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.
[Math] Computer program to solve a system of polynomial equations over a finite field
ag.algebraic-geometrycomputer-algebrafinite-fieldsmathematical-software
Best Answer
Magma. http://magma.maths.usyd.edu.au/magma/htmlhelp/text1282.htm#12832
You can also do it in Sage or Pari/GP with a bit of programming.