most recent 30 from http://mathoverflow.net 2013-05-22T16:40:11Z http://mathoverflow.net/feeds/question/11061 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/11061/computer-program-to-solve-a-system-of-polynomial-equations-over-a-finite-field Daniel Moseley 2010-01-07T19:17:08Z 2010-01-07T20:53:21Z

<p>I have a set of polynomial equations for which I want to know the solutions (actually really the number of solutions). It would be great if I could get a computer to do it, but I'm not sure exactly which programs will do things over finite fields. I surmise that Macaulay 2 may be able to do something like this, but I'm not quite sure how.</p>

http://mathoverflow.net/questions/11061/computer-program-to-solve-a-system-of-polynomial-equations-over-a-finite-field/11062#11062 Felipe Voloch 2010-01-07T19:26:21Z 2010-01-07T19:26:21Z

<p>Magma. <a href="http://magma.maths.usyd.edu.au/magma/htmlhelp/text1282.htm#12832" rel="nofollow">http://magma.maths.usyd.edu.au/magma/htmlhelp/text1282.htm#12832</a></p> <p>You can also do it in Sage or Pari/GP with a bit of programming.</p>

http://mathoverflow.net/questions/11061/computer-program-to-solve-a-system-of-polynomial-equations-over-a-finite-field/11067#11067 Steven Sam 2010-01-07T20:53:21Z 2010-01-07T20:53:21Z

<p>There is a package for doing this in Macaulay 2 also: <a href="http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.3.1/share/doc/Macaulay2/RationalPoints/html/index.html" rel="nofollow">http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.3.1/share/doc/Macaulay2/RationalPoints/html/index.html</a></p> <p>You might have to download the file and load it.</p> <p>It doesn't seem to have any shortcuts for just producing the number of points though, so I guess you can compare this with the one from magma to see which is faster.</p>