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sage.categories: Update # needs #38733

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Oct 12, 2024
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sage.categories: Update # needs #38733

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1cb84d8
sage.categories: Update # needs
mkoeppe Jun 9, 2024
4092691
src/sage/categories/semigroups.py: Fix # needs
mkoeppe Jun 22, 2024
1ffe438
src/sage/categories/triangular_kac_moody_algebras.py: Add # needs
mkoeppe Jul 26, 2024
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20 changes: 14 additions & 6 deletions src/sage/categories/finite_dimensional_algebras_with_basis.py
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Original file line number Diff line number Diff line change
Expand Up @@ -145,6 +145,7 @@ def radical_basis(self):
We compute the radical basis in a subalgebra using
the inherited product::

sage: # needs sage.modules
sage: scoeffs = {('a','e'): {'a':1}, ('b','e'): {'a':1, 'b':1},
....: ('c','d'): {'a':1}, ('c','e'): {'c':1}}
sage: L.<a,b,c,d,e> = LieAlgebra(QQ, scoeffs)
Expand All @@ -155,14 +156,14 @@ def radical_basis(self):

TESTS::

sage: A = KleinFourGroup().algebra(GF(2)) # needs sage.groups sage.modules
sage: A.radical_basis() # needs sage.groups sage.modules
sage: # needs sage.groups sage.modules
sage: A = KleinFourGroup().algebra(GF(2))
sage: A.radical_basis()
(() + (1,2)(3,4), (3,4) + (1,2)(3,4), (1,2) + (1,2)(3,4))

sage: A = KleinFourGroup().algebra(QQ, category=Monoids()) # needs sage.groups sage.modules
sage: A.radical_basis.__module__ # needs sage.groups sage.modules
sage: A = KleinFourGroup().algebra(QQ, category=Monoids())
sage: A.radical_basis.__module__
'sage.categories.finite_dimensional_algebras_with_basis'
sage: A.radical_basis() # needs sage.groups sage.modules
sage: A.radical_basis()
()
"""
F = self.base_ring()
Expand Down Expand Up @@ -421,6 +422,7 @@ def subalgebra(self, gens, category=None, *args, **opts):

EXAMPLES::

sage: # needs sage.modules
sage: scoeffs = {('a','e'): {'a':1}, ('b','e'): {'a':1, 'b':1},
....: ('c','d'): {'a':1}, ('c','e'): {'c':1}}
sage: L.<a,b,c,d,e> = LieAlgebra(QQ, scoeffs)
Expand All @@ -429,6 +431,7 @@ def subalgebra(self, gens, category=None, *args, **opts):
sage: A.dimension()
7

sage: # needs sage.modules
sage: L.<x,y,z> = LieAlgebra(GF(3), {('x','z'): {'x':1, 'y':1}, ('y','z'): {'y':1}})
sage: MS = MatrixSpace(L.base_ring(), L.dimension())
sage: gens = [b.adjoint_matrix() for b in L.basis()]
Expand Down Expand Up @@ -473,6 +476,7 @@ def ideal_submodule(self, gens, side='left', category=None, *args, **opts):

EXAMPLES::

sage: # needs sage.modules
sage: scoeffs = {('a','e'): {'a':1}, ('b','e'): {'a':1, 'b':1},
....: ('c','d'): {'a':1}, ('c','e'): {'c':1}}
sage: L.<a,b,c,d,e> = LieAlgebra(QQ, scoeffs)
Expand Down Expand Up @@ -1537,18 +1541,21 @@ def simple_module_parameterization(self):

EXAMPLES::

sage: # needs sage.modules
sage: TL = TemperleyLiebAlgebra(5, 30, QQ) # semisimple
sage: len(TL.radical_basis())
0
sage: TL.simple_module_parameterization()
(1, 3, 5)

sage: # needs sage.modules
sage: TL = TemperleyLiebAlgebra(5, 1, QQ) # not semisimple
sage: len(TL.radical_basis())
24
sage: TL.simple_module_parameterization()
(1, 3, 5)

sage: # needs sage.modules
sage: TL = TemperleyLiebAlgebra(6, 30, QQ) # semisimple
sage: all(TL.cell_module(la).dimension()
....: == TL.cell_module(la).simple_module().dimension()
Expand All @@ -1557,6 +1564,7 @@ def simple_module_parameterization(self):
sage: TL.simple_module_parameterization()
(0, 2, 4, 6)

sage: # needs sage.modules
sage: TL = TemperleyLiebAlgebra(6, 0, QQ) # not semisimple
sage: TL.simple_module_parameterization()
(2, 4, 6)
Expand Down
2 changes: 2 additions & 0 deletions src/sage/categories/semigroups.py
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Expand Up @@ -511,6 +511,7 @@ def representation(self, module, on_basis, side='left', *args, **kwargs):

EXAMPLES::

sage: # needs sage.groups
sage: G = CyclicPermutationGroup(3)
sage: M = algebras.Exterior(QQ, 'x', 3)
sage: def on_basis(g, m): # cyclically permute generators
Expand Down Expand Up @@ -1059,6 +1060,7 @@ def representation(self, module, on_basis, side='left', *args, **kwargs):

EXAMPLES::

sage: # needs sage.groups
sage: G = groups.permutation.Dihedral(5)
sage: CFM = CombinatorialFreeModule(GF(2), [1, 2, 3, 4, 5])
sage: A = G.algebra(GF(2))
Expand Down
5 changes: 5 additions & 0 deletions src/sage/categories/triangular_kac_moody_algebras.py
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Expand Up @@ -215,6 +215,7 @@ def _triangular_key(self, x):

EXAMPLES::

sage: # needs sage.combinat sage.modules
sage: L = lie_algebras.sl(QQ, 3)
sage: La = L.cartan_type().root_system().weight_lattice().fundamental_weights()
sage: sorted(L.basis().keys(), key=L._basis_key)
Expand Down Expand Up @@ -352,6 +353,7 @@ def _transpose_basis_mapping(self):

EXAMPLES::

sage: # needs sage.combinat sage.modules
sage: g = LieAlgebra(QQ, cartan_type=['A', 2])
sage: g._transpose_basis_mapping
{-alpha[1]: alpha[1],
Expand Down Expand Up @@ -384,6 +386,7 @@ def _transpose_on_basis(self, m):

EXAMPLES::

sage: # needs sage.combinat sage.modules
sage: g = LieAlgebra(QQ, cartan_type=['B', 2])
sage: B = g.basis()
sage: [(B[k], g._transpose_on_basis(k)) for k in B.keys()]
Expand All @@ -407,6 +410,7 @@ def transpose(self):

EXAMPLES::

sage: # needs sage.combinat sage.modules
sage: g = LieAlgebra(QQ, cartan_type=['B', 2])
sage: g.transpose
Generic endomorphism of Lie algebra of ['B', 2] in the Chevalley basis
Expand All @@ -425,6 +429,7 @@ def transpose(self):

EXAMPLES::

sage: # needs sage.combinat sage.modules
sage: g = LieAlgebra(QQ, cartan_type=['G', 2])
sage: for b in g.basis():
....: for bp in g.basis():
Expand Down
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