Choosing a fast computer algebra system that works in characteristic p? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T05:41:05Z http://mathoverflow.net/feeds/question/10233 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/10233/choosing-a-fast-computer-algebra-system-that-works-in-characteristic-p Choosing a fast computer algebra system that works in characteristic p? AP 2009-12-31T05:00:57Z 2009-12-31T08:06:22Z <p>Hi all,</p> <p>I want to compute in \$\mathbb{F}_q (x)((y))\$ i.e. a Laurent series ring over the rational functions over \$\mathbb{F}_q\$. The computations are fairly basic, but they involve raising to the qth power a lot. I thought that this would be easy (I thought that it will merely shirt powers around), so I tried it in SAGE. I have to say that I am highly impressed with the ease of programming in SAGE, but I think it is too big (and slow) for the calculation I need (I know that SAGE has lots of components (PARI, GAP, etc.) some of them may be what I need).</p> <p>So I wanted to ask the people who have more experience then me for a recommendation. Which algebra system is good at Laurent series over rational function fields in char p if you need to do a lot of raising to the qth power. </p> <p>~AP</p> http://mathoverflow.net/questions/10233/choosing-a-fast-computer-algebra-system-that-works-in-characteristic-p/10247#10247 Answer by David Lehavi for Choosing a fast computer algebra system that works in characteristic p? David Lehavi 2009-12-31T07:08:25Z 2009-12-31T07:08:25Z <p>My personal experience is a few years old, but I don't think things have changed much. Sage is (or actually, was) more about ease of use then about performance. The only three CAS's you want to consider are</p> <ul> <li>Singular (Macaulay 2 uses Singular's engine)</li> <li>Cocoa.</li> <li>Magma.</li> </ul> <p>Back then the fastest of the bunch was Magma, but not by much. Regarding ease of use, it was a tie between Macaulay 2 and Magma. </p> <p>And now to some criticism: I never looked at Magma's code (proprietary), but I did look at both Singular and Cocoa. None of them uses SSE/GPGPU, which could probably give you an acceleration factor of 10-100.</p>