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GModule work from OSCAR Workshop #4095
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d7b7045
add bad first attempt at `GModuleHom` type
mjrodgers f05a8ab
fix `irreducible_modules(QQ,G)` returning duplicate modules
mjrodgers 8a9d8de
fix variable name
mjrodgers 20c6825
add missing `}`
mjrodgers 00a2a51
extend the GHom's - almost useful now
fieker 40ab299
typos
fieker 2415646
proof of comcept: use map in restriction
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,93 @@ | ||
| mutable struct GModuleHom{ G, T1, T2} <: Map{GModule{G, T1}, GModule{G, T2}, OscarMap, GModuleHom} | ||
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| GM1::GModule{G, T1} | ||
| GM2::GModule{G, T2} | ||
| module_map::Map{T1, T2} | ||
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| function GModuleHom( | ||
| M1::GModule, | ||
| M2::GModule, | ||
| mp::Map; | ||
| check::Bool = false | ||
| ) | ||
| # Need to require that | ||
| # 1. Both GModules have the same group | ||
| # 2. The group action is respected | ||
| @req M1.G === M2.G "groups need to be identical" | ||
| @req domain(mp) === M1.M && codomain(mp) === M2.M "map need to map 1st module into 2nd" | ||
| #not every hom is a G-Hom...that is what check is supposed to do - eventually | ||
| #see 2. | ||
| if check #only works if mp is a morphism so that "*" and "==" are doing | ||
| #s.th. useful | ||
| @assert all(g->action(M1, g)*mp == mp*action(M2, g), gens(M1.G)) | ||
| end | ||
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| return new{typeof(M1.G), typeof(M1.M), typeof(M2.M)}(M1, M2, mp) | ||
| end | ||
| end | ||
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| function hom(M1::GModule{T}, M2::GModule{T}, mp::Map; check::Bool = true) where T <: AbstractAlgebra.Group | ||
| return GModuleHom(M1, M2, mp; check) | ||
| end | ||
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| function hom(M1::GModule{T}, M2::GModule{T}, mp::MatElem; check::Bool = true) where T <: AbstractAlgebra.Group | ||
| return GModuleHom(M1, M2, hom(M1.M, M2.M, mp); check) | ||
| end | ||
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| domain(M::GModuleHom) = M.GM1 | ||
| codomain(M::GModuleHom) = M.GM2 | ||
| parent(M::GModuleHom) = Hecke.MapParent(domain(M), codomain(M), "homomorphisms") | ||
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| mutable struct GModuleElem{T} | ||
| parent::GModule | ||
| data::T | ||
| end | ||
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| parent(a::GModuleElem) = a.parent | ||
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| function (C::GModule)(a::Union{ModuleElem, FinGenAbGroupElem}) | ||
| @req parent(a) === C.M "wrong parent for $a" | ||
| return GModuleElem(C, a) | ||
| end | ||
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| function ==(a::GModuleElem, b::GModuleElem) | ||
| @req parent(a) === parent(b) "parents differ" | ||
| return a.data == b.data | ||
| end | ||
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| function hash(a::GModuleElem, u::UInt) | ||
| return hash(a.data, u) | ||
| end | ||
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| function +(a::GModuleElem, b::GModuleElem) | ||
| @req parent(a) === parent(b) "parents differ" | ||
| return GModuleElem(parent(a), a.data + b.data) | ||
| end | ||
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| function -(a::GModuleElem, b::GModuleElem) | ||
| @req parent(a) === parent(b) "parents differ" | ||
| return GModuleElem(parent(a), a.data - b.data) | ||
| end | ||
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| function -(a::GModuleElem) | ||
| return GModuleElem(parent(a), -a.data) | ||
| end | ||
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| function *(a::GModuleElem, g::GroupElem) | ||
| @req parent(a).G === parent(g) "group element has wrong parent" | ||
| return GModuleElem(parent(a), action(parent(a), g, a.data)) | ||
| end | ||
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| function (A::GModuleHom)(a::GModuleElem) | ||
| @req parent(a) === domain(A) "element has wrong parent" | ||
| return GModuleElem(codomain(A), A.module_map(a.data)) | ||
| end | ||
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| function kernel(A::GModuleHom) | ||
| return sub(A, kernel(A.module_map)[2]) | ||
| end | ||
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| function image(A::GModuleHom) | ||
| return sub(A, image(A.module_map)[2]) | ||
| end | ||
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maybe add some tests for the new code?