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Added tests + more documentation
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Currently the package can install, all documentation loads, and all tests pass
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kellerlv committed Jun 17, 2024
1 parent b8c0f83 commit 74a6dfc
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Expand Up @@ -4,7 +4,8 @@ newPackage(
Version => "0.1",
Date => "September 27, 2023",
Authors => {
{Name => "Keller VandeBogert", Email => "[email protected]", HomePage => "todo"}},
{Name => "Keller VandeBogert", Email => "[email protected]", HomePage => "todo"},
{Name => "Michael DeBellevue", Email => "", HomePage => ""}},
Headline => "methods for working in the category of simplicial modules",
Keywords => {"Homological Algebra", "Algebraic Topology"},
PackageExports => {"Complexes", "SchurFunctors"},
Expand Down Expand Up @@ -72,19 +73,7 @@ load "./SimplicialModules/SimplicialModuleDOC.m2"
-- Tests
-----------------------------------------------------------------------------

TEST ///
Q = ZZ/101[x_1,x_2];
K1 = complex {matrix{{x_1}}};
K2 = complex {matrix{{x_2}}};
T1 = K1**K2
--T1.dd
T2 = prune simplicialTensor({K1,K2})
--T2.dd
phi1 = extend(T1,T2,id_(T1_0));
phi2 = extend(T2,T1,id_(T1_0));
--assert(phi1*phi2 == id_T1)
--assert(isNullHomotopic(phi2*phi1 - id_T2))
///
load "./SimplicialModules/SimplicialModuleTESTS1.m2"



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Expand Up @@ -3274,8 +3274,21 @@ doc ///
Text
If any of these identities fail, the function returns `false`. If all identities are satisfied, the function returns `true`.
Example
Q = ZZ/101[x_1..x_3]
R = QQ[a..d];
f0 = matrix {{-b^2+a*c, b*c-a*d, -c^2+b*d}}
f1 = map(source f0,, {{d, c}, {c, b}, {b, a}})
C = simplicialModule(complex {f0, f1}, 3, Degeneracy => true)
isSimplicial C
dd^C
ss^C
dd^C*ss^C --if C is simplicial, this should be all identity maps
Text
The zero simplicial module is well-defined.
Example
C = simplicialModule(R^0, 6, Degeneracy => true)
isSimplicial C
SeeAlso
isWellDefined
///


Expand Down Expand Up @@ -3309,8 +3322,21 @@ doc ///
since the @TO normalize@ command by default first checks if a simplicial module is obtained as a Dold-Kan image
before attempting a more costly computation.
Example
Q = ZZ/101[x_1..x_3]
R = ZZ/101[x_1..x_3];
K = koszulComplex vars R
S = simplicialModule(K,4, Degeneracy => true)
S.?complex
fS = forgetComplex S
components fS_3
ffS = forgetComplex(S, RememberSummands => false)
components ffS_3
Kn = normalize fS
Knn = normalize ffS
Kn.dd
K == prune Kn
SeeAlso
normalize
forgetDegeneracy
///


Expand All @@ -3331,12 +3357,19 @@ doc ///
The simplicial module S, but with no degeneracy maps stored.
Description
Text
This function removes the data of degeneracy maps from a simplicial module `S`, effectively forgetting the degeneracy structure. It is useful when the user wants to ignore degeneracy maps for the purpose of speeding up computations or simplifying the simplicial object.
Text
If `S` already contains a complex (`S.complex`), the function returns a new simplicial module with the same complex, face maps (`S.dd.map`), and top degree (`S.topDegree`), effectively preserving the complex while removing degeneracy maps.
If `S` does not have a complex, the function returns a new simplicial module with the underlying module (`S.module`), face maps (`S.dd.map`), and top degree (`S.topDegree`).
This function removes the data of degeneracy maps from a simplicial module `S`.
It is useful when the user wants to ignore degeneracy maps for the purpose of speeding up computations or simplifying the simplicial object.
Example
Q = ZZ/101[x_1..x_3]
Q = ZZ/101[a..d]
K = koszulComplex vars Q
S = simplicialModule(K, 6, Degeneracy => true)
elapsedTime S**S
fS = forgetDegeneracy S
elapsedTime fS**fS --faster when degeneracy is ignored
Text
The change in speed becomes much more noticeable as ranks get larger.
SeeAlso
forgetComplex
///


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