def _single_variate(base_ring, names, sparse):
"""
EXAMPLES::
sage: from sage.rings.polynomial.laurent_polynomial_ring import _single_variate
sage: _single_variate(QQ, ('x',), False)
Univariate Laurent Polynomial Ring in x over Rational Field
"""
############################################################
# This should later get moved to an actual single variate #
# implementation with valuation tracking, #
# but I don't want to right now. #
############################################################
# We need to come up with a name for the inverse that is easy to search
# for in a string *and* doesn't overlap with the name that we already have.
# For now, I'm going to use a name mangling with checking method.
names = normalize_names(1, names)
key = (base_ring, names, sparse)
P = _get_from_cache(key)
if P is not None:
return P
prepend_string = "qk"
while True:
if prepend_string in names:
prepend_string += 'k'
else:
break
R = _multi_variate_poly(base_ring, names, 1, sparse, 'degrevlex', None)
P = LaurentPolynomialRing_mpair(R, prepend_string, names)
_save_in_cache(key, P)
return P
def _single_variate(base_ring, names, sparse):
"""
EXAMPLES::
sage: from sage.rings.polynomial.laurent_polynomial_ring import _single_variate
sage: _single_variate(QQ, ('x',), False)
Univariate Laurent Polynomial Ring in x over Rational Field
"""
############################################################
# This should later get moved to an actual single variate #
# implementation with valuation tracking, #
# but I don't want to right now. #
############################################################
# We need to come up with a name for the inverse that is easy to search
# for in a string *and* doesn't overlap with the name that we already have.
# For now, I'm going to use a name mangling with checking method.
names = normalize_names(1, names)
key = (base_ring, names, sparse)
P = _get_from_cache(key)
if P is not None:
return P
prepend_string = "qk"
while True:
if prepend_string in names:
prepend_string += 'k'
else:
break
R = _multi_variate_poly(base_ring, names, 1, sparse, 'degrevlex', None)
P = LaurentPolynomialRing_mpair(R, prepend_string, names)
_save_in_cache(key, P)
return P
def _multi_variate(base_ring, names, n, sparse, order):
"""
EXAMPLES::
sage: from sage.rings.polynomial.laurent_polynomial_ring import _multi_variate
sage: _multi_variate(QQ, ('x','y'), 2, False, 'degrevlex')
Multivariate Laurent Polynomial Ring in x, y over Rational Field
"""
# We need to come up with a name for the inverse that is easy to search
# for in a string *and* doesn't overlap with the name that we already have.
# For now, I'm going to use a name mangling with checking method.
names = normalize_names(n, names)
from .term_order import TermOrder
order = TermOrder(order, n)
if isinstance(names, list):
names = tuple(names)
elif isinstance(names, str):
if ',' in names:
names = tuple(names.split(','))
key = (base_ring, names, n, sparse, order)
P = _get_from_cache(key)
if P is not None:
return P
prepend_string = "qk"
while True:
for a in names:
if prepend_string in a:
prepend_string += 'k'
break
else:
break
R = _multi_variate_poly(base_ring, names, n, sparse, order, None)
P = LaurentPolynomialRing_mpair(R, prepend_string, names)
_save_in_cache(key, P)
return P
def _multi_variate(base_ring, names, n, sparse, order):
"""
EXAMPLES::
sage: from sage.rings.polynomial.laurent_polynomial_ring import _multi_variate
sage: _multi_variate(QQ, ('x','y'), 2, False, 'degrevlex')
Multivariate Laurent Polynomial Ring in x, y over Rational Field
"""
# We need to come up with a name for the inverse that is easy to search
# for in a string *and* doesn't overlap with the name that we already have.
# For now, I'm going to use a name mangling with checking method.
names = normalize_names(n, names)
from term_order import TermOrder
order = TermOrder(order, n)
if isinstance(names, list):
names = tuple(names)
elif isinstance(names, str):
if ',' in names:
names = tuple(names.split(','))
key = (base_ring, names, n, sparse, order)
P = _get_from_cache(key)
if P is not None:
return P
prepend_string = "qk"
while True:
for a in names:
if prepend_string in a:
prepend_string += 'k'
break
else:
break
R = _multi_variate_poly(base_ring, names, n, sparse, order, None)
P = LaurentPolynomialRing_mpair(R, prepend_string, names)
_save_in_cache(key, P)
return P
