add hint to lift() function to docstring of groebner_basis()

malb commented 15 years ago

On [sage-support]:

On Tuesday 31 March 2009, Florian wrote: Hello everyone,

I've been trying to figure out whether the following functionality is implemented, but so far I could not. I was hoping that anyone would know if it existed and in that case what the syntax is.

Suppose you computed the reduced Groebner Basis G of an ideal I= (f1,...,fn) in some polynomial ring R, and suppose that that Groebner Basis turned out to be G=(1). Is there a function that finds some, maybe even all, combinations of coefficients h1,...,hn such that h1f1+...+hnfn=1?

This is basically a byproduct of e.g. the Buchberger Algorithm. The question is whether this information can be accessed.

Martin answers ... and William Stein replies:

Martin, since this is a frequently asked question, do you think something about this should be added to the groebner_basis docstring? The groebner_basis docstring is 3 pages right now, so this shouldn't be too far down there.

Component: commutative algebra

Keywords: Groebner basis

Author: Martin Albrecht

Reviewer: Burcin Erocal

Merged: 4.0.1.rc1

Issue created by migration from https://trac.sagemath.org/ticket/5656

malb commented 15 years ago

Attachment: gb_lift.patch.gz