def __init__(self, R, L): """ Initialize ``self``. TESTS:: sage: L = posets.BooleanLattice(4) sage: M = L.moebius_algebra(QQ) sage: TestSuite(M).run() """ cat = Algebras(R).Commutative().WithBasis() if L in FiniteEnumeratedSets(): cat = cat.FiniteDimensional() self._lattice = L self._category = cat Parent.__init__(self, base=R, category=self._category.WithRealizations())
def __init__(self, R, P, prefix='I'): """ Initialize ``self``. TESTS:: sage: P = posets.BooleanLattice(4) sage: I = P.incidence_algebra(QQ) sage: TestSuite(I).run() # long time """ cat = Algebras(R).WithBasis() if P in FiniteEnumeratedSets(): cat = cat.FiniteDimensional() self._poset = P CombinatorialFreeModule.__init__(self, R, map(tuple, P.relations()), prefix=prefix, category=cat)