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)