Fix some nasty bugs in GAP conversion

that only happen if an Oscar root system is known, and the Chevalley basis is different from the basis

experimental/LieAlgebras/src/iso_oscar_gap.jl

@@ -7,7 +7,7 @@
 function _iso_oscar_gap_lie_algebra_functions(
   LO::LieAlgebra{C}, LG::GapObj, coeffs_iso::MapFromFunc
 ) where {C<:FieldElem}
-  basis_LG = GAPWrap.Basis(LG)
+  basis_LG = GAPWrap.Basis(LG, GAPWrap.GeneratorsOfAlgebra(LG))
 
   f = function (x::LieAlgebraElem{C})
     cfs = GAP.Obj([coeffs_iso(c) for c in coefficients(x)])
@@ -34,8 +34,7 @@ function _iso_oscar_gap(LO::LinearLieAlgebra; set_attributes::Bool=true)
 
   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)
+    _iso_oscar_gap_set_root_system(LO, LG, f)
   end
 
   return MapFromFunc(LO, LG, f, finv)
@@ -64,14 +63,14 @@ function _iso_oscar_gap(LO::AbstractLieAlgebra; set_attributes::Bool=true)
 
   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)
+    _iso_oscar_gap_set_root_system(LO, LG, f)
   end
 
   return MapFromFunc(LO, LG, f, finv)
 end
 
-function _iso_oscar_gap_set_root_system(LG::GapObj, RO::RootSystem)
+function _iso_oscar_gap_set_root_system(LO::LieAlgebra, LG::GapObj, LO_to_LG::Function)
+  RO = root_system(LO)
   RG = GAP.Globals.Objectify(
     GAP.Globals.NewType(
       GAP.Globals.NewFamily(GAP.Obj("RootSystemFam"), GAP.Globals.IsObject),
@@ -84,10 +83,10 @@ function _iso_oscar_gap_set_root_system(LG::GapObj, RO::RootSystem)
   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]
+  chev_basisL = chevalley_basis(LO)
+  pos_root_vectorsG = GAP.Obj(LO_to_LG.(chev_basisL[1]))
+  neg_root_vectorsG = GAP.Obj(LO_to_LG.(chev_basisL[2]))
+  csa_basisG = GAP.Obj(LO_to_LG.(chev_basisL[3]))
   GAP.Globals.SetPositiveRootVectors(RG, pos_root_vectorsG)
   GAP.Globals.SetNegativeRootVectors(RG, neg_root_vectorsG)
   GAP.Globals.SetCanonicalGenerators(

experimental/LieAlgebras/test/LieAlgebraModule-test.jl

@@ -5,12 +5,14 @@
       L = special_linear_lie_algebra(QQ, 2)
       V = trivial_module(L, 0)
       lie_algebra_module_conformance_test(L, V)
+      @test dim(V) == 0
     end
 
     @testset "3-dim trivial module of so_3(QQ)" begin
       L = special_orthogonal_lie_algebra(QQ, 2)
       V = trivial_module(L, 3)
       lie_algebra_module_conformance_test(L, V)
+      @test dim(V) == 3
     end
 
     @testset "V of sl_2(QQ) using structure constants" begin
@@ -25,30 +27,35 @@
       L = special_linear_lie_algebra(QQ, 2)
       V = abstract_module(L, 2, sc)
       lie_algebra_module_conformance_test(L, V)
+      @test dim(V) == 2
     end
 
     @testset "λ = [1,1,0] of sl_4(QQ)" begin
       L = special_linear_lie_algebra(QQ, 4)
       V = simple_module(L, [1, 1, 0])
       lie_algebra_module_conformance_test(L, V)
+      @test dim(V) == 20
     end
 
-    @testset "λ = [1,1,0,0] of so_4(CF(4))" begin
+    @testset "λ = [1,1] of so_4(CF(4))" begin
       L = special_orthogonal_lie_algebra(cyclotomic_field(4)[1], 4)
-      V = simple_module(L, [1, 1, 0, 0])
+      V = simple_module(L, [1, 1])
       lie_algebra_module_conformance_test(L, V)
+      @test dim(V) == 4
     end
 
     @testset "λ = [0,1] of A_2(QQ)" begin
       L = lie_algebra(QQ, :A, 2)
       V = simple_module(L, [0, 1])
       lie_algebra_module_conformance_test(L, V)
+      @test dim(V) == 3
     end
 
     @testset "λ = [0,1,1] of B_3(QQ)" begin
       L = lie_algebra(QQ, :B, 3)
       V = simple_module(L, [0, 1, 1])
       lie_algebra_module_conformance_test(L, V)
+      @test dim(V) == 112
     end
 
     @testset "V of sl_4(QQ)" begin

experimental/LieAlgebras/test/iso_oscar_gap-test.jl

@@ -1,6 +1,6 @@
 import Oscar: GAPWrap
 
-function test_iso_oscar_gap(LO::LieAlgebra; num_random_tests::Int=10)
+function test_iso_oscar_gap(LO::LieAlgebra; num_random_tests::Int=25)
   iso = Oscar.iso_oscar_gap(LO)
   @test domain(iso) === LO
   LG = codomain(iso)
@@ -54,6 +54,7 @@ end
         lie_algebra(RO, sl2_struct_consts(RO), ["e", "f", "h"]),
         lie_algebra(RO, :A, 3),
         lie_algebra(RO, :B, 2),
+        (L0 = lie_algebra(RO, :B, 5); root_system(L0); L0),
       ]
 
       @testset for LO in lie_algebras
@@ -67,6 +68,7 @@ end
         special_linear_lie_algebra(RO, 3),
         special_orthogonal_lie_algebra(RO, 4),
         symplectic_lie_algebra(RO, 6),
+        (LO = special_linear_lie_algebra(RO, 4); root_system(LO); LO),
       ]
 
       @testset for LO in lie_algebras

src/GAP/wrappers.jl

@@ -108,6 +108,7 @@ GAP.@wrap FreeGroupOfFpGroup(x::GapObj)::GapObj
 GAP.@wrap FusionCharTableTom(x::GapObj, y::GapObj)::GapObj
 GAP.@wrap FusionConjugacyClasses(x::GapObj, y::GapObj)::GapObj
 GAP.@wrap GaloisCyc(x::GAP.Obj, GapInt)::GAP.Obj
+GAP.@wrap GeneratorsOfAlgebra(x::GapObj)::GapObj
 GAP.@wrap GeneratorsOfField(x::GapObj)::GapObj
 GAP.@wrap GeneratorsOfGroup(x::GapObj)::GapObj
 GAP.@wrap GenExpList(x::GapObj)::GapObj