本文整理汇总了Python中sage.rings.polynomial.polynomial_element.Polynomial.gcd方法的典型用法代码示例。如果您正苦于以下问题：Python Polynomial.gcd方法的具体用法？Python Polynomial.gcd怎么用？Python Polynomial.gcd使用的例子？那么, 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_element.Polynomial的用法示例。
在下文中一共展示了Polynomial.gcd方法的1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: gcd
# 需要导入模块: from sage.rings.polynomial.polynomial_element import Polynomial [as 别名]
# 或者: from sage.rings.polynomial.polynomial_element.Polynomial import gcd [as 别名]
def gcd(self,other,algorithm=None):
"""
Return the gcd of this polynomial and ``other``
INPUT:
- ``other`` -- a polynomial defined over the same ring as this
polynomial.
ALGORITHM:
Two algorithms are provided:
- ``generic``: Uses the generic implementation, which depends on the
base ring being a UFD or a field.
- ``dense``: The polynomials are converted to the dense representation,
their gcd is computed and is converted back to the sparse
representation.
Default is ``dense`` for polynomials over ZZ and ``generic`` in the
other cases.
EXAMPLES::
sage: R.<x> = PolynomialRing(ZZ,sparse=True)
sage: p = x^6 + 7*x^5 + 8*x^4 + 6*x^3 + 2*x^2 + x + 2
sage: q = 2*x^4 - x^3 - 2*x^2 - 4*x - 1
sage: gcd(p,q)
x^2 + x + 1
sage: gcd(p, q, algorithm = "dense")
x^2 + x + 1
sage: gcd(p, q, algorithm = "generic")
x^2 + x + 1
sage: gcd(p, q, algorithm = "foobar")
Traceback (most recent call last):
...
ValueError: Unknown algorithm 'foobar'
TESTS:
Check that :trac:`19676` is fixed::
sage: S.<y> = R[]
sage: x.gcd(y)
1
sage: (6*x).gcd(9)
3
"""
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
from sage.arith.all import lcm
if algorithm is None:
if self.base_ring() == ZZ:
algorithm = "dense"
else:
algorithm = "generic"
if algorithm=="dense":
S = self.parent()
# FLINT is faster but a bug makes the conversion extremely slow,
# so NTL is used in those cases where the conversion is too slow. Cf
# <https://groups.google.com/d/msg/sage-devel/6qhW90dgd1k/Hoq3N7fWe4QJ>
sd = self.degree()
od = other.degree()
if max(sd,od)<100 or \
min(len(self.__coeffs)/sd, len(other.__coeffs)/od)>.06:
implementation="FLINT"
else:
implementation="NTL"
D = PolynomialRing(S.base_ring(),'x',implementation=implementation)
g = D(self).gcd(D(other))
return S(g)
elif algorithm=="generic":
return Polynomial.gcd(self,other)
else:
raise ValueError("Unknown algorithm '%s'" % algorithm)