#17671: Implement xgcd for fraction fields
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Reporter: vdelecroix | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.5
Component: basic arithmetic | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/17671 | 401193ce270c603dc80ebc1028ff46d0eb662c6c
Dependencies: #17673 | Stopgaps:
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Comment (by bruno):
* In `src/sage/rings/arith.py`, lines 1901-1910, the introducing sentence
should to my mind be: `Here is an example of a xgcd for two polynomials
over the integers, where the linear combination is not the gcd but the gcd
multiplied by the resultant::`.
{{{#!python
Here is an example of a xgcd for two polynomials over the integers,
where the linear
combination is not the gcd but the resultant::
sage: R.<x> = ZZ[]
sage: gcd(2*x*(x-1), x^2)
x
sage: xgcd(2*x*(x-1), x^2)
(2*x, -1, 2)
sage: (2*(x-1)).resultant(x)
2
}}}
* I do not understand exactly what you want to do with your function
`_test_gcd_vs_xgcd()`: As discussed, it is not clear that the results
should always be the same.
* To answer your questions:
1. As I've said on sage-devel, I am clearly in favor of `gcd(RR(6),
RR(3)).parent()` to return `Real Field with 53 bits of precision` rather
than `Integer Ring`.
2. I would keep the name `xgcd` though, with a clear documentation.
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=f22ac97d0f1a45f8c23cf8b9064c0f652b6e6b30
f22ac97]||{{{trac #17671: (review) fix gcd/xgcd in QuotientFields}}}||
||[http://git.sagemath.org/sage.git/commit/?id=401193ce270c603dc80ebc1028ff46d0eb662c6c
401193c]||{{{trac #17671: fix xgcd of polynomial_field_generic}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/17671#comment:9>
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