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())
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())
