fix: group algebras of additive groups with sparse rep

[lgoettgens]

These were the necessary changes to make (sparse) group algebras with an (infinite) additive group that is not FinGenAbGroup.

To find these things, I defined a thin wrapper around FinGenAbGroup and tried to make that work with the existing things.

struct FooGroup <: AbstractAlgebra.AdditiveGroup
  G::FinGenAbGroup
end

struct FooGroupElem <: AbstractAlgebra.AdditiveGroupElem
  x::FinGenAbGroupElem
end

elem_type(::Type{FooGroup}) = FooGroupElem

parent_type(::Type{FooGroupElem}) = FooGroup

parent(x::FooGroupElem) = FooGroup(parent(x.x))

is_abelian(G::FooGroup) = is_abelian(G.G)

is_finite(G::FooGroup) = is_finite(G.G)

order(T, G::FooGroup) = order(T, G.G)

order(G::FooGroup) = order(G.G)

length(G::FooGroup) = length(G.G)

function Base.iterate(G::FooGroup)
  it = iterate(G.G)
  isnothing(it) && return nothing
  x, state = it
  return FooGroupElem(x), state
end

function Base.iterate(G::FooGroup, state)
  it = iterate(G.G, state)
  isnothing(it) && return nothing
  x, state = it
  return FooGroupElem(x), state
end

zero(G::FooGroup) = FooGroupElem(zero(G.G))

iszero(x::FooGroupElem) = iszero(x.x)

+(x::FooGroupElem, y::FooGroupElem) = FooGroupElem(x.x + y.x)

Base.hash(x::FooGroupElem, h::UInt) = hash(x.x, h)

Base.:(==)(x::FooGroupElem, y::FooGroupElem) = x.x == y.x

Base.rand(G::FooGroup) = FooGroupElem(rand(G.G))

export FooGroup, FooGroupElem

[codecov]

Codecov Report

Attention: Patch coverage is 81.57895% with 7 lines in your changes missing coverage. Please review.

Project coverage is 75.92%. Comparing base (0d6625a) to head (4b6c2e6).
Report is 3 commits behind head on master.

Files with missing lines	Patch %	Lines
src/AlgAss/AlgGrp.jl	78.12%	7 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1685      +/-   ##
==========================================
- Coverage   76.01%   75.92%   -0.09%     
==========================================
  Files         362      362              
  Lines      114299   114324      +25     
==========================================
- Hits        86882    86803      -79     
- Misses      27417    27521     +104     

Files with missing lines	Coverage Δ
src/AlgAss/Elem.jl	88.35% <100.00%> (+0.18%)	⬆️
src/AlgAss/Types.jl	85.22% <100.00%> (-0.17%)	⬇️
src/AlgAss/AlgGrp.jl	74.87% <78.12%> (+0.46%)	⬆️

... and 30 files with indirect coverage changes

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[thofma]

can you add a dummy print test? sprint("text/plain", QG) isa String or something like that?

[thofma]

Thanks, looks good. I wish those functions were part of the "Group interface".

[lgoettgens]

Yeah, something I might tackle in the future, depending on if my experiment with additive group algebras works out.

I have the feeling that I might find more things in here once I really start using group algebras in Oscar, but I would suggest that I then open another PR.

[thofma]

I will merge once it is green modulo julia nightly. The "sparse" group algebras are not really battle tested, but I hope that at least the "ring interface" might be happy now.