#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 | Resolution:
Keywords: polynomial gcd | Merged in:
Authors: Peter Bruin | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by pbruin:
Old description:
> 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.
New description:
The goal of this ticket is to implement a Cython method
`Field._gcd_univariate_polynomial()` using the standard Euclidean
algorithm. This is much faster than
`Fields.ParentMethods._gcd_univariate_polynomial()`, which calls
`EuclideanDomains.ElementMethods.gcd()`, since both are Python methods.
(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.
Similarly, to make `CC` and `QQbar` use the new method instead of Python
code, we also remove the now obsolete `Polynomial_generic_field.gcd()`.
--
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Ticket URL: <http://trac.sagemath.org/ticket/18461#comment:1>
Sage <http://www.sagemath.org>
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