def __init__(self,
base_ring,
name=None,
default_prec=20,
sparse=False,
use_lazy_mpoly_ring=False,
category=None):
"""
Initializes a power series ring.
INPUT:
- ``base_ring`` - a commutative ring
- ``name`` - name of the indeterminate
- ``default_prec`` - the default precision
- ``sparse`` - whether or not power series are
sparse
- ``use_lazy_mpoly_ring`` - if base ring is a poly ring compute with
multivariate polynomials instead of a univariate poly over the base
ring. Only use this for dense power series where you won't do too
much arithmetic, but the arithmetic you do must be fast. You must
explicitly call ``f.do_truncation()`` on an element
for it to truncate away higher order terms (this is called
automatically before printing).
"""
R = PolynomialRing(base_ring, name, sparse=sparse)
self.__poly_ring = R
self.__is_sparse = sparse
self.__params = (base_ring, name, default_prec, sparse)
if use_lazy_mpoly_ring and (is_MPolynomialRing(base_ring) or \
is_PolynomialRing(base_ring)):
K = base_ring
names = K.variable_names() + (name, )
self.__mpoly_ring = PolynomialRing(K.base_ring(), names=names)
assert is_MPolynomialRing(self.__mpoly_ring)
self.Element = power_series_mpoly.PowerSeries_mpoly
commutative_ring.CommutativeRing.__init__(
self,
base_ring,
names=name,
category=getattr(self, '_default_category', _CommutativeRings))
Nonexact.__init__(self, default_prec)
self.__generator = self.element_class(self,
R.gen(),
check=True,
is_gen=True)
def __init__(self, base_ring, name=None, default_prec=20, sparse=False,
use_lazy_mpoly_ring=False):
"""
Initializes a power series ring.
INPUT:
- ``base_ring`` - a commutative ring
- ``name`` - name of the indeterminate
- ``default_prec`` - the default precision
- ``sparse`` - whether or not power series are
sparse
- ``use_lazy_mpoly_ring`` - if base ring is a poly ring compute with
multivariate polynomials instead of a univariate poly over the base
ring. Only use this for dense power series where you won't do too
much arithmetic, but the arithmetic you do must be fast. You must
explicitly call ``f.do_truncation()`` on an element
for it to truncate away higher order terms (this is called
automatically before printing).
"""
R = PolynomialRing(base_ring, name, sparse=sparse)
self.__poly_ring = R
self.__is_sparse = sparse
self.__params = (base_ring, name, default_prec, sparse)
if use_lazy_mpoly_ring and (is_MPolynomialRing(base_ring) or \
is_PolynomialRing(base_ring)):
K = base_ring
names = K.variable_names() + (name,)
self.__mpoly_ring = PolynomialRing(K.base_ring(), names=names)
assert is_MPolynomialRing(self.__mpoly_ring)
self.Element = power_series_mpoly.PowerSeries_mpoly
commutative_ring.CommutativeRing.__init__(self, base_ring, names=name,
category=getattr(self,'_default_category',
_CommutativeRings))
Nonexact.__init__(self, default_prec)
self.__generator = self.element_class(self, R.gen(), check=True, is_gen=True)
def __init__(self, base_ring, name=None, default_prec=None, sparse=False,
use_lazy_mpoly_ring=False, category=None):
"""
Initializes a power series ring.
INPUT:
- ``base_ring`` - a commutative ring
- ``name`` - name of the indeterminate
- ``default_prec`` - the default precision
- ``sparse`` - whether or not power series are
sparse
- ``use_lazy_mpoly_ring`` - if base ring is a poly ring compute with
multivariate polynomials instead of a univariate poly over the base
ring. Only use this for dense power series where you won't do too
much arithmetic, but the arithmetic you do must be fast. You must
explicitly call ``f.do_truncation()`` on an element
for it to truncate away higher order terms (this is called
automatically before printing).
EXAMPLES:
This base class inherits from :class:`~sage.rings.ring.CommutativeRing`.
Since :trac:`11900`, it is also initialised as such, and since :trac:`14084`
it is actually initialised as an integral domain::
sage: R.<x> = ZZ[[]]
sage: R.category()
Category of integral domains
sage: TestSuite(R).run()
When the base ring `k` is a field, the ring `k[[x]]` is not only a
commutative ring, but also a complete discrete valuation ring (CDVR).
The appropriate (sub)category is automatically set in this case::
sage: k = GF(11)
sage: R.<x> = k[[]]
sage: R.category()
Category of complete discrete valuation rings
sage: TestSuite(R).run()
"""
R = PolynomialRing(base_ring, name, sparse=sparse)
self.__poly_ring = R
self.__is_sparse = sparse
if default_prec is None:
from sage.misc.defaults import series_precision
default_prec = series_precision()
self.__params = (base_ring, name, default_prec, sparse)
if use_lazy_mpoly_ring and (is_MPolynomialRing(base_ring) or \
is_PolynomialRing(base_ring)):
K = base_ring
names = K.variable_names() + (name,)
self.__mpoly_ring = PolynomialRing(K.base_ring(), names=names)
assert is_MPolynomialRing(self.__mpoly_ring)
self.Element = power_series_mpoly.PowerSeries_mpoly
commutative_ring.CommutativeRing.__init__(self, base_ring, names=name,
category=getattr(self,'_default_category',
_CommutativeRings))
Nonexact.__init__(self, default_prec)
self.__generator = self.element_class(self, R.gen(), check=True, is_gen=True)
def __init__(self,
base_ring,
name=None,
default_prec=None,
sparse=False,
use_lazy_mpoly_ring=False,
category=None):
"""
Initializes a power series ring.
INPUT:
- ``base_ring`` - a commutative ring
- ``name`` - name of the indeterminate
- ``default_prec`` - the default precision
- ``sparse`` - whether or not power series are
sparse
- ``use_lazy_mpoly_ring`` - if base ring is a poly ring compute with
multivariate polynomials instead of a univariate poly over the base
ring. Only use this for dense power series where you won't do too
much arithmetic, but the arithmetic you do must be fast. You must
explicitly call ``f.do_truncation()`` on an element
for it to truncate away higher order terms (this is called
automatically before printing).
EXAMPLES:
This base class inherits from :class:`~sage.rings.ring.CommutativeRing`.
Since :trac:`11900`, it is also initialised as such, and since :trac:`14084`
it is actually initialised as an integral domain::
sage: R.<x> = ZZ[[]]
sage: R.category()
Category of integral domains
sage: TestSuite(R).run()
When the base ring `k` is a field, the ring `k[[x]]` is not only a
commutative ring, but also a complete discrete valuation ring (CDVR).
The appropriate (sub)category is automatically set in this case::
sage: k = GF(11)
sage: R.<x> = k[[]]
sage: R.category()
Category of complete discrete valuation rings
sage: TestSuite(R).run()
It is checked that the default precision is non-negative
(see :trac:`19409`)::
sage: PowerSeriesRing(ZZ, 'x', default_prec=-5)
Traceback (most recent call last):
...
ValueError: default_prec (= -5) must be non-negative
"""
R = PolynomialRing(base_ring, name, sparse=sparse)
self.__poly_ring = R
self.__is_sparse = sparse
if default_prec is None:
from sage.misc.defaults import series_precision
default_prec = series_precision()
elif default_prec < 0:
raise ValueError("default_prec (= %s) must be non-negative" %
default_prec)
self.__params = (base_ring, name, default_prec, sparse)
if use_lazy_mpoly_ring and (is_MPolynomialRing(base_ring) or \
is_PolynomialRing(base_ring)):
K = base_ring
names = K.variable_names() + (name, )
self.__mpoly_ring = PolynomialRing(K.base_ring(), names=names)
assert is_MPolynomialRing(self.__mpoly_ring)
self.Element = power_series_mpoly.PowerSeries_mpoly
commutative_ring.CommutativeRing.__init__(
self,
base_ring,
names=name,
category=getattr(self, '_default_category', _CommutativeRings))
Nonexact.__init__(self, default_prec)
self.__generator = self.element_class(self,
R.gen(),
check=True,
is_gen=True)
