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Some fixes and performance improvements for iso_oscar_gap(::LieAlgebra) #4227

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merged 4 commits into from
Oct 22, 2024
Merged

Some fixes and performance improvements for iso_oscar_gap(::LieAlgebra) #4227

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241ac1f
Make `_iso_oscar_gap(::AbstractLieAlgeba)` way more efficient
lgoettgens Oct 22, 2024
68cdc5d
Move root system iso to its own function
lgoettgens Oct 22, 2024
dcbd2b9
Some type stability
lgoettgens Oct 22, 2024
0007d2c
Remove some unwanted iso caching
lgoettgens Oct 22, 2024
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8 changes: 2 additions & 6 deletions experimental/LieAlgebras/src/iso_gap_oscar.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -26,9 +26,7 @@ function _iso_gap_oscar_abstract_lie_algebra(
LO = _abstract_lie_algebra_from_GAP(LG, coeffs_iso, s)
finv, f = _iso_oscar_gap_lie_algebra_functions(LO, LG, inv(coeffs_iso))

iso = MapFromFunc(LG, LO, f, finv)
set_attribute!(LO, :iso_oscar_gap => inv(iso))
return iso
return MapFromFunc(LG, LO, f, finv)
end

function _iso_gap_oscar_linear_lie_algebra(
Expand All @@ -39,9 +37,7 @@ function _iso_gap_oscar_linear_lie_algebra(
LO = _linear_lie_algebra_from_GAP(LG, coeffs_iso, s)
finv, f = _iso_oscar_gap_lie_algebra_functions(LO, LG, inv(coeffs_iso))

iso = MapFromFunc(LG, LO, f, finv)
set_attribute!(LO, :iso_oscar_gap => inv(iso))
return iso
return MapFromFunc(LG, LO, f, finv)
end

function _abstract_lie_algebra_from_GAP(
Expand Down
78 changes: 44 additions & 34 deletions experimental/LieAlgebras/src/iso_oscar_gap.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -22,7 +22,7 @@
return (f, finv)
end

function _iso_oscar_gap(LO::LinearLieAlgebra)
function _iso_oscar_gap(LO::LinearLieAlgebra; set_attributes::Bool=true)
coeffs_iso = Oscar.iso_oscar_gap(coefficient_ring(LO))
LG = GAP.Globals.LieAlgebra(
codomain(coeffs_iso),
Expand All @@ -32,6 +32,12 @@

f, finv = _iso_oscar_gap_lie_algebra_functions(LO, LG, coeffs_iso)

if set_attributes && has_root_system(LO)
# we need to construct the root system in GAP as otherwise it may detect a different order of simple roots
RO = root_system(LO)
_iso_oscar_gap_set_root_system(LG, RO)

Check warning on line 38 in experimental/LieAlgebras/src/iso_oscar_gap.jl

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Codecov / codecov/patch

experimental/LieAlgebras/src/iso_oscar_gap.jl#L37-L38 

Added lines #L37 - L38 were not covered by tests
end

return MapFromFunc(LO, LG, f, finv)
end

Expand All @@ -41,52 +47,56 @@
[
[
begin
pairs = filter(pair -> !iszero(last(pair)), collect(enumerate(_matrix(xi * xj))))
(map(first, pairs), GAP.Obj[coeffs_iso(c) for c in map(last, pairs)])
end for xj in basis(LO)
] for xi in basis(LO)
pairs = collect(LO.struct_consts[i, j])
(first.(pairs), GAP.Obj[coeffs_iso(c) for c in last.(pairs)])
end for j in 1:dim(LO)
] for i in 1:dim(LO)
]
-1
coeffs_iso(zero(coefficient_ring(LO)))
]

LG = GAP.Globals.LieAlgebraByStructureConstants(
codomain(coeffs_iso), GAP.Obj(sc_table_G; recursive=true)
LG = GAPWrap.LieAlgebraByStructureConstants(
codomain(coeffs_iso), GapObj(sc_table_G; recursive=true)
)

f, finv = _iso_oscar_gap_lie_algebra_functions(LO, LG, coeffs_iso)

if set_attributes && has_root_system(LO)
# we need to construct the root system in GAP as otherwise it may detect a different order of simple roots
RO = root_system(LO)
RG = GAP.Globals.Objectify(
GAP.Globals.NewType(
GAP.Globals.NewFamily(GAP.Obj("RootSystemFam"), GAP.Globals.IsObject),
GAP.evalstr("IsAttributeStoringRep and IsRootSystemFromLieAlgebra")),
GAP.GapObj(Dict{Symbol,Any}()))
GAP.Globals.SetUnderlyingLieAlgebra(RG, LG)

cartan_trO = transpose(cartan_matrix(RO))
transform_root(r::RootSpaceElem) = GAP.Obj(coefficients(r) * cartan_trO)[1]
GAP.Globals.SetPositiveRoots(RG, GAP.Obj(transform_root.(positive_roots(RO))))
GAP.Globals.SetNegativeRoots(RG, GAP.Obj(transform_root.(negative_roots(RO))))
GAP.Globals.SetSimpleSystem(RG, GAP.Obj(transform_root.(simple_roots(RO))))
can_basisG = GAP.Globals.CanonicalBasis(LG)
pos_root_vectorsG = can_basisG[1:n_positive_roots(RO)]
neg_root_vectorsG = can_basisG[(n_positive_roots(RO) + 1):(2 * n_positive_roots(RO))]
csa_basisG = can_basisG[(2 * n_positive_roots(RO) + 1):end]
GAP.Globals.SetPositiveRootVectors(RG, pos_root_vectorsG)
GAP.Globals.SetNegativeRootVectors(RG, neg_root_vectorsG)
GAP.Globals.SetCanonicalGenerators(
RG, GAP.Obj([pos_root_vectorsG, neg_root_vectorsG, csa_basisG])
)
GAP.Globals.SetChevalleyBasis(
LG, GAP.Obj([pos_root_vectorsG, neg_root_vectorsG, csa_basisG])
)

GAP.Globals.SetCartanMatrix(RG, GAP.Obj(cartan_trO))
GAP.Globals.SetRootSystem(LG, RG)
_iso_oscar_gap_set_root_system(LG, RO)
end

return MapFromFunc(LO, LG, f, finv)
end

function _iso_oscar_gap_set_root_system(LG::GapObj, RO::RootSystem)
RG = GAP.Globals.Objectify(
GAP.Globals.NewType(
GAP.Globals.NewFamily(GAP.Obj("RootSystemFam"), GAP.Globals.IsObject),
GAP.evalstr("IsAttributeStoringRep and IsRootSystemFromLieAlgebra")),
GAP.GapObj(Dict{Symbol,Any}()))
GAP.Globals.SetUnderlyingLieAlgebra(RG, LG)

cartan_trO = transpose(cartan_matrix(RO))
transform_root(r::RootSpaceElem) = GAP.Obj(coefficients(r) * cartan_trO)[1]
GAP.Globals.SetPositiveRoots(RG, GAP.Obj(transform_root.(positive_roots(RO))))
GAP.Globals.SetNegativeRoots(RG, GAP.Obj(transform_root.(negative_roots(RO))))
GAP.Globals.SetSimpleSystem(RG, GAP.Obj(transform_root.(simple_roots(RO))))
can_basisG = GAP.Globals.CanonicalBasis(LG)
pos_root_vectorsG = can_basisG[1:n_positive_roots(RO)]
neg_root_vectorsG = can_basisG[(n_positive_roots(RO) + 1):(2 * n_positive_roots(RO))]
csa_basisG = can_basisG[(2 * n_positive_roots(RO) + 1):end]
GAP.Globals.SetPositiveRootVectors(RG, pos_root_vectorsG)
GAP.Globals.SetNegativeRootVectors(RG, neg_root_vectorsG)
GAP.Globals.SetCanonicalGenerators(
RG, GAP.Obj([pos_root_vectorsG, neg_root_vectorsG, csa_basisG])
)
GAP.Globals.SetChevalleyBasis(
LG, GAP.Obj([pos_root_vectorsG, neg_root_vectorsG, csa_basisG])
)

GAP.Globals.SetCartanMatrix(RG, GAP.Obj(cartan_trO))
GAP.Globals.SetRootSystem(LG, RG)
end
2 changes: 0 additions & 2 deletions experimental/LieAlgebras/test/iso_gap_oscar-test.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -6,8 +6,6 @@ function test_iso_gap_oscar(LG, oscarT; num_random_tests::Int=10)
LO = codomain(iso)
@test LO isa oscarT

@test codomain(Oscar.iso_oscar_gap(LO)) === LG

@test iso === Oscar.iso_gap_oscar(LG) # test caching

for _ in 1:num_random_tests
Expand Down
1 change: 0 additions & 1 deletion experimental/LieAlgebras/test/iso_oscar_gap-test.jl
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Expand Up @@ -5,7 +5,6 @@ function test_iso_oscar_gap(LO::LieAlgebra; num_random_tests::Int=10)
@test domain(iso) === LO
LG = codomain(iso)
@test GAPWrap.IsLieAlgebra(LG)
# @test codomain(Oscar.iso_gap_oscar(LG)) === LO

@test iso === Oscar.iso_oscar_gap(LO) # test caching

Expand Down
4 changes: 2 additions & 2 deletions src/GAP/iso_oscar_gap.jl
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Expand Up @@ -402,7 +402,7 @@ function _iso_oscar_gap(FO::QQAbField)
end

"""
Oscar.iso_oscar_gap(R) -> Map{T, GapObj}
Oscar.iso_oscar_gap(R::T) -> Map{T, GapObj}

Return an isomorphism `f` with domain `R`
and `codomain` a GAP object `S`.
Expand Down Expand Up @@ -481,7 +481,7 @@ true
structure is not fully supported in GAP will likely cause overhead
at runtime.
"""
@attr Map function iso_oscar_gap(F)
@attr Map{T, GapObj} function iso_oscar_gap(F::T) where T
return _iso_oscar_gap(F)
end

Expand Down
1 change: 1 addition & 0 deletions src/GAP/wrappers.jl
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Expand Up @@ -270,6 +270,7 @@ GAP.@wrap LargestMovedPoint(x::Any)::Int
GAP.@wrap LeftActingDomain(x::GapObj)::GapObj
GAP.@wrap LetterRepAssocWord(x::GapObj)::GapObj
GAP.@wrap LibInfoCharacterTable(x::GapObj)::GapObj
GAP.@wrap LieAlgebraByStructureConstants(x::GapObj, y::GapObj)::GapObj
GAP.@wrap LinearCharacters(x::GapObj)::GapObj
GAP.@wrap LinearCombination(x::GapObj, y::GapObj)::GapObj
GAP.@wrap ListPerm(x::GapObj)::GapObj
Expand Down
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