def zero(self): r""" EXAMPLES:: sage: from surface_dynamics.misc.multiplicative_multivariate_generating_series import MultiplicativeMultivariateGeneratingSeriesRing sage: M = MultiplicativeMultivariateGeneratingSeriesRing('x', 2) sage: M.zero() 0 sage: M.zero().parent() is M True sage: M.zero().is_zero() True """ return self._element_constructor_(QQ.zero())
def ConstantFormsSpaceFunctor(group): r""" Construction functor for the space of constant forms. When determining a common parent between a ring and a forms ring or space this functor is first applied to the ring. EXAMPLES:: sage: from sage.modular.modform_hecketriangle.functors import (ConstantFormsSpaceFunctor, FormsSpaceFunctor) sage: ConstantFormsSpaceFunctor(4) == FormsSpaceFunctor("holo", 4, 0, 1) True sage: ConstantFormsSpaceFunctor(4) ModularFormsFunctor(n=4, k=0, ep=1) """ return FormsSpaceFunctor("holo", group, QQ.zero(), ZZ.one())