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@@ -288,3 +288,4 @@ AllMarkovBases | |
| Tableaux | ||
| CpMackeyFunctors | ||
| JSONRPC | ||
| SimplicialModules | ||
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,208 @@ | ||
| newPackage( | ||
| "SimplicialModules", | ||
| AuxiliaryFiles => true, | ||
| Version => "0.1", | ||
| Date => "September 27, 2023", | ||
| Authors => { | ||
| {Name => "Keller VandeBogert", Email => "kvandebo@nd.edu", HomePage => "https://sites.google.com/view/kellervandebogert/home"}, | ||
| {Name => "Michael DeBellevue", Email => "", HomePage => ""}}, | ||
| Headline => "methods for working in the category of simplicial modules", | ||
| Keywords => {"Homological Algebra", "Commutative Algebra"}, | ||
| PackageExports => {"Complexes", "SchurFunctors"}, | ||
| PackageImports => {"Complexes"} | ||
| ) | ||
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| export {"SimplicialModule", | ||
| "SimplicialModuleMap", | ||
| "simplicialModule", | ||
| --"combineSFactors", | ||
| "forgetComplex", | ||
| "forgetDegeneracy", | ||
| "isSimplicialModule", | ||
| "isSimplicialMorphism", | ||
| "randomSimplicialMap", | ||
| "tensorwithComponents", | ||
| "topDegree", | ||
| "exteriorInclusion", | ||
| "extPower", | ||
| "naiveNorm", | ||
| "normalize", | ||
| "schurMap", | ||
| "simplicialTensor", | ||
| "symmetricQuotient", | ||
| "tensorLES", | ||
| --"CheckMap", | ||
| "CheckComplex", | ||
| "RememberSummands", | ||
| "Degeneracy", | ||
| "TopDegree", | ||
| "ss", | ||
| "complexLength", | ||
| "CheckSum", | ||
| "complexMap", | ||
| "summandSurjection" | ||
| } | ||
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| ------------------------------------------------------------------------------ | ||
| ------------------------------------------------------------------------------ | ||
| -- **CODE** -- | ||
| ------------------------------------------------------------------------------ | ||
| ------------------------------------------------------------------------------ | ||
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| load "./SimplicialModules/SimplicialMapUtilities_Modified.m2" | ||
| load "./SimplicialModules/SimplicialModule.m2" | ||
| load "./SimplicialModules/Normalization.m2" | ||
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| ----------------------------------------------------------------------------- | ||
| -- Documentation | ||
| ----------------------------------------------------------------------------- | ||
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| beginDocumentation() | ||
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| load "./SimplicialModules/SimplicialModuleDOC.m2" | ||
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| ----------------------------------------------------------------------------- | ||
| -- Tests | ||
| ----------------------------------------------------------------------------- | ||
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| load "./SimplicialModules/SimplicialModuleTESTS1.m2" | ||
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| ----------------------------------------------------------------------------- | ||
| -- Development | ||
| ----------------------------------------------------------------------------- | ||
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| end-- | ||
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| uninstallPackage "SimplicialModules" | ||
| restart | ||
| debug installPackage "SimplicialModules" | ||
| debug loadPackage("SimplicialModules", LoadDocumentation => true, Reload => true) | ||
| debug needsPackage "SimplicialModules" | ||
| check SimplicialModules | ||
| viewHelp SimplicialModules | ||
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| Q = QQ[x_1..x_3]; | ||
| K = koszulComplex vars Q; | ||
| isWellDefined simplicialModule(K, 4) --no degeneracy here | ||
| S = simplicialModule(K,4, Degeneracy => true) | ||
| S.dd**Q^1 | ||
| isWellDefined S | ||
| Sdegen = simplicialModule(K,4,Degeneracy => true) | ||
| S.dd | ||
| --S.ss --should return error, no such key | ||
| Sdegen.ss --this is the version that actually has degeneracy maps cached | ||
| simplicialModule(K, 5) | ||
| C = complex(Q^1, Base => 1) | ||
| simplicialModule(C, 3) | ||
| isWellDefined oo | ||
| simplicialModule(complex(Q^2, Base => 2), 6, Degeneracy => true) | ||
| isWellDefined oo --nice, now we can be confident the objects we are messing with actually make any sense | ||
| oo.ss | ||
| id_S | ||
| phi = exteriorInclusion(S); | ||
| prune phi | ||
| prune coker phi | ||
| K = koszulComplex {x_1,x_2} | ||
| Sn = simplicialModule(K, 4, Degeneracy => true) | ||
| phi = exteriorInclusion(K) | ||
| isCommutative phi | ||
| isWellDefined phi | ||
| isCommutative prune phi | ||
| isWellDefined prune phi | ||
| sphi = exteriorInclusion(Sn); | ||
| psphi = prune sphi; | ||
| isWellDefined (source psphi).cache.pruningMap | ||
| isCommutative (source psphi).cache.pruningMap | ||
| isSimplicialMorphism (source psphi).cache.pruningMap --pruningMaps are well-defined morphisms | ||
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| S = simplicialModule(K,6) | ||
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| p = randomComplexMap(K, K, Degree => 1, InternalDegree => 1) | ||
| sp = simplicialModule p | ||
| isWellDefined sp | ||
| isCommutative sp | ||
| normalize(sp, CheckComplex => false) | ||
| prune oo ---reobtain p | ||
| p' = randomComplexMap(K, K, Degree => -1) | ||
| sp' = simplicialModule p' | ||
| isWellDefined sp' | ||
| isCommutative sp' | ||
| normalize(sp', CheckComplex => false) | ||
| prune oo --reobtain p' | ||
| p = randomComplexMap(K, K, Degree => 1, Cycle => true, InternalDegree => 2) | ||
| sp = simplicialModule p | ||
| isWellDefined sp | ||
| isCommutative sp | ||
| normalize(sp, CheckComplex => false) | ||
| prune oo ---reobtain p | ||
| diffs = simplicialModule K.dd | ||
| isWellDefined diffs | ||
| isCommutative diffs | ||
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| image(id_S) == S | ||
| simplicialModule(id_K, 6) == id_S | ||
| isSimplicialMorphism id_S | ||
| simplicialModule(complex(Q^0), 6, Degeneracy => true) -- should be able to input 0 and get a well-defined output | ||
| isWellDefined oo | ||
| phi = randomSimplicialMap(S, S, Cycle => true, InternalDegree => 1) | ||
| isWellDefined phi | ||
| isCommutative phi | ||
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| bS = basis(0, forgetComplex S) | ||
| prune bS.dd | ||
| isWellDefined bS | ||
| isWellDefined prune bS | ||
| bid = basis(0, id_(forgetComplex S)) | ||
| isWellDefined bid | ||
| isCommutative bid | ||
| isWellDefined prune bid | ||
| isCommutative prune bid | ||
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| fS = forgetComplex S | ||
| fS.?ss | ||
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| bS = basis(1, forgetComplex S) | ||
| isWellDefined bS | ||
| prune bS.dd | ||
| isWellDefined oo | ||
| prune bS.ss | ||
| isWellDefined oo | ||
| normalize bS | ||
| prune oo | ||
| prune basis(1, K) | ||
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| bS = basis(3, forgetComplex S) | ||
| isWellDefined bS | ||
| prune bS.dd; | ||
| isWellDefined oo | ||
| prune bS.ss; | ||
| isWellDefined oo | ||
| normalize bS | ||
| prune oo | ||
| prune basis(3, koszulComplex vars Q) | ||
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| tS = truncate(1, S) | ||
| isWellDefined tS | ||
| prune tS | ||
| isWellDefined prune tS | ||
| tS = truncate(1, fS) | ||
| isWellDefined tS | ||
| prune tS | ||
| isWellDefined prune tS | ||
| isCommutative truncate(2, id_S) | ||
| isCommutative truncate(2, id_fS) | ||
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| K = koszulComplex {x_1,x_2} | ||
| isWellDefined (Sc = schurMap({1,1}, K)) | ||
| prune ext(2, K) | ||
| prune schurMap({2,1}, K, TopDegree => 4) | ||
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Having Complexes in both PackageImports and PackageExports is redundant
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What's the preferred threshold for test lengths? These tests took about half as long as those times on my computer, but I acknowledge 35 seconds is quite long. One issue with this is that simplicial objects are generally very big and computationally cumbersome, so it's hard to build nontrivial examples that also run quickly. I kind of knew the example sizes would be an issue here but wasn't sure what was considered acceptable.
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What's the main bottleneck? Have you profiled the test?
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No, I haven't profiled it mostly because I don't know how. For all of the slow tests it generally stems not from this package's constructors themselves, but the general slowness of applying Schur functors/exterior powers to large matrices (which are functions from other packages).