def _multi_variate(base_ring, names, n, sparse, order, implementation):
# if not sparse:
# raise ValueError, "A dense representation of multivariate polynomials is not supported"
sparse = False
# "True" would be correct, since there is no dense implementation of
# multivariate polynomials. However, traditionally, "False" is used in the key,
# even though it is meaningless.
if implementation is not None:
raise ValueError(
"The %s implementation is not known for multivariate polynomial rings"
% implementation)
names = normalize_names(n, names)
n = len(names)
import sage.rings.polynomial.multi_polynomial_ring as m
from sage.rings.polynomial.term_order import TermOrder
order = TermOrder(order, n)
key = (base_ring, names, n, sparse, order)
R = _get_from_cache(key)
if not R is None:
return R
from sage.rings.polynomial.multi_polynomial_libsingular import MPolynomialRing_libsingular
if isinstance(base_ring, ring.IntegralDomain):
if n < 1:
R = m.MPolynomialRing_polydict_domain(base_ring, n, names, order)
else:
try:
R = MPolynomialRing_libsingular(base_ring, n, names, order)
except (TypeError, NotImplementedError):
R = m.MPolynomialRing_polydict_domain(base_ring, n, names,
order)
else:
if not base_ring.is_zero():
try:
R = MPolynomialRing_libsingular(base_ring, n, names, order)
except (TypeError, NotImplementedError):
R = m.MPolynomialRing_polydict(base_ring, n, names, order)
else:
R = m.MPolynomialRing_polydict(base_ring, n, names, order)
_save_in_cache(key, R)
return R
def _multi_variate(base_ring,
names,
sparse=None,
order="degrevlex",
implementation=None):
# if not sparse:
# raise ValueError("a dense representation of multivariate polynomials is not supported")
sparse = False
if implementation is None:
force_singular = False
elif implementation == "singular":
force_singular = True
else:
raise ValueError(
"unknown implementation %r for multivariate polynomial rings" %
(implementation, ))
n = len(names)
from sage.rings.polynomial.term_order import TermOrder
order = TermOrder(order, n)
key = (base_ring, names, n, sparse, order)
R = _get_from_cache(key)
if not R is None:
return R
from sage.rings.polynomial.multi_polynomial_libsingular import MPolynomialRing_libsingular
try:
R = MPolynomialRing_libsingular(base_ring, n, names, order)
except (TypeError, NotImplementedError):
if force_singular:
raise
import sage.rings.polynomial.multi_polynomial_ring as m
if isinstance(base_ring, ring.IntegralDomain):
R = m.MPolynomialRing_polydict_domain(base_ring, n, names, order)
else:
R = m.MPolynomialRing_polydict(base_ring, n, names, order)
_save_in_cache(key, R)
return R