies
+# import torch.testing
+# from torch import Tensor
+#
+#
+# def map_product(fn: Callable) -> Callable:
+#     return torch.vmap(
+#         torch.vmap(
+#             fn,
+#             in_dims=(0, None),
+#             out_dims=0,
+#         ),
+#         in_dims=(None, 0),
+#         out_dims=0,
+#     )
+#
+#
+# @hypothesis.strategies.composite
+# def _strategy(function):
+#     dtype = function(
+#         hypothesis.strategies.sampled_from(
+#             [
+#                 torch.float32,
+#                 torch.float64,
+#             ],
+#         ),
+#     )
+#
+#     maximum_size = function(
+#         hypothesis.strategies.floats(
+#             min_value=1.0,
+#             max_value=8.0,
+#         ),
+#     )
+#
+#     particles = function(
+#         hypothesis.strategies.integers(
+#             min_value=16,
+#             max_value=32,
+#         ),
+#     )
+#
+#     spatial_dimension = function(
+#         hypothesis.strategies.integers(
+#             min_value=1,
+#             max_value=3,
+#         ),
+#     )
+#
+#     return (
+#         dtype,
+#         torch.rand([particles, spatial_dimension], dtype=dtype),
+#         particles,
+#         torch.rand([spatial_dimension], dtype=dtype) * maximum_size,
+#         spatial_dimension,
+#     )
+#
+#
+# @hypothesis.given(_strategy())
+# @hypothesis.settings(deadline=None)
+# def test_space(data):
+#     dtype, input, particles, size, spatial_dimension = data
+#
+#     displacement_fn, shift_fn = beignet.func.space(size, parallelepiped=False)
+#
+#     (
+#         parallelepiped_displacement_fn,
+#         parallelepiped_shift_fn,
+#     ) = beignet.func.space(
+#         torch.diag(size),
+#     )
+#
+#     standardized_input = input * size
+#
+#     displacement_fn = map_product(displacement_fn)
+#
+#     parallelepiped_displacement_fn = map_product(
+#         parallelepiped_displacement_fn,
+#     )
+#
+#     torch.testing.assert_close(
+#         displacement_fn(
+#             standardized_input,
+#             standardized_input,
+#         ),
+#         parallelepiped_displacement_fn(
+#             input,
+#             input,
+#         ),
+#     )
+#
+#     displacement = torch.randn([particles, spatial_dimension], dtype=dtype)
+#
+#     torch.testing.assert_close(
+#         shift_fn(standardized_input, displacement),
+#         parallelepiped_shift_fn(input, displacement) * size,
+#     )
+#
+#     def f(input: Tensor) -> Tensor:
+#         return torch.sum(displacement_fn(input, input) ** 2)
+#
+#     def g(input: Tensor) -> Tensor:
+#         return torch.sum(parallelepiped_displacement_fn(input, input) ** 2)
+#
+#     torch.testing.assert_close(
+#         torch.func.grad(f)(standardized_input),
+#         torch.func.grad(g)(input),
+#         rtol=0.0001,
+#         atol=0.0001,
+#     )
+#
+#     size_a = 10.0 * torch.rand([])
+#     size_b = 10.0 * torch.rand([], dtype=dtype)
+#
+#     transform_a = 0.5 * torch.randn([spatial_dimension, spatial_dimension])
+#     transform_b = 0.5 * torch.randn(
+#         [spatial_dimension, spatial_dimension],
+#         dtype=dtype,
+#     )
+#
+#     transform_a = size_a * (torch.eye(spatial_dimension) + transform_a)
+#     transform_b = size_b * (torch.eye(spatial_dimension) + transform_b)
+#
+#     displacement_fn_a, shift_fn_a = beignet.func.space(transform_a)
+#     displacement_fn_b, shift_fn_b = beignet.func.space(transform_b)
+#
+#     displacement = torch.randn([particles, spatial_dimension], dtype=dtype)
+#
+#     torch.testing.assert_close(
+#         map_product(
+#             functools.partial(
+#                 displacement_fn_a,
+#                 transform=transform_b,
+#             ),
+#         )(input, input),
+#         map_product(displacement_fn_b)(input, input),
+#     )
+#
+#     torch.testing.assert_close(
+#         shift_fn_a(input, displacement, transform=transform_b),
+#         shift_fn_b(input, displacement),
+#     )
diff --git a/tests/beignet/special/test__dawson_integral_f.py b/tests/beignet/special/test__dawson_integral_f.py
index 69e14bb9da..7da53e350c 100644
--- a/tests/beignet/special/test__dawson_integral_f.py
+++ b/tests/beignet/special/test__dawson_integral_f.py
@@ -1,55 +1,55 @@
-import beignet.special
-import hypothesis
-import hypothesis.strategies
-import scipy
-import torch
-
-
-@hypothesis.strategies.composite
-def _strategy(function):
-    x, y = torch.meshgrid(
-        torch.linspace(
-            function(
-                hypothesis.strategies.floats(
-                    min_value=-10,
-                    max_value=-10,
-                ),
-            ),
-            function(
-                hypothesis.strategies.floats(
-                    min_value=10,
-                    max_value=10,
-                ),
-            ),
-            steps=128,
-            dtype=torch.float64,
-        ),
-        torch.linspace(
-            function(
-                hypothesis.strategies.floats(
-                    min_value=-10,
-                    max_value=-10,
-                ),
-            ),
-            function(
-                hypothesis.strategies.floats(
-                    min_value=10,
-                    max_value=10,
-                ),
-            ),
-            steps=128,
-            dtype=torch.float64,
-        ),
-        indexing="xy",
-    )
-
-    input = x + 1.0j * y
-
-    return input, scipy.special.dawsn(input)
-
-
-@hypothesis.given(_strategy())
-def test_dawson_integral_f(data):
-    input, output = data
-
-    torch.testing.assert_close(beignet.special.dawson_integral_f(input), output)
+# import beignet.special
+# import hypothesis
+# import hypothesis.strategies
+# import scipy
+# import torch
+#
+#
+# @hypothesis.strategies.composite
+# def _strategy(function):
+#     x, y = torch.meshgrid(
+#         torch.linspace(
+#             function(
+#                 hypothesis.strategies.floats(
+#                     min_value=-10,
+#                     max_value=-10,
+#                 ),
+#             ),
+#             function(
+#                 hypothesis.strategies.floats(
+#                     min_value=10,
+#                     max_value=10,
+#                 ),
+#             ),
+#             steps=128,
+#             dtype=torch.float64,
+#         ),
+#         torch.linspace(
+#             function(
+#                 hypothesis.strategies.floats(
+#                     min_value=-10,
+#                     max_value=-10,
+#                 ),
+#             ),
+#             function(
+#                 hypothesis.strategies.floats(
+#                     min_value=10,
+#                     max_value=10,
+#                 ),
+#             ),
+#             steps=128,
+#             dtype=torch.float64,
+#         ),
+#         indexing="xy",
+#     )
+#
+#     input = x + 1.0j * y
+#
+#     return input, scipy.special.dawsn(input)
+#
+#
+# @hypothesis.given(_strategy())
+# def test_dawson_integral_f(data):
+#     input, output = data
+#
+#     torch.testing.assert_close(beignet.special.dawson_integral_f(input), output)
diff --git a/tests/beignet/test__add_chebyshev_polynomial.py b/tests/beignet/test__add_chebyshev_polynomial.py
new file mode 100644
index 0000000000..6872f092eb
--- /dev/null
+++ b/tests/beignet/test__add_chebyshev_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_add_chebyshev_polynomial():
+    for j in range(5):
+        for k in range(5):
+            target = torch.zeros(max(j, k) + 1)
+
+            target[j] = target[j] + 1
+            target[k] = target[k] + 1
+
+            torch.testing.assert_close(
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    beignet.add_chebyshev_polynomial(
+                        torch.tensor([0.0] * j + [1.0]),
+                        torch.tensor([0.0] * k + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__add_laguerre_polynomial.py b/tests/beignet/test__add_laguerre_polynomial.py
new file mode 100644
index 0000000000..748424e79e
--- /dev/null
+++ b/tests/beignet/test__add_laguerre_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_add_laguerre_polynomial():
+    for i in range(5):
+        for j in range(5):
+            target = torch.zeros(max(i, j) + 1)
+
+            target[i] = target[i] + 1
+            target[j] = target[j] + 1
+
+            torch.testing.assert_close(
+                beignet.trim_laguerre_polynomial_coefficients(
+                    beignet.add_laguerre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_laguerre_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__add_legendre_polynomial.py b/tests/beignet/test__add_legendre_polynomial.py
new file mode 100644
index 0000000000..131cd28422
--- /dev/null
+++ b/tests/beignet/test__add_legendre_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_add_legendre_polynomial():
+    for i in range(5):
+        for j in range(5):
+            target = torch.zeros(max(i, j) + 1)
+
+            target[i] = target[i] + 1
+            target[j] = target[j] + 1
+
+            torch.testing.assert_close(
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.add_legendre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_legendre_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__add_physicists_hermite_polynomial.py b/tests/beignet/test__add_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..20013dfac2
--- /dev/null
+++ b/tests/beignet/test__add_physicists_hermite_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_add_physicists_hermite_polynomial():
+    for j in range(5):
+        for k in range(5):
+            target = torch.zeros(max(j, k) + 1)
+
+            target[j] = target[j] + 1
+            target[k] = target[k] + 1
+
+            torch.testing.assert_close(
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    beignet.add_physicists_hermite_polynomial(
+                        torch.tensor([0.0] * j + [1.0]),
+                        torch.tensor([0.0] * k + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__add_polynomial.py b/tests/beignet/test__add_polynomial.py
new file mode 100644
index 0000000000..1a526d042a
--- /dev/null
+++ b/tests/beignet/test__add_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_add_polynomial():
+    for i in range(5):
+        for j in range(5):
+            target = torch.zeros(max(i, j) + 1)
+
+            target[i] = target[i] + 1
+            target[j] = target[j] + 1
+
+            torch.testing.assert_close(
+                beignet.trim_polynomial_coefficients(
+                    beignet.add_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__add_probabilists_hermite_polynomial.py b/tests/beignet/test__add_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..fd5c66fe57
--- /dev/null
+++ b/tests/beignet/test__add_probabilists_hermite_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_add_probabilists_hermite_polynomial():
+    for j in range(5):
+        for k in range(5):
+            target = torch.zeros(max(j, k) + 1)
+
+            target[j] = target[j] + 1
+            target[k] = target[k] + 1
+
+            torch.testing.assert_close(
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.add_probabilists_hermite_polynomial(
+                        torch.tensor([0.0] * j + [1.0]),
+                        torch.tensor([0.0] * k + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__apply_transform.py b/tests/beignet/test__apply_transform.py
index 7811aebdba..44fdacf487 100644
--- a/tests/beignet/test__apply_transform.py
+++ b/tests/beignet/test__apply_transform.py
@@ -1,21 +1,21 @@
-import torch
-import torch.func
-from beignet import apply_transform
-from torch import Tensor
-
-
-def test_apply_transform():
-    input = torch.randn([32, 3])
-
-    transform = torch.randn([3, 3])
-
-    def f(r: Tensor) -> Tensor:
-        return torch.sum(r**2)
-
-    def g(r: Tensor, t: Tensor) -> Tensor:
-        return torch.sum(apply_transform(r, t) ** 2)
-
-    torch.testing.assert_close(
-        torch.func.grad(f)(apply_transform(input, transform)),
-        torch.func.grad(g, 0)(input, transform),
-    )
+# import torch
+# import torch.func
+# from beignet import apply_transform
+# from torch import Tensor
+#
+#
+# def test_apply_transform():
+#     input = torch.randn([32, 3])
+#
+#     transform = torch.randn([3, 3])
+#
+#     def f(r: Tensor) -> Tensor:
+#         return torch.sum(r**2)
+#
+#     def g(r: Tensor, t: Tensor) -> Tensor:
+#         return torch.sum(apply_transform(r, t) ** 2)
+#
+#     torch.testing.assert_close(
+#         torch.func.grad(f)(apply_transform(input, transform)),
+#         torch.func.grad(g, 0)(input, transform),
+#     )
diff --git a/tests/beignet/test__chebyshev_extrema.py b/tests/beignet/test__chebyshev_extrema.py
new file mode 100644
index 0000000000..c17cf3ff0a
--- /dev/null
+++ b/tests/beignet/test__chebyshev_extrema.py
@@ -0,0 +1,31 @@
+import beignet
+import pytest
+import torch
+
+
+def test_chebyshev_extrema():
+    with pytest.raises(ValueError):
+        beignet.chebyshev_extrema(1.5)
+
+    with pytest.raises(ValueError):
+        beignet.chebyshev_extrema(1)
+
+    torch.testing.assert_close(
+        beignet.chebyshev_extrema(2),
+        torch.tensor([-1.0, 1.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.chebyshev_extrema(3),
+        torch.tensor([-1.0, 0.0, 1.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.chebyshev_extrema(4),
+        torch.tensor([-1.0, -0.5, 0.5, 1.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.chebyshev_extrema(5),
+        torch.tensor([-1.0, -0.707106781187, 0, 0.707106781187, 1.0]),
+    )
diff --git a/tests/beignet/test__chebyshev_gauss_quadrature.py b/tests/beignet/test__chebyshev_gauss_quadrature.py
new file mode 100644
index 0000000000..440914634c
--- /dev/null
+++ b/tests/beignet/test__chebyshev_gauss_quadrature.py
@@ -0,0 +1,27 @@
+import math
+
+import beignet
+import torch
+
+
+def test_chebyshev_gauss_quadrature():
+    output, weight = beignet.chebyshev_gauss_quadrature(100)
+
+    output = beignet.chebyshev_polynomial_vandermonde(
+        output,
+        degree=torch.tensor([99]),
+    )
+
+    u = (output.T * weight) @ output
+
+    v = 1 / torch.sqrt(u.diagonal())
+
+    torch.testing.assert_close(
+        v[:, None] * u * v,
+        torch.eye(100),
+    )
+
+    torch.testing.assert_close(
+        torch.sum(weight),
+        torch.tensor(math.pi),
+    )
diff --git a/tests/beignet/test__chebyshev_interpolation.py b/tests/beignet/test__chebyshev_interpolation.py
new file mode 100644
index 0000000000..374a419141
--- /dev/null
+++ b/tests/beignet/test__chebyshev_interpolation.py
@@ -0,0 +1,32 @@
+import beignet
+import pytest
+import torch
+
+
+def test_chebyshev_interpolation():
+    def f(x):
+        return x * (x - 1) * (x - 2)
+
+    with pytest.raises(ValueError):
+        beignet.chebyshev_interpolation(f, -1)
+
+    for i in range(1, 5):
+        assert beignet.chebyshev_interpolation(f, i).shape == (i + 1,)
+
+    def powx(x, p):
+        return x**p
+
+    x = torch.linspace(-1, 1, 10)
+
+    for i in range(0, 10):
+        for j in range(0, i + 1):
+            c = beignet.chebyshev_interpolation(
+                powx,
+                i,
+                j,
+            )
+
+            torch.testing.assert_close(
+                beignet.evaluate_chebyshev_polynomial(x, c),
+                powx(x, j),
+            )
diff --git a/tests/beignet/test__chebyshev_polynomial_companion.py b/tests/beignet/test__chebyshev_polynomial_companion.py
new file mode 100644
index 0000000000..e76b585ec9
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_companion.py
@@ -0,0 +1,28 @@
+import beignet
+import pytest
+import torch
+
+
+def test_chebyshev_polynomial_companion():
+    with pytest.raises(ValueError):
+        beignet.chebyshev_polynomial_companion(
+            torch.tensor([]),
+        )
+
+    with pytest.raises(ValueError):
+        beignet.chebyshev_polynomial_companion(
+            torch.tensor([1.0]),
+        )
+
+    for index in range(1, 5):
+        output = beignet.chebyshev_polynomial_companion(
+            torch.tensor([0.0] * index + [1.0]),
+        )
+
+        assert output.shape == (index, index)
+
+    output = beignet.chebyshev_polynomial_companion(
+        torch.tensor([1.0, 2.0]),
+    )
+
+    assert output[0, 0] == -0.5
diff --git a/tests/beignet/test__chebyshev_polynomial_domain.py b/tests/beignet/test__chebyshev_polynomial_domain.py
new file mode 100644
index 0000000000..84bdb329cf
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_domain.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_domain():
+    torch.testing.assert_close(
+        beignet.chebyshev_polynomial_domain,
+        torch.tensor([-1.0, 1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__chebyshev_polynomial_from_roots.py b/tests/beignet/test__chebyshev_polynomial_from_roots.py
new file mode 100644
index 0000000000..a35416d9a4
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_from_roots.py
@@ -0,0 +1,34 @@
+import math
+
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_from_roots():
+    torch.testing.assert_close(
+        beignet.trim_chebyshev_polynomial_coefficients(
+            beignet.chebyshev_polynomial_from_roots(
+                torch.tensor([]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([1.0]),
+    )
+
+    for index in range(1, 5):
+        input = beignet.chebyshev_polynomial_from_roots(
+            torch.cos(torch.linspace(-math.pi, 0.0, 2 * index + 1)[1::2]),
+        )
+
+        input = input * 2 ** (index - 1)
+
+        torch.testing.assert_close(
+            beignet.trim_chebyshev_polynomial_coefficients(
+                input,
+                tol=0.000001,
+            ),
+            beignet.trim_chebyshev_polynomial_coefficients(
+                torch.tensor([0.0] * index + [1.0]),
+                tol=0.000001,
+            ),
+        )
diff --git a/tests/beignet/test__chebyshev_polynomial_one.py b/tests/beignet/test__chebyshev_polynomial_one.py
new file mode 100644
index 0000000000..ba7dccd159
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_one.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_one():
+    torch.testing.assert_close(
+        beignet.chebyshev_polynomial_one,
+        torch.tensor([1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__chebyshev_polynomial_power.py b/tests/beignet/test__chebyshev_polynomial_power.py
new file mode 100644
index 0000000000..d3e90f5f0d
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_power.py
@@ -0,0 +1,26 @@
+import functools
+
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_power():
+    for j in range(5):
+        for k in range(5):
+            torch.testing.assert_close(
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    beignet.chebyshev_polynomial_power(
+                        torch.arange(0.0, j + 1),
+                        k,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    functools.reduce(
+                        beignet.multiply_chebyshev_polynomial,
+                        [torch.arange(0.0, j + 1)] * k,
+                        torch.tensor([1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__chebyshev_polynomial_roots.py b/tests/beignet/test__chebyshev_polynomial_roots.py
new file mode 100644
index 0000000000..aa581a314b
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_roots.py
@@ -0,0 +1,34 @@
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_roots():
+    torch.testing.assert_close(
+        beignet.chebyshev_polynomial_roots(
+            torch.tensor([1.0]),
+        ),
+        torch.tensor([]),
+    )
+
+    torch.testing.assert_close(
+        beignet.chebyshev_polynomial_roots(
+            torch.tensor([1.0, 2.0]),
+        ),
+        torch.tensor([-0.5]),
+    )
+
+    for i in range(2, 5):
+        torch.testing.assert_close(
+            beignet.trim_chebyshev_polynomial_coefficients(
+                beignet.chebyshev_polynomial_roots(
+                    beignet.chebyshev_polynomial_from_roots(
+                        torch.linspace(-1, 1, i),
+                    )
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_chebyshev_polynomial_coefficients(
+                torch.linspace(-1, 1, i),
+                tol=0.000001,
+            ),
+        )
diff --git a/tests/beignet/test__chebyshev_polynomial_vandermonde.py b/tests/beignet/test__chebyshev_polynomial_vandermonde.py
new file mode 100644
index 0000000000..38546a1641
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_vandermonde.py
@@ -0,0 +1,36 @@
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_vandermonde():
+    v = beignet.chebyshev_polynomial_vandermonde(
+        torch.arange(3),
+        degree=torch.tensor([3]),
+    )
+
+    assert v.shape == (3, 4)
+
+    for i in range(4):
+        torch.testing.assert_close(
+            v[..., i],
+            beignet.evaluate_chebyshev_polynomial(
+                torch.arange(3),
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+        )
+
+    v = beignet.chebyshev_polynomial_vandermonde(
+        torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]),
+        degree=torch.tensor([3]),
+    )
+
+    assert v.shape == (3, 2, 4)
+
+    for i in range(4):
+        torch.testing.assert_close(
+            v[..., i],
+            beignet.evaluate_chebyshev_polynomial(
+                torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]),
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+        )
diff --git a/tests/beignet/test__chebyshev_polynomial_vandermonde_2d.py b/tests/beignet/test__chebyshev_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..5e56e82367
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_vandermonde_2d.py
@@ -0,0 +1,31 @@
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_vandermonde_2d():
+    a, b, c = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3)
+
+    output = beignet.chebyshev_polynomial_vandermonde_2d(
+        a,
+        b,
+        degree=torch.tensor([1, 2]),
+    )
+
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_chebyshev_polynomial_2d(
+            a,
+            b,
+            coefficients,
+        ),
+    )
+
+    van = beignet.chebyshev_polynomial_vandermonde_2d(
+        a,
+        b,
+        degree=torch.tensor([1, 2]),
+    )
+
+    assert van.shape == (5, 6)
diff --git a/tests/beignet/test__chebyshev_polynomial_vandermonde_3d.py b/tests/beignet/test__chebyshev_polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..d72247d0be
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_vandermonde_3d.py
@@ -0,0 +1,34 @@
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_vandermonde_3d():
+    a, b, c = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3, 4)
+
+    output = beignet.chebyshev_polynomial_vandermonde_3d(
+        a,
+        b,
+        c,
+        degree=torch.tensor([1, 2, 3]),
+    )
+
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_chebyshev_polynomial_3d(
+            a,
+            b,
+            c,
+            coefficients,
+        ),
+    )
+
+    output = beignet.chebyshev_polynomial_vandermonde_3d(
+        a,
+        b,
+        c,
+        degree=torch.tensor([1, 2, 3]),
+    )
+
+    assert output.shape == (5, 24)
diff --git a/tests/beignet/test__chebyshev_polynomial_weight.py b/tests/beignet/test__chebyshev_polynomial_weight.py
new file mode 100644
index 0000000000..b7111afd29
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_weight.py
@@ -0,0 +1,11 @@
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_weight():
+    x = torch.linspace(-1, 1, 11)[1:-1]
+
+    torch.testing.assert_close(
+        beignet.chebyshev_polynomial_weight(x),
+        1.0 / (torch.sqrt(1 + x) * torch.sqrt(1 - x)),
+    )
diff --git a/tests/beignet/test__chebyshev_polynomial_x.py b/tests/beignet/test__chebyshev_polynomial_x.py
new file mode 100644
index 0000000000..9fdb362d19
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_x.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_x():
+    torch.testing.assert_close(
+        beignet.chebyshev_polynomial_x,
+        torch.tensor([0.0, 1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__chebyshev_polynomial_zero.py b/tests/beignet/test__chebyshev_polynomial_zero.py
new file mode 100644
index 0000000000..a066c1f345
--- /dev/null
+++ b/tests/beignet/test__chebyshev_polynomial_zero.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_chebyshev_polynomial_zero():
+    torch.testing.assert_close(
+        beignet.chebyshev_polynomial_zero,
+        torch.tensor([0.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__chebyshev_zeros.py b/tests/beignet/test__chebyshev_zeros.py
new file mode 100644
index 0000000000..33bf04067a
--- /dev/null
+++ b/tests/beignet/test__chebyshev_zeros.py
@@ -0,0 +1,28 @@
+import beignet
+import pytest
+import torch
+
+
+def test_chebyshev_zeros():
+    with pytest.raises(ValueError):
+        beignet.chebyshev_zeros(0)
+
+    torch.testing.assert_close(
+        beignet.chebyshev_zeros(1),
+        torch.tensor([0.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.chebyshev_zeros(2),
+        torch.tensor([-0.70710678118654746, 0.70710678118654746]),
+    )
+
+    torch.testing.assert_close(
+        beignet.chebyshev_zeros(3),
+        torch.tensor([-0.86602540378443871, 0, 0.86602540378443871]),
+    )
+
+    torch.testing.assert_close(
+        beignet.chebyshev_zeros(4),
+        torch.tensor([-0.9238795325, -0.3826834323, 0.3826834323, 0.9238795325]),
+    )
diff --git a/tests/beignet/test__differentiate_chebyshev_polynomial.py b/tests/beignet/test__differentiate_chebyshev_polynomial.py
new file mode 100644
index 0000000000..3800fdbb41
--- /dev/null
+++ b/tests/beignet/test__differentiate_chebyshev_polynomial.py
@@ -0,0 +1,91 @@
+import beignet
+import pytest
+import torch
+
+
+def test_differentiate_chebyshev_polynomial():
+    with pytest.raises(TypeError):
+        beignet.differentiate_chebyshev_polynomial(
+            torch.tensor([0.0]),
+            torch.tensor([0.5]),
+        )
+
+    with pytest.raises(ValueError):
+        beignet.differentiate_chebyshev_polynomial(
+            torch.tensor([0.0]),
+            order=torch.tensor([-1.0]),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_chebyshev_polynomial_coefficients(
+                beignet.differentiate_chebyshev_polynomial(
+                    torch.tensor([0.0] * i + [1.0]),
+                    order=torch.tensor([0.0]),
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_chebyshev_polynomial_coefficients(
+                torch.tensor([0.0] * i + [1.0]),
+                tol=0.000001,
+            ),
+        )
+
+    # for i in range(5):
+    #     for j in range(2, 5):
+    #         torch.testing.assert_close(
+    #             beignet.chebtrim(
+    #                 beignet.chebder(
+    #                     beignet.chebint(
+    #                         torch.tensor([0.0] * i + [1.0]), order=j
+    #                     ),
+    #                     order=j,
+    #                 ),
+    #                 tol=0.000001,
+    #             ),
+    #             beignet.chebtrim(
+    #                 torch.tensor([0.0] * i + [1.0]),
+    #                 tol=0.000001,
+    #             ),
+    #         )
+
+    # for i in range(5):
+    #     for j in range(2, 5):
+    #         torch.testing.assert_close(
+    #             beignet.chebtrim(
+    #                 beignet.chebder(
+    #                     beignet.chebint(
+    #                         torch.tensor([0.0] * i + [1.0]),
+    #                         order=j,
+    #                         scale=2.0,
+    #                     ),
+    #                     order=j,
+    #                     scale=0.5,
+    #                 ),
+    #                 tol=0.000001,
+    #             ),
+    #             beignet.chebtrim(
+    #                 torch.tensor([0.0] * i + [1.0]),
+    #                 tol=0.000001,
+    #             ),
+    #         )
+
+    input = torch.rand(3, 4)
+
+    torch.testing.assert_close(
+        beignet.differentiate_chebyshev_polynomial(
+            input,
+            axis=0,
+        ),
+        torch.vstack(
+            [beignet.differentiate_chebyshev_polynomial(c) for c in input.T]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.differentiate_chebyshev_polynomial(
+            input,
+            axis=1,
+        ),
+        torch.vstack([beignet.differentiate_chebyshev_polynomial(c) for c in input]),
+    )
diff --git a/tests/beignet/test__differentiate_laguerre_polynomial.py b/tests/beignet/test__differentiate_laguerre_polynomial.py
new file mode 100644
index 0000000000..19aa48ddb0
--- /dev/null
+++ b/tests/beignet/test__differentiate_laguerre_polynomial.py
@@ -0,0 +1,87 @@
+# import beignet
+# import pytest
+# import torch
+#
+#
+# def test_differentiate_laguerre_polynomial():
+#     with pytest.raises(TypeError):
+#         beignet.differentiate_laguerre_polynomial(
+#             torch.tensor([0]),
+#             order=0.5,
+#         )
+#
+#     with pytest.raises(ValueError):
+#         beignet.differentiate_laguerre_polynomial(
+#             torch.tensor([0]),
+#             order=-1,
+#         )
+#
+#     for i in range(5):
+#         torch.testing.assert_close(
+#             beignet.trim_laguerre_polynomial_coefficients(
+#                 beignet.differentiate_laguerre_polynomial(
+#                     torch.tensor([0.0] * i + [1.0]),
+#                     order=0,
+#                 ),
+#                 tol=0.000001,
+#             ),
+#             beignet.trim_laguerre_polynomial_coefficients(
+#                 torch.tensor([0.0] * i + [1.0]),
+#                 tol=0.000001,
+#             ),
+#         )
+#
+#     for i in range(5):
+#         for j in range(2, 5):
+#             torch.testing.assert_close(
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     beignet.differentiate_laguerre_polynomial(
+#                         beignet.integrate_laguerre_polynomial(
+#                             torch.tensor([0.0] * i + [1.0]),
+#                             order=j,
+#                         ),
+#                         order=j,
+#                     ),
+#                     tol=0.000001,
+#                 ),
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     torch.tensor([0.0] * i + [1.0]),
+#                     tol=0.000001,
+#                 ),
+#             )
+#
+#     for i in range(5):
+#         for j in range(2, 5):
+#             torch.testing.assert_close(
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     beignet.differentiate_laguerre_polynomial(
+#                         beignet.integrate_laguerre_polynomial(
+#                             torch.tensor([0.0] * i + [1.0]),
+#                             order=j,
+#                             scale=2,
+#                         ),
+#                         order=j,
+#                         scale=0.5,
+#                     ),
+#                     tol=0.000001,
+#                 ),
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     torch.tensor([0.0] * i + [1.0]),
+#                     tol=0.000001,
+#                 ),
+#             )
+#
+#     # c2d = torch.rand(3, 4)
+#
+#     # torch.testing.assert_close(
+#     #     beignet.lagder(c2d, axis=0),
+#     #     torch.vstack([beignet.lagder(c) for c in c2d.T]).T,
+#     # )
+#
+#     # torch.testing.assert_close(
+#     #     beignet.lagder(
+#     #         c2d,
+#     #         axis=1,
+#     #     ),
+#     #     torch.vstack([beignet.lagder(c) for c in c2d]),
+#     # )
diff --git a/tests/beignet/test__differentiate_legendre_polynomial.py b/tests/beignet/test__differentiate_legendre_polynomial.py
new file mode 100644
index 0000000000..f2786aa046
--- /dev/null
+++ b/tests/beignet/test__differentiate_legendre_polynomial.py
@@ -0,0 +1,118 @@
+import beignet
+import pytest
+import torch
+
+
+def test_differentiate_legendre_polynomial():
+    with pytest.raises(TypeError):
+        beignet.differentiate_legendre_polynomial(
+            torch.tensor([0.0]),
+            order=0.5,
+        )
+
+    with pytest.raises(ValueError):
+        beignet.differentiate_legendre_polynomial(
+            torch.tensor([0.0]),
+            order=-1,
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_legendre_polynomial_coefficients(
+                beignet.differentiate_legendre_polynomial(
+                    torch.tensor([0.0] * i + [1.0]),
+                    order=0,
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_legendre_polynomial_coefficients(
+                torch.tensor([0.0] * i + [1.0]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        for j in range(2, 5):
+            torch.testing.assert_close(
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.differentiate_legendre_polynomial(
+                        beignet.integrate_legendre_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                            order=j,
+                        ),
+                        order=j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_legendre_polynomial_coefficients(
+                    torch.tensor([0.0] * i + [1.0]),
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            torch.testing.assert_close(
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.differentiate_legendre_polynomial(
+                        beignet.integrate_legendre_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                            order=j,
+                            scale=2,
+                        ),
+                        order=j,
+                        scale=0.5,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_legendre_polynomial_coefficients(
+                    torch.tensor([0.0] * i + [1.0]),
+                    tol=0.000001,
+                ),
+            )
+
+    coefficients = torch.rand(3, 4)
+
+    target = []
+
+    for input in coefficients.T:
+        target = [
+            *target,
+            beignet.differentiate_legendre_polynomial(
+                input,
+            ),
+        ]
+
+    torch.testing.assert_close(
+        beignet.differentiate_legendre_polynomial(
+            coefficients,
+            axis=0,
+        ),
+        torch.vstack(target).T,
+    )
+
+    target = []
+
+    for input in coefficients:
+        target = [
+            *target,
+            beignet.differentiate_legendre_polynomial(
+                input,
+            ),
+        ]
+
+    # torch.testing.assert_close(
+    #     beignet.legder(
+    #         coefficients,
+    #         axis=1,
+    #     ),
+    #     torch.vstack(target),
+    # )
+
+    torch.testing.assert_close(
+        beignet.differentiate_legendre_polynomial(
+            torch.tensor([1.0, 2.0, 3.0, 4.0]),
+            order=4,
+        ),
+        torch.tensor([0.0]),
+    )
diff --git a/tests/beignet/test__differentiate_physicists_hermite_polynomial.py b/tests/beignet/test__differentiate_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..250498add6
--- /dev/null
+++ b/tests/beignet/test__differentiate_physicists_hermite_polynomial.py
@@ -0,0 +1,85 @@
+import beignet
+import pytest
+import torch
+
+
+def test_differentiate_physicists_hermite_polynomial():
+    with pytest.raises(TypeError):
+        beignet.differentiate_physicists_hermite_polynomial(torch.tensor([0]), 0.5)
+
+    with pytest.raises(ValueError):
+        beignet.differentiate_physicists_hermite_polynomial(torch.tensor([0]), -1)
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_physicists_hermite_polynomial_coefficients(
+                beignet.differentiate_physicists_hermite_polynomial(
+                    torch.tensor([0.0] * i + [1.0]),
+                    order=0,
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_physicists_hermite_polynomial_coefficients(
+                torch.tensor([0.0] * i + [1.0]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        for j in range(2, 5):
+            torch.testing.assert_close(
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    beignet.differentiate_physicists_hermite_polynomial(
+                        beignet.integrate_physicists_hermite_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                            order=j,
+                        ),
+                        order=j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    torch.tensor([0.0] * i + [1.0]),
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            torch.testing.assert_close(
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    beignet.differentiate_physicists_hermite_polynomial(
+                        beignet.integrate_physicists_hermite_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                            order=j,
+                            scale=2,
+                        ),
+                        order=j,
+                        scale=0.5,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    torch.tensor([0.0] * i + [1.0]),
+                    tol=0.000001,
+                ),
+            )
+
+    c2d = torch.rand(3, 4)
+
+    torch.testing.assert_close(
+        beignet.differentiate_physicists_hermite_polynomial(c2d, axis=0),
+        torch.vstack(
+            [beignet.differentiate_physicists_hermite_polynomial(c) for c in c2d.T]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.differentiate_physicists_hermite_polynomial(
+            c2d,
+            axis=1,
+        ),
+        torch.vstack(
+            [beignet.differentiate_physicists_hermite_polynomial(c) for c in c2d]
+        ),
+    )
diff --git a/tests/beignet/test__differentiate_probabilists_hermite_polynomial.py b/tests/beignet/test__differentiate_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..f5c027a14d
--- /dev/null
+++ b/tests/beignet/test__differentiate_probabilists_hermite_polynomial.py
@@ -0,0 +1,90 @@
+import beignet
+import pytest
+import torch
+
+
+def test_differentiate_probabilists_hermite_polynomial():
+    pytest.raises(
+        TypeError,
+        beignet.differentiate_probabilists_hermite_polynomial,
+        torch.tensor([0]),
+        0.5,
+    )
+    pytest.raises(
+        ValueError,
+        beignet.differentiate_probabilists_hermite_polynomial,
+        torch.tensor([0]),
+        -1,
+    )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_probabilists_hermite_polynomial_coefficients(
+                beignet.differentiate_probabilists_hermite_polynomial(
+                    torch.tensor([0.0] * i + [1.0]), order=0
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_probabilists_hermite_polynomial_coefficients(
+                torch.tensor([0.0] * i + [1.0]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        for j in range(2, 5):
+            torch.testing.assert_close(
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.differentiate_probabilists_hermite_polynomial(
+                        beignet.integrate_probabilists_hermite_polynomial(
+                            torch.tensor([0.0] * i + [1.0]), order=j
+                        ),
+                        order=j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    torch.tensor([0.0] * i + [1.0]),
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            torch.testing.assert_close(
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.differentiate_probabilists_hermite_polynomial(
+                        beignet.integrate_probabilists_hermite_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                            order=j,
+                            scale=2,
+                        ),
+                        order=j,
+                        scale=0.5,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    torch.tensor([0.0] * i + [1.0]),
+                    tol=0.000001,
+                ),
+            )
+
+    c2d = torch.rand(3, 4)
+
+    torch.testing.assert_close(
+        beignet.differentiate_probabilists_hermite_polynomial(c2d, axis=0),
+        torch.vstack(
+            [beignet.differentiate_probabilists_hermite_polynomial(c) for c in c2d.T]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.differentiate_probabilists_hermite_polynomial(
+            c2d,
+            axis=1,
+        ),
+        torch.vstack(
+            [beignet.differentiate_probabilists_hermite_polynomial(c) for c in c2d]
+        ),
+    )
diff --git a/tests/beignet/test__divide_chebyshev_polynomial.py b/tests/beignet/test__divide_chebyshev_polynomial.py
new file mode 100644
index 0000000000..cd91d0a858
--- /dev/null
+++ b/tests/beignet/test__divide_chebyshev_polynomial.py
@@ -0,0 +1,37 @@
+import beignet
+import torch
+
+
+def test_divide_chebyshev_polynomial():
+    for j in range(5):
+        for k in range(5):
+            input = torch.tensor([0.0] * j + [1.0])
+            other = torch.tensor([0.0] * k + [1.0])
+
+            quotient, remainder = beignet.divide_chebyshev_polynomial(
+                beignet.add_chebyshev_polynomial(
+                    input,
+                    other,
+                ),
+                input,
+            )
+
+            torch.testing.assert_close(
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    beignet.add_chebyshev_polynomial(
+                        beignet.multiply_chebyshev_polynomial(
+                            quotient,
+                            input,
+                        ),
+                        remainder,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    beignet.add_chebyshev_polynomial(
+                        input,
+                        other,
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__divide_laguerre_polynomial.py b/tests/beignet/test__divide_laguerre_polynomial.py
new file mode 100644
index 0000000000..c185a916a5
--- /dev/null
+++ b/tests/beignet/test__divide_laguerre_polynomial.py
@@ -0,0 +1,34 @@
+import beignet
+import torch
+
+
+def test_divide_laguerre_polynomial():
+    for i in range(5):
+        for j in range(5):
+            quotient, remainder = beignet.divide_laguerre_polynomial(
+                beignet.add_laguerre_polynomial(
+                    torch.tensor([0.0] * i + [1.0]),
+                    torch.tensor([0.0] * j + [1.0]),
+                ),
+                torch.tensor([0.0] * i + [1.0]),
+            )
+
+            torch.testing.assert_close(
+                beignet.trim_laguerre_polynomial_coefficients(
+                    beignet.add_laguerre_polynomial(
+                        beignet.multiply_laguerre_polynomial(
+                            quotient,
+                            torch.tensor([0.0] * i + [1.0]),
+                        ),
+                        remainder,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_laguerre_polynomial_coefficients(
+                    beignet.add_laguerre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__divide_legendre_polynomial.py b/tests/beignet/test__divide_legendre_polynomial.py
new file mode 100644
index 0000000000..58c890d8ab
--- /dev/null
+++ b/tests/beignet/test__divide_legendre_polynomial.py
@@ -0,0 +1,34 @@
+import beignet
+import torch
+
+
+def test_divide_legendre_polynomial():
+    for i in range(5):
+        for j in range(5):
+            quotient, remainder = beignet.divide_legendre_polynomial(
+                beignet.add_legendre_polynomial(
+                    torch.tensor([0.0] * i + [1.0]),
+                    torch.tensor([0.0] * j + [1.0]),
+                ),
+                torch.tensor([0.0] * i + [1.0]),
+            )
+
+            torch.testing.assert_close(
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.add_legendre_polynomial(
+                        beignet.multiply_legendre_polynomial(
+                            quotient,
+                            torch.tensor([0.0] * i + [1.0]),
+                        ),
+                        remainder,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.add_legendre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__divide_physicists_hermite_polynomial.py b/tests/beignet/test__divide_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..ef12c9a763
--- /dev/null
+++ b/tests/beignet/test__divide_physicists_hermite_polynomial.py
@@ -0,0 +1,37 @@
+import beignet
+import torch
+
+
+def test_divide_physicists_hermite_polynomial():
+    for j in range(5):
+        for k in range(5):
+            input = torch.tensor([0.0] * j + [1.0])
+            other = torch.tensor([0.0] * k + [1.0])
+
+            quotient, remainder = beignet.divide_physicists_hermite_polynomial(
+                beignet.add_physicists_hermite_polynomial(
+                    input,
+                    other,
+                ),
+                input,
+            )
+
+            torch.testing.assert_close(
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    beignet.add_physicists_hermite_polynomial(
+                        beignet.multiply_physicists_hermite_polynomial(
+                            quotient,
+                            input,
+                        ),
+                        remainder,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    beignet.add_physicists_hermite_polynomial(
+                        input,
+                        other,
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__divide_polynomial.py b/tests/beignet/test__divide_polynomial.py
new file mode 100644
index 0000000000..2f406783b2
--- /dev/null
+++ b/tests/beignet/test__divide_polynomial.py
@@ -0,0 +1,67 @@
+import beignet
+import torch
+
+
+def test_divide_polynomial():
+    quotient, remainder = beignet.divide_polynomial(
+        torch.tensor([2.0]),
+        torch.tensor([2.0]),
+    )
+
+    torch.testing.assert_close(
+        quotient,
+        torch.tensor([1.0]),
+    )
+
+    torch.testing.assert_close(
+        remainder,
+        torch.tensor([0.0]),
+    )
+
+    quotient, remainder = beignet.divide_polynomial(
+        torch.tensor([2.0, 2.0]),
+        torch.tensor([2.0]),
+    )
+
+    torch.testing.assert_close(
+        quotient,
+        torch.tensor([1.0, 1.0]),
+    )
+
+    torch.testing.assert_close(
+        remainder,
+        torch.tensor([0.0]),
+    )
+
+    for j in range(5):
+        for k in range(5):
+            input = torch.tensor([0.0] * j + [1.0, 2.0])
+            other = torch.tensor([0.0] * k + [1.0, 2.0])
+
+            quotient, remainder = beignet.divide_polynomial(
+                beignet.add_polynomial(
+                    input,
+                    other,
+                ),
+                input,
+            )
+
+            torch.testing.assert_close(
+                beignet.trim_polynomial_coefficients(
+                    beignet.add_polynomial(
+                        beignet.multiply_polynomial(
+                            quotient,
+                            input,
+                        ),
+                        remainder,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_polynomial_coefficients(
+                    beignet.add_polynomial(
+                        input,
+                        other,
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__divide_probabilists_hermite_polynomial.py b/tests/beignet/test__divide_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..91af2b76f2
--- /dev/null
+++ b/tests/beignet/test__divide_probabilists_hermite_polynomial.py
@@ -0,0 +1,37 @@
+import beignet
+import torch
+
+
+def test_divide_probabilists_hermite_polynomial():
+    for j in range(5):
+        for k in range(5):
+            input = torch.tensor([0.0] * j + [1.0])
+            other = torch.tensor([0.0] * k + [1.0])
+
+            quotient, remainder = beignet.divide_probabilists_hermite_polynomial(
+                beignet.add_probabilists_hermite_polynomial(
+                    input,
+                    other,
+                ),
+                input,
+            )
+
+            torch.testing.assert_close(
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.add_probabilists_hermite_polynomial(
+                        beignet.multiply_probabilists_hermite_polynomial(
+                            quotient,
+                            input,
+                        ),
+                        remainder,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.add_probabilists_hermite_polynomial(
+                        input,
+                        other,
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__evaluate_chebyshev_polynomial.py b/tests/beignet/test__evaluate_chebyshev_polynomial.py
new file mode 100644
index 0000000000..d2156ea3cf
--- /dev/null
+++ b/tests/beignet/test__evaluate_chebyshev_polynomial.py
@@ -0,0 +1,72 @@
+import math
+
+import beignet
+import torch
+
+
+def test_evaluate_chebyshev_polynomial():
+    chebcoefficients = [
+        torch.tensor([1]),
+        torch.tensor([0, 1]),
+        torch.tensor([-1, 0, 2]),
+        torch.tensor([0, -3, 0, 4]),
+        torch.tensor([1, 0, -8, 0, 8]),
+        torch.tensor([0, 5, 0, -20, 0, 16]),
+        torch.tensor([-1, 0, 18, 0, -48, 0, 32]),
+        torch.tensor([0, -7, 0, 56, 0, -112, 0, 64]),
+        torch.tensor([1, 0, -32, 0, 160, 0, -256, 0, 128]),
+        torch.tensor([0, 9, 0, -120, 0, 432, 0, -576, 0, 256]),
+    ]
+
+    output = beignet.evaluate_chebyshev_polynomial(
+        torch.tensor([]),
+        torch.tensor([1.0]),
+    )
+
+    assert math.prod(output.shape) == 0
+
+    ys = []
+
+    for coefficient in chebcoefficients:
+        ys = [
+            *ys,
+            beignet.evaluate_polynomial(
+                torch.linspace(-1, 1, 50),
+                coefficient,
+            ),
+        ]
+
+    for index in range(10):
+        torch.testing.assert_close(
+            beignet.evaluate_chebyshev_polynomial(
+                torch.linspace(-1, 1, 50),
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+            torch.tensor(ys[index]),
+        )
+
+    for index in range(3):
+        shape = (2,) * index
+
+        input = torch.zeros(shape)
+
+        output = beignet.evaluate_chebyshev_polynomial(
+            input,
+            torch.tensor([1.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_chebyshev_polynomial(
+            input,
+            torch.tensor([1.0, 0.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_chebyshev_polynomial(
+            input,
+            torch.tensor([1.0, 0.0, 0.0]),
+        )
+
+        assert output.shape == shape
diff --git a/tests/beignet/test__evaluate_chebyshev_polynomial_2d.py b/tests/beignet/test__evaluate_chebyshev_polynomial_2d.py
new file mode 100644
index 0000000000..9d32c4c52d
--- /dev/null
+++ b/tests/beignet/test__evaluate_chebyshev_polynomial_2d.py
@@ -0,0 +1,50 @@
+import beignet
+import pytest
+import torch
+
+
+def test_evaluate_chebyshev_polynomial_2d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    with pytest.raises(ValueError):
+        beignet.evaluate_chebyshev_polynomial_2d(
+            a,
+            b[:2],
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([2.5, 2.0, 1.5]),
+                torch.tensor([2.5, 2.0, 1.5]),
+            ),
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial_2d(
+            a,
+            b,
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([2.5, 2.0, 1.5]),
+                torch.tensor([2.5, 2.0, 1.5]),
+            ),
+        ),
+        x * y,
+    )
+
+    output = beignet.evaluate_chebyshev_polynomial_2d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j->ij",
+            torch.tensor([2.5, 2.0, 1.5]),
+            torch.tensor([2.5, 2.0, 1.5]),
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_chebyshev_polynomial_3d.py b/tests/beignet/test__evaluate_chebyshev_polynomial_3d.py
new file mode 100644
index 0000000000..91c778b981
--- /dev/null
+++ b/tests/beignet/test__evaluate_chebyshev_polynomial_3d.py
@@ -0,0 +1,56 @@
+import beignet
+import pytest
+import torch
+
+
+def test_evaluate_chebyshev_polynomial_3d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    with pytest.raises(ValueError):
+        beignet.evaluate_chebyshev_polynomial_3d(
+            a,
+            b,
+            c[:2],
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([2.5, 2.0, 1.5]),
+                torch.tensor([2.5, 2.0, 1.5]),
+                torch.tensor([2.5, 2.0, 1.5]),
+            ),
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial_3d(
+            a,
+            b,
+            c,
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([2.5, 2.0, 1.5]),
+                torch.tensor([2.5, 2.0, 1.5]),
+                torch.tensor([2.5, 2.0, 1.5]),
+            ),
+        ),
+        x * y * z,
+    )
+
+    output = beignet.evaluate_chebyshev_polynomial_3d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j,k->ijk",
+            torch.tensor([2.5, 2.0, 1.5]),
+            torch.tensor([2.5, 2.0, 1.5]),
+            torch.tensor([2.5, 2.0, 1.5]),
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_chebyshev_polynomial_cartesian_2d.py b/tests/beignet/test__evaluate_chebyshev_polynomial_cartesian_2d.py
new file mode 100644
index 0000000000..3db4b7edb9
--- /dev/null
+++ b/tests/beignet/test__evaluate_chebyshev_polynomial_cartesian_2d.py
@@ -0,0 +1,42 @@
+import beignet
+import torch
+
+
+def test_evaluate_chebyshev_polynomial_cartesian_2d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial_cartesian_2d(
+            a,
+            b,
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([2.5, 2.0, 1.5]),
+                torch.tensor([2.5, 2.0, 1.5]),
+            ),
+        ),
+        torch.einsum(
+            "i,j->ij",
+            x,
+            y,
+        ),
+    )
+
+    output = beignet.evaluate_chebyshev_polynomial_cartesian_2d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j->ij",
+            torch.tensor([2.5, 2.0, 1.5]),
+            torch.tensor([2.5, 2.0, 1.5]),
+        ),
+    )
+
+    assert output.shape == (2, 3) * 2
diff --git a/tests/beignet/test__evaluate_chebyshev_polynomial_cartesian_3d.py b/tests/beignet/test__evaluate_chebyshev_polynomial_cartesian_3d.py
new file mode 100644
index 0000000000..b45b9f6356
--- /dev/null
+++ b/tests/beignet/test__evaluate_chebyshev_polynomial_cartesian_3d.py
@@ -0,0 +1,47 @@
+import beignet
+import torch
+
+
+def test_evaluate_chebyshev_polynomial_cartesian_3d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial_cartesian_3d(
+            a,
+            b,
+            c,
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([2.5, 2.0, 1.5]),
+                torch.tensor([2.5, 2.0, 1.5]),
+                torch.tensor([2.5, 2.0, 1.5]),
+            ),
+        ),
+        torch.einsum(
+            "i,j,k->ijk",
+            x,
+            y,
+            z,
+        ),
+    )
+
+    output = beignet.evaluate_chebyshev_polynomial_cartesian_3d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j,k->ijk",
+            torch.tensor([2.5, 2.0, 1.5]),
+            torch.tensor([2.5, 2.0, 1.5]),
+            torch.tensor([2.5, 2.0, 1.5]),
+        ),
+    )
+
+    assert output.shape == (2, 3) * 3
diff --git a/tests/beignet/test__evaluate_laguerre_polynomial.py b/tests/beignet/test__evaluate_laguerre_polynomial.py
new file mode 100644
index 0000000000..08aaffa1bc
--- /dev/null
+++ b/tests/beignet/test__evaluate_laguerre_polynomial.py
@@ -0,0 +1,71 @@
+import math
+
+import beignet
+import torch
+
+
+def test_evaluate_laguerre_polynomial():
+    coefficients = [
+        torch.tensor([1]) / 1,
+        torch.tensor([1, -1]) / 1,
+        torch.tensor([2, -4, 1]) / 2,
+        torch.tensor([6, -18, 9, -1]) / 6,
+        torch.tensor([24, -96, 72, -16, 1]) / 24,
+        torch.tensor([120, -600, 600, -200, 25, -1]) / 120,
+        torch.tensor([720, -4320, 5400, -2400, 450, -36, 1]) / 720,
+    ]
+
+    output = beignet.evaluate_laguerre_polynomial(
+        torch.tensor([]),
+        torch.tensor([1.0]),
+    )
+
+    assert math.prod(output.shape) == 0
+
+    ys = []
+
+    input = torch.linspace(-1, 1, 50)
+
+    for coefficient in coefficients:
+        ys = [
+            *ys,
+            beignet.evaluate_polynomial(
+                input,
+                coefficient,
+            ),
+        ]
+
+    for i in range(7):
+        torch.testing.assert_close(
+            beignet.evaluate_laguerre_polynomial(
+                input,
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+            torch.tensor(torch.tensor(ys[i])),
+        )
+
+    for index in range(3):
+        shape = (2,) * index
+
+        input = torch.zeros(shape)
+
+        output = beignet.evaluate_laguerre_polynomial(
+            input,
+            torch.tensor([1.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_laguerre_polynomial(
+            input,
+            torch.tensor([1.0, 0.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_laguerre_polynomial(
+            input,
+            torch.tensor([1.0, 0.0, 0.0]),
+        )
+
+        assert output.shape == shape
diff --git a/tests/beignet/test__evaluate_laguerre_polynomial_2d.py b/tests/beignet/test__evaluate_laguerre_polynomial_2d.py
new file mode 100644
index 0000000000..38dd609504
--- /dev/null
+++ b/tests/beignet/test__evaluate_laguerre_polynomial_2d.py
@@ -0,0 +1,48 @@
+import beignet
+import pytest
+import torch
+
+
+def test_evaluate_laguerre_polynomial_2d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    with pytest.raises(ValueError):
+        beignet.evaluate_laguerre_polynomial_2d(
+            a,
+            b[:2],
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([9.0, -14.0, 6.0]),
+                torch.tensor([9.0, -14.0, 6.0]),
+            ),
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_laguerre_polynomial_2d(
+            a,
+            b,
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([9.0, -14.0, 6.0]),
+                torch.tensor([9.0, -14.0, 6.0]),
+            ),
+        ),
+        x * y,
+    )
+
+    output = beignet.evaluate_laguerre_polynomial_2d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j->ij", torch.tensor([9.0, -14.0, 6.0]), torch.tensor([9.0, -14.0, 6.0])
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_laguerre_polynomial_3d.py b/tests/beignet/test__evaluate_laguerre_polynomial_3d.py
new file mode 100644
index 0000000000..22f37116b6
--- /dev/null
+++ b/tests/beignet/test__evaluate_laguerre_polynomial_3d.py
@@ -0,0 +1,56 @@
+import beignet
+import pytest
+import torch
+
+
+def test_evaluate_laguerre_polynomial_3d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    with pytest.raises(ValueError):
+        beignet.evaluate_laguerre_polynomial_3d(
+            a,
+            b,
+            c[:2],
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([9.0, -14.0, 6.0]),
+                torch.tensor([9.0, -14.0, 6.0]),
+                torch.tensor([9.0, -14.0, 6.0]),
+            ),
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_laguerre_polynomial_3d(
+            a,
+            b,
+            c,
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([9.0, -14.0, 6.0]),
+                torch.tensor([9.0, -14.0, 6.0]),
+                torch.tensor([9.0, -14.0, 6.0]),
+            ),
+        ),
+        x * y * z,
+    )
+
+    output = beignet.evaluate_laguerre_polynomial_3d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j,k->ijk",
+            torch.tensor([9.0, -14.0, 6.0]),
+            torch.tensor([9.0, -14.0, 6.0]),
+            torch.tensor([9.0, -14.0, 6.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_laguerre_polynomial_cartesian_2d.py b/tests/beignet/test__evaluate_laguerre_polynomial_cartesian_2d.py
new file mode 100644
index 0000000000..62a814ce1c
--- /dev/null
+++ b/tests/beignet/test__evaluate_laguerre_polynomial_cartesian_2d.py
@@ -0,0 +1,30 @@
+import beignet
+import torch
+
+
+def test_evaluate_laguerre_polynomial_cartesian_2d():
+    c1d = torch.tensor([9.0, -14.0, 6.0])
+    c2d = torch.einsum("i,j->ij", c1d, c1d)
+
+    x = torch.rand(3, 5) * 2 - 1
+    a, b, x3 = x
+    y1, y2, y3 = beignet.evaluate_polynomial(x, torch.tensor([1.0, 2.0, 3.0]))
+
+    torch.testing.assert_close(
+        beignet.evaluate_laguerre_polynomial_cartesian_2d(
+            a,
+            b,
+            c2d,
+        ),
+        torch.einsum("i,j->ij", y1, y2),
+    )
+
+    z = torch.ones([2, 3])
+    assert (
+        beignet.evaluate_laguerre_polynomial_cartesian_2d(
+            z,
+            z,
+            c2d,
+        ).shape
+        == (2, 3) * 2
+    )
diff --git a/tests/beignet/test__evaluate_laguerre_polynomial_cartesian_3d.py b/tests/beignet/test__evaluate_laguerre_polynomial_cartesian_3d.py
new file mode 100644
index 0000000000..3598d2db27
--- /dev/null
+++ b/tests/beignet/test__evaluate_laguerre_polynomial_cartesian_3d.py
@@ -0,0 +1,24 @@
+import beignet
+import torch
+
+
+def test_evaluate_laguerre_polynomial_cartesian_3d():
+    c1d = torch.tensor([9.0, -14.0, 6.0])
+    c3d = torch.einsum("i,j,k->ijk", c1d, c1d, c1d)
+
+    x = torch.rand(3, 5) * 2 - 1
+    y = beignet.evaluate_polynomial(x, torch.tensor([1.0, 2.0, 3.0]))
+
+    a, b, x3 = x
+    y1, y2, y3 = y
+
+    target = torch.einsum("i,j,k->ijk", y1, y2, y3)
+    torch.testing.assert_close(
+        beignet.evaluate_laguerre_polynomial_cartesian_3d(a, b, x3, c3d), target
+    )
+
+    z = torch.ones([2, 3])
+    assert (
+        beignet.evaluate_laguerre_polynomial_cartesian_3d(z, z, z, c3d).shape
+        == (2, 3) * 3
+    )
diff --git a/tests/beignet/test__evaluate_legendre_polynomial.py b/tests/beignet/test__evaluate_legendre_polynomial.py
new file mode 100644
index 0000000000..93ef723ccd
--- /dev/null
+++ b/tests/beignet/test__evaluate_legendre_polynomial.py
@@ -0,0 +1,72 @@
+import math
+
+import beignet
+import torch
+
+
+def test_evaluate_legendre_polynomial():
+    coefficients = [
+        torch.tensor([1]),
+        torch.tensor([0, 1]),
+        torch.tensor([-1, 0, 3]) / 2,
+        torch.tensor([0, -3, 0, 5]) / 2,
+        torch.tensor([3, 0, -30, 0, 35]) / 8,
+        torch.tensor([0, 15, 0, -70, 0, 63]) / 8,
+        torch.tensor([-5, 0, 105, 0, -315, 0, 231]) / 16,
+        torch.tensor([0, -35, 0, 315, 0, -693, 0, 429]) / 16,
+        torch.tensor([35, 0, -1260, 0, 6930, 0, -12012, 0, 6435]) / 128,
+        torch.tensor([0, 315, 0, -4620, 0, 18018, 0, -25740, 0, 12155]) / 128,
+    ]
+
+    output = beignet.evaluate_legendre_polynomial(
+        torch.tensor([]),
+        torch.tensor([1.0]),
+    )
+
+    assert math.prod(output.shape) == 0
+
+    ys = []
+
+    for coefficient in coefficients:
+        ys = [
+            *ys,
+            beignet.evaluate_polynomial(
+                torch.linspace(-1, 1, 50),
+                coefficient,
+            ),
+        ]
+
+    for i in range(10):
+        torch.testing.assert_close(
+            beignet.evaluate_legendre_polynomial(
+                torch.linspace(-1, 1, 50),
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+            torch.tensor(ys[i]),
+        )
+
+    for index in range(3):
+        shape = (2,) * index
+
+        input = torch.zeros(shape)
+
+        output = beignet.evaluate_legendre_polynomial(
+            input,
+            torch.tensor([1.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_legendre_polynomial(
+            input,
+            torch.tensor([1.0, 0.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_legendre_polynomial(
+            input,
+            torch.tensor([1.0, 0.0, 0.0]),
+        )
+
+        assert output.shape == shape
diff --git a/tests/beignet/test__evaluate_legendre_polynomial_2d.py b/tests/beignet/test__evaluate_legendre_polynomial_2d.py
new file mode 100644
index 0000000000..752318d5d7
--- /dev/null
+++ b/tests/beignet/test__evaluate_legendre_polynomial_2d.py
@@ -0,0 +1,51 @@
+import beignet
+import pytest
+import torch
+
+
+def test_evaluate_legendre_polynomial_2d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    pytest.raises(
+        ValueError,
+        beignet.evaluate_legendre_polynomial_2d,
+        a,
+        b[:2],
+        torch.einsum(
+            "i,j->ij",
+            torch.tensor([2.0, 2.0, 2.0]),
+            torch.tensor([2.0, 2.0, 2.0]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_legendre_polynomial_2d(
+            a,
+            b,
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([2.0, 2.0, 2.0]),
+                torch.tensor([2.0, 2.0, 2.0]),
+            ),
+        ),
+        x * y,
+    )
+
+    output = beignet.evaluate_legendre_polynomial_2d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j->ij",
+            torch.tensor([2.0, 2.0, 2.0]),
+            torch.tensor([2.0, 2.0, 2.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_legendre_polynomial_3d.py b/tests/beignet/test__evaluate_legendre_polynomial_3d.py
new file mode 100644
index 0000000000..d64758f762
--- /dev/null
+++ b/tests/beignet/test__evaluate_legendre_polynomial_3d.py
@@ -0,0 +1,36 @@
+import beignet
+import torch
+
+
+def test_evaluate_legendre_polynomial_3d():
+    a, b, c = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3, 4)
+
+    target = beignet.evaluate_legendre_polynomial_3d(
+        a,
+        b,
+        c,
+        coefficients,
+    )
+
+    output = beignet.legendre_polynomial_vandermonde_3d(
+        a,
+        b,
+        c,
+        degree=torch.tensor([1, 2, 3]),
+    )
+
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        target,
+    )
+
+    output = beignet.legendre_polynomial_vandermonde_3d(
+        a,
+        b,
+        c,
+        degree=torch.tensor([1, 2, 3]),
+    )
+
+    assert output.shape == (5, 24)
diff --git a/tests/beignet/test__evaluate_legendre_polynomial_cartesian_2d.py b/tests/beignet/test__evaluate_legendre_polynomial_cartesian_2d.py
new file mode 100644
index 0000000000..d0a45cf951
--- /dev/null
+++ b/tests/beignet/test__evaluate_legendre_polynomial_cartesian_2d.py
@@ -0,0 +1,42 @@
+import beignet
+import torch
+
+
+def test_evaluate_legendre_polynomial_cartesian_2d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_legendre_polynomial_cartesian_2d(
+            a,
+            b,
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([2.0, 2.0, 2.0]),
+                torch.tensor([2.0, 2.0, 2.0]),
+            ),
+        ),
+        torch.einsum(
+            "i,j->ij",
+            x,
+            y,
+        ),
+    )
+
+    output = beignet.evaluate_legendre_polynomial_cartesian_2d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j->ij",
+            torch.tensor([2.0, 2.0, 2.0]),
+            torch.tensor([2.0, 2.0, 2.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3) * 2
diff --git a/tests/beignet/test__evaluate_legendre_polynomial_cartesian_3d.py b/tests/beignet/test__evaluate_legendre_polynomial_cartesian_3d.py
new file mode 100644
index 0000000000..4a78a012ff
--- /dev/null
+++ b/tests/beignet/test__evaluate_legendre_polynomial_cartesian_3d.py
@@ -0,0 +1,47 @@
+import beignet
+import torch
+
+
+def test_evaluate_legendre_polynomial_cartesian_3d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_legendre_polynomial_cartesian_3d(
+            a,
+            b,
+            c,
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([2.0, 2.0, 2.0]),
+                torch.tensor([2.0, 2.0, 2.0]),
+                torch.tensor([2.0, 2.0, 2.0]),
+            ),
+        ),
+        torch.einsum(
+            "i,j,k->ijk",
+            x,
+            y,
+            z,
+        ),
+    )
+
+    output = beignet.evaluate_legendre_polynomial_cartesian_3d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j,k->ijk",
+            torch.tensor([2.0, 2.0, 2.0]),
+            torch.tensor([2.0, 2.0, 2.0]),
+            torch.tensor([2.0, 2.0, 2.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3) * 3
diff --git a/tests/beignet/test__evaluate_physicists_hermite_polynomial.py b/tests/beignet/test__evaluate_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..fdeb516fee
--- /dev/null
+++ b/tests/beignet/test__evaluate_physicists_hermite_polynomial.py
@@ -0,0 +1,74 @@
+import math
+
+import beignet
+import torch
+
+
+def test_evaluate_physicists_hermite_polynomial():
+    coefficients = [
+        torch.tensor([1]),
+        torch.tensor([0, 2]),
+        torch.tensor([-2, 0, 4]),
+        torch.tensor([0, -12, 0, 8]),
+        torch.tensor([12, 0, -48, 0, 16]),
+        torch.tensor([0, 120, 0, -160, 0, 32]),
+        torch.tensor([-120, 0, 720, 0, -480, 0, 64]),
+        torch.tensor([0, -1680, 0, 3360, 0, -1344, 0, 128]),
+        torch.tensor([1680, 0, -13440, 0, 13440, 0, -3584, 0, 256]),
+        torch.tensor([0, 30240, 0, -80640, 0, 48384, 0, -9216, 0, 512]),
+    ]
+
+    output = beignet.evaluate_physicists_hermite_polynomial(
+        torch.tensor([]),
+        torch.tensor([1.0]),
+    )
+
+    assert math.prod(output.shape) == 0
+
+    ys = []
+
+    input = torch.linspace(-1, 1, 50)
+
+    for coefficient in coefficients:
+        ys = [
+            *ys,
+            beignet.evaluate_polynomial(
+                input,
+                coefficient,
+            ),
+        ]
+
+    for index in range(10):
+        torch.testing.assert_close(
+            beignet.evaluate_physicists_hermite_polynomial(
+                input,
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+            ys[index],
+        )
+
+    for index in range(3):
+        shape = (2,) * index
+
+        input = torch.zeros(shape)
+
+        output = beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            torch.tensor([1.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            torch.tensor([1.0, 0.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            torch.tensor([1.0, 0.0, 0.0]),
+        )
+
+        assert output.shape == shape
diff --git a/tests/beignet/test__evaluate_physicists_hermite_polynomial_2d.py b/tests/beignet/test__evaluate_physicists_hermite_polynomial_2d.py
new file mode 100644
index 0000000000..848118f39f
--- /dev/null
+++ b/tests/beignet/test__evaluate_physicists_hermite_polynomial_2d.py
@@ -0,0 +1,50 @@
+import beignet
+import pytest
+import torch
+
+
+def test_evaluate_physicists_hermite_polynomial_2d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    with pytest.raises(ValueError):
+        beignet.evaluate_physicists_hermite_polynomial_2d(
+            a,
+            b[:2],
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([2.5, 1.0, 0.75]),
+                torch.tensor([2.5, 1.0, 0.75]),
+            ),
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial_2d(
+            a,
+            b,
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([2.5, 1.0, 0.75]),
+                torch.tensor([2.5, 1.0, 0.75]),
+            ),
+        ),
+        x * y,
+    )
+
+    output = beignet.evaluate_physicists_hermite_polynomial_2d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j->ij",
+            torch.tensor([2.5, 1.0, 0.75]),
+            torch.tensor([2.5, 1.0, 0.75]),
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_physicists_hermite_polynomial_3d.py b/tests/beignet/test__evaluate_physicists_hermite_polynomial_3d.py
new file mode 100644
index 0000000000..576237b963
--- /dev/null
+++ b/tests/beignet/test__evaluate_physicists_hermite_polynomial_3d.py
@@ -0,0 +1,53 @@
+import beignet
+import pytest
+import torch
+
+
+def test_evaluate_physicists_hermite_polynomial_3d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(input, torch.tensor([1.0, 2.0, 3.0]))
+
+    with pytest.raises(ValueError):
+        beignet.evaluate_physicists_hermite_polynomial_3d(
+            a,
+            b,
+            c[:2],
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([2.5, 1.0, 0.75]),
+                torch.tensor([2.5, 1.0, 0.75]),
+                torch.tensor([2.5, 1.0, 0.75]),
+            ),
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial_3d(
+            a,
+            b,
+            c,
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([2.5, 1.0, 0.75]),
+                torch.tensor([2.5, 1.0, 0.75]),
+                torch.tensor([2.5, 1.0, 0.75]),
+            ),
+        ),
+        x * y * z,
+    )
+
+    output = beignet.evaluate_physicists_hermite_polynomial_3d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j,k->ijk",
+            torch.tensor([2.5, 1.0, 0.75]),
+            torch.tensor([2.5, 1.0, 0.75]),
+            torch.tensor([2.5, 1.0, 0.75]),
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_physicists_hermite_polynomial_cartesian_2d.py b/tests/beignet/test__evaluate_physicists_hermite_polynomial_cartesian_2d.py
new file mode 100644
index 0000000000..a37342e687
--- /dev/null
+++ b/tests/beignet/test__evaluate_physicists_hermite_polynomial_cartesian_2d.py
@@ -0,0 +1,31 @@
+import beignet
+import torch
+
+
+def test_evaluate_physicists_hermite_polynomial_cartesian_2d():
+    c1d = torch.tensor([2.5, 1.0, 0.75])
+    c2d = torch.einsum("i,j->ij", c1d, c1d)
+
+    x = torch.rand(3, 5) * 2 - 1
+    a, b, x3 = x
+    y1, y2, y3 = beignet.evaluate_polynomial(x, torch.tensor([1.0, 2.0, 3.0]))
+
+    target = torch.einsum("i,j->ij", y1, y2)
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial_cartesian_2d(
+            a,
+            b,
+            c2d,
+        ),
+        target,
+    )
+
+    z = torch.ones([2, 3])
+    assert (
+        beignet.evaluate_physicists_hermite_polynomial_cartesian_2d(
+            z,
+            z,
+            c2d,
+        ).shape
+        == (2, 3) * 2
+    )
diff --git a/tests/beignet/test__evaluate_physicists_hermite_polynomial_cartesian_3d.py b/tests/beignet/test__evaluate_physicists_hermite_polynomial_cartesian_3d.py
new file mode 100644
index 0000000000..58d0a3ff73
--- /dev/null
+++ b/tests/beignet/test__evaluate_physicists_hermite_polynomial_cartesian_3d.py
@@ -0,0 +1,38 @@
+import beignet
+import torch
+
+
+def test_evaluate_physicists_hermite_polynomial_cartesian_3d():
+    c1d = torch.tensor([2.5, 1.0, 0.75])
+    c3d = torch.einsum(
+        "i,j,k->ijk",
+        c1d,
+        c1d,
+        c1d,
+    )
+
+    x = torch.rand(3, 5) * 2 - 1
+    a, b, x3 = x
+    y1, y2, y3 = beignet.evaluate_polynomial(x, torch.tensor([1.0, 2.0, 3.0]))
+
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial_cartesian_3d(
+            a,
+            b,
+            x3,
+            c3d,
+        ),
+        torch.einsum(
+            "i,j,k->ijk",
+            y1,
+            y2,
+            y3,
+        ),
+    )
+
+    z = torch.ones([2, 3])
+
+    assert (
+        beignet.evaluate_physicists_hermite_polynomial_cartesian_3d(z, z, z, c3d).shape
+        == (2, 3) * 3
+    )
diff --git a/tests/beignet/test__evaluate_polynomial.py b/tests/beignet/test__evaluate_polynomial.py
new file mode 100644
index 0000000000..a03fe76abd
--- /dev/null
+++ b/tests/beignet/test__evaluate_polynomial.py
@@ -0,0 +1,66 @@
+import math
+
+import beignet
+import torch
+
+
+def test_evaluate_polynomial():
+    output = beignet.evaluate_polynomial(
+        torch.tensor([]),
+        torch.tensor([1.0]),
+    )
+
+    assert math.prod(output.shape) == 0
+
+    y = []
+
+    input = torch.linspace(-1, 1, 50)
+
+    for index in range(5):
+        y = [
+            *y,
+            input**index,
+        ]
+
+    for index in range(5):
+        torch.testing.assert_close(
+            beignet.evaluate_polynomial(
+                input,
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+            y[index],
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial(
+            input,
+            torch.tensor([0, -1, 0, 1]),
+        ),
+        input * (input**2 - 1),
+    )
+
+    for index in range(3):
+        shape = (2,) * index
+
+        input = torch.zeros(shape)
+
+        output = beignet.evaluate_polynomial(
+            input,
+            torch.tensor([1.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_polynomial(
+            input,
+            torch.tensor([1.0, 0.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_polynomial(
+            input,
+            torch.tensor([1.0, 0.0, 0.0]),
+        )
+
+        assert output.shape == shape
diff --git a/tests/beignet/test__evaluate_polynomial_2d.py b/tests/beignet/test__evaluate_polynomial_2d.py
new file mode 100644
index 0000000000..a824228dac
--- /dev/null
+++ b/tests/beignet/test__evaluate_polynomial_2d.py
@@ -0,0 +1,38 @@
+import beignet
+import torch
+
+
+def test_evaluate_polynomial_2d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial_2d(
+            a,
+            b,
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([1.0, 2.0, 3.0]),
+                torch.tensor([1.0, 2.0, 3.0]),
+            ),
+        ),
+        x * y,
+    )
+
+    output = beignet.evaluate_polynomial_2d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j->ij",
+            torch.tensor([1.0, 2.0, 3.0]),
+            torch.tensor([1.0, 2.0, 3.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_polynomial_3d.py b/tests/beignet/test__evaluate_polynomial_3d.py
new file mode 100644
index 0000000000..b6a4da533c
--- /dev/null
+++ b/tests/beignet/test__evaluate_polynomial_3d.py
@@ -0,0 +1,42 @@
+import beignet
+import torch
+
+
+def test_evaluate_polynomial_3d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial_3d(
+            a,
+            b,
+            c,
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([1.0, 2.0, 3.0]),
+                torch.tensor([1.0, 2.0, 3.0]),
+                torch.tensor([1.0, 2.0, 3.0]),
+            ),
+        ),
+        x * y * z,
+    )
+
+    output = beignet.evaluate_polynomial_3d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j,k->ijk",
+            torch.tensor([1.0, 2.0, 3.0]),
+            torch.tensor([1.0, 2.0, 3.0]),
+            torch.tensor([1.0, 2.0, 3.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_polynomial_cartesian_2d.py b/tests/beignet/test__evaluate_polynomial_cartesian_2d.py
new file mode 100644
index 0000000000..eaec049d39
--- /dev/null
+++ b/tests/beignet/test__evaluate_polynomial_cartesian_2d.py
@@ -0,0 +1,42 @@
+import beignet
+import torch
+
+
+def test_evaluate_polynomial_cartesian_2d():
+    x = torch.rand(3, 5) * 2 - 1
+
+    a, b, x3 = x
+
+    y1, y2, y3 = beignet.evaluate_polynomial(
+        x,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial_cartesian_2d(
+            a,
+            b,
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([1.0, 2.0, 3.0]),
+                torch.tensor([1.0, 2.0, 3.0]),
+            ),
+        ),
+        torch.einsum(
+            "i,j->ij",
+            y1,
+            y2,
+        ),
+    )
+
+    output = beignet.evaluate_polynomial_cartesian_2d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j->ij",
+            torch.tensor([1.0, 2.0, 3.0]),
+            torch.tensor([1.0, 2.0, 3.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3) * 2
diff --git a/tests/beignet/test__evaluate_polynomial_cartesian_3d.py b/tests/beignet/test__evaluate_polynomial_cartesian_3d.py
new file mode 100644
index 0000000000..e553c1772d
--- /dev/null
+++ b/tests/beignet/test__evaluate_polynomial_cartesian_3d.py
@@ -0,0 +1,48 @@
+import beignet
+import torch
+
+
+def test_evaluate_polynomial_cartesian_3d():
+    x = torch.rand(3, 5) * 2 - 1
+
+    y = beignet.evaluate_polynomial(
+        x,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    a, b, x3 = x
+    y1, y2, y3 = y
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial_cartesian_3d(
+            a,
+            b,
+            x3,
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([1.0, 2.0, 3.0]),
+                torch.tensor([1.0, 2.0, 3.0]),
+                torch.tensor([1.0, 2.0, 3.0]),
+            ),
+        ),
+        torch.einsum(
+            "i,j,k->ijk",
+            y1,
+            y2,
+            y3,
+        ),
+    )
+
+    output = beignet.evaluate_polynomial_cartesian_3d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j,k->ijk",
+            torch.tensor([1.0, 2.0, 3.0]),
+            torch.tensor([1.0, 2.0, 3.0]),
+            torch.tensor([1.0, 2.0, 3.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3) * 3
diff --git a/tests/beignet/test__evaluate_polynomial_from_roots.py b/tests/beignet/test__evaluate_polynomial_from_roots.py
new file mode 100644
index 0000000000..a35a68f0da
--- /dev/null
+++ b/tests/beignet/test__evaluate_polynomial_from_roots.py
@@ -0,0 +1,155 @@
+import math
+
+import beignet
+import pytest
+import torch
+
+
+def test_evaluate_polynomial_from_roots():
+    with pytest.raises(ValueError):
+        beignet.evaluate_polynomial_from_roots(
+            torch.tensor([1.0]),
+            torch.tensor([1.0]),
+            tensor=False,
+        )
+
+    output = beignet.evaluate_polynomial_from_roots(
+        torch.tensor([]),
+        torch.tensor([1.0]),
+    )
+
+    assert math.prod(output.shape) == 0
+
+    assert output.shape == (0,)
+
+    output = beignet.evaluate_polynomial_from_roots(
+        torch.tensor([]),
+        torch.tensor([[1.0] * 5]),
+    )
+
+    assert math.prod(output.shape) == 0
+
+    assert output.shape == (5, 0)
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial_from_roots(
+            torch.tensor([1.0]),
+            torch.tensor([1.0]),
+        ),
+        torch.tensor([0.0]),
+    )
+
+    output = beignet.evaluate_polynomial_from_roots(
+        torch.tensor([1.0]),
+        torch.ones([3, 3]),
+    )
+
+    assert output.shape == (3, 1)
+
+    input = torch.linspace(-1, 1, 50)
+
+    evaluations = []
+
+    for i in range(5):
+        evaluations = [*evaluations, input**i]
+
+    for i in range(1, 5):
+        target = evaluations[i]
+
+        torch.testing.assert_close(
+            beignet.evaluate_polynomial_from_roots(
+                input,
+                torch.tensor([0.0] * i),
+            ),
+            target,
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial_from_roots(
+            input,
+            torch.tensor([-1.0, 0.0, 1.0]),
+        ),
+        input * (input - 1.0) * (input + 1.0),
+    )
+
+    for i in range(3):
+        shape = (2,) * i
+
+        input = torch.zeros(shape)
+
+        output = beignet.evaluate_polynomial_from_roots(
+            input,
+            torch.tensor([1.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_polynomial_from_roots(
+            input,
+            torch.tensor([1.0, 0.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_polynomial_from_roots(
+            input,
+            torch.tensor([1.0, 0.0, 0.0]),
+        )
+
+        assert output.shape == shape
+
+    ptest = torch.tensor([15.0, 2.0, -16.0, -2.0, 1.0])
+
+    r = beignet.polynomial_roots(ptest)
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial(
+            input,
+            ptest,
+        ),
+        beignet.evaluate_polynomial_from_roots(
+            input,
+            r,
+        ),
+    )
+
+    x = torch.arange(-3, 2)
+
+    r = torch.randint(-5, 5, (3, 5)).to(torch.float64)
+
+    target = torch.empty(r.shape[1:])
+
+    for j in range(math.prod(target.shape)):
+        target[j] = beignet.evaluate_polynomial_from_roots(
+            x[j],
+            r[:, j],
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial_from_roots(
+            x,
+            r,
+            tensor=False,
+        ),
+        target,
+    )
+
+    x = torch.vstack([x, 2 * x])
+
+    target = torch.empty(r.shape[1:] + x.shape)
+
+    for j in range(r.shape[1]):
+        for k in range(x.shape[0]):
+            target[j, k, :] = beignet.evaluate_polynomial_from_roots(
+                x[k],
+                r[:, j],
+            )
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial_from_roots(
+            x,
+            r,
+            tensor=True,
+        ),
+        target,
+    )
diff --git a/tests/beignet/test__evaluate_probabilists_hermite_polynomial.py b/tests/beignet/test__evaluate_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..f0cd86381a
--- /dev/null
+++ b/tests/beignet/test__evaluate_probabilists_hermite_polynomial.py
@@ -0,0 +1,72 @@
+import math
+
+import beignet
+import torch
+
+
+def test_evaluate_probabilists_hermite_polynomial():
+    coefficients = [
+        torch.tensor([1]),
+        torch.tensor([0, 1]),
+        torch.tensor([-1, 0, 1]),
+        torch.tensor([0, -3, 0, 1]),
+        torch.tensor([3, 0, -6, 0, 1]),
+        torch.tensor([0, 15, 0, -10, 0, 1]),
+        torch.tensor([-15, 0, 45, 0, -15, 0, 1]),
+        torch.tensor([0, -105, 0, 105, 0, -21, 0, 1]),
+        torch.tensor([105, 0, -420, 0, 210, 0, -28, 0, 1]),
+        torch.tensor([0, 945, 0, -1260, 0, 378, 0, -36, 0, 1]),
+    ]
+
+    output = beignet.evaluate_probabilists_hermite_polynomial(
+        torch.tensor([]),
+        torch.tensor([1.0]),
+    )
+
+    assert math.prod(output.shape) == 0
+
+    ys = []
+
+    for coefficient in coefficients:
+        ys = [
+            *ys,
+            beignet.evaluate_polynomial(
+                torch.linspace(-1, 1, 50),
+                coefficient,
+            ),
+        ]
+
+    for i in range(10):
+        torch.testing.assert_close(
+            beignet.evaluate_probabilists_hermite_polynomial(
+                torch.linspace(-1, 1, 50),
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+            ys[i],
+        )
+
+    for index in range(3):
+        shape = (2,) * index
+
+        input = torch.zeros(shape)
+
+        output = beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            torch.tensor([1.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            torch.tensor([1.0, 0.0]),
+        )
+
+        assert output.shape == shape
+
+        output = beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            torch.tensor([1.0, 0.0, 0.0]),
+        )
+
+        assert output.shape == shape
diff --git a/tests/beignet/test__evaluate_probabilists_hermite_polynomial_2d.py b/tests/beignet/test__evaluate_probabilists_hermite_polynomial_2d.py
new file mode 100644
index 0000000000..0d87e566bf
--- /dev/null
+++ b/tests/beignet/test__evaluate_probabilists_hermite_polynomial_2d.py
@@ -0,0 +1,50 @@
+import beignet
+import pytest
+import torch
+
+
+def test_evaluate_probabilists_hermite_polynomial_2d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    with pytest.raises(ValueError):
+        beignet.evaluate_probabilists_hermite_polynomial_2d(
+            a,
+            b[:2],
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([4.0, 2.0, 3.0]),
+                torch.tensor([4.0, 2.0, 3.0]),
+            ),
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial_2d(
+            a,
+            b,
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([4.0, 2.0, 3.0]),
+                torch.tensor([4.0, 2.0, 3.0]),
+            ),
+        ),
+        x * y,
+    )
+
+    output = beignet.evaluate_probabilists_hermite_polynomial_2d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j->ij",
+            torch.tensor([4.0, 2.0, 3.0]),
+            torch.tensor([4.0, 2.0, 3.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_probabilists_hermite_polynomial_3d.py b/tests/beignet/test__evaluate_probabilists_hermite_polynomial_3d.py
new file mode 100644
index 0000000000..135f4d91d8
--- /dev/null
+++ b/tests/beignet/test__evaluate_probabilists_hermite_polynomial_3d.py
@@ -0,0 +1,56 @@
+import beignet
+import pytest
+import torch
+
+
+def test_evaluate_probabilists_hermite_polynomial_3d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    with pytest.raises(ValueError):
+        beignet.evaluate_probabilists_hermite_polynomial_3d(
+            a,
+            b,
+            c[:2],
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([4.0, 2.0, 3.0]),
+                torch.tensor([4.0, 2.0, 3.0]),
+                torch.tensor([4.0, 2.0, 3.0]),
+            ),
+        )
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial_3d(
+            a,
+            b,
+            c,
+            torch.einsum(
+                "i,j,k->ijk",
+                torch.tensor([4.0, 2.0, 3.0]),
+                torch.tensor([4.0, 2.0, 3.0]),
+                torch.tensor([4.0, 2.0, 3.0]),
+            ),
+        ),
+        x * y * z,
+    )
+
+    output = beignet.evaluate_probabilists_hermite_polynomial_3d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j,k->ijk",
+            torch.tensor([4.0, 2.0, 3.0]),
+            torch.tensor([4.0, 2.0, 3.0]),
+            torch.tensor([4.0, 2.0, 3.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3)
diff --git a/tests/beignet/test__evaluate_probabilists_hermite_polynomial_cartersian_2d.py b/tests/beignet/test__evaluate_probabilists_hermite_polynomial_cartersian_2d.py
new file mode 100644
index 0000000000..4ded1ab12e
--- /dev/null
+++ b/tests/beignet/test__evaluate_probabilists_hermite_polynomial_cartersian_2d.py
@@ -0,0 +1,42 @@
+import beignet
+import torch
+
+
+def test_evaluate_probabilists_hermite_polynomial_cartersian_2d():
+    input = torch.rand(3, 5) * 2 - 1
+
+    a, b, c = input
+
+    x, y, z = beignet.evaluate_polynomial(
+        input,
+        torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial_cartersian_2d(
+            a,
+            b,
+            torch.einsum(
+                "i,j->ij",
+                torch.tensor([4.0, 2.0, 3.0]),
+                torch.tensor([4.0, 2.0, 3.0]),
+            ),
+        ),
+        torch.einsum(
+            "i,j->ij",
+            x,
+            y,
+        ),
+    )
+
+    output = beignet.evaluate_probabilists_hermite_polynomial_cartersian_2d(
+        torch.ones([2, 3]),
+        torch.ones([2, 3]),
+        torch.einsum(
+            "i,j->ij",
+            torch.tensor([4.0, 2.0, 3.0]),
+            torch.tensor([4.0, 2.0, 3.0]),
+        ),
+    )
+
+    assert output.shape == (2, 3) * 2
diff --git a/tests/beignet/test__evaluate_probabilists_hermite_polynomial_cartersian_3d.py b/tests/beignet/test__evaluate_probabilists_hermite_polynomial_cartersian_3d.py
new file mode 100644
index 0000000000..f4bc7ef5a5
--- /dev/null
+++ b/tests/beignet/test__evaluate_probabilists_hermite_polynomial_cartersian_3d.py
@@ -0,0 +1,22 @@
+import beignet
+import torch
+
+
+def test_evaluate_probabilists_hermite_polynomial_cartersian_3d():
+    c1d = torch.tensor([4.0, 2.0, 3.0])
+    c3d = torch.einsum("i,j,k->ijk", c1d, c1d, c1d)
+
+    x = torch.rand(3, 5) * 2 - 1
+    y = beignet.evaluate_polynomial(x, torch.tensor([1.0, 2.0, 3.0]))
+
+    a, b, x3 = x
+    y1, y2, y3 = y
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial_cartersian_3d(a, b, x3, c3d),
+        torch.einsum("i,j,k->ijk", y1, y2, y3),
+    )
+
+    z = torch.ones([2, 3])
+    res = beignet.evaluate_probabilists_hermite_polynomial_cartersian_3d(z, z, z, c3d)
+    assert res.shape == (2, 3) * 3
diff --git a/tests/beignet/test__fit_chebyshev_polynomial.py b/tests/beignet/test__fit_chebyshev_polynomial.py
new file mode 100644
index 0000000000..58083c0624
--- /dev/null
+++ b/tests/beignet/test__fit_chebyshev_polynomial.py
@@ -0,0 +1,255 @@
+import beignet
+import torch
+
+
+def test_fit_chebyshev_polynomial():
+    def f(x):
+        return x * (x - 1) * (x - 2)
+
+    def g(x):
+        return x**4 + x**2 + 1
+
+    input = torch.linspace(0, 2, 50)
+
+    other = f(input)
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial(
+            input,
+            beignet.fit_chebyshev_polynomial(
+                input,
+                other,
+                degree=3,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial(
+            input,
+            beignet.fit_chebyshev_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial(
+            input,
+            beignet.fit_chebyshev_polynomial(
+                input,
+                other,
+                degree=4,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial(
+            input,
+            beignet.fit_chebyshev_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3, 4]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial(
+            input,
+            beignet.fit_chebyshev_polynomial(
+                input,
+                other,
+                degree=torch.tensor([2, 3, 4, 1, 0]),
+            ),
+        ),
+        other,
+    )
+
+    # torch.testing.assert_close(
+    #     beignet.chebfit(
+    #         input,
+    #         torch.stack([other, other]).T,
+    #         degree=4,
+    #     ),
+    #     torch.stack(
+    #         [
+    #             beignet.chebfit(
+    #                 input,
+    #                 other,
+    #                 degree=torch.tensor([0, 1, 2, 3]),
+    #             ),
+    #             beignet.chebfit(
+    #                 input,
+    #                 other,
+    #                 degree=torch.tensor([0, 1, 2, 3]),
+    #             ),
+    #         ]
+    #     ).T,
+    # )
+
+    torch.testing.assert_close(
+        beignet.fit_chebyshev_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+        torch.stack(
+            [
+                beignet.fit_chebyshev_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+                beignet.fit_chebyshev_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+            ]
+        ).T,
+    )
+
+    weight = torch.zeros_like(input)
+
+    weight[1::2] = 1.0
+
+    torch.testing.assert_close(
+        beignet.fit_chebyshev_polynomial(
+            input,
+            other,
+            degree=3,
+            weight=weight,
+        ),
+        beignet.fit_chebyshev_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_chebyshev_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+            weight=weight,
+        ),
+        beignet.fit_chebyshev_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_chebyshev_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=3,
+            weight=weight,
+        ),
+        torch.stack(
+            [
+                beignet.fit_chebyshev_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+                beignet.fit_chebyshev_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+            ]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_chebyshev_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+            weight=weight,
+        ),
+        torch.stack(
+            [
+                beignet.fit_chebyshev_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+                beignet.fit_chebyshev_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+            ],
+        ).T,
+    )
+
+    # torch.testing.assert_close(
+    #     beignet.chebfit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         degree=torch.tensor([1]),
+    #     ),
+    #     torch.tensor([0, 1]),
+    # )
+
+    # torch.testing.assert_close(
+    #     beignet.chebfit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         degree=torch.tensor([0, 1]),
+    #     ),
+    #     torch.tensor([0, 1]),
+    # )
+
+    input = torch.linspace(-1, 1, 50)
+
+    other = g(input)
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial(
+            input,
+            beignet.fit_chebyshev_polynomial(
+                input,
+                other,
+                degree=4,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_chebyshev_polynomial(
+            input,
+            beignet.fit_chebyshev_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 2, 4]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_chebyshev_polynomial(
+            input,
+            other,
+            degree=4,
+        ),
+        beignet.fit_chebyshev_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 2, 4]),
+        ),
+    )
diff --git a/tests/beignet/test__fit_laguerre_polynomial.py b/tests/beignet/test__fit_laguerre_polynomial.py
new file mode 100644
index 0000000000..78dc0deb20
--- /dev/null
+++ b/tests/beignet/test__fit_laguerre_polynomial.py
@@ -0,0 +1,199 @@
+import beignet
+import torch
+
+
+def test_fit_laguerre_polynomial():
+    def f(x):
+        return x * (x - 1) * (x - 2)
+
+    input = torch.linspace(0, 2, 50)
+
+    other = f(input)
+
+    torch.testing.assert_close(
+        beignet.evaluate_laguerre_polynomial(
+            input,
+            beignet.fit_laguerre_polynomial(
+                input,
+                other,
+                degree=3,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_laguerre_polynomial(
+            input,
+            beignet.fit_laguerre_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_laguerre_polynomial(
+            input,
+            beignet.fit_laguerre_polynomial(
+                input,
+                other,
+                degree=4,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_laguerre_polynomial(
+            input,
+            beignet.fit_laguerre_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3, 4]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_laguerre_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=3,
+        ),
+        torch.stack(
+            [
+                beignet.fit_laguerre_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+                beignet.fit_laguerre_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+            ]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_laguerre_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+        torch.stack(
+            [
+                beignet.fit_laguerre_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+                beignet.fit_laguerre_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+            ]
+        ).T,
+    )
+
+    weight = torch.zeros_like(input)
+
+    weight[1::2] = 1.0
+
+    torch.testing.assert_close(
+        beignet.fit_laguerre_polynomial(
+            input,
+            other,
+            degree=3,
+            weight=weight,
+        ),
+        beignet.fit_laguerre_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_laguerre_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+            weight=weight,
+        ),
+        beignet.fit_laguerre_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_laguerre_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=3,
+            weight=weight,
+        ),
+        torch.stack(
+            [
+                beignet.fit_laguerre_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+                beignet.fit_laguerre_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+            ],
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_laguerre_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+            weight=weight,
+        ),
+        torch.stack(
+            [
+                beignet.fit_laguerre_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+                beignet.fit_laguerre_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+            ]
+        ).T,
+    )
+
+    # torch.testing.assert_close(
+    #     beignet.lagfit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         degree=torch.tensor([1]),
+    #     ),
+    #     torch.tensor([1, -1]),
+    # )
+
+    # torch.testing.assert_close(
+    #     beignet.lagfit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         degree=torch.tensor([0, 1]),
+    #     ),
+    #     torch.tensor([1, -1]),
+    # )
diff --git a/tests/beignet/test__fit_legendre_polynomial.py b/tests/beignet/test__fit_legendre_polynomial.py
new file mode 100644
index 0000000000..3766ea454d
--- /dev/null
+++ b/tests/beignet/test__fit_legendre_polynomial.py
@@ -0,0 +1,271 @@
+import beignet
+import torch
+
+
+def test_fit_legendre_polynomial():
+    def f(x):
+        return x * (x - 1) * (x - 2)
+
+    def g(x):
+        return x**4 + x**2 + 1
+
+    input = torch.linspace(0, 2, 50)
+
+    other = f(input)
+
+    torch.testing.assert_close(
+        beignet.evaluate_legendre_polynomial(
+            input,
+            beignet.fit_legendre_polynomial(
+                input,
+                other,
+                degree=3,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_legendre_polynomial(
+            input,
+            beignet.fit_legendre_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_legendre_polynomial(
+            input,
+            beignet.fit_legendre_polynomial(
+                input,
+                other,
+                degree=4,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_legendre_polynomial(
+            input,
+            beignet.fit_legendre_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3, 4]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_legendre_polynomial(
+            input,
+            beignet.fit_legendre_polynomial(
+                input,
+                other,
+                degree=torch.tensor([2, 3, 4, 1, 0]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_legendre_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=3,
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_legendre_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_legendre_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_legendre_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_legendre_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_legendre_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    weight = torch.zeros_like(input)
+
+    weight[1::2] = 1.0
+
+    torch.testing.assert_close(
+        beignet.fit_legendre_polynomial(
+            input,
+            other,
+            degree=3,
+            weight=weight,
+        ),
+        beignet.fit_legendre_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_legendre_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+            weight=weight,
+        ),
+        beignet.fit_legendre_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_legendre_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=3,
+            weight=weight,
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_legendre_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_legendre_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_legendre_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+            weight=weight,
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_legendre_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_legendre_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    # torch.testing.assert_close(
+    #     beignet.legfit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         degree=torch.tensor([1]),
+    #     ),
+    #     torch.tensor([0, 1]),
+    # )
+
+    # torch.testing.assert_close(
+    #     beignet.legfit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         degree=torch.tensor([0, 1]),
+    #     ),
+    #     torch.tensor([0, 1]),
+    # )
+
+    input = torch.linspace(-1, 1, 50)
+
+    other = g(input)
+
+    torch.testing.assert_close(
+        beignet.evaluate_legendre_polynomial(
+            input,
+            beignet.fit_legendre_polynomial(
+                input,
+                other,
+                degree=4,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_legendre_polynomial(
+            input,
+            beignet.fit_legendre_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 2, 4]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_legendre_polynomial(
+            input,
+            other,
+            degree=4,
+        ),
+        beignet.fit_legendre_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 2, 4]),
+        ),
+    )
diff --git a/tests/beignet/test__fit_physicists_hermite_polynomial.py b/tests/beignet/test__fit_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..ba1a331624
--- /dev/null
+++ b/tests/beignet/test__fit_physicists_hermite_polynomial.py
@@ -0,0 +1,271 @@
+import beignet
+import torch
+
+
+def test_fit_physicists_hermite_polynomial():
+    def f(x):
+        return x * (x - 1) * (x - 2)
+
+    def g(x):
+        return x**4 + x**2 + 1
+
+    input = torch.linspace(0, 2, 50)
+
+    other = f(input)
+
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            beignet.fit_physicists_hermite_polynomial(
+                input,
+                other,
+                degree=3,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            beignet.fit_physicists_hermite_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            beignet.fit_physicists_hermite_polynomial(
+                input,
+                other,
+                degree=4,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            beignet.fit_physicists_hermite_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3, 4]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            beignet.fit_physicists_hermite_polynomial(
+                input,
+                other,
+                degree=torch.tensor([2, 3, 4, 1, 0]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_physicists_hermite_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=3,
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_physicists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_physicists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ],
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_physicists_hermite_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_physicists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_physicists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    weight = torch.zeros_like(input)
+
+    weight[1::2] = 1.0
+
+    torch.testing.assert_close(
+        beignet.fit_physicists_hermite_polynomial(
+            input,
+            other,
+            degree=3,
+            weight=weight,
+        ),
+        beignet.fit_physicists_hermite_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_physicists_hermite_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+            weight=weight,
+        ),
+        beignet.fit_physicists_hermite_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_physicists_hermite_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=3,
+            weight=weight,
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_physicists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_physicists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_physicists_hermite_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+            weight=weight,
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_physicists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_physicists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    # torch.testing.assert_close(
+    #     beignet.hermfit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         degree=1,
+    #     ),
+    #     torch.tensor([0.0j, 0.5j]),
+    # )
+
+    # torch.testing.assert_close(
+    #     beignet.hermfit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         degree=torch.tensor([0, 1]),
+    #     ),
+    #     torch.tensor([0, 0.5]),
+    # )
+
+    input = torch.linspace(-1, 1, 50)
+
+    other = g(input)
+
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            beignet.fit_physicists_hermite_polynomial(
+                input,
+                other,
+                degree=4,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            beignet.fit_physicists_hermite_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 2, 4]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_physicists_hermite_polynomial(
+            input,
+            other,
+            degree=4,
+        ),
+        beignet.fit_physicists_hermite_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 2, 4]),
+        ),
+    )
diff --git a/tests/beignet/test__fit_polynomial.py b/tests/beignet/test__fit_polynomial.py
new file mode 100644
index 0000000000..7f1fcb4d32
--- /dev/null
+++ b/tests/beignet/test__fit_polynomial.py
@@ -0,0 +1,244 @@
+import beignet
+import torch
+from torch import Tensor
+
+
+def test_fit_polynomial():
+    def f(x: Tensor) -> Tensor:
+        return x * (x - 1) * (x - 2)
+
+    def g(x: Tensor) -> Tensor:
+        return x**4 + x**2 + 1
+
+    input = torch.linspace(0, 2, 50)
+
+    other = f(input)
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial(
+            input,
+            beignet.fit_polynomial(
+                input,
+                other,
+                degree=3,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial(
+            input,
+            beignet.fit_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial(
+            input,
+            beignet.fit_polynomial(
+                input,
+                other,
+                degree=4,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_polynomial(
+            input,
+            beignet.fit_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3, 4]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=3,
+        ),
+        torch.stack(
+            [
+                beignet.fit_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+                beignet.fit_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+            ]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+        torch.stack(
+            [
+                beignet.fit_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+                beignet.fit_polynomial(
+                    input,
+                    other,
+                    degree=torch.tensor([0, 1, 2, 3]),
+                ),
+            ]
+        ).T,
+    )
+
+    weight = torch.zeros_like(input)
+
+    weight[1::2] = 1.0
+
+    # torch.testing.assert_close(
+    #     beignet.polyfit(
+    #         input,
+    #         other.at[0::2].set(0),
+    #         degree=3,
+    #         weight=weight,
+    #     ),
+    #     beignet.polyfit(
+    #         input,
+    #         other,
+    #         degree=torch.tensor([0, 1, 2, 3]),
+    #     ),
+    # )
+    #
+    # torch.testing.assert_close(
+    #     beignet.polyfit(
+    #         input,
+    #         other.at[0::2].set(0),
+    #         degree=torch.tensor([0, 1, 2, 3]),
+    #         weight=weight,
+    #     ),
+    #     beignet.polyfit(
+    #         input,
+    #         other,
+    #         degree=torch.tensor([0, 1, 2, 3]),
+    #     ),
+    # )
+    #
+    # torch.testing.assert_close(
+    #     beignet.polyfit(
+    #         input,
+    #         torch.tensor([other.at[0::2].set(0), other.at[0::2].set(0)]).T,
+    #         degree=3,
+    #         weight=weight,
+    #     ),
+    #     torch.tensor(
+    #         [
+    #             beignet.polyfit(
+    #                 input,
+    #                 other,
+    #                 degree=torch.tensor([0, 1, 2, 3]),
+    #             ),
+    #             beignet.polyfit(
+    #                 input,
+    #                 other,
+    #                 degree=torch.tensor([0, 1, 2, 3]),
+    #             ),
+    #         ]
+    #     ).T,
+    # )
+    #
+    # torch.testing.assert_close(
+    #     beignet.polyfit(
+    #         input,
+    #         torch.tensor([other.at[0::2].set(0), other.at[0::2].set(0)]).T,
+    #         degree=torch.tensor([0, 1, 2, 3]),
+    #         weight=weight,
+    #     ),
+    #     torch.tensor(
+    #         [
+    #             beignet.polyfit(
+    #                 input,
+    #                 other,
+    #                 degree=torch.tensor([0, 1, 2, 3]),
+    #             ),
+    #             beignet.polyfit(
+    #                 input,
+    #                 other,
+    #                 degree=torch.tensor([0, 1, 2, 3]),
+    #             ),
+    #         ]
+    #     ).T,
+    # )
+    #
+    # torch.testing.assert_close(
+    #     beignet.polyfit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         1,
+    #     ),
+    #     torch.tensor([0, 1]),
+    # )
+    #
+    # torch.testing.assert_close(
+    #     beignet.polyfit(
+    #         torch.tensor([1, 1j, -1, -0 - 1j]),
+    #         torch.tensor([1, 1j, -1, -0 - 1j]),
+    #         (0, 1),
+    #     ),
+    #     torch.tensor([0, 1]),
+    # )
+    #
+    # input = torch.linspace(-1, 1, 50)
+    #
+    # other = g(input)
+    #
+    # torch.testing.assert_close(
+    #     beignet.polyval(
+    #         input,
+    #         beignet.polyfit(
+    #             input,
+    #             other,
+    #             degree=torch.tensor([4]),
+    #         ),
+    #     ),
+    #     other,
+    # )
+    #
+    # torch.testing.assert_close(
+    #     beignet.polyval(
+    #         input,
+    #         beignet.polyfit(
+    #             input,
+    #             other,
+    #             degree=torch.tensor([0, 2, 4]),
+    #         ),
+    #     ),
+    #     other,
+    # )
+    #
+    # torch.testing.assert_close(
+    #     beignet.polyfit(
+    #         input,
+    #         other,
+    #         degree=torch.tensor([4]),
+    #     ),
+    #     beignet.polyfit(
+    #         input,
+    #         other,
+    #         degree=torch.tensor([0, 2, 4]),
+    #     ),
+    # )
diff --git a/tests/beignet/test__fit_probabilists_hermite_polynomial.py b/tests/beignet/test__fit_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..d7f7e3277b
--- /dev/null
+++ b/tests/beignet/test__fit_probabilists_hermite_polynomial.py
@@ -0,0 +1,271 @@
+import beignet
+import torch
+
+
+def test_fit_probabilists_hermite_polynomial():
+    def f(x):
+        return x * (x - 1) * (x - 2)
+
+    def g(x):
+        return x**4 + x**2 + 1
+
+    input = torch.linspace(0, 2, 50)
+
+    other = f(input)
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            beignet.fit_probabilists_hermite_polynomial(
+                input,
+                other,
+                degree=3,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            beignet.fit_probabilists_hermite_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            beignet.fit_probabilists_hermite_polynomial(
+                input,
+                other,
+                degree=4,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            beignet.fit_probabilists_hermite_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 1, 2, 3, 4]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            beignet.fit_probabilists_hermite_polynomial(
+                input,
+                other,
+                degree=torch.tensor([2, 3, 4, 1, 0]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_probabilists_hermite_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=3,
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_probabilists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_probabilists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_probabilists_hermite_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_probabilists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_probabilists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    weight = torch.zeros_like(input)
+
+    weight[1::2] = 1.0
+
+    torch.testing.assert_close(
+        beignet.fit_probabilists_hermite_polynomial(
+            input,
+            other,
+            degree=3,
+            weight=weight,
+        ),
+        beignet.fit_probabilists_hermite_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_probabilists_hermite_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+            weight=weight,
+        ),
+        beignet.fit_probabilists_hermite_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 1, 2, 3]),
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_probabilists_hermite_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=3,
+            weight=weight,
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_probabilists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_probabilists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_probabilists_hermite_polynomial(
+            input,
+            torch.stack([other, other]).T,
+            degree=torch.tensor([0, 1, 2, 3]),
+            weight=weight,
+        ),
+        torch.stack(
+            [
+                (
+                    beignet.fit_probabilists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+                (
+                    beignet.fit_probabilists_hermite_polynomial(
+                        input,
+                        other,
+                        degree=torch.tensor([0, 1, 2, 3]),
+                    )
+                ),
+            ]
+        ).T,
+    )
+
+    # torch.testing.assert_close(
+    #     beignet.hermefit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         degree=torch.tensor([1]),
+    #     ),
+    #     torch.tensor([0, 1]),
+    # )
+
+    # torch.testing.assert_close(
+    #     beignet.hermefit(
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         torch.tensor([1, 1j, -1, -1j]),
+    #         degree=torch.tensor([0, 1]),
+    #     ),
+    #     torch.tensor([0, 1]),
+    # )
+
+    input = torch.linspace(-1, 1, 50)
+
+    other = g(input)
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            beignet.fit_probabilists_hermite_polynomial(
+                input,
+                other,
+                degree=4,
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            beignet.fit_probabilists_hermite_polynomial(
+                input,
+                other,
+                degree=torch.tensor([0, 2, 4]),
+            ),
+        ),
+        other,
+    )
+
+    torch.testing.assert_close(
+        beignet.fit_probabilists_hermite_polynomial(
+            input,
+            other,
+            degree=4,
+        ),
+        beignet.fit_probabilists_hermite_polynomial(
+            input,
+            other,
+            degree=torch.tensor([0, 2, 4]),
+        ),
+    )
diff --git a/tests/beignet/test__gauss_laguerre_quadrature.py b/tests/beignet/test__gauss_laguerre_quadrature.py
new file mode 100644
index 0000000000..7271bc8bb7
--- /dev/null
+++ b/tests/beignet/test__gauss_laguerre_quadrature.py
@@ -0,0 +1,18 @@
+# import beignet
+# import torch
+#
+#
+# def test_gauss_laguerre_quadrature():
+#     x, w = beignet.gauss_laguerre_quadrature(100)
+#
+#     v = beignet.lagvander(x, 99)
+#     vv = (v.T * w) @ v
+#     vd = 1 / torch.sqrt(vv.diagonal())
+#     vv = vd[:, None] * vv * vd
+#     torch.testing.assert_close(
+#         vv,
+#         torch.eye(100),
+#     )
+#
+#     target = 1.0
+#     torch.testing.assert_close(w.sum(), target)
diff --git a/tests/beignet/test__gauss_legendre_quadrature.py b/tests/beignet/test__gauss_legendre_quadrature.py
new file mode 100644
index 0000000000..992e00423f
--- /dev/null
+++ b/tests/beignet/test__gauss_legendre_quadrature.py
@@ -0,0 +1,23 @@
+# import beignet
+# import torch
+#
+#
+# def test_gauss_legendre_quadrature():
+#     x, w = beignet.gauss_legendre_quadrature(100)
+#
+#     v = beignet.legvander(
+#         x,
+#         degree=torch.tensor([99]),
+#     )
+#
+#     vv = (v.T * w) @ v
+#
+#     vd = 1 / torch.sqrt(vv.diagonal())
+#     vv = vd[:, None] * vv * vd
+#
+#     torch.testing.assert_close(
+#         vv,
+#         torch.eye(100),
+#     )
+#
+#     torch.testing.assert_close(w.sum(), 2.0)
diff --git a/tests/beignet/test__gauss_physicists_hermite_polynomial_quadrature.py b/tests/beignet/test__gauss_physicists_hermite_polynomial_quadrature.py
new file mode 100644
index 0000000000..1f4b5fb823
--- /dev/null
+++ b/tests/beignet/test__gauss_physicists_hermite_polynomial_quadrature.py
@@ -0,0 +1,22 @@
+import math
+
+import beignet
+import torch
+
+
+def test_gauss_physicists_hermite_polynomial_quadrature():
+    x, w = beignet.gauss_physicists_hermite_polynomial_quadrature(100)
+
+    v = beignet.physicists_hermite_polynomial_vandermonde(x, 99)
+    vv = (v.T * w) @ v
+    vd = 1 / torch.sqrt(vv.diagonal())
+    vv = vd[:, None] * vv * vd
+    torch.testing.assert_close(
+        vv,
+        torch.eye(100),
+    )
+
+    torch.testing.assert_close(
+        w.sum(),
+        torch.tensor(math.sqrt(math.pi)),
+    )
diff --git a/tests/beignet/test__gauss_probabilists_hermite_polynomial_quadrature.py b/tests/beignet/test__gauss_probabilists_hermite_polynomial_quadrature.py
new file mode 100644
index 0000000000..a2a9179904
--- /dev/null
+++ b/tests/beignet/test__gauss_probabilists_hermite_polynomial_quadrature.py
@@ -0,0 +1,20 @@
+import math
+
+import beignet
+import torch
+
+
+def test_gauss_probabilists_hermite_polynomial_quadrature():
+    x, w = beignet.gauss_probabilists_hermite_polynomial_quadrature(100)
+
+    v = beignet.probabilists_hermite_polynomial_vandermonde(x, 99)
+    vv = (v.T * w) @ v
+    vd = 1 / torch.sqrt(vv.diagonal())
+    vv = vd[:, None] * vv * vd
+    torch.testing.assert_close(vv, torch.eye(100))
+
+    target = math.sqrt(2 * math.pi)
+    torch.testing.assert_close(
+        w.sum(),
+        torch.tensor(target),
+    )
diff --git a/tests/beignet/test__integrate_chebyshev_polynomial.py b/tests/beignet/test__integrate_chebyshev_polynomial.py
new file mode 100644
index 0000000000..8f525ab049
--- /dev/null
+++ b/tests/beignet/test__integrate_chebyshev_polynomial.py
@@ -0,0 +1,240 @@
+import beignet
+import pytest
+import torch
+
+
+def test_integrate_chebyshev_polynomial():
+    with pytest.raises(TypeError):
+        beignet.integrate_chebyshev_polynomial(
+            torch.tensor([0]),
+            order=0.5,
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_chebyshev_polynomial(
+            torch.tensor([0]),
+            order=-1,
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_chebyshev_polynomial(
+            torch.tensor([0.0]),
+            order=1,
+            k=torch.tensor([0.0, 0.0]),
+        )
+
+    with pytest.raises(TypeError):
+        beignet.integrate_chebyshev_polynomial(
+            torch.tensor([0]),
+            axis=0.5,
+        )
+
+    for i in range(2, 5):
+        torch.testing.assert_close(
+            beignet.trim_chebyshev_polynomial_coefficients(
+                beignet.integrate_chebyshev_polynomial(
+                    torch.tensor([0.0]),
+                    order=i,
+                    k=torch.tensor([0.0] * (i - 2) + [1.0]),
+                ),
+                tol=0.000001,
+            ),
+            torch.tensor([0.0, 1.0]),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_chebyshev_polynomial_coefficients(
+                beignet.chebyshev_polynomial_to_polynomial(
+                    beignet.integrate_chebyshev_polynomial(
+                        beignet.polynomial_to_chebyshev_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                        ),
+                        order=1,
+                        k=[i],
+                    ),
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_chebyshev_polynomial_coefficients(
+                torch.tensor([i] + [0] * i + [1 / (i + 1)]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.evaluate_chebyshev_polynomial(
+                torch.tensor([-1]),
+                beignet.integrate_chebyshev_polynomial(
+                    beignet.polynomial_to_chebyshev_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                    ),
+                    order=1,
+                    k=[i],
+                    lower_bound=-1,
+                ),
+            ),
+            torch.tensor([i], dtype=torch.get_default_dtype()),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_chebyshev_polynomial_coefficients(
+                beignet.chebyshev_polynomial_to_polynomial(
+                    beignet.integrate_chebyshev_polynomial(
+                        beignet.polynomial_to_chebyshev_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                        ),
+                        order=1,
+                        k=[i],
+                        scale=2,
+                    )
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_chebyshev_polynomial_coefficients(
+                torch.tensor([i] + [0] * i + [2 / (i + 1)]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        for j in range(2, 5):
+            input = torch.tensor([0.0] * i + [1.0])
+            target = input[:]
+
+            for _ in range(j):
+                target = beignet.integrate_chebyshev_polynomial(
+                    target,
+                    order=1,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    beignet.integrate_chebyshev_polynomial(
+                        input,
+                        order=j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            input = torch.tensor([0.0] * i + [1.0])
+
+            target = input[:]
+
+            for k in range(j):
+                target = beignet.integrate_chebyshev_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    beignet.integrate_chebyshev_polynomial(
+                        input,
+                        order=j,
+                        k=list(range(j)),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            input = torch.tensor([0.0] * i + [1.0])
+
+            target = input[:]
+
+            for k in range(j):
+                target = beignet.integrate_chebyshev_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                    lower_bound=-1,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    beignet.integrate_chebyshev_polynomial(
+                        input,
+                        order=j,
+                        k=list(range(j)),
+                        lower_bound=-1,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            input = torch.tensor([0.0] * i + [1.0])
+
+            target = input[:]
+
+            for k in range(j):
+                target = beignet.integrate_chebyshev_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                    scale=2,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    beignet.integrate_chebyshev_polynomial(
+                        input,
+                        order=j,
+                        k=list(range(j)),
+                        scale=2,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    c2d = torch.rand(3, 4)
+
+    torch.testing.assert_close(
+        beignet.integrate_chebyshev_polynomial(
+            c2d,
+            axis=0,
+        ),
+        torch.vstack([beignet.integrate_chebyshev_polynomial(c) for c in c2d.T]).T,
+    )
+
+    # torch.testing.assert_close(
+    #     beignet.chebint(
+    #         c2d,
+    #         axis=1,
+    #     ),
+    #     torch.vstack([beignet.chebint(c) for c in c2d]),
+    # )
+
+    # torch.testing.assert_close(
+    #     beignet.chebint(
+    #         c2d,
+    #         k=3,
+    #         axis=1,
+    #     ),
+    #     torch.vstack([beignet.chebint(c, k=3) for c in c2d]),
+    # )
diff --git a/tests/beignet/test__integrate_laguerre_polynomial.py b/tests/beignet/test__integrate_laguerre_polynomial.py
new file mode 100644
index 0000000000..4d4ea45d7d
--- /dev/null
+++ b/tests/beignet/test__integrate_laguerre_polynomial.py
@@ -0,0 +1,245 @@
+# import beignet
+# import pytest
+# import torch
+#
+#
+# def test_integrate_laguerre_polynomial():
+#     with pytest.raises(TypeError):
+#         beignet.integrate_laguerre_polynomial(
+#             torch.tensor([0]),
+#             0.5,
+#         )
+#
+#     with pytest.raises(ValueError):
+#         beignet.integrate_laguerre_polynomial(
+#             torch.tensor([0]),
+#             -1,
+#         )
+#
+#     with pytest.raises(ValueError):
+#         beignet.integrate_laguerre_polynomial(
+#             torch.tensor([0]),
+#             1,
+#             torch.tensor([0, 0]),
+#         )
+#
+#     with pytest.raises(ValueError):
+#         beignet.integrate_laguerre_polynomial(
+#             torch.tensor([0]),
+#             lower_bound=[0],
+#         )
+#
+#     with pytest.raises(ValueError):
+#         beignet.integrate_laguerre_polynomial(
+#             torch.tensor([0]),
+#             scale=[0],
+#         )
+#
+#     with pytest.raises(TypeError):
+#         beignet.integrate_laguerre_polynomial(
+#             torch.tensor([0]),
+#             axis=0.5,
+#         )
+#
+#     for i in range(2, 5):
+#         torch.testing.assert_close(
+#             beignet.trim_laguerre_polynomial_coefficients(
+#                 beignet.integrate_laguerre_polynomial(
+#                     torch.tensor([0.0]),
+#                     order=i,
+#                     k=([0.0] * (i - 2) + [1.0]),
+#                 ),
+#                 tol=0.000001,
+#             ),
+#             torch.tensor([1.0, -1.0]),
+#         )
+#
+#     for i in range(5):
+#         torch.testing.assert_close(
+#             beignet.trim_laguerre_polynomial_coefficients(
+#                 beignet.laguerre_polynomial_to_polynomial(
+#                     beignet.integrate_laguerre_polynomial(
+#                         beignet.polynomial_to_laguerre_polynomial(
+#                             torch.tensor([0.0] * i + [1.0]),
+#                         ),
+#                         order=1,
+#                         k=[i],
+#                     ),
+#                 ),
+#                 tol=0.000001,
+#             ),
+#             beignet.trim_laguerre_polynomial_coefficients(
+#                 torch.tensor([i] + [0.0] * i + [1.0 / (i + 1.0)]),
+#                 tol=0.000001,
+#             ),
+#         )
+#
+#     for i in range(5):
+#         torch.testing.assert_close(
+#             beignet.evaluate_laguerre_polynomial(
+#                 torch.tensor([-1.0]),
+#                 beignet.integrate_laguerre_polynomial(
+#                     beignet.polynomial_to_laguerre_polynomial(
+#                         torch.tensor([0.0] * i + [1.0]),
+#                     ),
+#                     order=1,
+#                     k=[i],
+#                     lower_bound=-1,
+#                 ),
+#             ),
+#             torch.tensor([i], dtype=torch.get_default_dtype()),
+#         )
+#
+#     for i in range(5):
+#         torch.testing.assert_close(
+#             beignet.trim_laguerre_polynomial_coefficients(
+#                 beignet.laguerre_polynomial_to_polynomial(
+#                     beignet.integrate_laguerre_polynomial(
+#                         beignet.polynomial_to_laguerre_polynomial(
+#                             torch.tensor([0.0] * i + [1.0]),
+#                         ),
+#                         order=1,
+#                         k=[i],
+#                         scale=2,
+#                     ),
+#                 ),
+#                 tol=0.000001,
+#             ),
+#             beignet.trim_laguerre_polynomial_coefficients(
+#                 torch.tensor([i] + [0.0] * i + [2.0 / (i + 1)]),
+#                 tol=0.000001,
+#             ),
+#         )
+#
+#     for i in range(5):
+#         for j in range(2, 5):
+#             target = torch.tensor([0.0] * i + [1.0])[:]
+#
+#             for _ in range(j):
+#                 target = beignet.integrate_laguerre_polynomial(
+#                     target,
+#                     order=1,
+#                 )
+#
+#             torch.testing.assert_close(
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     beignet.integrate_laguerre_polynomial(
+#                         torch.tensor([0.0] * i + [1.0]),
+#                         order=j,
+#                     ),
+#                     tol=0.000001,
+#                 ),
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     target,
+#                     tol=0.000001,
+#                 ),
+#             )
+#
+#     for i in range(5):
+#         for j in range(2, 5):
+#             target = torch.tensor([0.0] * i + [1.0])[:]
+#
+#             for k in range(j):
+#                 target = beignet.integrate_laguerre_polynomial(
+#                     target,
+#                     order=1,
+#                     k=[k],
+#                 )
+#
+#             torch.testing.assert_close(
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     beignet.integrate_laguerre_polynomial(
+#                         torch.tensor([0.0] * i + [1.0]),
+#                         order=j,
+#                         k=list(range(j)),
+#                     ),
+#                     tol=0.000001,
+#                 ),
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     target,
+#                     tol=0.000001,
+#                 ),
+#             )
+#
+#     for i in range(5):
+#         for j in range(2, 5):
+#             target = torch.tensor([0.0] * i + [1.0])[:]
+#
+#             for k in range(j):
+#                 target = beignet.integrate_laguerre_polynomial(
+#                     target,
+#                     order=1,
+#                     k=[k],
+#                     lower_bound=-1,
+#                 )
+#
+#             torch.testing.assert_close(
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     beignet.integrate_laguerre_polynomial(
+#                         torch.tensor([0.0] * i + [1.0]),
+#                         order=j,
+#                         k=list(range(j)),
+#                         lower_bound=-1,
+#                     ),
+#                     tol=0.000001,
+#                 ),
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     target,
+#                     tol=0.000001,
+#                 ),
+#             )
+#
+#     for i in range(5):
+#         for j in range(2, 5):
+#             target = torch.tensor([0.0] * i + [1.0])[:]
+#
+#             for k in range(j):
+#                 target = beignet.integrate_laguerre_polynomial(
+#                     target,
+#                     order=1,
+#                     k=[k],
+#                     scale=2,
+#                 )
+#
+#             torch.testing.assert_close(
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     beignet.integrate_laguerre_polynomial(
+#                         torch.tensor([0.0] * i + [1.0]),
+#                         order=j,
+#                         k=list(range(j)),
+#                         scale=2,
+#                     ),
+#                     tol=0.000001,
+#                 ),
+#                 beignet.trim_laguerre_polynomial_coefficients(
+#                     target,
+#                     tol=0.000001,
+#                 ),
+#             )
+#
+#     c2d = torch.rand(3, 4)
+#
+#     torch.testing.assert_close(
+#         beignet.integrate_laguerre_polynomial(
+#             c2d,
+#             axis=0,
+#         ),
+#         torch.vstack([beignet.integrate_laguerre_polynomial(c) for c in c2d.T]).T,
+#     )
+#
+#     torch.testing.assert_close(
+#         beignet.integrate_laguerre_polynomial(
+#             c2d,
+#             axis=1,
+#         ),
+#         torch.vstack([beignet.integrate_laguerre_polynomial(c) for c in c2d]),
+#     )
+#
+#     torch.testing.assert_close(
+#         beignet.integrate_laguerre_polynomial(
+#             c2d,
+#             k=3,
+#             axis=1,
+#         ),
+#         torch.vstack([beignet.integrate_laguerre_polynomial(c, k=3) for c in c2d]),
+#     )
diff --git a/tests/beignet/test__integrate_legendre_polynomial.py b/tests/beignet/test__integrate_legendre_polynomial.py
new file mode 100644
index 0000000000..42bf104ea3
--- /dev/null
+++ b/tests/beignet/test__integrate_legendre_polynomial.py
@@ -0,0 +1,259 @@
+import beignet
+import pytest
+import torch
+
+
+def test_integrate_legendre_polynomial():
+    with pytest.raises(TypeError):
+        beignet.integrate_legendre_polynomial(
+            torch.tensor([0]),
+            0.5,
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_legendre_polynomial(
+            torch.tensor([0]),
+            -1,
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_legendre_polynomial(
+            torch.tensor([0]),
+            1,
+            torch.tensor([0, 0]),
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_legendre_polynomial(
+            torch.tensor([0]),
+            lower_bound=[0],
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_legendre_polynomial(
+            torch.tensor([0]),
+            scale=[0],
+        )
+
+    with pytest.raises(TypeError):
+        beignet.integrate_legendre_polynomial(
+            torch.tensor([0]),
+            axis=0.5,
+        )
+
+    for i in range(2, 5):
+        output = beignet.integrate_legendre_polynomial(
+            torch.tensor([0.0]),
+            order=i,
+            k=[0.0] * (i - 2) + [1.0],
+        )
+        torch.testing.assert_close(
+            beignet.trim_legendre_polynomial_coefficients(
+                output,
+                tol=0.000001,
+            ),
+            torch.tensor([0.0, 1.0]),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_legendre_polynomial_coefficients(
+                beignet.legendre_polynomial_to_polynomial(
+                    beignet.integrate_legendre_polynomial(
+                        beignet.polynomial_to_legendre_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                        ),
+                        order=1,
+                        k=[i],
+                    )
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_legendre_polynomial_coefficients(
+                torch.tensor([i] + [0.0] * i + [1 / (i + 1)]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.evaluate_legendre_polynomial(
+                torch.tensor([-1]),
+                beignet.integrate_legendre_polynomial(
+                    beignet.polynomial_to_legendre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                    ),
+                    order=1,
+                    k=[i],
+                    lower_bound=-1,
+                ),
+            ),
+            torch.tensor([i], dtype=torch.get_default_dtype()),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_legendre_polynomial_coefficients(
+                beignet.legendre_polynomial_to_polynomial(
+                    beignet.integrate_legendre_polynomial(
+                        beignet.polynomial_to_legendre_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                        ),
+                        order=1,
+                        k=[i],
+                        scale=2,
+                    )
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_legendre_polynomial_coefficients(
+                torch.tensor([i] + [0.0] * i + [2 / (i + 1)]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for _ in range(j):
+                target = beignet.integrate_legendre_polynomial(
+                    target,
+                    order=1,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.integrate_legendre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_legendre_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for k in range(j):
+                target = beignet.integrate_legendre_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.integrate_legendre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                        k=list(range(j)),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_legendre_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for k in range(j):
+                target = beignet.integrate_legendre_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                    lower_bound=-1,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.integrate_legendre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                        k=list(range(j)),
+                        lower_bound=-1,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_legendre_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for k in range(j):
+                target = beignet.integrate_legendre_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                    scale=2,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.integrate_legendre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                        k=list(range(j)),
+                        scale=2,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_legendre_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    c2d = torch.rand(3, 4)
+
+    torch.testing.assert_close(
+        beignet.integrate_legendre_polynomial(c2d, axis=0),
+        torch.vstack([beignet.integrate_legendre_polynomial(c) for c in c2d.T]).T,
+    )
+
+    target = [beignet.integrate_legendre_polynomial(c) for c in c2d]
+
+    target = torch.vstack(target)
+
+    torch.testing.assert_close(
+        beignet.integrate_legendre_polynomial(
+            c2d,
+            axis=1,
+        ),
+        target,
+    )
+
+    target = [beignet.integrate_legendre_polynomial(c, k=3) for c in c2d]
+
+    target = torch.vstack(target)
+
+    torch.testing.assert_close(
+        beignet.integrate_legendre_polynomial(
+            c2d,
+            k=3,
+            axis=1,
+        ),
+        target,
+    )
+
+    torch.testing.assert_close(
+        beignet.integrate_legendre_polynomial(
+            torch.tensor([1, 2, 3]),
+            order=0,
+        ),
+        torch.tensor([1, 2, 3]),
+    )
diff --git a/tests/beignet/test__integrate_physicists_hermite_polynomial.py b/tests/beignet/test__integrate_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..b8d981054b
--- /dev/null
+++ b/tests/beignet/test__integrate_physicists_hermite_polynomial.py
@@ -0,0 +1,257 @@
+import beignet
+import pytest
+import torch
+
+
+def test_integrate_physicists_hermite_polynomial():
+    with pytest.raises(TypeError):
+        beignet.integrate_physicists_hermite_polynomial(
+            torch.tensor([0.0]),
+            order=0.5,
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_physicists_hermite_polynomial(
+            torch.tensor([0]),
+            order=-1,
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_physicists_hermite_polynomial(
+            torch.tensor([0]),
+            order=1,
+            k=torch.tensor([0, 0]),
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_physicists_hermite_polynomial(
+            torch.tensor([0]),
+            lower_bound=[0],
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_physicists_hermite_polynomial(
+            torch.tensor([0]),
+            scale=[0],
+        )
+
+    with pytest.raises(TypeError):
+        beignet.integrate_physicists_hermite_polynomial(
+            torch.tensor([0]),
+            axis=0.5,
+        )
+
+    for i in range(2, 5):
+        torch.testing.assert_close(
+            beignet.trim_physicists_hermite_polynomial_coefficients(
+                beignet.integrate_physicists_hermite_polynomial(
+                    torch.tensor([0.0]),
+                    order=i,
+                    k=([0.0] * (i - 2) + [1.0]),
+                ),
+                tol=0.000001,
+            ),
+            torch.tensor([0.0, 0.5]),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_physicists_hermite_polynomial_coefficients(
+                beignet.physicists_hermite_polynomial_to_polynomial(
+                    beignet.integrate_physicists_hermite_polynomial(
+                        beignet.polynomial_to_physicists_hermite_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                        ),
+                        order=1,
+                        k=[i],
+                    )
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_physicists_hermite_polynomial_coefficients(
+                torch.tensor([i] + [0.0] * i + [1.0 / (i + 1)]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.evaluate_physicists_hermite_polynomial(
+                torch.tensor([-1.0]),
+                beignet.integrate_physicists_hermite_polynomial(
+                    beignet.polynomial_to_physicists_hermite_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                    ),
+                    order=1,
+                    k=[i],
+                    lower_bound=-1,
+                ),
+            ),
+            torch.tensor([i], dtype=torch.get_default_dtype()),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_physicists_hermite_polynomial_coefficients(
+                beignet.physicists_hermite_polynomial_to_polynomial(
+                    beignet.integrate_physicists_hermite_polynomial(
+                        beignet.polynomial_to_physicists_hermite_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                        ),
+                        order=1,
+                        k=[i],
+                        scale=2,
+                    ),
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_physicists_hermite_polynomial_coefficients(
+                torch.tensor([i] + [0.0] * i + [2.0 / (i + 1.0)]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for _ in range(j):
+                target = beignet.integrate_physicists_hermite_polynomial(
+                    target,
+                    order=1,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    beignet.integrate_physicists_hermite_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            pol = torch.tensor([0.0] * i + [1.0])
+
+            target = pol[:]
+
+            for k in range(j):
+                target = beignet.integrate_physicists_hermite_polynomial(
+                    target, order=1, k=[k]
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    beignet.integrate_physicists_hermite_polynomial(
+                        pol,
+                        order=j,
+                        k=list(range(j)),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            pol = torch.tensor([0.0] * i + [1.0])
+            target = pol[:]
+            for k in range(j):
+                target = beignet.integrate_physicists_hermite_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                    lower_bound=-1,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    beignet.integrate_physicists_hermite_polynomial(
+                        pol,
+                        order=j,
+                        k=list(range(j)),
+                        lower_bound=-1,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            pol = torch.tensor([0.0] * i + [1.0])
+            target = pol[:]
+            for k in range(j):
+                target = beignet.integrate_physicists_hermite_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                    scale=2,
+                )
+
+            # torch.testing.assert_close(
+            #     beignet.hermtrim(
+            #         beignet.hermint(
+            #             pol,
+            #             order=j,
+            #             k=list(range(j)),
+            #             scale=2,
+            #         ),
+            #         tol=0.000001,
+            #     ),
+            #     beignet.hermtrim(
+            #         target,
+            #         tol=0.000001,
+            #     ),
+            # )
+
+    c2d = torch.rand(3, 4)
+
+    target = torch.vstack(
+        [beignet.integrate_physicists_hermite_polynomial(c) for c in c2d.T]
+    ).T
+
+    torch.testing.assert_close(
+        beignet.integrate_physicists_hermite_polynomial(
+            c2d,
+            axis=0,
+        ),
+        target,
+    )
+
+    target = torch.vstack(
+        [beignet.integrate_physicists_hermite_polynomial(c) for c in c2d]
+    )
+
+    torch.testing.assert_close(
+        beignet.integrate_physicists_hermite_polynomial(
+            c2d,
+            axis=1,
+        ),
+        target,
+    )
+
+    target = torch.vstack(
+        [beignet.integrate_physicists_hermite_polynomial(c, k=3) for c in c2d]
+    )
+
+    torch.testing.assert_close(
+        beignet.integrate_physicists_hermite_polynomial(
+            c2d,
+            k=3,
+            axis=1,
+        ),
+        target,
+    )
diff --git a/tests/beignet/test__integrate_polynomial.py b/tests/beignet/test__integrate_polynomial.py
new file mode 100644
index 0000000000..bb4ad0c81a
--- /dev/null
+++ b/tests/beignet/test__integrate_polynomial.py
@@ -0,0 +1,222 @@
+import beignet
+import pytest
+import torch
+
+
+def test_integrate_polynomial():
+    with pytest.raises(TypeError):
+        beignet.integrate_polynomial(
+            torch.tensor([0.0]),
+            order=0.5,
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_polynomial(
+            torch.tensor([0.0]),
+            order=-1,
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_polynomial(
+            torch.tensor([0.0]),
+            order=1,
+            k=[0, 0],
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_polynomial(
+            torch.tensor([0.0]),
+            lower_bound=[0],
+        )
+
+    with pytest.raises(ValueError):
+        beignet.integrate_polynomial(
+            torch.tensor([0.0]),
+            scale=[0],
+        )
+
+    with pytest.raises(TypeError):
+        beignet.integrate_polynomial(
+            torch.tensor([0.0]),
+            axis=0.5,
+        )
+
+    for i in range(2, 5):
+        torch.testing.assert_close(
+            beignet.trim_polynomial_coefficients(
+                beignet.integrate_polynomial(
+                    torch.tensor([0.0]),
+                    order=i,
+                    k=[0.0] * (i - 2) + [1.0],
+                ),
+            ),
+            torch.tensor([0.0, 1.0]),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_polynomial_coefficients(
+                beignet.integrate_polynomial(
+                    torch.tensor([0.0] * i + [1.0]),
+                    order=1,
+                    k=[i],
+                ),
+            ),
+            beignet.trim_polynomial_coefficients(
+                torch.tensor([i] + [0.0] * i + [1.0 / (i + 1.0)]),
+            ),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.evaluate_polynomial(
+                torch.tensor([-1.0]),
+                beignet.integrate_polynomial(
+                    torch.tensor([0.0] * i + [1.0]),
+                    order=1,
+                    k=[i],
+                    lower_bound=-1,
+                ),
+            ),
+            torch.tensor([i], dtype=torch.get_default_dtype()),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_polynomial_coefficients(
+                beignet.integrate_polynomial(
+                    torch.tensor([0.0] * i + [1.0]),
+                    order=1,
+                    k=[i],
+                    scale=2,
+                ),
+            ),
+            beignet.trim_polynomial_coefficients(
+                torch.tensor([i] + [0.0] * i + [2.0 / (i + 1.0)]),
+            ),
+        )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for _ in range(j):
+                target = beignet.integrate_polynomial(
+                    target,
+                    order=1,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_polynomial_coefficients(
+                    beignet.integrate_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                    ),
+                ),
+                beignet.trim_polynomial_coefficients(
+                    target,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for k in range(j):
+                target = beignet.integrate_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_polynomial_coefficients(
+                    beignet.integrate_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                        k=list(range(j)),
+                    ),
+                ),
+                beignet.trim_polynomial_coefficients(
+                    target,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for k in range(j):
+                target = beignet.integrate_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                    lower_bound=-1,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_polynomial_coefficients(
+                    beignet.integrate_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                        k=list(range(j)),
+                        lower_bound=-1,
+                    ),
+                ),
+                beignet.trim_polynomial_coefficients(
+                    target,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for k in range(j):
+                target = beignet.integrate_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                    scale=2,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_polynomial_coefficients(
+                    beignet.integrate_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                        k=list(range(j)),
+                        scale=2,
+                    ),
+                ),
+                beignet.trim_polynomial_coefficients(
+                    target,
+                ),
+            )
+
+    c2d = torch.rand(3, 6)
+
+    torch.testing.assert_close(
+        beignet.integrate_polynomial(
+            c2d,
+            dim=0,
+        ),
+        torch.vstack([beignet.integrate_polynomial(c) for c in c2d.T]).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.integrate_polynomial(
+            c2d,
+            dim=1,
+        ),
+        torch.vstack([beignet.integrate_polynomial(c) for c in c2d]),
+    )
+
+    torch.testing.assert_close(
+        beignet.integrate_polynomial(
+            c2d,
+            k=3,
+            dim=1,
+        ),
+        torch.vstack([beignet.integrate_polynomial(c, k=3) for c in c2d]),
+    )
diff --git a/tests/beignet/test__integrate_probabilists_hermite_polynomial.py b/tests/beignet/test__integrate_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..67a492ce0d
--- /dev/null
+++ b/tests/beignet/test__integrate_probabilists_hermite_polynomial.py
@@ -0,0 +1,251 @@
+import beignet
+import pytest
+import torch
+
+
+def test_integrate_probabilists_hermite_polynomial():
+    pytest.raises(
+        TypeError,
+        beignet.integrate_probabilists_hermite_polynomial,
+        torch.tensor([0]),
+        0.5,
+    )
+    pytest.raises(
+        ValueError,
+        beignet.integrate_probabilists_hermite_polynomial,
+        torch.tensor([0]),
+        -1,
+    )
+    pytest.raises(
+        ValueError,
+        beignet.integrate_probabilists_hermite_polynomial,
+        torch.tensor([0]),
+        1,
+        [0, 0],
+    )
+    pytest.raises(
+        ValueError,
+        beignet.integrate_probabilists_hermite_polynomial,
+        torch.tensor([0]),
+        lower_bound=[0],
+    )
+    pytest.raises(
+        ValueError,
+        beignet.integrate_probabilists_hermite_polynomial,
+        torch.tensor([0]),
+        scale=[0],
+    )
+    pytest.raises(
+        TypeError,
+        beignet.integrate_probabilists_hermite_polynomial,
+        torch.tensor([0]),
+        axis=0.5,
+    )
+
+    for i in range(2, 5):
+        torch.testing.assert_close(
+            beignet.trim_probabilists_hermite_polynomial_coefficients(
+                beignet.integrate_probabilists_hermite_polynomial(
+                    torch.tensor([0.0]),
+                    order=i,
+                    k=([0.0] * (i - 2) + [1.0]),
+                ),
+                tol=0.000001,
+            ),
+            torch.tensor([0.0, 1.0]),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_probabilists_hermite_polynomial_coefficients(
+                beignet.probabilists_hermite_polynomial_to_polynomial(
+                    beignet.integrate_probabilists_hermite_polynomial(
+                        beignet.polynomial_to_probabilists_hermite_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                        ),
+                        order=1,
+                        k=[i],
+                    ),
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_probabilists_hermite_polynomial_coefficients(
+                torch.tensor([i] + [0.0] * i + [1.0 / (i + 1.0)]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.evaluate_probabilists_hermite_polynomial(
+                torch.tensor([-1]),
+                beignet.integrate_probabilists_hermite_polynomial(
+                    beignet.polynomial_to_probabilists_hermite_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                    ),
+                    order=1,
+                    k=[i],
+                    lower_bound=-1,
+                ),
+            ),
+            torch.tensor([i], dtype=torch.get_default_dtype()),
+        )
+
+    for i in range(5):
+        torch.testing.assert_close(
+            beignet.trim_probabilists_hermite_polynomial_coefficients(
+                beignet.probabilists_hermite_polynomial_to_polynomial(
+                    beignet.integrate_probabilists_hermite_polynomial(
+                        beignet.polynomial_to_probabilists_hermite_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                        ),
+                        order=1,
+                        k=[i],
+                        scale=2,
+                    ),
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_probabilists_hermite_polynomial_coefficients(
+                torch.tensor([i] + [0.0] * i + [2.0 / (i + 1.0)]),
+                tol=0.000001,
+            ),
+        )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for _ in range(j):
+                target = beignet.integrate_probabilists_hermite_polynomial(
+                    target,
+                    order=1,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.integrate_probabilists_hermite_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+            for k in range(j):
+                target = beignet.integrate_probabilists_hermite_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.integrate_probabilists_hermite_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                        k=list(range(j)),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for k in range(j):
+                target = beignet.integrate_probabilists_hermite_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                    lower_bound=-1,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.integrate_probabilists_hermite_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                        k=list(range(j)),
+                        lower_bound=-1,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    for i in range(5):
+        for j in range(2, 5):
+            target = torch.tensor([0.0] * i + [1.0])[:]
+
+            for k in range(j):
+                target = beignet.integrate_probabilists_hermite_polynomial(
+                    target,
+                    order=1,
+                    k=[k],
+                    scale=2,
+                )
+
+            torch.testing.assert_close(
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.integrate_probabilists_hermite_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        order=j,
+                        k=list(range(j)),
+                        scale=2,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
+
+    c2d = torch.rand(3, 4)
+
+    torch.testing.assert_close(
+        beignet.integrate_probabilists_hermite_polynomial(
+            c2d,
+            axis=0,
+        ),
+        torch.vstack(
+            [beignet.integrate_probabilists_hermite_polynomial(c) for c in c2d.T]
+        ).T,
+    )
+
+    torch.testing.assert_close(
+        beignet.integrate_probabilists_hermite_polynomial(
+            c2d,
+            axis=1,
+        ),
+        torch.vstack(
+            [beignet.integrate_probabilists_hermite_polynomial(c) for c in c2d]
+        ),
+    )
+
+    torch.testing.assert_close(
+        beignet.integrate_probabilists_hermite_polynomial(
+            c2d,
+            k=3,
+            axis=1,
+        ),
+        torch.vstack(
+            [beignet.integrate_probabilists_hermite_polynomial(c, k=3) for c in c2d]
+        ),
+    )
diff --git a/tests/beignet/test__laguerre_polynomial_companion.py b/tests/beignet/test__laguerre_polynomial_companion.py
new file mode 100644
index 0000000000..97573f0755
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_companion.py
@@ -0,0 +1,28 @@
+import beignet
+import pytest
+import torch
+
+
+def test_laguerre_polynomial_companion():
+    with pytest.raises(ValueError):
+        beignet.laguerre_polynomial_companion(
+            torch.tensor([]),
+        )
+
+    with pytest.raises(ValueError):
+        beignet.laguerre_polynomial_companion(
+            torch.tensor([1.0]),
+        )
+
+    for index in range(1, 5):
+        output = beignet.laguerre_polynomial_companion(
+            torch.tensor([0.0] * index + [1.0]),
+        )
+
+        assert output.shape == (index, index)
+
+    output = beignet.laguerre_polynomial_companion(
+        torch.tensor([1.0, 2.0]),
+    )
+
+    assert output[0, 0] == 1.5
diff --git a/tests/beignet/test__laguerre_polynomial_domain.py b/tests/beignet/test__laguerre_polynomial_domain.py
new file mode 100644
index 0000000000..8ac3bfa56c
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_domain.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_domain():
+    torch.testing.assert_close(
+        beignet.laguerre_polynomial_domain,
+        torch.tensor([0.0, 1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__laguerre_polynomial_from_roots.py b/tests/beignet/test__laguerre_polynomial_from_roots.py
new file mode 100644
index 0000000000..32536b3c3f
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_from_roots.py
@@ -0,0 +1,44 @@
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_from_roots():
+    torch.testing.assert_close(
+        beignet.trim_laguerre_polynomial_coefficients(
+            beignet.laguerre_polynomial_from_roots(
+                torch.tensor([]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([1.0]),
+    )
+
+    # for i in range(1, 5):
+    #     roots = torch.linspace(-math.pi, 0, 2 * i + 1)
+    #
+    #     roots = roots[1::2]
+    #
+    #     roots = torch.cos(roots)
+    #
+    #     output = beignet.lag2poly(
+    #         beignet.lagfromroots(
+    #             roots,
+    #         ),
+    #     )
+    #
+    #     torch.testing.assert_close(
+    #         output,
+    #         torch.tensor([1.0]),
+    #     )
+    #
+    #     output = beignet.lagval(
+    #         roots,
+    #         beignet.lagfromroots(
+    #             roots,
+    #         ),
+    #     )
+    #
+    #     torch.testing.assert_close(
+    #         output,
+    #         torch.tensor([0.0]),
+    #     )
diff --git a/tests/beignet/test__laguerre_polynomial_one.py b/tests/beignet/test__laguerre_polynomial_one.py
new file mode 100644
index 0000000000..48ef608b1b
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_one.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_one():
+    torch.testing.assert_close(
+        beignet.laguerre_polynomial_one,
+        torch.tensor([1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__laguerre_polynomial_power.py b/tests/beignet/test__laguerre_polynomial_power.py
new file mode 100644
index 0000000000..da9c5756d6
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_power.py
@@ -0,0 +1,26 @@
+import functools
+
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_power():
+    for i in range(5):
+        for j in range(5):
+            torch.testing.assert_close(
+                beignet.trim_laguerre_polynomial_coefficients(
+                    beignet.laguerre_polynomial_power(
+                        torch.arange(0.0, i + 1),
+                        j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_laguerre_polynomial_coefficients(
+                    functools.reduce(
+                        beignet.multiply_laguerre_polynomial,
+                        [torch.arange(0.0, i + 1)] * j,
+                        torch.tensor([1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__laguerre_polynomial_roots.py b/tests/beignet/test__laguerre_polynomial_roots.py
new file mode 100644
index 0000000000..af062e20dc
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_roots.py
@@ -0,0 +1,34 @@
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_roots():
+    torch.testing.assert_close(
+        beignet.laguerre_polynomial_roots(
+            torch.tensor([1.0]),
+        ),
+        torch.tensor([]),
+    )
+
+    torch.testing.assert_close(
+        beignet.laguerre_polynomial_roots(
+            torch.tensor([0.0, 1.0]),
+        ),
+        torch.tensor([1.0]),
+    )
+
+    for index in range(2, 5):
+        torch.testing.assert_close(
+            beignet.trim_laguerre_polynomial_coefficients(
+                beignet.laguerre_polynomial_roots(
+                    beignet.laguerre_polynomial_from_roots(
+                        torch.linspace(0, 3, index),
+                    ),
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_laguerre_polynomial_coefficients(
+                torch.linspace(0, 3, index),
+                tol=0.000001,
+            ),
+        )
diff --git a/tests/beignet/test__laguerre_polynomial_to_polynomial.py b/tests/beignet/test__laguerre_polynomial_to_polynomial.py
new file mode 100644
index 0000000000..8824ee585d
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_to_polynomial.py
@@ -0,0 +1,22 @@
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_to_polynomial():
+    coefficients = [
+        torch.tensor([1.0]) / 1,
+        torch.tensor([1.0, -1]) / 1,
+        torch.tensor([2.0, -4, 1]) / 2,
+        torch.tensor([6.0, -18, 9, -1]) / 6,
+        torch.tensor([24.0, -96, 72, -16, 1]) / 24,
+        torch.tensor([120.0, -600, 600, -200, 25, -1]) / 120,
+        torch.tensor([720.0, -4320, 5400, -2400, 450, -36, 1]) / 720,
+    ]
+
+    for index in range(7):
+        torch.testing.assert_close(
+            beignet.laguerre_polynomial_to_polynomial(
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+            coefficients[index],
+        )
diff --git a/tests/beignet/test__laguerre_polynomial_vandermonde.py b/tests/beignet/test__laguerre_polynomial_vandermonde.py
new file mode 100644
index 0000000000..da9b4d0c0c
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_vandermonde.py
@@ -0,0 +1,34 @@
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_vandermonde():
+    x = torch.arange(3)
+
+    v = beignet.laguerre_polynomial_vandermonde(x, 3)
+
+    assert v.shape == (3, 4)
+
+    for i in range(4):
+        torch.testing.assert_close(
+            v[..., i],
+            beignet.evaluate_laguerre_polynomial(
+                x,
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+        )
+
+    x = torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])
+
+    v = beignet.laguerre_polynomial_vandermonde(x, 3)
+
+    assert v.shape == (3, 2, 4)
+
+    for i in range(4):
+        torch.testing.assert_close(
+            v[..., i],
+            beignet.evaluate_laguerre_polynomial(
+                x,
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+        )
diff --git a/tests/beignet/test__laguerre_polynomial_vandermonde_2d.py b/tests/beignet/test__laguerre_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..ed2fdcb699
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_vandermonde_2d.py
@@ -0,0 +1,27 @@
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_vandermonde_2d():
+    a, b, c = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3)
+
+    output = beignet.laguerre_polynomial_vandermonde_2d(
+        a,
+        b,
+        torch.tensor([1, 2]),
+    )
+
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_laguerre_polynomial_2d(a, b, coefficients),
+    )
+
+    output = beignet.laguerre_polynomial_vandermonde_2d(
+        a,
+        b,
+        torch.tensor([1, 2]),
+    )
+
+    assert output.shape == (5, 6)
diff --git a/tests/beignet/test__laguerre_polynomial_vandermonde_3d.py b/tests/beignet/test__laguerre_polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..1d86e86b33
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_vandermonde_3d.py
@@ -0,0 +1,33 @@
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_vandermonde_3d():
+    a, b, c = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3, 4)
+
+    output = beignet.laguerre_polynomial_vandermonde_3d(
+        a,
+        b,
+        c,
+        degree=torch.tensor([1, 2, 3]),
+    )
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_laguerre_polynomial_3d(
+            a,
+            b,
+            c,
+            coefficients,
+        ),
+    )
+
+    output = beignet.laguerre_polynomial_vandermonde_3d(
+        a,
+        b,
+        c,
+        degree=torch.tensor([1, 2, 3]),
+    )
+
+    assert output.shape == (5, 24)
diff --git a/tests/beignet/test__laguerre_polynomial_weight.py b/tests/beignet/test__laguerre_polynomial_weight.py
new file mode 100644
index 0000000000..7d7bca8917
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_weight.py
@@ -0,0 +1,11 @@
+# import beignet
+# import torch
+#
+#
+# def test_laguerre_polynomial_weight():
+#     torch.testing.assert_close(
+#         beignet.laguerre_polynomial_weight(
+#             torch.linspace(0, 10, 11),
+#         ),
+#         torch.exp(-torch.linspace(0, 10, 11)),
+#     )
diff --git a/tests/beignet/test__laguerre_polynomial_x.py b/tests/beignet/test__laguerre_polynomial_x.py
new file mode 100644
index 0000000000..ef4871b109
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_x.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_x():
+    torch.testing.assert_close(
+        beignet.laguerre_polynomial_x,
+        torch.tensor([1.0, -1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__laguerre_polynomial_zero.py b/tests/beignet/test__laguerre_polynomial_zero.py
new file mode 100644
index 0000000000..d3abaf610c
--- /dev/null
+++ b/tests/beignet/test__laguerre_polynomial_zero.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_laguerre_polynomial_zero():
+    torch.testing.assert_close(
+        beignet.laguerre_polynomial_zero,
+        torch.tensor([0.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__legendre_polynomial_companion.py b/tests/beignet/test__legendre_polynomial_companion.py
new file mode 100644
index 0000000000..bee23fed33
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_companion.py
@@ -0,0 +1,20 @@
+import beignet
+import pytest
+import torch
+
+
+def test_legendre_polynomial_companion():
+    with pytest.raises(ValueError):
+        beignet.legendre_polynomial_companion(torch.tensor([]))
+
+    with pytest.raises(ValueError):
+        beignet.legendre_polynomial_companion(torch.tensor([1]))
+
+    for index in range(1, 5):
+        output = beignet.legendre_polynomial_companion(
+            torch.tensor([0.0] * index + [1.0]),
+        )
+
+        assert output.shape == (index, index)
+
+    assert beignet.legendre_polynomial_companion(torch.tensor([1, 2]))[0, 0] == -0.5
diff --git a/tests/beignet/test__legendre_polynomial_domain.py b/tests/beignet/test__legendre_polynomial_domain.py
new file mode 100644
index 0000000000..e4983e95c2
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_domain.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_legendre_polynomial_domain():
+    torch.testing.assert_close(
+        beignet.legendre_polynomial_domain,
+        torch.tensor([-1.0, 1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__legendre_polynomial_from_roots.py b/tests/beignet/test__legendre_polynomial_from_roots.py
new file mode 100644
index 0000000000..915f2ac63d
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_from_roots.py
@@ -0,0 +1,52 @@
+import math
+
+import beignet
+import torch
+
+
+def test_legendre_polynomial_from_roots():
+    torch.testing.assert_close(
+        beignet.trim_legendre_polynomial_coefficients(
+            beignet.legendre_polynomial_from_roots(
+                torch.tensor([]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([1.0]),
+    )
+
+    for index in range(1, 5):
+        input = torch.linspace(-math.pi, 0, 2 * index + 1)[1::2]
+
+        output = beignet.legendre_polynomial_from_roots(
+            torch.cos(
+                input,
+            ),
+        )
+
+        assert output.shape[-1] == index + 1
+
+        # torch.testing.assert_close(
+        #     beignet.leg2poly(
+        #         beignet.legfromroots(
+        #             torch.cos(
+        #                 input,
+        #             ),
+        #         )
+        #     )[-1],
+        #     torch.tensor([1.0]),
+        # )
+
+        # torch.testing.assert_close(
+        #     beignet.legval(
+        #         torch.cos(
+        #             input,
+        #         ),
+        #         beignet.legfromroots(
+        #             torch.cos(
+        #                 input,
+        #             ),
+        #         ),
+        #     ),
+        #     torch.tensor([0.0]),
+        # )
diff --git a/tests/beignet/test__legendre_polynomial_one.py b/tests/beignet/test__legendre_polynomial_one.py
new file mode 100644
index 0000000000..9f153ebd61
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_one.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_legendre_polynomial_one():
+    torch.testing.assert_close(
+        beignet.legendre_polynomial_one,
+        torch.tensor([1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__legendre_polynomial_power.py b/tests/beignet/test__legendre_polynomial_power.py
new file mode 100644
index 0000000000..d1f3c05706
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_power.py
@@ -0,0 +1,26 @@
+import functools
+
+import beignet
+import torch
+
+
+def test_legendre_polynomial_power():
+    for i in range(5):
+        for j in range(5):
+            torch.testing.assert_close(
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.legendre_polynomial_power(
+                        torch.arange(0.0, i + 1),
+                        j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_legendre_polynomial_coefficients(
+                    functools.reduce(
+                        beignet.multiply_legendre_polynomial,
+                        [torch.arange(0.0, i + 1)] * j,
+                        torch.tensor([1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__legendre_polynomial_roots.py b/tests/beignet/test__legendre_polynomial_roots.py
new file mode 100644
index 0000000000..94fc165601
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_roots.py
@@ -0,0 +1,32 @@
+import beignet
+import torch
+
+
+def test_legendre_polynomial_roots():
+    torch.testing.assert_close(
+        beignet.legendre_polynomial_roots(
+            torch.tensor([1.0]),
+        ),
+        torch.tensor([]),
+    )
+
+    torch.testing.assert_close(
+        beignet.legendre_polynomial_roots(torch.tensor([1.0, 2.0])),
+        torch.tensor([-0.5]),
+    )
+
+    for index in range(2, 5):
+        torch.testing.assert_close(
+            beignet.trim_legendre_polynomial_coefficients(
+                beignet.legendre_polynomial_roots(
+                    beignet.legendre_polynomial_from_roots(
+                        torch.linspace(-1, 1, index),
+                    ),
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_legendre_polynomial_coefficients(
+                torch.linspace(-1, 1, index),
+                tol=0.000001,
+            ),
+        )
diff --git a/tests/beignet/test__legendre_polynomial_to_polynomial.py b/tests/beignet/test__legendre_polynomial_to_polynomial.py
new file mode 100644
index 0000000000..8b429ad2d8
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_to_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_legendre_polynomial_to_polynomial():
+    coefficients = [
+        torch.tensor([1.0]),
+        torch.tensor([0.0, 1.0]),
+        torch.tensor([-1.0, 0.0, 3.0]) / 2.0,
+        torch.tensor([0.0, -3.0, 0.0, 5.0]) / 2.0,
+        torch.tensor([3.0, 0.0, -30, 0, 35]) / 8,
+        torch.tensor([0.0, 15.0, 0, -70, 0, 63]) / 8,
+        torch.tensor([-5.0, 0.0, 105, 0, -315, 0, 231]) / 16,
+        torch.tensor([0.0, -35.0, 0, 315, 0, -693, 0, 429]) / 16,
+        torch.tensor([35.0, 0.0, -1260, 0, 6930, 0, -12012, 0, 6435]) / 128,
+        torch.tensor([0.0, 315.0, 0, -4620, 0, 18018, 0, -25740, 0, 12155]) / 128,
+    ]
+
+    for index in range(10):
+        torch.testing.assert_close(
+            beignet.legendre_polynomial_to_polynomial(
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+            coefficients[index],
+        )
diff --git a/tests/beignet/test__legendre_polynomial_vandermonde.py b/tests/beignet/test__legendre_polynomial_vandermonde.py
new file mode 100644
index 0000000000..6d940528a3
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_vandermonde.py
@@ -0,0 +1,47 @@
+import beignet
+import pytest
+import torch
+
+
+def test_legendre_polynomial_vandermonde():
+    x = torch.arange(3)
+
+    v = beignet.legendre_polynomial_vandermonde(
+        x,
+        degree=3,
+    )
+
+    assert v.shape == (3, 4)
+
+    for index in range(4):
+        torch.testing.assert_close(
+            v[..., index],
+            beignet.evaluate_legendre_polynomial(
+                x,
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+        )
+
+    x = torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])
+
+    v = beignet.legendre_polynomial_vandermonde(
+        x,
+        degree=3,
+    )
+
+    assert v.shape == (3, 2, 4)
+
+    for index in range(4):
+        torch.testing.assert_close(
+            v[..., index],
+            beignet.evaluate_legendre_polynomial(
+                x,
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+        )
+
+    with pytest.raises(ValueError):
+        beignet.legendre_polynomial_vandermonde(
+            torch.tensor([1, 2, 3]),
+            -1,
+        )
diff --git a/tests/beignet/test__legendre_polynomial_vandermonde_2d.py b/tests/beignet/test__legendre_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..89cb4d8379
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_vandermonde_2d.py
@@ -0,0 +1,30 @@
+import beignet
+import torch
+
+
+def test_legendre_polynomial_vandermonde_2d():
+    a, b, x3 = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3)
+
+    output = beignet.legendre_polynomial_vandermonde_2d(
+        a,
+        b,
+        degree=torch.tensor([1, 2]),
+    )
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_legendre_polynomial_2d(
+            a,
+            b,
+            coefficients,
+        ),
+    )
+
+    output = beignet.legendre_polynomial_vandermonde_2d(
+        a,
+        b,
+        degree=torch.tensor([1, 2]),
+    )
+
+    assert output.shape == (5, 6)
diff --git a/tests/beignet/test__legendre_polynomial_weight.py b/tests/beignet/test__legendre_polynomial_weight.py
new file mode 100644
index 0000000000..06c5dd9dc1
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_weight.py
@@ -0,0 +1,11 @@
+# import beignet
+# import torch
+#
+#
+# def test_legendre_polynomial_weight():
+#     torch.testing.assert_close(
+#         beignet.legendre_polynomial_weight(
+#             torch.linspace(-1, 1, 11),
+#         ),
+#         torch.tensor([1.0]),
+#     )
diff --git a/tests/beignet/test__legendre_polynomial_x.py b/tests/beignet/test__legendre_polynomial_x.py
new file mode 100644
index 0000000000..62f5dbb548
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_x.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_legendre_polynomial_x():
+    torch.testing.assert_close(
+        beignet.legendre_polynomial_x,
+        torch.tensor([0.0, 1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__legendre_polynomial_zero.py b/tests/beignet/test__legendre_polynomial_zero.py
new file mode 100644
index 0000000000..73df136f33
--- /dev/null
+++ b/tests/beignet/test__legendre_polynomial_zero.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_legendre_polynomial_zero():
+    torch.testing.assert_close(
+        beignet.legendre_polynomial_zero,
+        torch.tensor([0.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__linear_chebyshev_polynomial.py b/tests/beignet/test__linear_chebyshev_polynomial.py
new file mode 100644
index 0000000000..290e8c0cd9
--- /dev/null
+++ b/tests/beignet/test__linear_chebyshev_polynomial.py
@@ -0,0 +1,9 @@
+import beignet
+import torch
+
+
+def test_linear_chebyshev_polynomial():
+    torch.testing.assert_close(
+        beignet.linear_chebyshev_polynomial(3.0, 4.0),
+        torch.tensor([3.0, 4.0]),
+    )
diff --git a/tests/beignet/test__linear_legendre_polynomial.py b/tests/beignet/test__linear_legendre_polynomial.py
new file mode 100644
index 0000000000..052e097c97
--- /dev/null
+++ b/tests/beignet/test__linear_legendre_polynomial.py
@@ -0,0 +1,17 @@
+import beignet
+import torch
+
+
+def test_linear_legendre_polynomial():
+    torch.testing.assert_close(
+        beignet.linear_legendre_polynomial(3.0, 4.0),
+        torch.tensor([3.0, 4.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_legendre_polynomial_coefficients(
+            beignet.linear_legendre_polynomial(3.0, 0.0),
+            tol=0.000001,
+        ),
+        torch.tensor([3.0]),
+    )
diff --git a/tests/beignet/test__linear_physicists_hermite_polynomial.py b/tests/beignet/test__linear_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..0a1a1c5f05
--- /dev/null
+++ b/tests/beignet/test__linear_physicists_hermite_polynomial.py
@@ -0,0 +1,9 @@
+import beignet
+import torch
+
+
+def test_linear_physicists_hermite_polynomial():
+    torch.testing.assert_close(
+        beignet.linear_physicists_hermite_polynomial(3, 4),
+        torch.tensor([3.0, 2.0]),
+    )
diff --git a/tests/beignet/test__linear_polynomial.py b/tests/beignet/test__linear_polynomial.py
new file mode 100644
index 0000000000..45d6580644
--- /dev/null
+++ b/tests/beignet/test__linear_polynomial.py
@@ -0,0 +1,14 @@
+import beignet
+import torch
+
+
+def test_linear_polynomial():
+    torch.testing.assert_close(
+        beignet.linear_polynomial(3.0, 4.0),
+        torch.tensor([3.0, 4.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.linear_polynomial(3.0, 0.0),
+        torch.tensor([3.0, 0.0]),
+    )
diff --git a/tests/beignet/test__linear_probabilists_hermite_polynomial.py b/tests/beignet/test__linear_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..fc03535123
--- /dev/null
+++ b/tests/beignet/test__linear_probabilists_hermite_polynomial.py
@@ -0,0 +1,9 @@
+import beignet
+import torch
+
+
+def test_linear_probabilists_hermite_polynomial():
+    torch.testing.assert_close(
+        beignet.linear_probabilists_hermite_polynomial(3.0, 4.0),
+        torch.tensor([3.0, 4.0]),
+    )
diff --git a/tests/beignet/test__multiply_chebyshev_polynomial.py b/tests/beignet/test__multiply_chebyshev_polynomial.py
new file mode 100644
index 0000000000..23b65b0d63
--- /dev/null
+++ b/tests/beignet/test__multiply_chebyshev_polynomial.py
@@ -0,0 +1,28 @@
+import beignet
+import torch
+
+
+def test_multiply_chebyshev_polynomial():
+    for j in range(5):
+        for k in range(5):
+            target = torch.zeros(j + k + 1)
+
+            target[abs(j + k)] = target[abs(j + k)] + 0.5
+            target[abs(j - k)] = target[abs(j - k)] + 0.5
+
+            input = torch.tensor([0.0] * j + [1.0])
+            other = torch.tensor([0.0] * k + [1.0])
+
+            torch.testing.assert_close(
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    beignet.multiply_chebyshev_polynomial(
+                        input,
+                        other,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__multiply_chebyshev_polynomial_by_x.py b/tests/beignet/test__multiply_chebyshev_polynomial_by_x.py
new file mode 100644
index 0000000000..775788fc01
--- /dev/null
+++ b/tests/beignet/test__multiply_chebyshev_polynomial_by_x.py
@@ -0,0 +1,35 @@
+import beignet
+import torch
+
+
+def test_multiply_chebyshev_polynomial_by_x():
+    torch.testing.assert_close(
+        beignet.trim_chebyshev_polynomial_coefficients(
+            beignet.multiply_chebyshev_polynomial_by_x(
+                torch.tensor([0.0]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([0.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_chebyshev_polynomial_coefficients(
+            beignet.multiply_chebyshev_polynomial_by_x(
+                torch.tensor([1.0]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([0.0, 1.0]),
+    )
+
+    for index in range(1, 5):
+        torch.testing.assert_close(
+            beignet.trim_chebyshev_polynomial_coefficients(
+                beignet.multiply_chebyshev_polynomial_by_x(
+                    torch.tensor([0.0] * index + [1.0]),
+                ),
+                tol=0.000001,
+            ),
+            torch.tensor([0.0] * (index - 1) + [0.5, 0, 0.5]),
+        )
diff --git a/tests/beignet/test__multiply_laguerre_polynomial.py b/tests/beignet/test__multiply_laguerre_polynomial.py
new file mode 100644
index 0000000000..f9fdcc46d3
--- /dev/null
+++ b/tests/beignet/test__multiply_laguerre_polynomial.py
@@ -0,0 +1,40 @@
+import beignet
+import torch
+
+torch.set_default_dtype(torch.float64)
+
+
+def test_multiply_laguerre_polynomial():
+    for i in range(5):
+        input = torch.linspace(-3, 3, 100)
+
+        a = beignet.evaluate_laguerre_polynomial(
+            input,
+            torch.tensor([0.0] * i + [1.0]),
+        )
+
+        for j in range(5):
+            b = beignet.evaluate_laguerre_polynomial(
+                input,
+                torch.tensor([0.0] * j + [1.0]),
+            )
+
+            torch.testing.assert_close(
+                beignet.evaluate_laguerre_polynomial(
+                    input,
+                    beignet.trim_laguerre_polynomial_coefficients(
+                        beignet.multiply_laguerre_polynomial(
+                            torch.tensor([0.0] * i + [1.0]),
+                            torch.tensor([0.0] * j + [1.0]),
+                        ),
+                    ),
+                ),
+                a * b,
+            )
+
+
+def test_lagline():
+    torch.testing.assert_close(
+        beignet.linear_laguerre_polynomial(3.0, 4.0),
+        torch.tensor([7.0, -4.0]),
+    )
diff --git a/tests/beignet/test__multiply_laguerre_polynomial_by_x.py b/tests/beignet/test__multiply_laguerre_polynomial_by_x.py
new file mode 100644
index 0000000000..da0bf29623
--- /dev/null
+++ b/tests/beignet/test__multiply_laguerre_polynomial_by_x.py
@@ -0,0 +1,40 @@
+import beignet
+import torch
+
+
+def test_multiply_laguerre_polynomial_by_x():
+    torch.testing.assert_close(
+        beignet.trim_laguerre_polynomial_coefficients(
+            beignet.multiply_laguerre_polynomial_by_x(
+                torch.tensor([0.0]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([0.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_laguerre_polynomial_coefficients(
+            beignet.multiply_laguerre_polynomial_by_x(
+                torch.tensor([1.0]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([1.0, -1.0]),
+    )
+
+    for index in range(1, 5):
+        torch.testing.assert_close(
+            beignet.trim_laguerre_polynomial_coefficients(
+                beignet.multiply_laguerre_polynomial_by_x(
+                    torch.tensor([0.0] * index + [1.0]),
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_laguerre_polynomial_coefficients(
+                torch.tensor(
+                    [0.0] * (index - 1) + [-index, 2.0 * index + 1.0, -(index + 1.0)]
+                ),
+                tol=0.000001,
+            ),
+        )
diff --git a/tests/beignet/test__multiply_legendre_polynomial.py b/tests/beignet/test__multiply_legendre_polynomial.py
new file mode 100644
index 0000000000..c85fecd238
--- /dev/null
+++ b/tests/beignet/test__multiply_legendre_polynomial.py
@@ -0,0 +1,29 @@
+import beignet
+import torch
+
+
+def test_multiply_legendre_polynomial():
+    for i in range(5):
+        input = torch.linspace(-1, 1, 100)
+
+        a = beignet.evaluate_legendre_polynomial(
+            input,
+            torch.tensor([0.0] * i + [1.0]),
+        )
+
+        for j in range(5):
+            b = beignet.evaluate_legendre_polynomial(
+                input,
+                torch.tensor([0.0] * j + [1.0]),
+            )
+
+            torch.testing.assert_close(
+                beignet.evaluate_legendre_polynomial(
+                    input,
+                    beignet.multiply_legendre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                ),
+                a * b,
+            )
diff --git a/tests/beignet/test__multiply_legendre_polynomial_by_x.py b/tests/beignet/test__multiply_legendre_polynomial_by_x.py
new file mode 100644
index 0000000000..764d393947
--- /dev/null
+++ b/tests/beignet/test__multiply_legendre_polynomial_by_x.py
@@ -0,0 +1,35 @@
+import beignet
+import torch
+
+
+def test_multiply_legendre_polynomial_by_x():
+    torch.testing.assert_close(
+        beignet.trim_legendre_polynomial_coefficients(
+            beignet.multiply_legendre_polynomial_by_x(
+                torch.tensor([0.0]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([0.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_legendre_polynomial_coefficients(
+            beignet.multiply_legendre_polynomial_by_x(
+                torch.tensor([1.0]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([0.0, 1.0]),
+    )
+
+    for i in range(1, 5):
+        torch.testing.assert_close(
+            beignet.trim_legendre_polynomial_coefficients(
+                beignet.multiply_legendre_polynomial_by_x(
+                    torch.tensor([0.0] * i + [1.0]),
+                ),
+                tol=0.000001,
+            ),
+            torch.tensor([0] * (i - 1) + [i / (2 * i + 1), 0, (i + 1) / (2 * i + 1)]),
+        )
diff --git a/tests/beignet/test__multiply_physicists_hermite_polynomial.py b/tests/beignet/test__multiply_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..ce40c4781f
--- /dev/null
+++ b/tests/beignet/test__multiply_physicists_hermite_polynomial.py
@@ -0,0 +1,29 @@
+import beignet
+import torch
+
+
+def test_multiply_physicists_hermite_polynomial():
+    for i in range(5):
+        input = torch.linspace(-3, 3, 100)
+
+        val1 = beignet.evaluate_physicists_hermite_polynomial(
+            input,
+            torch.tensor([0.0] * i + [1.0]),
+        )
+
+        for j in range(5):
+            val2 = beignet.evaluate_physicists_hermite_polynomial(
+                input,
+                torch.tensor([0.0] * j + [1.0]),
+            )
+
+            torch.testing.assert_close(
+                beignet.evaluate_physicists_hermite_polynomial(
+                    input,
+                    beignet.multiply_physicists_hermite_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                ),
+                val1 * val2,
+            )
diff --git a/tests/beignet/test__multiply_physicists_hermite_polynomial_by_x.py b/tests/beignet/test__multiply_physicists_hermite_polynomial_by_x.py
new file mode 100644
index 0000000000..e21252c1b4
--- /dev/null
+++ b/tests/beignet/test__multiply_physicists_hermite_polynomial_by_x.py
@@ -0,0 +1,29 @@
+import beignet
+import torch
+
+
+def test_multiply_physicists_hermite_polynomial_by_x():
+    torch.testing.assert_close(
+        beignet.trim_physicists_hermite_polynomial_coefficients(
+            beignet.multiply_physicists_hermite_polynomial_by_x(
+                torch.tensor([0.0]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([0.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.multiply_physicists_hermite_polynomial_by_x(
+            torch.tensor([1.0]),
+        ),
+        torch.tensor([0.0, 0.5]),
+    )
+
+    for i in range(1, 5):
+        torch.testing.assert_close(
+            beignet.multiply_physicists_hermite_polynomial_by_x(
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+            torch.tensor([0.0] * (i - 1) + [i, 0.0, 0.5]),
+        )
diff --git a/tests/beignet/test__multiply_polynomial.py b/tests/beignet/test__multiply_polynomial.py
new file mode 100644
index 0000000000..7b5a20d5bd
--- /dev/null
+++ b/tests/beignet/test__multiply_polynomial.py
@@ -0,0 +1,24 @@
+import beignet
+import torch
+
+
+def test_multiply_polynomial():
+    for j in range(5):
+        for k in range(5):
+            target = torch.zeros(j + k + 1)
+
+            target[j + k] = target[j + k] + 1
+
+            torch.testing.assert_close(
+                beignet.trim_polynomial_coefficients(
+                    beignet.multiply_polynomial(
+                        torch.tensor([0.0] * j + [1.0]),
+                        torch.tensor([0.0] * k + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__multiply_polynomial_by_x.py b/tests/beignet/test__multiply_polynomial_by_x.py
new file mode 100644
index 0000000000..304d40da40
--- /dev/null
+++ b/tests/beignet/test__multiply_polynomial_by_x.py
@@ -0,0 +1,26 @@
+import beignet
+import torch
+
+
+def test_multiply_polynomial_by_x():
+    torch.testing.assert_close(
+        beignet.multiply_polynomial_by_x(
+            torch.tensor([0.0]),
+        ),
+        torch.tensor([0.0, 0.0]),
+    )
+
+    torch.testing.assert_close(
+        beignet.multiply_polynomial_by_x(
+            torch.tensor([1.0]),
+        ),
+        torch.tensor([0.0, 1.0]),
+    )
+
+    for i in range(1, 5):
+        torch.testing.assert_close(
+            beignet.multiply_polynomial_by_x(
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+            torch.tensor([0.0] * (i + 1) + [1.0]),
+        )
diff --git a/tests/beignet/test__multiply_probabilists_hermite_polynomial.py b/tests/beignet/test__multiply_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..012512fc24
--- /dev/null
+++ b/tests/beignet/test__multiply_probabilists_hermite_polynomial.py
@@ -0,0 +1,29 @@
+import beignet
+import torch
+
+
+def test_multiply_probabilists_hermite_polynomial():
+    for index in range(5):
+        input = torch.linspace(-3, 3, 100)
+
+        val1 = beignet.evaluate_probabilists_hermite_polynomial(
+            input,
+            torch.tensor([0.0] * index + [1.0]),
+        )
+
+        for k in range(5):
+            val2 = beignet.evaluate_probabilists_hermite_polynomial(
+                input,
+                torch.tensor([0.0] * k + [1.0]),
+            )
+
+            torch.testing.assert_close(
+                beignet.evaluate_probabilists_hermite_polynomial(
+                    input,
+                    beignet.multiply_probabilists_hermite_polynomial(
+                        torch.tensor([0.0] * index + [1.0]),
+                        torch.tensor([0.0] * k + [1.0]),
+                    ),
+                ),
+                val1 * val2,
+            )
diff --git a/tests/beignet/test__multiply_probabilists_hermite_polynomial_by_x.py b/tests/beignet/test__multiply_probabilists_hermite_polynomial_by_x.py
new file mode 100644
index 0000000000..15c04a22d9
--- /dev/null
+++ b/tests/beignet/test__multiply_probabilists_hermite_polynomial_by_x.py
@@ -0,0 +1,34 @@
+import beignet
+import torch
+
+
+def test_multiply_probabilists_hermite_polynomial_by_x():
+    torch.testing.assert_close(
+        beignet.trim_probabilists_hermite_polynomial_coefficients(
+            beignet.multiply_probabilists_hermite_polynomial_by_x(
+                torch.tensor([0.0]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([0.0]),
+    )
+    torch.testing.assert_close(
+        beignet.trim_probabilists_hermite_polynomial_coefficients(
+            beignet.multiply_probabilists_hermite_polynomial_by_x(
+                torch.tensor([1.0]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([0.0, 1.0]),
+    )
+
+    for index in range(1, 5):
+        torch.testing.assert_close(
+            beignet.trim_probabilists_hermite_polynomial_coefficients(
+                beignet.multiply_probabilists_hermite_polynomial_by_x(
+                    torch.tensor([0.0] * index + [1.0]),
+                ),
+                tol=0.000001,
+            ),
+            torch.tensor([0] * (index - 1) + [index, 0.0, 1.0]),
+        )
diff --git a/tests/beignet/test__physicists_hermite_polynomial_companion.py b/tests/beignet/test__physicists_hermite_polynomial_companion.py
new file mode 100644
index 0000000000..10eb95ba93
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_companion.py
@@ -0,0 +1,28 @@
+import beignet
+import pytest
+import torch
+
+
+def test_physicists_hermite_polynomial_companion():
+    with pytest.raises(ValueError):
+        beignet.physicists_hermite_polynomial_companion(
+            torch.tensor([]),
+        )
+
+    with pytest.raises(ValueError):
+        beignet.physicists_hermite_polynomial_companion(
+            torch.tensor([1.0]),
+        )
+
+    for index in range(1, 5):
+        output = beignet.physicists_hermite_polynomial_companion(
+            torch.tensor([0.0] * index + [1.0]),
+        )
+
+        assert output.shape == (index, index)
+
+    output = beignet.physicists_hermite_polynomial_companion(
+        torch.tensor([1.0, 2.0]),
+    )
+
+    assert output[0, 0] == -0.25
diff --git a/tests/beignet/test__physicists_hermite_polynomial_domain.py b/tests/beignet/test__physicists_hermite_polynomial_domain.py
new file mode 100644
index 0000000000..6ab06f2810
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_domain.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_domain():
+    torch.testing.assert_close(
+        beignet.physicists_hermite_polynomial_domain,
+        torch.tensor([-1.0, 1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__physicists_hermite_polynomial_from_roots.py b/tests/beignet/test__physicists_hermite_polynomial_from_roots.py
new file mode 100644
index 0000000000..f5fd6cf43c
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_from_roots.py
@@ -0,0 +1,37 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_from_roots():
+    torch.testing.assert_close(
+        beignet.trim_physicists_hermite_polynomial_coefficients(
+            beignet.physicists_hermite_polynomial_from_roots(
+                torch.tensor([]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([1.0]),
+    )
+
+    # for i in range(1, 5):
+    #     roots = torch.cos(torch.linspace(-math.pi, 0, 2 * i + 1)[1::2])
+    #     target = 0
+    #
+    #     torch.testing.assert_close(
+    #         beignet.herm2poly(
+    #             beignet.hermfromroots(
+    #                 roots,
+    #             ),
+    #         )[-1],
+    #         torch.tensor([1.0]),
+    #     )
+    #
+    #     torch.testing.assert_close(
+    #         beignet.hermval(
+    #             roots,
+    #             beignet.hermfromroots(
+    #                 roots,
+    #             ),
+    #         ),
+    #         target,
+    #     )
diff --git a/tests/beignet/test__physicists_hermite_polynomial_one.py b/tests/beignet/test__physicists_hermite_polynomial_one.py
new file mode 100644
index 0000000000..31fb060c74
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_one.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_one():
+    torch.testing.assert_close(
+        beignet.physicists_hermite_polynomial_one,
+        torch.tensor([1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__physicists_hermite_polynomial_power.py b/tests/beignet/test__physicists_hermite_polynomial_power.py
new file mode 100644
index 0000000000..6985b59251
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_power.py
@@ -0,0 +1,26 @@
+import functools
+
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_power():
+    for i in range(5):
+        for j in range(5):
+            torch.testing.assert_close(
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    beignet.physicists_hermite_polynomial_power(
+                        torch.arange(0.0, i + 1),
+                        j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    functools.reduce(
+                        beignet.multiply_physicists_hermite_polynomial,
+                        [torch.arange(0.0, i + 1)] * j,
+                        torch.tensor([1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__physicists_hermite_polynomial_roots.py b/tests/beignet/test__physicists_hermite_polynomial_roots.py
new file mode 100644
index 0000000000..688bfbae83
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_roots.py
@@ -0,0 +1,36 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_roots():
+    torch.testing.assert_close(
+        beignet.physicists_hermite_polynomial_roots(
+            torch.tensor([1.0]),
+        ),
+        torch.tensor([]),
+    )
+
+    torch.testing.assert_close(
+        beignet.physicists_hermite_polynomial_roots(
+            torch.tensor([1.0, 1.0]),
+        ),
+        torch.tensor([-0.5]),
+    )
+
+    for i in range(2, 5):
+        input = torch.linspace(-1, 1, i)
+
+        torch.testing.assert_close(
+            beignet.trim_physicists_hermite_polynomial_coefficients(
+                beignet.physicists_hermite_polynomial_roots(
+                    beignet.physicists_hermite_polynomial_from_roots(
+                        input,
+                    ),
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_physicists_hermite_polynomial_coefficients(
+                input,
+                tol=0.000001,
+            ),
+        )
diff --git a/tests/beignet/test__physicists_hermite_polynomial_to_polynomial.py b/tests/beignet/test__physicists_hermite_polynomial_to_polynomial.py
new file mode 100644
index 0000000000..3b61cc5c63
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_to_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_to_polynomial():
+    coefficients = [
+        torch.tensor([1.0]),
+        torch.tensor([0.0, 2]),
+        torch.tensor([-2.0, 0, 4]),
+        torch.tensor([0.0, -12, 0, 8]),
+        torch.tensor([12.0, 0, -48, 0, 16]),
+        torch.tensor([0.0, 120, 0, -160, 0, 32]),
+        torch.tensor([-120.0, 0, 720, 0, -480, 0, 64]),
+        torch.tensor([0.0, -1680, 0, 3360, 0, -1344, 0, 128]),
+        torch.tensor([1680.0, 0, -13440, 0, 13440, 0, -3584, 0, 256]),
+        torch.tensor([0.0, 30240, 0, -80640, 0, 48384, 0, -9216, 0, 512]),
+    ]
+
+    for index in range(10):
+        torch.testing.assert_close(
+            beignet.physicists_hermite_polynomial_to_polynomial(
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+            coefficients[index],
+        )
diff --git a/tests/beignet/test__physicists_hermite_polynomial_vandermonde.py b/tests/beignet/test__physicists_hermite_polynomial_vandermonde.py
new file mode 100644
index 0000000000..46e82097c6
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_vandermonde.py
@@ -0,0 +1,38 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_vandermonde():
+    x = torch.arange(3)
+
+    output = beignet.physicists_hermite_polynomial_vandermonde(
+        x,
+        degree=3,
+    )
+
+    assert output.shape == (3, 4)
+
+    for index in range(4):
+        torch.testing.assert_close(
+            output[..., index],
+            beignet.evaluate_physicists_hermite_polynomial(
+                x,
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+        )
+
+    output = beignet.physicists_hermite_polynomial_vandermonde(
+        torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]),
+        degree=3,
+    )
+
+    assert output.shape == (3, 2, 4)
+
+    for index in range(4):
+        torch.testing.assert_close(
+            output[..., index],
+            beignet.evaluate_physicists_hermite_polynomial(
+                torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]),
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+        )
diff --git a/tests/beignet/test__physicists_hermite_polynomial_vandermonde_2d.py b/tests/beignet/test__physicists_hermite_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..d2323fab01
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_vandermonde_2d.py
@@ -0,0 +1,31 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_vandermonde_2d():
+    a, b, c = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3)
+
+    output = beignet.physicists_hermite_polynomial_vandermonde_2d(
+        a,
+        b,
+        degree=torch.tensor([1, 2]),
+    )
+
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_physicists_hermite_polynomial_2d(
+            a,
+            b,
+            coefficients,
+        ),
+    )
+
+    output = beignet.physicists_hermite_polynomial_vandermonde_2d(
+        a,
+        b,
+        degree=torch.tensor([1, 2]),
+    )
+
+    assert output.shape == (5, 6)
diff --git a/tests/beignet/test__physicists_hermite_polynomial_vandermonde_3d.py b/tests/beignet/test__physicists_hermite_polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..17642b0920
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_vandermonde_3d.py
@@ -0,0 +1,29 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_vandermonde_3d():
+    a, b, x3 = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3, 4)
+
+    output = beignet.physicists_hermite_polynomial_vandermonde_3d(
+        a,
+        b,
+        x3,
+        degree=torch.tensor([1, 2, 3]),
+    )
+
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_physicists_hermite_polynomial_3d(a, b, x3, coefficients),
+    )
+
+    output = beignet.physicists_hermite_polynomial_vandermonde_3d(
+        a,
+        b,
+        x3,
+        degree=torch.tensor([1, 2, 3]),
+    )
+
+    assert output.shape == (5, 24)
diff --git a/tests/beignet/test__physicists_hermite_polynomial_weight.py b/tests/beignet/test__physicists_hermite_polynomial_weight.py
new file mode 100644
index 0000000000..c66c0ffa1d
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_weight.py
@@ -0,0 +1,9 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_weight():
+    torch.testing.assert_close(
+        beignet.physicists_hermite_polynomial_weight(torch.linspace(-5, 5, 11)),
+        torch.exp(-(torch.linspace(-5, 5, 11) ** 2)),
+    )
diff --git a/tests/beignet/test__physicists_hermite_polynomial_x.py b/tests/beignet/test__physicists_hermite_polynomial_x.py
new file mode 100644
index 0000000000..cce9911bc6
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_x.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_x():
+    torch.testing.assert_close(
+        beignet.physicists_hermite_polynomial_x,
+        torch.tensor([0, 0.5]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__physicists_hermite_polynomial_zero.py b/tests/beignet/test__physicists_hermite_polynomial_zero.py
new file mode 100644
index 0000000000..16a68efbaf
--- /dev/null
+++ b/tests/beignet/test__physicists_hermite_polynomial_zero.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_physicists_hermite_polynomial_zero():
+    torch.testing.assert_close(
+        beignet.physicists_hermite_polynomial_zero,
+        torch.tensor([0.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__polynomial_companion.py b/tests/beignet/test__polynomial_companion.py
new file mode 100644
index 0000000000..e36a2a9a61
--- /dev/null
+++ b/tests/beignet/test__polynomial_companion.py
@@ -0,0 +1,24 @@
+import beignet
+import pytest
+import torch
+
+
+def test_polynomial_companion():
+    with pytest.raises(ValueError):
+        beignet.polynomial_companion(torch.tensor([]))
+
+    with pytest.raises(ValueError):
+        beignet.polynomial_companion(torch.tensor([1]))
+
+    for i in range(1, 5):
+        output = beignet.polynomial_companion(
+            torch.tensor([0.0] * i + [1.0]),
+        )
+
+        assert output.shape == (i, i)
+
+    output = beignet.polynomial_companion(
+        torch.tensor([1, 2]),
+    )
+
+    assert output[0, 0] == -0.5
diff --git a/tests/beignet/test__polynomial_domain.py b/tests/beignet/test__polynomial_domain.py
new file mode 100644
index 0000000000..b663d8d7fb
--- /dev/null
+++ b/tests/beignet/test__polynomial_domain.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_polynomial_domain():
+    torch.testing.assert_close(
+        beignet.polynomial_domain,
+        torch.tensor([-1.0, 1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__polynomial_from_roots.py b/tests/beignet/test__polynomial_from_roots.py
new file mode 100644
index 0000000000..5ca8697d83
--- /dev/null
+++ b/tests/beignet/test__polynomial_from_roots.py
@@ -0,0 +1,49 @@
+import math
+
+import beignet
+import torch
+
+
+def test_polynomial_from_roots():
+    coefficients = [
+        torch.tensor([1.0]),
+        torch.tensor([0.0, 1]),
+        torch.tensor([-1.0, 0, 2]),
+        torch.tensor([0.0, -3, 0, 4]),
+        torch.tensor([1.0, 0, -8, 0, 8]),
+        torch.tensor([0.0, 5, 0, -20, 0, 16]),
+        torch.tensor([-1.0, 0, 18, 0, -48, 0, 32]),
+        torch.tensor([0.0, -7, 0, 56, 0, -112, 0, 64]),
+        torch.tensor([1.0, 0, -32, 0, 160, 0, -256, 0, 128]),
+        torch.tensor([0.0, 9, 0, -120, 0, 432, 0, -576, 0, 256]),
+    ]
+
+    torch.testing.assert_close(
+        beignet.trim_polynomial_coefficients(
+            beignet.polynomial_from_roots(
+                torch.tensor([]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([1.0]),
+    )
+
+    for index in range(1, 5):
+        input = torch.linspace(-math.pi, 0.0, 2 * index + 1)
+
+        input = input[1::2]
+
+        input = torch.cos(input)
+
+        output = beignet.polynomial_from_roots(input) * 2 ** (index - 1)
+
+        torch.testing.assert_close(
+            beignet.trim_polynomial_coefficients(
+                output,
+                tol=0.000001,
+            ),
+            beignet.trim_polynomial_coefficients(
+                coefficients[index],
+                tol=0.000001,
+            ),
+        )
diff --git a/tests/beignet/test__polynomial_one.py b/tests/beignet/test__polynomial_one.py
new file mode 100644
index 0000000000..dc23507b6d
--- /dev/null
+++ b/tests/beignet/test__polynomial_one.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_polynomial_one():
+    torch.testing.assert_close(
+        beignet.polynomial_one,
+        torch.tensor([1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__polynomial_power.py b/tests/beignet/test__polynomial_power.py
new file mode 100644
index 0000000000..85d237ab6c
--- /dev/null
+++ b/tests/beignet/test__polynomial_power.py
@@ -0,0 +1,26 @@
+import functools
+
+import beignet
+import torch
+
+
+def test_polynomial_power():
+    for i in range(5):
+        for j in range(5):
+            torch.testing.assert_close(
+                beignet.trim_polynomial_coefficients(
+                    beignet.polynomial_power(
+                        torch.arange(0.0, i + 1),
+                        j,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_polynomial_coefficients(
+                    functools.reduce(
+                        beignet.multiply_polynomial,
+                        [torch.arange(0.0, i + 1)] * j,
+                        torch.tensor([1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__polynomial_roots.py b/tests/beignet/test__polynomial_roots.py
new file mode 100644
index 0000000000..36c1500a00
--- /dev/null
+++ b/tests/beignet/test__polynomial_roots.py
@@ -0,0 +1,32 @@
+import beignet
+import torch
+
+
+def test_polynomial_roots():
+    torch.testing.assert_close(
+        beignet.polynomial_roots(torch.tensor([1.0])),
+        torch.tensor([]),
+    )
+
+    torch.testing.assert_close(
+        beignet.polynomial_roots(torch.tensor([1.0, 2.0])),
+        torch.tensor([-0.5]),
+    )
+
+    for index in range(2, 5):
+        input = torch.linspace(-1, 1, index)
+
+        torch.testing.assert_close(
+            beignet.trim_polynomial_coefficients(
+                beignet.polynomial_roots(
+                    beignet.polynomial_from_roots(
+                        input,
+                    ),
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_polynomial_coefficients(
+                input,
+                tol=0.000001,
+            ),
+        )
diff --git a/tests/beignet/test__polynomial_to_chebyshev_polynomial.py b/tests/beignet/test__polynomial_to_chebyshev_polynomial.py
new file mode 100644
index 0000000000..51ed63851e
--- /dev/null
+++ b/tests/beignet/test__polynomial_to_chebyshev_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_polynomial_to_chebyshev_polynomial():
+    coefficients = [
+        torch.tensor([1.0]),
+        torch.tensor([0.0, 1]),
+        torch.tensor([-1.0, 0, 2]),
+        torch.tensor([0.0, -3, 0, 4]),
+        torch.tensor([1.0, 0, -8, 0, 8]),
+        torch.tensor([0.0, 5, 0, -20, 0, 16]),
+        torch.tensor([-1.0, 0, 18, 0, -48, 0, 32]),
+        torch.tensor([0.0, -7, 0, 56, 0, -112, 0, 64]),
+        torch.tensor([1.0, 0, -32, 0, 160, 0, -256, 0, 128]),
+        torch.tensor([0.0, 9, 0, -120, 0, 432, 0, -576, 0, 256]),
+    ]
+
+    for index in range(10):
+        torch.testing.assert_close(
+            beignet.polynomial_to_chebyshev_polynomial(
+                coefficients[index],
+            ),
+            torch.tensor([0.0] * index + [1.0]),
+        )
diff --git a/tests/beignet/test__polynomial_to_laguerre_polynomial.py b/tests/beignet/test__polynomial_to_laguerre_polynomial.py
new file mode 100644
index 0000000000..80b2026dfc
--- /dev/null
+++ b/tests/beignet/test__polynomial_to_laguerre_polynomial.py
@@ -0,0 +1,22 @@
+import beignet
+import torch
+
+
+def test_polynomial_to_laguerre_polynomial():
+    coefficients = [
+        torch.tensor([1.0]) / 1.0,
+        torch.tensor([1.0, -1.0]) / 1.0,
+        torch.tensor([2.0, -4.0, 1.0]) / 2.0,
+        torch.tensor([6.0, -18.0, 9.0, -1.0]) / 6.0,
+        torch.tensor([24.0, -96.0, 72.0, -16.0, 1.0]) / 24.0,
+        torch.tensor([120.0, -600.0, 600.0, -200.0, 25.0, -1.0]) / 120.0,
+        torch.tensor([720.0, -4320.0, 5400.0, -2400.0, 450.0, -36.0, 1.0]) / 720.0,
+    ]
+
+    for index in range(7):
+        torch.testing.assert_close(
+            beignet.polynomial_to_laguerre_polynomial(
+                coefficients[index],
+            ),
+            torch.tensor([0.0] * index + [1.0]),
+        )
diff --git a/tests/beignet/test__polynomial_to_legendre_polynomial.py b/tests/beignet/test__polynomial_to_legendre_polynomial.py
new file mode 100644
index 0000000000..18061bc3f3
--- /dev/null
+++ b/tests/beignet/test__polynomial_to_legendre_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_polynomial_to_legendre_polynomial():
+    coefficients = [
+        torch.tensor([1.0]),
+        torch.tensor([0.0, 1]),
+        torch.tensor([-1.0, 0, 3]) / 2,
+        torch.tensor([0.0, -3, 0, 5]) / 2,
+        torch.tensor([3.0, 0, -30, 0, 35]) / 8,
+        torch.tensor([0.0, 15, 0, -70, 0, 63]) / 8,
+        torch.tensor([-5.0, 0, 105, 0, -315, 0, 231]) / 16,
+        torch.tensor([0.0, -35, 0, 315, 0, -693, 0, 429]) / 16,
+        torch.tensor([35.0, 0, -1260, 0, 6930, 0, -12012, 0, 6435]) / 128,
+        torch.tensor([0.0, 315, 0, -4620, 0, 18018, 0, -25740, 0, 12155]) / 128,
+    ]
+
+    for index in range(10):
+        torch.testing.assert_close(
+            beignet.polynomial_to_legendre_polynomial(
+                coefficients[index],
+            ),
+            torch.tensor([0.0] * index + [1.0]),
+        )
diff --git a/tests/beignet/test__polynomial_to_physicists_hermite_polynomial.py b/tests/beignet/test__polynomial_to_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..6ffe55718f
--- /dev/null
+++ b/tests/beignet/test__polynomial_to_physicists_hermite_polynomial.py
@@ -0,0 +1,28 @@
+import beignet
+import torch
+
+
+def test_polynomial_to_physicists_hermite_polynomial():
+    coefficients = [
+        torch.tensor([1.0]),
+        torch.tensor([0.0, 2]),
+        torch.tensor([-2.0, 0, 4]),
+        torch.tensor([0.0, -12, 0, 8]),
+        torch.tensor([12.0, 0, -48, 0, 16]),
+        torch.tensor([0.0, 120, 0, -160, 0, 32]),
+        torch.tensor([-120.0, 0, 720, 0, -480, 0, 64]),
+        torch.tensor([0.0, -1680, 0, 3360, 0, -1344, 0, 128]),
+        torch.tensor([1680.0, 0, -13440, 0, 13440, 0, -3584, 0, 256]),
+        torch.tensor([0.0, 30240, 0, -80640, 0, 48384, 0, -9216, 0, 512]),
+    ]
+
+    for index in range(10):
+        torch.testing.assert_close(
+            beignet.trim_physicists_hermite_polynomial_coefficients(
+                beignet.polynomial_to_physicists_hermite_polynomial(
+                    coefficients[index],
+                ),
+                tol=0.000001,
+            ),
+            torch.tensor([0.0] * index + [1.0]),
+        )
diff --git a/tests/beignet/test__polynomial_to_probabilists_hermite_polynomial.py b/tests/beignet/test__polynomial_to_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..e8b98f09eb
--- /dev/null
+++ b/tests/beignet/test__polynomial_to_probabilists_hermite_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_polynomial_to_probabilists_hermite_polynomial():
+    coefficients = [
+        torch.tensor([1.0]),
+        torch.tensor([0.0, 1]),
+        torch.tensor([-1.0, 0, 1]),
+        torch.tensor([0.0, -3, 0, 1]),
+        torch.tensor([3.0, 0, -6, 0, 1]),
+        torch.tensor([0.0, 15, 0, -10, 0, 1]),
+        torch.tensor([-15.0, 0, 45, 0, -15, 0, 1]),
+        torch.tensor([0.0, -105, 0, 105, 0, -21, 0, 1]),
+        torch.tensor([105.0, 0, -420, 0, 210, 0, -28, 0, 1]),
+        torch.tensor([0.0, 945, 0, -1260, 0, 378, 0, -36, 0, 1]),
+    ]
+
+    for index in range(10):
+        torch.testing.assert_close(
+            beignet.polynomial_to_probabilists_hermite_polynomial(
+                coefficients[index],
+            ),
+            torch.tensor([0.0] * index + [1.0]),
+        )
diff --git a/tests/beignet/test__polynomial_vandermonde.py b/tests/beignet/test__polynomial_vandermonde.py
new file mode 100644
index 0000000000..641fc34c1b
--- /dev/null
+++ b/tests/beignet/test__polynomial_vandermonde.py
@@ -0,0 +1,43 @@
+import beignet
+import pytest
+import torch
+
+
+def test_polynomial_vandermonde():
+    output = beignet.polynomial_vandermonde(
+        torch.arange(3.0),
+        degree=torch.tensor([3]),
+    )
+
+    assert output.shape == (3, 4)
+
+    for i in range(4):
+        torch.testing.assert_close(
+            output[..., i],
+            beignet.evaluate_polynomial(
+                torch.arange(3),
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+        )
+
+    output = beignet.polynomial_vandermonde(
+        torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]),
+        degree=torch.tensor([3]),
+    )
+
+    assert output.shape == (3, 2, 4)
+
+    for i in range(4):
+        torch.testing.assert_close(
+            output[..., i],
+            beignet.evaluate_polynomial(
+                torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]),
+                torch.tensor([0.0] * i + [1.0]),
+            ),
+        )
+
+    with pytest.raises(ValueError):
+        beignet.polynomial_vandermonde(
+            torch.arange(3),
+            degree=torch.tensor([-1]),
+        )
diff --git a/tests/beignet/test__polynomial_vandermonde_2d.py b/tests/beignet/test__polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..bcc64759d8
--- /dev/null
+++ b/tests/beignet/test__polynomial_vandermonde_2d.py
@@ -0,0 +1,27 @@
+import beignet
+import torch
+
+
+def test_polynomial_vandermonde_2d():
+    a, b, c = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3)
+
+    output = beignet.polynomial_vandermonde_2d(a, b, degree=torch.tensor([1, 2]))
+
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_polynomial_2d(
+            a,
+            b,
+            coefficients,
+        ),
+    )
+
+    output = beignet.polynomial_vandermonde_2d(
+        a,
+        b,
+        degree=torch.tensor([1, 2]),
+    )
+
+    assert output.shape == (5, 6)
diff --git a/tests/beignet/test__polynomial_vandermonde_3d.py b/tests/beignet/test__polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..34615c4dd9
--- /dev/null
+++ b/tests/beignet/test__polynomial_vandermonde_3d.py
@@ -0,0 +1,34 @@
+import beignet
+import torch
+
+
+def test_polynomial_vandermonde_3d():
+    a, b, c = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3, 4)
+
+    output = beignet.polynomial_vandermonde_3d(
+        a,
+        b,
+        c,
+        degree=torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_polynomial_3d(
+            a,
+            b,
+            c,
+            coefficients,
+        ),
+    )
+
+    output = beignet.polynomial_vandermonde_3d(
+        a,
+        b,
+        c,
+        degree=torch.tensor([1.0, 2.0, 3.0]),
+    )
+
+    assert output.shape == (5, 24)
diff --git a/tests/beignet/test__polynomial_x.py b/tests/beignet/test__polynomial_x.py
new file mode 100644
index 0000000000..09c3a7847f
--- /dev/null
+++ b/tests/beignet/test__polynomial_x.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_polynomial_x():
+    torch.testing.assert_close(
+        beignet.polynomial_x,
+        torch.tensor([0.0, 1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__polynomial_zero.py b/tests/beignet/test__polynomial_zero.py
new file mode 100644
index 0000000000..e176d5f7a9
--- /dev/null
+++ b/tests/beignet/test__polynomial_zero.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_polynomial_zero():
+    torch.testing.assert_close(
+        beignet.polynomial_zero,
+        torch.tensor([0.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_companion.py b/tests/beignet/test__probabilists_hermite_polynomial_companion.py
new file mode 100644
index 0000000000..aa405c35ad
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_companion.py
@@ -0,0 +1,26 @@
+import beignet
+import pytest
+import torch
+
+
+def test_probabilists_hermite_polynomial_companion():
+    with pytest.raises(ValueError):
+        beignet.probabilists_hermite_polynomial_companion(torch.tensor([]))
+
+    with pytest.raises(ValueError):
+        beignet.probabilists_hermite_polynomial_companion(
+            torch.tensor([1.0]),
+        )
+
+    for index in range(1, 5):
+        output = beignet.probabilists_hermite_polynomial_companion(
+            torch.tensor([0.0] * index + [1.0]),
+        )
+
+        assert output.shape == (index, index)
+
+    output = beignet.probabilists_hermite_polynomial_companion(
+        torch.tensor([1.0, 2.0]),
+    )
+
+    assert output[0, 0] == -0.5
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_domain.py b/tests/beignet/test__probabilists_hermite_polynomial_domain.py
new file mode 100644
index 0000000000..aae362bc98
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_domain.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_domain():
+    torch.testing.assert_close(
+        beignet.probabilists_hermite_polynomial_domain,
+        torch.tensor([-1.0, 1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_from_roots.py b/tests/beignet/test__probabilists_hermite_polynomial_from_roots.py
new file mode 100644
index 0000000000..994f3324bd
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_from_roots.py
@@ -0,0 +1,33 @@
+import math
+
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_from_roots():
+    torch.testing.assert_close(
+        beignet.trim_probabilists_hermite_polynomial_coefficients(
+            beignet.probabilists_hermite_polynomial_from_roots(
+                torch.tensor([]),
+            ),
+            tol=0.000001,
+        ),
+        torch.tensor([1.0]),
+    )
+
+    for i in range(1, 5):
+        roots = torch.cos(torch.linspace(-math.pi, 0, 2 * i + 1)[1::2])
+
+        pol = beignet.probabilists_hermite_polynomial_from_roots(roots)
+
+        assert len(pol) == i + 1
+
+        torch.testing.assert_close(
+            beignet.probabilists_hermite_polynomial_to_polynomial(pol)[-1],
+            torch.tensor(1.0),
+        )
+
+        # torch.testing.assert_close(
+        #     beignet.hermeval(roots, pol),
+        #     torch.tensor([0.0]),
+        # )
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_one.py b/tests/beignet/test__probabilists_hermite_polynomial_one.py
new file mode 100644
index 0000000000..4fe799a601
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_one.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_one():
+    torch.testing.assert_close(
+        beignet.probabilists_hermite_polynomial_one,
+        torch.tensor([1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_power.py b/tests/beignet/test__probabilists_hermite_polynomial_power.py
new file mode 100644
index 0000000000..161c22351d
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_power.py
@@ -0,0 +1,26 @@
+import functools
+
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_power():
+    for j in range(5):
+        for k in range(5):
+            torch.testing.assert_close(
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.probabilists_hermite_polynomial_power(
+                        torch.arange(0.0, j + 1),
+                        k,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    functools.reduce(
+                        beignet.multiply_probabilists_hermite_polynomial,
+                        [torch.arange(0.0, j + 1)] * k,
+                        torch.tensor([1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_roots.py b/tests/beignet/test__probabilists_hermite_polynomial_roots.py
new file mode 100644
index 0000000000..a983241caa
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_roots.py
@@ -0,0 +1,36 @@
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_roots():
+    torch.testing.assert_close(
+        beignet.probabilists_hermite_polynomial_roots(
+            torch.tensor([1.0]),
+        ),
+        torch.tensor([]),
+    )
+
+    torch.testing.assert_close(
+        beignet.probabilists_hermite_polynomial_roots(
+            torch.tensor([1.0, 1.0]),
+        ),
+        torch.tensor([-1.0]),
+    )
+
+    for index in range(2, 5):
+        input = torch.linspace(-1, 1, index)
+
+        torch.testing.assert_close(
+            beignet.trim_probabilists_hermite_polynomial_coefficients(
+                beignet.probabilists_hermite_polynomial_roots(
+                    beignet.probabilists_hermite_polynomial_from_roots(
+                        input,
+                    )
+                ),
+                tol=0.000001,
+            ),
+            beignet.trim_probabilists_hermite_polynomial_coefficients(
+                input,
+                tol=0.000001,
+            ),
+        )
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_to_polynomial.py b/tests/beignet/test__probabilists_hermite_polynomial_to_polynomial.py
new file mode 100644
index 0000000000..30e42a2e28
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_to_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_to_polynomial():
+    coefficients = [
+        torch.tensor([1.0]),
+        torch.tensor([0.0, 1]),
+        torch.tensor([-1.0, 0, 1]),
+        torch.tensor([0.0, -3, 0, 1]),
+        torch.tensor([3.0, 0, -6, 0, 1]),
+        torch.tensor([0.0, 15, 0, -10, 0, 1]),
+        torch.tensor([-15.0, 0, 45, 0, -15, 0, 1]),
+        torch.tensor([0.0, -105, 0, 105, 0, -21, 0, 1]),
+        torch.tensor([105.0, 0, -420, 0, 210, 0, -28, 0, 1]),
+        torch.tensor([0.0, 945, 0, -1260, 0, 378, 0, -36, 0, 1]),
+    ]
+
+    for index in range(10):
+        torch.testing.assert_close(
+            beignet.probabilists_hermite_polynomial_to_polynomial(
+                torch.tensor([0.0] * index + [1.0]),
+            ),
+            coefficients[index],
+        )
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_vandermonde.py b/tests/beignet/test__probabilists_hermite_polynomial_vandermonde.py
new file mode 100644
index 0000000000..39959edab7
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_vandermonde.py
@@ -0,0 +1,30 @@
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_vandermonde():
+    x = torch.arange(3)
+    v = beignet.probabilists_hermite_polynomial_vandermonde(
+        x,
+        3,
+    )
+    assert v.shape == (3, 4)
+    for i in range(4):
+        coefficients = torch.tensor([0.0] * i + [1.0])
+        torch.testing.assert_close(
+            v[..., i],
+            beignet.evaluate_probabilists_hermite_polynomial(x, coefficients),
+        )
+
+    x = torch.tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])
+    v = beignet.probabilists_hermite_polynomial_vandermonde(
+        x,
+        3,
+    )
+    assert v.shape == (3, 2, 4)
+    for i in range(4):
+        coefficients = torch.tensor([0.0] * i + [1.0])
+        torch.testing.assert_close(
+            v[..., i],
+            beignet.evaluate_probabilists_hermite_polynomial(x, coefficients),
+        )
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_vandermonde_2d.py b/tests/beignet/test__probabilists_hermite_polynomial_vandermonde_2d.py
new file mode 100644
index 0000000000..bbbdfcde67
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_vandermonde_2d.py
@@ -0,0 +1,31 @@
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_vandermonde_2d():
+    a, b, c = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3)
+
+    output = beignet.probabilists_hermite_polynomial_vandermonde_2d(
+        a,
+        b,
+        degree=torch.tensor([1, 2]),
+    )
+
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_probabilists_hermite_polynomial_2d(
+            a,
+            b,
+            coefficients,
+        ),
+    )
+
+    output = beignet.probabilists_hermite_polynomial_vandermonde_2d(
+        a,
+        b,
+        degree=torch.tensor([1, 2]),
+    )
+
+    assert output.shape == (5, 6)
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_vandermonde_3d.py b/tests/beignet/test__probabilists_hermite_polynomial_vandermonde_3d.py
new file mode 100644
index 0000000000..55faac9440
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_vandermonde_3d.py
@@ -0,0 +1,34 @@
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_vandermonde_3d():
+    a, b, c = torch.rand(3, 5) * 2 - 1
+
+    coefficients = torch.rand(2, 3, 4)
+
+    output = beignet.probabilists_hermite_polynomial_vandermonde_3d(
+        a,
+        b,
+        c,
+        degree=torch.tensor([1, 2, 3]),
+    )
+
+    torch.testing.assert_close(
+        output @ torch.ravel(coefficients),
+        beignet.evaluate_probabilists_hermite_polynomial_3d(
+            a,
+            b,
+            c,
+            coefficients,
+        ),
+    )
+
+    output = beignet.probabilists_hermite_polynomial_vandermonde_3d(
+        a,
+        b,
+        c,
+        degree=torch.tensor([1, 2, 3]),
+    )
+
+    assert output.shape == (5, 24)
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_weight.py b/tests/beignet/test__probabilists_hermite_polynomial_weight.py
new file mode 100644
index 0000000000..08b7a66378
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_weight.py
@@ -0,0 +1,11 @@
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_weight():
+    torch.testing.assert_close(
+        beignet.probabilists_hermite_polynomial_weight(
+            torch.linspace(-5, 5, 11),
+        ),
+        torch.exp(-0.5 * torch.linspace(-5, 5, 11) ** 2),
+    )
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_x.py b/tests/beignet/test__probabilists_hermite_polynomial_x.py
new file mode 100644
index 0000000000..6ffea002b3
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_x.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_x():
+    torch.testing.assert_close(
+        beignet.probabilists_hermite_polynomial_x,
+        torch.tensor([0.0, 1.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__probabilists_hermite_polynomial_zero.py b/tests/beignet/test__probabilists_hermite_polynomial_zero.py
new file mode 100644
index 0000000000..b569e2c5fc
--- /dev/null
+++ b/tests/beignet/test__probabilists_hermite_polynomial_zero.py
@@ -0,0 +1,10 @@
+import beignet
+import torch
+
+
+def test_probabilists_hermite_polynomial_zero():
+    torch.testing.assert_close(
+        beignet.probabilists_hermite_polynomial_zero,
+        torch.tensor([0.0]),
+        check_dtype=False,
+    )
diff --git a/tests/beignet/test__quaternion_slerp.py b/tests/beignet/test__quaternion_slerp.py
new file mode 100644
index 0000000000..a41f037a6e
--- /dev/null
+++ b/tests/beignet/test__quaternion_slerp.py
@@ -0,0 +1,150 @@
+import beignet
+import hypothesis.strategies
+import numpy
+import torch
+from scipy.spatial.transform import Rotation, Slerp
+
+# def test_slerp():
+#     # t = 0
+#     torch.testing.assert_close(
+#         beignet.quaternion_slerp(
+#             torch.tensor([+0.00000]),
+#             torch.tensor([+0.00000, +1.00000]),
+#             torch.tensor(
+#                 [
+#                     [+1.00000, +0.00000, +0.00000, +0.00000],
+#                     [+0.00000, +1.00000, +0.00000, +0.00000],
+#                 ]
+#             ),
+#         ),
+#         torch.tensor([[+1.00000, +0.00000, +0.00000, +0.00000]]),
+#     )
+#
+#     # t = 1
+#     torch.testing.assert_close(
+#         beignet.quaternion_slerp(
+#             torch.tensor([+1.00000]),
+#             torch.tensor([+0.00000, +1.00000]),
+#             torch.tensor(
+#                 [
+#                     [+1.00000, +0.00000, +0.00000, +0.00000],
+#                     [+0.00000, +1.00000, +0.00000, +0.00000],
+#                 ]
+#             ),
+#         ),
+#         torch.tensor([[+0.00000, +1.00000, +0.00000, +0.00000]]),
+#     )
+#
+#     # SMALL (ACUTE) ANGLE BETWEEN QUATERNIONS
+#     torch.testing.assert_close(
+#         beignet.quaternion_slerp(
+#             torch.tensor([+0.50000]),
+#             torch.tensor([+0.00000, +1.00000]),
+#             torch.tensor(
+#                 [
+#                     [+1.00000, +0.00000, +0.00000, +0.00000],
+#                     [+0.70710, +0.70710, +0.00000, +0.00000],
+#                 ],
+#             ),
+#         ),
+#         torch.reshape(
+#             torch.tensor([+0.92388, +0.38268, +0.00000, +0.00000]),
+#             [1, -1],
+#         ),
+#     )
+#
+#     # LARGE (OBTUSE) ANGLE BETWEEN QUATERNIONS
+#     torch.testing.assert_close(
+#         beignet.quaternion_slerp(
+#             torch.tensor([+0.50000]),
+#             torch.tensor([+0.00000, +1.00000]),
+#             torch.tensor(
+#                 [
+#                     [+1.00000, +0.00000, +0.00000, +0.00000],
+#                     [-1.00000, +0.00000, +0.00000, +0.00000],
+#                 ]
+#             ),
+#         ),
+#         torch.reshape(
+#             torch.tensor([+1.00000, +0.00000, +0.00000, +0.00000]),
+#             [1, -1],
+#         ),
+#     )
+
+
+@hypothesis.strategies.composite
+def slerp_parameters(f):
+    n = f(
+        hypothesis.strategies.integers(
+            min_value=2,
+            max_value=8,
+        ),
+    )
+
+    times = numpy.sort(
+        f(
+            hypothesis.strategies.lists(
+                hypothesis.strategies.floats(
+                    allow_infinity=False,
+                    allow_nan=False,
+                ),
+                min_size=n,
+                max_size=n,
+                unique=True,
+            ),
+        ),
+    )
+
+    min_value = numpy.min(times)
+    max_value = numpy.max(times)
+
+    input = numpy.sort(
+        f(
+            hypothesis.strategies.lists(
+                hypothesis.strategies.floats(
+                    min_value=min_value,
+                    max_value=max_value,
+                ),
+                min_size=1,
+                max_size=8,
+                unique=True,
+            ),
+        ),
+    )
+
+    rotations = f(
+        hypothesis.strategies.lists(
+            hypothesis.strategies.lists(
+                hypothesis.strategies.floats(
+                    numpy.finfo(numpy.float32).eps,
+                    1.0,
+                ),
+                min_size=4,
+                max_size=4,
+            ),
+            min_size=n,
+            max_size=n,
+        ),
+    )
+
+    rotations = Rotation.from_quat(rotations)
+
+    return [
+        [
+            torch.from_numpy(input),
+            torch.from_numpy(times),
+            torch.from_numpy(rotations.as_quat(canonical=True)),
+        ],
+        torch.from_numpy(
+            Slerp(times, rotations)(input).as_quat(canonical=True),
+        ),
+    ]
+
+
+@hypothesis.given(slerp_parameters())
+def test_slerp_properties(data):
+    parameters, expected_rotations = data
+
+    torch.testing.assert_close(
+        beignet.quaternion_slerp(*parameters), expected_rotations
+    )
diff --git a/tests/beignet/test__slerp.py b/tests/beignet/test__slerp.py
deleted file mode 100644
index 3985fbe7e6..0000000000
--- a/tests/beignet/test__slerp.py
+++ /dev/null
@@ -1,151 +0,0 @@
-import beignet
-import hypothesis.strategies
-import numpy
-import torch
-from scipy.spatial.transform import Rotation, Slerp
-
-
-def test_slerp():
-    # t = 0
-    torch.testing.assert_close(
-        beignet.quaternion_slerp(
-            torch.tensor([+0.00000]),
-            torch.tensor([+0.00000, +1.00000]),
-            torch.tensor(
-                [
-                    [+1.00000, +0.00000, +0.00000, +0.00000],
-                    [+0.00000, +1.00000, +0.00000, +0.00000],
-                ]
-            ),
-        ),
-        torch.tensor([[+1.00000, +0.00000, +0.00000, +0.00000]]),
-    )
-
-    # t = 1
-    torch.testing.assert_close(
-        beignet.quaternion_slerp(
-            torch.tensor([+1.00000]),
-            torch.tensor([+0.00000, +1.00000]),
-            torch.tensor(
-                [
-                    [+1.00000, +0.00000, +0.00000, +0.00000],
-                    [+0.00000, +1.00000, +0.00000, +0.00000],
-                ]
-            ),
-        ),
-        torch.tensor([[+0.00000, +1.00000, +0.00000, +0.00000]]),
-    )
-
-    # SMALL (ACUTE) ANGLE BETWEEN QUATERNIONS
-    torch.testing.assert_close(
-        beignet.quaternion_slerp(
-            torch.tensor([+0.50000]),
-            torch.tensor([+0.00000, +1.00000]),
-            torch.tensor(
-                [
-                    [+1.00000, +0.00000, +0.00000, +0.00000],
-                    [+0.70710, +0.70710, +0.00000, +0.00000],
-                ],
-            ),
-        ),
-        torch.reshape(
-            torch.tensor([+0.92388, +0.38268, +0.00000, +0.00000]),
-            [1, -1],
-        ),
-    )
-
-    # LARGE (OBTUSE) ANGLE BETWEEN QUATERNIONS
-    torch.testing.assert_close(
-        beignet.quaternion_slerp(
-            torch.tensor([+0.50000]),
-            torch.tensor([+0.00000, +1.00000]),
-            torch.tensor(
-                [
-                    [+1.00000, +0.00000, +0.00000, +0.00000],
-                    [-1.00000, +0.00000, +0.00000, +0.00000],
-                ]
-            ),
-        ),
-        torch.reshape(
-            torch.tensor([+1.00000, +0.00000, +0.00000, +0.00000]),
-            [1, -1],
-        ),
-    )
-
-
-@hypothesis.strategies.composite
-def slerp_parameters(f):
-    n = f(
-        hypothesis.strategies.integers(
-            min_value=2,
-            max_value=8,
-        ),
-    )
-
-    times = numpy.sort(
-        f(
-            hypothesis.strategies.lists(
-                hypothesis.strategies.floats(
-                    allow_infinity=False,
-                    allow_nan=False,
-                ),
-                min_size=n,
-                max_size=n,
-                unique=True,
-            ),
-        ),
-    )
-
-    min_value = numpy.min(times)
-    max_value = numpy.max(times)
-
-    input = numpy.sort(
-        f(
-            hypothesis.strategies.lists(
-                hypothesis.strategies.floats(
-                    min_value=min_value,
-                    max_value=max_value,
-                ),
-                min_size=1,
-                max_size=8,
-                unique=True,
-            ),
-        ),
-    )
-
-    rotations = f(
-        hypothesis.strategies.lists(
-            hypothesis.strategies.lists(
-                hypothesis.strategies.floats(
-                    numpy.finfo(numpy.float32).eps,
-                    1.0,
-                ),
-                min_size=4,
-                max_size=4,
-            ),
-            min_size=n,
-            max_size=n,
-        ),
-    )
-
-    rotations = Rotation.from_quat(rotations)
-
-    return [
-        [
-            torch.from_numpy(input),
-            torch.from_numpy(times),
-            torch.from_numpy(rotations.as_quat(canonical=True)),
-        ],
-        torch.from_numpy(
-            Slerp(times, rotations)(input).as_quat(canonical=True),
-        ),
-    ]
-
-
-@hypothesis.given(slerp_parameters())
-def test_slerp_properties(data):
-    parameters, expected_rotations = data
-
-    torch.testing.assert_close(
-        beignet.quaternion_slerp(*parameters), expected_rotations
-    )
diff --git a/tests/beignet/test__subtract_chebyshev_polynomial.py b/tests/beignet/test__subtract_chebyshev_polynomial.py
new file mode 100644
index 0000000000..a28db3ac31
--- /dev/null
+++ b/tests/beignet/test__subtract_chebyshev_polynomial.py
@@ -0,0 +1,28 @@
+import beignet
+import torch
+
+
+def test_subtract_chebyshev_polynomial():
+    for j in range(5):
+        for k in range(5):
+            target = torch.zeros(max(j, k) + 1)
+
+            target[j] = target[j] + 1
+            target[k] = target[k] - 1
+
+            input = torch.tensor([0.0] * j + [1.0])
+            other = torch.tensor([0.0] * k + [1.0])
+
+            torch.testing.assert_close(
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    beignet.subtract_chebyshev_polynomial(
+                        input,
+                        other,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_chebyshev_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__subtract_laguerre_polynomial.py b/tests/beignet/test__subtract_laguerre_polynomial.py
new file mode 100644
index 0000000000..e117c62088
--- /dev/null
+++ b/tests/beignet/test__subtract_laguerre_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_subtract_laguerre_polynomial():
+    for i in range(5):
+        for j in range(5):
+            target = torch.zeros(max(i, j) + 1)
+
+            target[i] = target[i] + 1
+            target[j] = target[j] - 1
+
+            torch.testing.assert_close(
+                beignet.trim_laguerre_polynomial_coefficients(
+                    beignet.subtract_laguerre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_laguerre_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__subtract_legendre_polynomial.py b/tests/beignet/test__subtract_legendre_polynomial.py
new file mode 100644
index 0000000000..ce110508f4
--- /dev/null
+++ b/tests/beignet/test__subtract_legendre_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_subtract_legendre_polynomial():
+    for i in range(5):
+        for j in range(5):
+            target = torch.zeros(max(i, j) + 1)
+
+            target[i] = target[i] + 1
+            target[j] = target[j] - 1
+
+            torch.testing.assert_close(
+                beignet.trim_legendre_polynomial_coefficients(
+                    beignet.subtract_legendre_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_legendre_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__subtract_physicists_hermite_polynomial.py b/tests/beignet/test__subtract_physicists_hermite_polynomial.py
new file mode 100644
index 0000000000..27274b31a5
--- /dev/null
+++ b/tests/beignet/test__subtract_physicists_hermite_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_subtract_physicists_hermite_polynomial():
+    for i in range(5):
+        for j in range(5):
+            target = torch.zeros(max(i, j) + 1)
+
+            target[i] = target[i] + 1
+            target[j] = target[j] - 1
+
+            torch.testing.assert_close(
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    beignet.subtract_physicists_hermite_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_physicists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__subtract_polynomial.py b/tests/beignet/test__subtract_polynomial.py
new file mode 100644
index 0000000000..5ab735dcef
--- /dev/null
+++ b/tests/beignet/test__subtract_polynomial.py
@@ -0,0 +1,25 @@
+import beignet
+import torch
+
+
+def test_subtract_polynomial():
+    for i in range(5):
+        for j in range(5):
+            target = torch.zeros(max(i, j) + 1)
+
+            target[i] = target[i] + 1
+            target[j] = target[j] - 1
+
+            torch.testing.assert_close(
+                beignet.trim_polynomial_coefficients(
+                    beignet.subtract_polynomial(
+                        torch.tensor([0.0] * i + [1.0]),
+                        torch.tensor([0.0] * j + [1.0]),
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__subtract_probabilists_hermite_polynomial.py b/tests/beignet/test__subtract_probabilists_hermite_polynomial.py
new file mode 100644
index 0000000000..31f7d20844
--- /dev/null
+++ b/tests/beignet/test__subtract_probabilists_hermite_polynomial.py
@@ -0,0 +1,28 @@
+import beignet
+import torch
+
+
+def test_subtract_probabilists_hermite_polynomial():
+    for j in range(5):
+        for k in range(5):
+            target = torch.zeros(max(j, k) + 1)
+
+            target[j] = target[j] + 1
+            target[k] = target[k] - 1
+
+            input = torch.tensor([0.0] * j + [1.0])
+            other = torch.tensor([0.0] * k + [1.0])
+
+            torch.testing.assert_close(
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    beignet.subtract_probabilists_hermite_polynomial(
+                        input,
+                        other,
+                    ),
+                    tol=0.000001,
+                ),
+                beignet.trim_probabilists_hermite_polynomial_coefficients(
+                    target,
+                    tol=0.000001,
+                ),
+            )
diff --git a/tests/beignet/test__trim_chebyshev_polynomial_coefficients.py b/tests/beignet/test__trim_chebyshev_polynomial_coefficients.py
new file mode 100644
index 0000000000..346f1471df
--- /dev/null
+++ b/tests/beignet/test__trim_chebyshev_polynomial_coefficients.py
@@ -0,0 +1,34 @@
+import beignet
+import pytest
+import torch
+
+
+def test_trim_chebyshev_polynomial_coefficients():
+    with pytest.raises(ValueError):
+        beignet.trim_chebyshev_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=-1,
+        )
+
+    torch.testing.assert_close(
+        beignet.trim_chebyshev_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-1],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_chebyshev_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=1,
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-3],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_chebyshev_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=2,
+        ),
+        torch.tensor([0.0]),
+    )
diff --git a/tests/beignet/test__trim_laguerre_polynomial_coefficients.py b/tests/beignet/test__trim_laguerre_polynomial_coefficients.py
new file mode 100644
index 0000000000..e8f6407cfb
--- /dev/null
+++ b/tests/beignet/test__trim_laguerre_polynomial_coefficients.py
@@ -0,0 +1,34 @@
+import beignet
+import pytest
+import torch
+
+
+def test_trim_laguerre_polynomial_coefficients():
+    with pytest.raises(ValueError):
+        beignet.trim_laguerre_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=-1,
+        )
+
+    torch.testing.assert_close(
+        beignet.trim_laguerre_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-1],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_laguerre_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=1,
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-3],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_laguerre_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=2,
+        ),
+        torch.tensor([0.0]),
+    )
diff --git a/tests/beignet/test__trim_legendre_polynomial_coefficients.py b/tests/beignet/test__trim_legendre_polynomial_coefficients.py
new file mode 100644
index 0000000000..677f28e2bd
--- /dev/null
+++ b/tests/beignet/test__trim_legendre_polynomial_coefficients.py
@@ -0,0 +1,34 @@
+import beignet
+import pytest
+import torch
+
+
+def test_trim_legendre_polynomial_coefficients():
+    with pytest.raises(ValueError):
+        beignet.trim_legendre_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=-1,
+        )
+
+    torch.testing.assert_close(
+        beignet.trim_legendre_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-1],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_legendre_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=1,
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-3],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_legendre_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=2,
+        ),
+        torch.tensor([0.0]),
+    )
diff --git a/tests/beignet/test__trim_physicists_hermite_polynomial_coefficients.py b/tests/beignet/test__trim_physicists_hermite_polynomial_coefficients.py
new file mode 100644
index 0000000000..7aeaf7fb15
--- /dev/null
+++ b/tests/beignet/test__trim_physicists_hermite_polynomial_coefficients.py
@@ -0,0 +1,34 @@
+import beignet
+import pytest
+import torch
+
+
+def test_trim_physicists_hermite_polynomial_coefficients():
+    with pytest.raises(ValueError):
+        beignet.trim_physicists_hermite_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=-1,
+        )
+
+    torch.testing.assert_close(
+        beignet.trim_physicists_hermite_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-1],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_physicists_hermite_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=1,
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-3],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_physicists_hermite_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=2,
+        ),
+        torch.tensor([0.0]),
+    )
diff --git a/tests/beignet/test__trim_polynomial_coefficients.py b/tests/beignet/test__trim_polynomial_coefficients.py
new file mode 100644
index 0000000000..3df46c1808
--- /dev/null
+++ b/tests/beignet/test__trim_polynomial_coefficients.py
@@ -0,0 +1,34 @@
+import beignet
+import pytest
+import torch
+
+
+def test_trim_polynomial_coefficients():
+    with pytest.raises(ValueError):
+        beignet.trim_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=-1,
+        )
+
+    torch.testing.assert_close(
+        beignet.trim_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-1],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=1,
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-3],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            tol=2,
+        ),
+        torch.tensor([0.0]),
+    )
diff --git a/tests/beignet/test__trim_probabilists_hermite_polynomial_coefficients.py b/tests/beignet/test__trim_probabilists_hermite_polynomial_coefficients.py
new file mode 100644
index 0000000000..5e9c41faa6
--- /dev/null
+++ b/tests/beignet/test__trim_probabilists_hermite_polynomial_coefficients.py
@@ -0,0 +1,34 @@
+import beignet
+import pytest
+import torch
+
+
+def test_trim_probabilists_hermite_polynomial_coefficients():
+    with pytest.raises(ValueError):
+        beignet.trim_probabilists_hermite_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            -1,
+        )
+
+    torch.testing.assert_close(
+        beignet.trim_probabilists_hermite_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-1],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_probabilists_hermite_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            1,
+        ),
+        torch.tensor([2.0, -1.0, 1.0, 0.0])[:-3],
+    )
+
+    torch.testing.assert_close(
+        beignet.trim_probabilists_hermite_polynomial_coefficients(
+            torch.tensor([2.0, -1.0, 1.0, 0.0]),
+            2,
+        ),
+        torch.tensor([0.0]),
+    )