def __init__(self, R):
"""
Initialize ``self``.
EXAMPLES::
sage: L = lie_algebras.regular_vector_fields(QQ)
sage: TestSuite(L).run()
"""
cat = LieAlgebras(R).WithBasis()
InfinitelyGeneratedLieAlgebra.__init__(self, R, index_set=ZZ, category=cat)
IndexedGenerators.__init__(self, ZZ, prefix='d', bracket='[')
def __init__(self, R, index_set, prefix='L', **kwds):
"""
Initialize ``self``.
EXAMPLES::
sage: L = LieAlgebra(QQ, index_set=ZZ, abelian=True)
sage: TestSuite(L).run()
"""
cat = LieAlgebras(R).WithBasis()
InfinitelyGeneratedLieAlgebra.__init__(self, R, category=cat)
IndexedGenerators.__init__(self, index_set, prefix=prefix, **kwds)
def __init__(self, R):
"""
Initialize ``self``.
EXAMPLES::
sage: d = lie_algebras.VirasoroAlgebra(QQ)
sage: TestSuite(d).run()
"""
cat = LieAlgebras(R).WithBasis()
InfinitelyGeneratedLieAlgebra.__init__(self, R, index_set=ZZ, category=cat)
IndexedGenerators.__init__(self, ZZ, prefix='d', bracket='[',
sorting_key=_basis_key)
def __init__(self, R):
"""
Initialize ``self``.
EXAMPLES::
sage: d = lie_algebras.VirasoroAlgebra(QQ)
sage: TestSuite(d).run()
"""
cat = LieAlgebras(R).WithBasis().Graded()
InfinitelyGeneratedLieAlgebra.__init__(self,
R,
index_set=ZZ,
category=cat)
IndexedGenerators.__init__(self,
ZZ,
prefix='d',
bracket='[',
sorting_key=_basis_key)
def __init__(self, R):
r"""
Initialize ``self``.
EXAMPLES::
sage: L = lie_algebras.RankTwoHeisenbergVirasoro(QQ)
sage: TestSuite(L).run()
"""
cat = LieAlgebras(R).WithBasis()
self._KI = FiniteEnumeratedSet([1, 2, 3, 4])
self._V = ZZ**2
d = {'K': self._KI, 'E': self._V, 't': self._V}
indices = DisjointUnionEnumeratedSets(d, keepkey=True, facade=True)
InfinitelyGeneratedLieAlgebra.__init__(self,
R,
index_set=indices,
category=cat)
IndexedGenerators.__init__(self, indices, sorting_key=self._basis_key)
def __init__(self, R):
r"""
Initialize ``self``.
EXAMPLES::
sage: ACE = lie_algebras.AlternatingCentralExtensionOnsagerAlgebra(QQ)
sage: TestSuite(ACE).run()
sage: B = ACE.basis()
sage: A1, A2, Am2 = B[0,1], B[0,2], B[0,-2]
sage: B1, B2, Bm2 = B[1,1], B[1,2], B[1,-2]
sage: TestSuite(ACE).run(elements=[A1,A2,Am2,B1,B2,Bm2,ACE.an_element()])
"""
cat = LieAlgebras(R).WithBasis()
from sage.rings.integer_ring import ZZ
from sage.sets.disjoint_union_enumerated_sets import DisjointUnionEnumeratedSets
I = DisjointUnionEnumeratedSets([ZZ, ZZ], keepkey=True, facade=True)
IndexedGenerators.__init__(self, I)
InfinitelyGeneratedLieAlgebra.__init__(self,
R,
index_set=I,
category=cat)