def _single_variate(base_ring, name, sparse, implementation):
import sage.rings.polynomial.polynomial_ring as m
name = normalize_names(1, name)
key = (base_ring, name, sparse, implementation if not sparse else None)
R = _get_from_cache(key)
if not R is None:
return R
if isinstance(base_ring, ring.CommutativeRing):
if is_IntegerModRing(base_ring) and not sparse:
n = base_ring.order()
if n.is_prime():
R = m.PolynomialRing_dense_mod_p(base_ring,
name,
implementation=implementation)
elif n > 1:
R = m.PolynomialRing_dense_mod_n(base_ring,
name,
implementation=implementation)
else: # n == 1!
R = m.PolynomialRing_integral_domain(
base_ring, name) # specialized code breaks in this case.
elif is_FiniteField(base_ring) and not sparse:
R = m.PolynomialRing_dense_finite_field(
base_ring, name, implementation=implementation)
elif isinstance(base_ring, padic_base_leaves.pAdicFieldCappedRelative):
R = m.PolynomialRing_dense_padic_field_capped_relative(
base_ring, name)
elif isinstance(base_ring, padic_base_leaves.pAdicRingCappedRelative):
R = m.PolynomialRing_dense_padic_ring_capped_relative(
base_ring, name)
elif isinstance(base_ring, padic_base_leaves.pAdicRingCappedAbsolute):
R = m.PolynomialRing_dense_padic_ring_capped_absolute(
base_ring, name)
elif isinstance(base_ring, padic_base_leaves.pAdicRingFixedMod):
R = m.PolynomialRing_dense_padic_ring_fixed_mod(base_ring, name)
elif base_ring.is_field(proof=False):
R = m.PolynomialRing_field(base_ring, name, sparse)
elif base_ring.is_integral_domain(proof=False):
R = m.PolynomialRing_integral_domain(base_ring, name, sparse,
implementation)
else:
R = m.PolynomialRing_commutative(base_ring, name, sparse)
else:
R = m.PolynomialRing_general(base_ring, name, sparse)
if hasattr(R, '_implementation_names'):
for name in R._implementation_names:
real_key = key[0:3] + (name, )
_save_in_cache(real_key, R)
else:
_save_in_cache(key, R)
return R
def _single_variate(base_ring,
name,
sparse=None,
implementation=None,
order=None):
# The "order" argument is unused, but we allow it (and ignore it)
# for consistency with the multi-variate case.
sparse = bool(sparse)
if sparse:
implementation = None
key = (base_ring, name, sparse, implementation)
R = _get_from_cache(key)
if R is not None:
return R
import sage.rings.polynomial.polynomial_ring as m
if isinstance(base_ring, ring.CommutativeRing):
if is_IntegerModRing(base_ring) and not sparse:
n = base_ring.order()
if n.is_prime():
R = m.PolynomialRing_dense_mod_p(base_ring,
name,
implementation=implementation)
elif n > 1:
R = m.PolynomialRing_dense_mod_n(base_ring,
name,
implementation=implementation)
else: # n == 1!
R = m.PolynomialRing_integral_domain(
base_ring, name) # specialized code breaks in this case.
elif is_FiniteField(base_ring) and not sparse:
R = m.PolynomialRing_dense_finite_field(
base_ring, name, implementation=implementation)
elif isinstance(base_ring, padic_base_leaves.pAdicFieldCappedRelative):
R = m.PolynomialRing_dense_padic_field_capped_relative(
base_ring, name)
elif isinstance(base_ring, padic_base_leaves.pAdicRingCappedRelative):
R = m.PolynomialRing_dense_padic_ring_capped_relative(
base_ring, name)
elif isinstance(base_ring, padic_base_leaves.pAdicRingCappedAbsolute):
R = m.PolynomialRing_dense_padic_ring_capped_absolute(
base_ring, name)
elif isinstance(base_ring, padic_base_leaves.pAdicRingFixedMod):
R = m.PolynomialRing_dense_padic_ring_fixed_mod(base_ring, name)
elif base_ring in _CompleteDiscreteValuationRings:
R = m.PolynomialRing_cdvr(base_ring, name, sparse)
elif base_ring in _CompleteDiscreteValuationFields:
R = m.PolynomialRing_cdvf(base_ring, name, sparse)
elif base_ring.is_field(proof=False):
R = m.PolynomialRing_field(base_ring, name, sparse)
elif base_ring.is_integral_domain(proof=False):
R = m.PolynomialRing_integral_domain(base_ring, name, sparse,
implementation)
else:
R = m.PolynomialRing_commutative(base_ring, name, sparse)
else:
R = m.PolynomialRing_general(base_ring, name, sparse)
if hasattr(R, '_implementation_names'):
for name in R._implementation_names:
real_key = key[0:3] + (name, )
_save_in_cache(real_key, R)
else:
_save_in_cache(key, R)
return R