def __init__(self, base_ring, n, names, order):
from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
order = TermOrder(order, n)
MPolynomialRing_generic.__init__(self, base_ring, n, names, order)
# Construct the generators
v = [0 for _ in xrange(n)]
one = base_ring(1)
self._gens = []
C = self._poly_class()
for i in xrange(n):
v[i] = 1 # int's!
self._gens.append(C(self, {tuple(v): one}))
v[i] = 0
self._gens = tuple(self._gens)
self._zero_tuple = tuple(v)
self._has_singular = can_convert_to_singular(self)
# This polynomial ring should belong to Algebras(base_ring).
# Algebras(...).parent_class, which was called from MPolynomialRing_generic.__init__,
# tries to provide a conversion from the base ring, if it does not exist.
# This is for algebras that only do the generic stuff in their initialisation.
# But here, we want to use PolynomialBaseringInjection. Hence, we need to
# wipe the memory and construct the conversion from scratch.
if n:
from sage.rings.polynomial.polynomial_element import PolynomialBaseringInjection
base_inject = PolynomialBaseringInjection(base_ring, self)
self.register_coercion(base_inject)
def __init__(self, base_ring, n, names, order):
from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
order = TermOrder(order,n)
MPolynomialRing_generic.__init__(self, base_ring, n, names, order)
# Construct the generators
v = [0 for _ in xrange(n)]
one = base_ring(1);
self._gens = []
C = self._poly_class()
for i in xrange(n):
v[i] = 1 # int's!
self._gens.append(C(self, {tuple(v):one}))
v[i] = 0
self._gens = tuple(self._gens)
self._zero_tuple = tuple(v)
self._has_singular = can_convert_to_singular(self)
# This polynomial ring should belong to Algebras(base_ring).
# Algebras(...).parent_class, which was called from MPolynomialRing_generic.__init__,
# tries to provide a conversion from the base ring, if it does not exist.
# This is for algebras that only do the generic stuff in their initialisation.
# But here, we want to use PolynomialBaseringInjection. Hence, we need to
# wipe the memory and construct the conversion from scratch.
if n:
from sage.rings.polynomial.polynomial_element import PolynomialBaseringInjection
base_inject = PolynomialBaseringInjection(base_ring, self)
self.register_coercion(base_inject)
def __init__(self, base_ring, n, names, order):
from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
order = TermOrder(order, n)
# MPolynomialRing_base.__init__() normally initialises the base ring,
# but it also needs the generators to construct a coercion map from the
# base ring, and the base ring must be set to initialise the generators.
# We set the base ring manually to break this circular dependency.
self._base = base_ring
# Construct the generators
v = [0] * n
one = base_ring.one()
self._gens = []
for i in range(n):
v[i] = 1 # int's!
self._gens.append(self.Element_hidden(self, {tuple(v): one}))
v[i] = 0
self._gens = tuple(self._gens)
self._zero_tuple = tuple(v)
MPolynomialRing_base.__init__(self, base_ring, n, names, order)
self._has_singular = can_convert_to_singular(self)