本文整理汇总了Python中sage.rings.polynomial.polynomial_ring_constructor.PolynomialRing.parent方法的典型用法代码示例。如果您正苦于以下问题：Python PolynomialRing.parent方法的具体用法？Python PolynomialRing.parent怎么用？Python PolynomialRing.parent使用的例子？那么恭喜您, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类sage.rings.polynomial.polynomial_ring_constructor.PolynomialRing的用法示例。
在下文中一共展示了PolynomialRing.parent方法的4个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: quantum_group
# 需要导入模块: from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing [as 别名]
# 或者: from sage.rings.polynomial.polynomial_ring_constructor.PolynomialRing import parent [as 别名]
def quantum_group(self, q=None, c=None):
r"""
Return the quantum group of ``self``.
The corresponding quantum group is the
:class:`~sage.algebras.lie_algebras.onsager.QuantumOnsagerAlgebra`.
The parameter `c` must be such that `c(1) = 1`
INPUT:
- ``q`` -- (optional) the quantum parameter; the default
is `q \in R(q)`, where `R` is the base ring of ``self``
- ``c`` -- (optional) the parameter `c`; the default is ``q``
EXAMPLES::
sage: O = lie_algebras.OnsagerAlgebra(QQ)
sage: Q = O.quantum_group()
sage: Q
q-Onsager algebra with c=q over Fraction Field of
Univariate Polynomial Ring in q over Rational Field
"""
if q is None:
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
q = PolynomialRing(self.base_ring(), 'q').fraction_field().gen()
if c is None:
c = q
else:
c = q.parent()(c)
return QuantumOnsagerAlgebra(self, q, c)示例2: q_dimension
# 需要导入模块: from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing [as 别名]
# 或者: from sage.rings.polynomial.polynomial_ring_constructor.PolynomialRing import parent [as 别名]
#.........这里部分代码省略.........
sage: TP.cardinality()
25600
sage: qdim = TP.q_dimension(use_product=True); qdim # long time
q^32 + 2*q^31 + 8*q^30 + 15*q^29 + 34*q^28 + 63*q^27 + 110*q^26
+ 175*q^25 + 276*q^24 + 389*q^23 + 550*q^22 + 725*q^21
+ 930*q^20 + 1131*q^19 + 1362*q^18 + 1548*q^17 + 1736*q^16
+ 1858*q^15 + 1947*q^14 + 1944*q^13 + 1918*q^12 + 1777*q^11
+ 1628*q^10 + 1407*q^9 + 1186*q^8 + 928*q^7 + 720*q^6
+ 498*q^5 + 342*q^4 + 201*q^3 + 117*q^2 + 48*q + 26
sage: qdim(1) # long time
25600
sage: TP.q_dimension() == qdim # long time
True
The `q`-dimensions of infinite crystals are returned
as formal power series::
sage: C = crystals.LSPaths(['A',2,1], [1,0,0])
sage: C.q_dimension(prec=5)
1 + q + 2*q^2 + 2*q^3 + 4*q^4 + O(q^5)
sage: C.q_dimension(prec=10)
1 + q + 2*q^2 + 2*q^3 + 4*q^4 + 5*q^5 + 7*q^6
+ 9*q^7 + 13*q^8 + 16*q^9 + O(q^10)
sage: qdim = C.q_dimension(); qdim
1 + q + 2*q^2 + 2*q^3 + 4*q^4 + 5*q^5 + 7*q^6
+ 9*q^7 + 13*q^8 + 16*q^9 + 22*q^10 + O(x^11)
sage: qdim.compute_coefficients(15)
sage: qdim
1 + q + 2*q^2 + 2*q^3 + 4*q^4 + 5*q^5 + 7*q^6
+ 9*q^7 + 13*q^8 + 16*q^9 + 22*q^10 + 27*q^11
+ 36*q^12 + 44*q^13 + 57*q^14 + 70*q^15 + O(x^16)
REFERENCES:
.. [Kac] Victor G. Kac. *Infinite-dimensional Lie Algebras*.
Third edition. Cambridge University Press, Cambridge, 1990.
"""
from sage.rings.all import ZZ
WLR = self.weight_lattice_realization()
I = self.index_set()
mg = self.highest_weight_vectors()
max_deg = float('inf') if prec is None else prec - 1
def iter_by_deg(gens):
next = set(gens)
deg = -1
while next and deg < max_deg:
deg += 1
yield len(next)
todo = next
next = set([])
while todo:
x = todo.pop()
for i in I:
y = x.f(i)
if y is not None:
next.add(y)
# def iter_by_deg
from sage.categories.finite_crystals import FiniteCrystals
if self in FiniteCrystals():
if q is None:
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
q = PolynomialRing(ZZ, 'q').gen(0)
if use_product:
# Since we are in the classical case, all roots occur with multiplicity 1
pos_coroots = map(lambda x: x.associated_coroot(), WLR.positive_roots())
rho = WLR.rho()
P = q.parent()
ret = P.zero()
for v in self.highest_weight_vectors():
hw = v.weight()
ret += P.prod((1 - q**(rho+hw).scalar(ac)) / (1 - q**rho.scalar(ac))
for ac in pos_coroots)
# We do a cast since the result would otherwise live in the fraction field
return P(ret)
elif prec is None:
# If we're here, we may not be a finite crystal.
# In fact, we're probably infinite.
from sage.combinat.species.series import LazyPowerSeriesRing
if q is None:
P = LazyPowerSeriesRing(ZZ, names='q')
else:
P = q.parent()
if not isinstance(P, LazyPowerSeriesRing):
raise TypeError("the parent of q must be a lazy power series ring")
ret = P(iter_by_deg(mg))
ret.compute_coefficients(10)
return ret
from sage.rings.power_series_ring import PowerSeriesRing, PowerSeriesRing_generic
if q is None:
q = PowerSeriesRing(ZZ, 'q', default_prec=prec).gen(0)
P = q.parent()
ret = P.sum(c * q**deg for deg,c in enumerate(iter_by_deg(mg)))
if ret.degree() == max_deg and isinstance(P, PowerSeriesRing_generic):
ret = P(ret, prec)
return ret示例3: Polynomial_padic_capped_relative_dense
# 需要导入模块: from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing [as 别名]
# 或者: from sage.rings.polynomial.polynomial_ring_constructor.PolynomialRing import parent [as 别名]
class Polynomial_padic_capped_relative_dense(Polynomial_generic_domain):
def __init__(self, parent, x=None, check=True, is_gen=False, construct = False, absprec = infinity, relprec = infinity):
"""
TESTS:
sage: K = Qp(13,7)
sage: R.<t> = K[]
sage: R([K(13), K(1)])
(1 + O(13^7))*t + (13 + O(13^8))
sage: T.<t> = ZZ[]
sage: R(t + 2)
(1 + O(13^7))*t + (2 + O(13^7))
"""
Polynomial.__init__(self, parent, is_gen=is_gen)
parentbr = parent.base_ring()
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
if construct:
(self._poly, self._valbase, self._relprecs, self._normalized, self._valaddeds, self._list) = x #the last two of these may be None
return
elif is_gen:
self._poly = PolynomialRing(ZZ, parent.variable_name()).gen()
self._valbase = 0
self._valaddeds = [infinity, 0]
self._relprecs = [infinity, parentbr.precision_cap()]
self._normalized = True
self._list = None
return
#First we list the types that are turned into Polynomials
if isinstance(x, ZZX):
x = Polynomial_integer_dense(PolynomialRing(ZZ, parent.variable_name()), x, construct = True)
elif isinstance(x, fraction_field_element.FractionFieldElement) and \
x.denominator() == 1:
#Currently we ignore precision information in the denominator. This should be changed eventually
x = x.numerator()
#We now coerce various types into lists of coefficients. There are fast pathways for some types of polynomials
if isinstance(x, Polynomial):
if x.parent() is self.parent():
if not absprec is infinity or not relprec is infinity:
x._normalize()
self._poly = x._poly
self._valbase = x._valbase
self._valaddeds = x._valaddeds
self._relprecs = x._relprecs
self._normalized = x._normalized
self._list = x._list
if not absprec is infinity or not relprec is infinity:
self._adjust_prec_info(absprec, relprec)
return
elif x.base_ring() is ZZ:
self._poly = x
self._valbase = Integer(0)
p = parentbr.prime()
self._relprecs = [c.valuation(p) + parentbr.precision_cap() for c in x.list()]
self._comp_valaddeds()
self._normalized = len(self._valaddeds) == 0 or (min(self._valaddeds) == 0)
self._list = None
if not absprec is infinity or not relprec is infinity:
self._adjust_prec_info(absprec, relprec)
return
else:
x = [parentbr(a) for a in x.list()]
check = False
elif isinstance(x, dict):
zero = parentbr.zero_element()
n = max(x.keys())
v = [zero for _ in xrange(n + 1)]
for i, z in x.iteritems():
v[i] = z
x = v
elif isinstance(x, pari_gen):
x = [parentbr(w) for w in x.list()]
check = False
#The default behavior if we haven't already figured out what the type is is to assume it coerces into the base_ring as a constant polynomial
elif not isinstance(x, list):
x = [x] # constant polynomial
# In contrast to other polynomials, the zero element is not distinguished
# by having its list empty. Instead, it has list [0]
if not x:
x = [parentbr.zero_element()]
if check:
x = [parentbr(z) for z in x]
# Remove this -- for p-adics this is terrible, since it kills any non exact zero.
#if len(x) == 1 and not x[0]:
# x = []
self._list = x
self._valaddeds = [a.valuation() for a in x]
self._valbase = sage.rings.padics.misc.min(self._valaddeds)
if self._valbase is infinity:
self._valaddeds = []
self._relprecs = []
self._poly = PolynomialRing(ZZ, parent.variable_name())()
self._normalized = True
if not absprec is infinity or not relprec is infinity:
self._adjust_prec_info(absprec, relprec)
else:
self._valaddeds = [c - self._valbase for c in self._valaddeds]
#.........这里部分代码省略.........
示例4: Polynomial_padic_capped_relative_dense
# 需要导入模块: from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing [as 别名]
# 或者: from sage.rings.polynomial.polynomial_ring_constructor.PolynomialRing import parent [as 别名]
class Polynomial_padic_capped_relative_dense(Polynomial_generic_domain, Polynomial_padic):
def __init__(self, parent, x=None, check=True, is_gen=False, construct = False, absprec = infinity, relprec = infinity):
"""
TESTS::
sage: K = Qp(13,7)
sage: R.<t> = K[]
sage: R([K(13), K(1)])
(1 + O(13^7))*t + (13 + O(13^8))
sage: T.<t> = ZZ[]
sage: R(t + 2)
(1 + O(13^7))*t + (2 + O(13^7))
Check that :trac:`13620` has been fixed::
sage: f = R.zero()
sage: R(f.dict())
0
"""
Polynomial.__init__(self, parent, is_gen=is_gen)
parentbr = parent.base_ring()
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
if construct:
(self._poly, self._valbase, self._relprecs, self._normalized, self._valaddeds, self._list) = x #the last two of these may be None
return
elif is_gen:
self._poly = PolynomialRing(ZZ, parent.variable_name()).gen()
self._valbase = 0
self._valaddeds = [infinity, 0]
self._relprecs = [infinity, parentbr.precision_cap()]
self._normalized = True
self._list = None
return
#First we list the types that are turned into Polynomials
if isinstance(x, ZZX):
x = Polynomial_integer_dense(PolynomialRing(ZZ, parent.variable_name()), x, construct = True)
elif isinstance(x, fraction_field_element.FractionFieldElement) and \
x.denominator() == 1:
#Currently we ignore precision information in the denominator. This should be changed eventually
x = x.numerator()
#We now coerce various types into lists of coefficients. There are fast pathways for some types of polynomials
if isinstance(x, Polynomial):
if x.parent() is self.parent():
if not absprec is infinity or not relprec is infinity:
x._normalize()
self._poly = x._poly
self._valbase = x._valbase
self._valaddeds = x._valaddeds
self._relprecs = x._relprecs
self._normalized = x._normalized
self._list = x._list
if not absprec is infinity or not relprec is infinity:
self._adjust_prec_info(absprec, relprec)
return
elif x.base_ring() is ZZ:
self._poly = x
self._valbase = Integer(0)
p = parentbr.prime()
self._relprecs = [c.valuation(p) + parentbr.precision_cap() for c in x.list()]
self._comp_valaddeds()
self._normalized = len(self._valaddeds) == 0 or (min(self._valaddeds) == 0)
self._list = None
if not absprec is infinity or not relprec is infinity:
self._adjust_prec_info(absprec, relprec)
return
else:
x = [parentbr(a) for a in x.list()]
check = False
elif isinstance(x, dict):
zero = parentbr.zero()
n = max(x.keys()) if x else 0
v = [zero for _ in xrange(n + 1)]
for i, z in x.iteritems():
v[i] = z
x = v
elif isinstance(x, pari_gen):
x = [parentbr(w) for w in x.list()]
check = False
#The default behavior if we haven't already figured out what the type is is to assume it coerces into the base_ring as a constant polynomial
elif not isinstance(x, list):
x = [x] # constant polynomial
# In contrast to other polynomials, the zero element is not distinguished
# by having its list empty. Instead, it has list [0]
if not x:
x = [parentbr.zero()]
if check:
x = [parentbr(z) for z in x]
# Remove this -- for p-adics this is terrible, since it kills any non exact zero.
#if len(x) == 1 and not x[0]:
# x = []
self._list = x
self._valaddeds = [a.valuation() for a in x]
self._valbase = sage.rings.padics.misc.min(self._valaddeds)
if self._valbase is infinity:
#.........这里部分代码省略.........