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Is there any easy way to parallel gröbnerbasis computations in sage?

asked 2016-05-24 14:35:00 +0200

mathguy gravatar image

Hi, I have a problem I am currently working on where I wish to eliminate variables from a system of polynomials. I have managed to do it in several cases, but for large systems to check my hypothesis the memory usage becomes very large, and the computations take a long time. Therefore I wondered if there is any easy way to optimalize the gröbner basis computation in sage. I am currently using the .elimination_ideal([]) environment, but it turns out to be very ineffective in the examples I am computing. I figured out that one of the limitations is that the eliminate function runs on only one core of the computer. So I therefore thought that in order to speed up the computations, then one could parallelize the function. However, it turns out that all current environments on sage including @fork, @parallel and parallelism.set() does not help at all in this case, since the process still runs on only one core.

Any good ideas out there?

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Can you provide some explicit examples that other users can play with to investigate your question?

slelievre gravatar imageslelievre ( 2016-05-24 16:06:33 +0200 )edit

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answered 2016-05-24 16:07:58 +0200

tmonteil gravatar image

updated 2016-05-24 16:09:49 +0200

There is no parallel computation of Groebner basis in Sage. However, .elimination_ideal([]) uses a algorithm provided by SIngular which is not the fastest available, and you can not change it in this method. You can specify which algorithm in the .groebner_basis() method.

A good candidate is the following:

Install giacpy from your terminal:

sage -i giacpy

Then, you can get the Groebner Basis from within Sage as follows:

sage: G = I.groebner_basis(algorithm='giac:gbasis')

You can get all possible algorithms by doing

sage: G = I.groebner_basis?

Please tell us if it was faster.

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Asked: 2016-05-24 14:26:36 +0200

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Last updated: May 24 '16