#18461: Implement Field._gcd_univariate_polynomial()
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Reporter: pbruin | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.8
Component: basic arithmetic | Keywords: polynomial gcd
Merged in: | Authors: Peter Bruin
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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We implement `Field._gcd_univariate_polynomial()` using the standard
Euclidean algorithm. This is much faster than the existing Python method
`Fields.ParentMethods._gcd_univariate_polynomial()` (which calls
`EuclideanDomains.ElementMethods.gcd()`). (The
`_gcd_univariate_polynomial` mechanism was introduced in #13442.)
The following bug can then be fixed by just removing
`PolynomialRealDense.gcd()`, which does not take into account the case
where one of the arguments of `gcd` is zero:
{{{
sage: R.<x> = RR[]
sage: x.gcd(R.zero())
Traceback (most recent call last):
...
TypeError: 'MinusInfinity' object cannot be interpreted as an index
}}}
Removing this method ''without'' implementing
`Field._gcd_univariate_polynomial()` (falling back on Python code) is
about twice as slow; with this ticket there is no slowdown.
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Ticket URL: <http://trac.sagemath.org/ticket/18461>
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