class AbstractMSumRing(Parent):
def __init__(self, *args):
if len(args) == 1 and isinstance(args[0], AbstractMSumRing):
self._laurent_polynomial_ring = args[0]._laurent_polynomial_ring
self._free_module = args[0]._free_module
self._laurent_polynomial_ring_extra_var = args[0]._laurent_polynomial_ring_extra_var
else:
from sage.rings.polynomial.laurent_polynomial_ring import LaurentPolynomialRing
from sage.modules.free_module import FreeModule
self._laurent_polynomial_ring = LaurentPolynomialRing(QQ, *args)
dim = ZZ(self._laurent_polynomial_ring.ngens())
self._free_module = FreeModule(ZZ, dim)
# univariate extension of the polynomial ring
# (needed in several algorithms)
self._laurent_polynomial_ring_extra_var = self._laurent_polynomial_ring['EXTRA_VAR']
Parent.__init__(self, category=Rings())
def ngens(self):
return self.laurent_polynomial_ring().ngens()
def free_module(self):
return self._free_module
def polynomial_ring(self):
raise ValueError
def polynomial_ring_extra_var(self):
raise ValueError
def laurent_polynomial_ring(self):
return self._laurent_polynomial_ring
def laurent_polynomial_ring_extra_var(self):
return self._laurent_polynomial_ring_extra_var
def with_extra_var(self):
return self['EXTRA_VAR']
@cached_method
def zero(self):
r"""
EXAMPLES::
sage: from surface_dynamics.misc.multivariate_generating_series import MultivariateGeneratingSeriesRing
sage: M = MultivariateGeneratingSeriesRing('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())
@cached_method
def one(self):
r"""
EXAMPLES::
sage: from surface_dynamics.misc.multivariate_generating_series import MultivariateGeneratingSeriesRing
sage: M = MultivariateGeneratingSeriesRing('x', 2)
sage: M.zero()
0
sage: M.zero().parent() is M
True
sage: M.one().is_one()
True
"""
return self._element_constructor_(QQ.one())
def term(self, num, den):
r"""
Return the term ``num / den``.
INPUT:
- ``num`` - a Laurent polynomial
- ``den`` - a list of pairs ``(vector, power)`` or a dictionary
whose keys are the vectors and the values the powers. The
vector ``v = (v_0, v_1, \ldots)`` with power ``n`` corresponds
to the factor `(1 - x_0^{v_0} x_1^{v_1} \ldots x_k^{v_k})^n`.
EXAMPLES::
sage: from surface_dynamics.misc.multivariate_generating_series import MultivariateGeneratingSeriesRing
sage: M = MultivariateGeneratingSeriesRing('x', 3)
sage: M.term(1, [([1,1,0],1),([1,0,-1],2)])
(1)/((1 - x0*x2^-1)^2*(1 - x0*x1))
sage: M.term(1, {(1,1,0): 1, (1,0,-1): 2})
(1)/((1 - x0*x2^-1)^2*(1 - x0*x1))
"""
return self.element_class(self, [(den, num)])
def _element_constructor_(self, arg):
r"""
TESTS::
sage: from surface_dynamics.misc.multivariate_generating_series import MultivariateGeneratingSeriesRing
sage: M = MultivariateGeneratingSeriesRing('x', 2)
sage: M(1)
(1)
sage: R = M.laurent_polynomial_ring()
sage: M(R.0)
(x0)
"""
num = self._laurent_polynomial_ring(arg)
return self.element_class(self, [([], num)])
