[sage-devel] Re: Solving a gcd equation for polynomials

2011-05-29 Thread Rob Beezer
On May 29, 2:09 am, javier wrote: > I have been looking at the paper and at first glance don't see any > reason that would prevent the stabilization algorithm from working > over any Euclidean domain, as there you have division with remainder, > gcd, xgcd, all ideals are principal, sum of ideals i

[sage-devel] Re: Solving a gcd equation for polynomials

2011-05-29 Thread javier
I have been looking at the paper and at first glance don't see any reason that would prevent the stabilization algorithm from working over any Euclidean domain, as there you have division with remainder, gcd, xgcd, all ideals are principal, sum of ideals is generated by the gcd and so on. The only

[sage-devel] Re: Solving a gcd equation for polynomials

2011-05-28 Thread Rob Beezer
On May 25, 2:22 pm, John Cremona wrote: > If no-one else is more explicit I'll look for a reference tomorrow. For the record, off-list John Cremona pointed me to "Fast Algorithms for Linear Algebra mod N" by Storjohann and Mulders, where this is called "stablization of p and q mod r" and the

Re: [sage-devel] Re: Solving a gcd equation for polynomials

2011-05-25 Thread John Cremona
Something very similar to this is needed for modular symbols, with the ring ZZ instead of polynomials, so there is likely to be a function somewhere which does this and could be adapted. If no-one else is more explicit I'll look for a reference tomorrow. John On Wed, May 25, 2011 at 10:16 PM, Ro

[sage-devel] Re: Solving a gcd equation for polynomials

2011-05-25 Thread Rob Beezer
Thanks, Georg. I know Euclidean rings, but did not recognize the requested function as a defining property. I usually teach them as "admitting" the "degree" function. So that may help me go fishing. If anybody knows the code well enough to know such a thing is *not* available, that'd be helpful

[sage-devel] Re: Solving a gcd equation for polynomials

2011-05-25 Thread Georg S. Weber
On 25 Mai, 08:18, Rob Beezer wrote: > I'm wondering if Sage has the following function for polynomials over > a field.  Mostly, I don't know if it is a common thing to expect, and > if so, I have no idea what it would be called.  So a pointer would be > of real help, if it  exists.  The paper I