ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 18 Jan 2012 05:32:31 -0600Faugère's F4 Algorithmhttp://ask.sagemath.org/question/8638/faugeres-f4-algorithm/There are many places online which mention that Faugère's F4 (and even F5) algorithms are included (or were going to be included) in Sage, but the only result in the documentation I can find is here:
http://www.sagemath.org/doc/reference/sage/rings/polynomial/pbori.html?highlight=faugere#sage.rings.polynomial.pbori.GroebnerStrategy.faugere_step_dense
Does anyone know if it is currently included in Sage?Tue, 17 Jan 2012 15:40:56 -0600http://ask.sagemath.org/question/8638/faugeres-f4-algorithm/Answer by Simon King for <p>There are many places online which mention that Faugère's F4 (and even F5) algorithms are included (or were going to be included) in Sage, but the only result in the documentation I can find is here:
<a href="http://www.sagemath.org/doc/reference/sage/rings/polynomial/pbori.html?highlight=faugere#sage.rings.polynomial.pbori.GroebnerStrategy.faugere_step_dense">http://www.sagemath.org/doc/reference...</a></p>
<p>Does anyone know if it is currently included in Sage?</p>
http://ask.sagemath.org/question/8638/faugeres-f4-algorithm/?answer=13139#post-id-13139As much as I know, there are only toy implementations of F5 in Sage (and I don't recall how it is available) - that's to say, they are good for educational purposes, but it would be much more efficient to use the default ways of computing Gröbner bases.
Note that Michael Brickenstein's "slimgb" (which is often used in Singular and thus also in Sage) is sometimes referred to as a version of F4. If you create a multivariate ideal `J` and want to compute its Gröbner basis with a particular algorithm, you can use something like
J.groebner_basis(algorithm='slimgb')Tue, 17 Jan 2012 19:13:21 -0600http://ask.sagemath.org/question/8638/faugeres-f4-algorithm/?answer=13139#post-id-13139Comment by process91 for <p>As much as I know, there are only toy implementations of F5 in Sage (and I don't recall how it is available) - that's to say, they are good for educational purposes, but it would be much more efficient to use the default ways of computing Gröbner bases.</p>
<p>Note that Michael Brickenstein's "slimgb" (which is often used in Singular and thus also in Sage) is sometimes referred to as a version of F4. If you create a multivariate ideal <code>J</code> and want to compute its Gröbner basis with a particular algorithm, you can use something like</p>
<pre><code>J.groebner_basis(algorithm='slimgb')
</code></pre>
http://ask.sagemath.org/question/8638/faugeres-f4-algorithm/?comment=20504#post-id-20504Thanks, that is what I have found as well. It looks like the command is actually J.groebner_basis('singular:slimgb')Wed, 18 Jan 2012 05:32:31 -0600http://ask.sagemath.org/question/8638/faugeres-f4-algorithm/?comment=20504#post-id-20504