Hello
2015-01-25 19:14 UTC+01:00, Álinson S Xavier <[email protected]>:
> Vincent Delecroix <[email protected]> wrote:
>> Anyway, the answer you got is perfectly valid and it would actually
>> make confusion to not return the trivial answer (1, 1/a, 0) in the
>> case of fields. Do you still think this is a bug?
>
> I am not sure. This behavior did cause a subtle bug in my application.
> I made sure the arguments to xgcd were rational numbers with denominator
> one, but I forgot to actually cast them into integers.
>
> It also disagrees with the gcd function:
>
> sage: gcd(6/1,2/1)
> 2
> sage: xgcd(6/1,2/1)
> (1, 1/6, 0)
Right, this is unfortunate. But the answer is still valid (since 2 is
a unit of the rational numbers). The problem comes from the fact that
all "quotient fields" (fields that come from the quotient of a ring)
have a custom gcd function that takes care of that but no associated
xgcd. I opened a ticket for that at
http://trac.sagemath.org/ticket/17671
(this is the way things are modified in Sage)
It should be fixed in the next release in which you will have
{{{
sage: gcd(6/1,2/1)
2
sage: xgcd(6/1,2/1)
(2, 0, 1)
}}}
Thanks for you report and your insistence ;-)
Vincent
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