diff --git a/M2/Macaulay2/packages/HolonomicSystems/DOC/Dsystems.m2 b/M2/Macaulay2/packages/HolonomicSystems/DOC/Dsystems.m2 index 87754913ce6..de05c4dbf9c 100644 --- a/M2/Macaulay2/packages/HolonomicSystems/DOC/Dsystems.m2 +++ b/M2/Macaulay2/packages/HolonomicSystems/DOC/Dsystems.m2 @@ -11,7 +11,7 @@ doc /// D:PolynomialRing Outputs :Ideal - the toric ideal of the matrix $A$ in the polynomial ring of the partials inside of the Weyl algerba $D$. + the toric ideal of the matrix $A$ in the polynomial ring of the partials inside of the Weyl algebra $D$. Description Text A $d \times n$ integer matrix $A$ determines a GKZ hypergeometric system of PDEs diff --git a/M2/Macaulay2/packages/LLLBases.m2 b/M2/Macaulay2/packages/LLLBases.m2 index b353f6112e7..84fbf460e15 100644 --- a/M2/Macaulay2/packages/LLLBases.m2 +++ b/M2/Macaulay2/packages/LLLBases.m2 @@ -946,9 +946,9 @@ document { }, SUBSECTION "Orthogonalization Strategy", UL { - {"default -- Classical Gramm-Schmidt Orthogonalization, ", + {"default -- Classical Gram-Schmidt Orthogonalization, ", "This choice uses classical methods for computing - the Gramm-Schmidt othogonalization. + the Gram-Schmidt orthogonalization. It is fast but prone to stability problems. This strategy was first proposed by Schnorr and Euchner in the paper mentioned above. diff --git a/M2/Macaulay2/packages/MatchingFields.m2 b/M2/Macaulay2/packages/MatchingFields.m2 index 367d20caa87..ed04731c27b 100644 --- a/M2/Macaulay2/packages/MatchingFields.m2 +++ b/M2/Macaulay2/packages/MatchingFields.m2 @@ -978,7 +978,7 @@ matchingFieldFromPermutationNoScaling(ZZ, ZZ, List) := opts -> (Lk, Ln, S) -> ( -- 7) if not then d = d+1 and go back to step 2 -- 8) reduce the matching field ideal gens modulo the full GB and check if the result is zero -- --- In the homgeneous case, it suffices to compute a GB up to degree limit d (step 1) +-- In the homogeneous case, it suffices to compute a GB up to degree limit d (step 1) -- so we can forgo the while loop isToricDegeneration = method () diff --git a/M2/Macaulay2/packages/MonodromySolver/under-construction-examples/deprecated-examples/example-trace.m2 b/M2/Macaulay2/packages/MonodromySolver/under-construction-examples/deprecated-examples/example-trace.m2 index cf405e694ea..cfde5ee5b97 100644 --- a/M2/Macaulay2/packages/MonodromySolver/under-construction-examples/deprecated-examples/example-trace.m2 +++ b/M2/Macaulay2/packages/MonodromySolver/under-construction-examples/deprecated-examples/example-trace.m2 @@ -109,7 +109,7 @@ R = C[x_1..x_n] F = apply(n-m, i->sub(random(d,CC[x_1..x_n]),R)) -- V(F) = intersection of n-m hypersurfaces of degree d A = genericMatrix(C,n,m) B = genericMatrix(C,b_1,1,m) -L = flatten entries (vars R * A + B) -- slice of complimentary dimension +L = flatten entries (vars R * A + B) -- slice of complementary dimension G = polySystem(F|L) clearAll() diff --git a/M2/Macaulay2/packages/NumericalSemigroups.m2 b/M2/Macaulay2/packages/NumericalSemigroups.m2 index 6718eece6c3..15c27c0499b 100644 --- a/M2/Macaulay2/packages/NumericalSemigroups.m2 +++ b/M2/Macaulay2/packages/NumericalSemigroups.m2 @@ -2097,7 +2097,7 @@ Outputs degrees of a basis of T^1(semigroupRing L) Description Text - T^1(B) is the tangent space to the versal deformaion of + T^1(B) is the tangent space to the versal deformation of the ring B, and is finite dimensional when B has isolated singularity. If B = S/I is a Cohen presentation, then T^1(B) = coker Hom(Omega_S, B) -> Hom(I/I^2, B). diff --git a/M2/Macaulay2/packages/PlaneCurveLinearSeries.m2 b/M2/Macaulay2/packages/PlaneCurveLinearSeries.m2 index 4fff75a4294..99543f5ef01 100644 --- a/M2/Macaulay2/packages/PlaneCurveLinearSeries.m2 +++ b/M2/Macaulay2/packages/PlaneCurveLinearSeries.m2 @@ -479,7 +479,7 @@ Outputs Description Text Implements the additive inverse in the group law on the smooth points of - a plane curve E of genus 1, represented by its homogeneouos coordinate ring, + a plane curve E of genus 1, represented by its homogeneous coordinate ring, with chosen zero point o. Example S = QQ[x,y,z] diff --git a/M2/Macaulay2/packages/TateOnProducts.m2 b/M2/Macaulay2/packages/TateOnProducts.m2 index 0f64b2cd031..d58ae5d26bd 100644 --- a/M2/Macaulay2/packages/TateOnProducts.m2 +++ b/M2/Macaulay2/packages/TateOnProducts.m2 @@ -856,7 +856,7 @@ viewHelp TateOnProducts lastQuadrantComplex=method() lastQuadrantComplex(ChainComplex,List) := (C,c) -> ( - -- c index of the lower corner of the complentary first quadrant + -- c index of the lower corner of the complementary first quadrant lastQuadrantComplex1(C,c-toList(#c:1))) diff --git a/M2/Macaulay2/packages/TropicalToric/ToricCycleDoc.m2 b/M2/Macaulay2/packages/TropicalToric/ToricCycleDoc.m2 index cb1fc962a3f..664efd9901b 100644 --- a/M2/Macaulay2/packages/TropicalToric/ToricCycleDoc.m2 +++ b/M2/Macaulay2/packages/TropicalToric/ToricCycleDoc.m2 @@ -326,7 +326,7 @@ doc /// The set of torus-invariant cycles forms an abelian group under addition. The basic operations arising from this structure, including addition, subtraction, negation, and scalar - multplication by integers, are available. + multiplication by integers, are available. Text We illustrate a few of the possibilities on one variety. Example diff --git a/M2/Macaulay2/packages/TropicalToric/TropicalToricCode.m2 b/M2/Macaulay2/packages/TropicalToric/TropicalToricCode.m2 index 60cba5d4abb..0c9dcd12619 100644 --- a/M2/Macaulay2/packages/TropicalToric/TropicalToricCode.m2 +++ b/M2/Macaulay2/packages/TropicalToric/TropicalToricCode.m2 @@ -31,7 +31,7 @@ refineMultiplicity (TropicalCycle, NormalToricVariety) := (T,X) ->( --input: normal toric varieties X,X' such that the identity on the lattices induces -- a toric map phi:X' -> X, --- list mult of multiplcities of cones of X' of dimension k +-- list mult of multiplicities of cones of X' of dimension k --output: list of degrees deg([Y'] * phi^*(V(sigma)), where [Y'] is the class of the cycle -- Y' in X' corresponding to the Minkowski weight given by mult. -- Note that here [Y'] * V(sigma') = mult_sigma' for every cone sigma' of X'.