feat: group algebras with sparse representation #1655

thofma · 2024-10-18T19:41:42Z

Due to popular demand, group algebras with sparse representation (aka "don't crash with large groups"). Needs some work/clean up:

julia> G = SymmetricGroup(10)
Full symmetric group over 10 elements

julia> QG = group_algebra(QQ, G; sparse = true)
Group algebra
  of full symmetric group over 10 elements
  over rational field

julia> a = QG(rand(G)); b = QG(rand(G));

julia> c = (a + b) * (a - b)
(1,2,4,8,7)(3,9,10,5,6) - (1,4,9)(2,10,3,6,7,5,8) + (1,7,3,8,6,10,4)(2,9,5) - (1,2,6)(3,9)(4,5)

@royess this might interest you. It is similar to your approach.

Small todo:

Add a FG(::Dict) constructor.
Add tests.
Add documentation.

codecov · 2024-10-21T21:33:34Z

Codecov Report

Attention: Patch coverage is 91.08280% with 14 lines in your changes missing coverage. Please review.

Project coverage is 75.82%. Comparing base (2af99ca) to head (2c131f3).

Files with missing lines	Patch %	Lines
src/AlgAss/Elem.jl	83.33%	13 Missing ⚠️
src/AlgAss/AlgGrp.jl	85.71%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1655      +/-   ##
==========================================
- Coverage   75.85%   75.82%   -0.04%     
==========================================
  Files         361      361              
  Lines      113719   113797      +78     
==========================================
+ Hits        86262    86284      +22     
- Misses      27457    27513      +56

Files with missing lines	Coverage Δ
src/AlgAss/AbsAlgAss.jl	`88.26% <100.00%> (+0.06%)`	⬆️
src/AlgAss/Types.jl	`85.79% <100.00%> (+2.89%)`	⬆️
src/Grp/GenGrp.jl	`70.11% <100.00%> (+0.11%)`	⬆️
src/GrpAb/GrpAbFinGen.jl	`75.92% <100.00%> (-0.07%)`	⬇️
src/AlgAss/AlgGrp.jl	`74.28% <85.71%> (+1.21%)`	⬆️
src/AlgAss/Elem.jl	`88.29% <83.33%> (-0.32%)`	⬇️

... and 26 files with indirect coverage changes

lgoettgens · 2024-10-22T09:33:56Z

Does this change allow me to work with group algebras of infinite groups as well?

thofma · 2024-10-22T10:47:43Z

Yes:

julia> F = free_group(2)
Free group of rank 2

julia> x, y = gens(F);

julia> QF = group_algebra(QQ, F; sparse = true)
Group algebra
  of free group of rank 2
  over rational field

julia> (QF(x) + QF(y))^2
f1^2 + f1*f2 + f2*f1 + f2^2

Fe-r-oz · 2024-10-22T19:31:27Z

This is wonderful! I will shift to sparse = true as soon as this is merged! Thank you.

fingolfin

Great! Some quick comments and questions (all nitpicks, not meant to block anything)

fingolfin · 2024-10-23T12:33:00Z

docs/src/manual/algebras/groupalgebras.md

+```jldoctest
+julia> G = abelian_group([2, 2]); a = G([0, 1]);
+
+julia> QG = group_algebra(QQ, G);
+
+julia> x = QG(a)
+[0, 0, 1, 0]
+```
+


Seems a bit redundant to me given the example right afterwards. But perhaps that just me (definitely is a matter of taste anyway).

Suggested change

```jldoctest

julia> G = abelian_group([2, 2]); a = G([0, 1]);

julia> QG = group_algebra(QQ, G);

julia> x = QG(a)

[0, 0, 1, 0]

```

Alternatively, how about turning this into a "running" example, with the codeblocks connected with help of a label? I.e. using the ```jldoctest mylabel syntax. Then the definitions of G and QG don't have to be repeated three times.

fingolfin · 2024-10-23T12:35:52Z

docs/src/manual/algebras/groupalgebras.md

+
+julia> QG = group_algebra(QQ, G);
+
+julia> QG(Dict(a => 2, zero(G) => 1)) == 2 * QG(a) + 1 * QG(zero(G))


How about also supporting this syntax?

Suggested change

julia> QG(Dict(a => 2, zero(G) => 1)) == 2 * QG(a) + 1 * QG(zero(G))

julia> QG(a => 2, zero(G) => 1) == 2 * QG(a) + 1 * QG(zero(G))

fingolfin · 2024-10-23T12:36:41Z

src/AlgAss/AlgGrp.jl

@@ -59,17 +59,25 @@ end
 ################################################################################

 @doc raw"""
-    group_algebra(K::Ring, G; op = *) -> GroupAlgebra
+    group_algebra(K::Ring, G::Group; sparse::Bool = false,


Is op omitted on purpose (just wondering, as it is still there in the implementation)

fingolfin · 2024-10-24T07:38:00Z

src/AlgAss/Types.jl

@@ -130,6 +130,13 @@ end
 @attributes mutable struct GroupAlgebra{T, S, R} <: AbstractAssociativeAlgebra{T}
  base_ring::Ring
  group::S
+  # We represent elements using a coefficient vector,


Suggested change

# We represent elements using a coefficient vector,

# If `sparse` is false we represent elements using a coefficient vector,

fingolfin · 2024-10-24T07:40:46Z

src/AlgAss/Types.jl

+        A.ind += 1
+        resize!(A.base_to_group, max(A.ind, length(A.base_to_group)))
+        A.base_to_group[A.ind] = g
+        return A.ind


So when would length(A.base_to_group) ever exceed A.ind? Right now I am wondering why you even need A.ind and can't just do this:

Suggested change

A.ind += 1

resize!(A.base_to_group, max(A.ind, length(A.base_to_group)))

A.base_to_group[A.ind] = g

return A.ind

push!(A.base_to_group, g)

return length(A.base_to_group)

fingolfin · 2024-10-24T07:45:01Z

src/AlgAss/Types.jl


-      A.one = v
+      if !A.sparse


Merge this with preceding end into an else?

thofma marked this pull request as draft October 18, 2024 19:41

feat: group algebras with sparse representation

d76c540

thofma force-pushed the th/grpalg branch 2 times, most recently from 032ba33 to d4cbc4f Compare October 21, 2024 20:17

hmmm

2c131f3

thofma force-pushed the th/grpalg branch from d4cbc4f to 2c131f3 Compare October 21, 2024 20:34

thofma marked this pull request as ready for review October 21, 2024 21:11

This was referenced Oct 22, 2024

Implementing Bivariate Bicycle Codes using 2BGA as the parent via Hecke's Group Algebra QuantumSavory/QuantumClifford.jl#399

Open

Haah's cubic code using abelian group ℤ₃ˣ³ via Hecke's Group Algebra QuantumSavory/QuantumClifford.jl#388

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feat: group algebras with sparse representation #1655

feat: group algebras with sparse representation #1655

thofma commented Oct 18, 2024 •

edited

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lgoettgens commented Oct 22, 2024

thofma commented Oct 22, 2024

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fingolfin Oct 23, 2024

fingolfin Oct 23, 2024

fingolfin Oct 23, 2024

fingolfin Oct 24, 2024

fingolfin Oct 24, 2024

fingolfin Oct 24, 2024


		julia> QG = group_algebra(QQ, G);

		julia> QG(Dict(a => 2, zero(G) => 1)) == 2 * QG(a) + 1 * QG(zero(G))

	julia> QG(Dict(a => 2, zero(G) => 1)) == 2 * QG(a) + 1 * QG(zero(G))
	julia> QG(a => 2, zero(G) => 1) == 2 * QG(a) + 1 * QG(zero(G))

	# We represent elements using a coefficient vector,
	# If `sparse` is false we represent elements using a coefficient vector,

feat: group algebras with sparse representation #1655

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feat: group algebras with sparse representation #1655

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thofma commented Oct 18, 2024 • edited Loading

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thofma commented Oct 18, 2024 •

edited

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