A function to compute Bezout coefficients ?

[ablondin]

Hello, everyone !

I've been looking for a function that allows one to compute Bezout
coefficients of two numbers (say natural numbers). There is the GCD
function, but I haven't found anything about Bezout coefficients. This
is not complicated to write one, but it would be better if it was
included somehwere in Sage. Is there already something like that ?

Thank you for your help !

Alex

[Mike Hansen]

Hello,

> I've been looking for a function that allows one to compute Bezout
> coefficients of two numbers (say natural numbers). There is the GCD
> function, but I haven't found anything about Bezout coefficients. This
> is not complicated to write one, but it would be better if it was
> included somehwere in Sage. Is there already something like that ?

You should use xgcd:

sage: xgcd(5, 7)
(1, 3, -2)
sage: g,a,b = xgcd(5, 7)
sage: a*5 + b*7
1

--Mike

[Tim Daly]

Is anyone else getting duplicate copies of Sage messages? -- Tim

[ablondin]

Thanks !
I would never have guessed the name !
Alex

[Robert Bradshaw]

On May 25, 2010, at 1:42 PM, ablondin wrote:

> Thanks !
> I would never have guessed the name !
> Alex

And I had never heard of the term "Bezout coefficients" :). The is an
abbreviation for "extended gcd."

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[ablondin]

In fact, I'm not sure the term "Bezout coefficients" is standard, but
you can find it on Wikipedia.
http://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity
They also call these "Bezout numbers", since they're linked to the
Bezout identity.
Alex

On 25 mai, 16:44, Robert Bradshaw <rober...@math.washington.edu>
wrote:

[Florent Hivert]

Hi There,

On Tue, May 25, 2010 at 01:44:10PM -0700, Robert Bradshaw wrote:
> On May 25, 2010, at 1:42 PM, ablondin wrote:
>
>> Thanks !
>> I would never have guessed the name !
>> Alex
>
> And I had never heard of the term "Bezout coefficients" :). The is an
> abbreviation for "extended gcd."

I think this is pretty standard in the French community. According to
Alexandre it seems to be standard also in the French speaking community ;-)

Cheers,

Florent