Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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.

share|improve this question

2 Answers 2

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.

share|improve this answer
2  
While you're here, let me ask: Is there a command to count points without listing them? Of course, I can get the length of a list, but I am thinking about situations where the list would be very long and I could save time by not generating it. For a trivial example, something that could tell me that A^n has q^n points without taking time proportional to q^n. –  David Speyer Jan 7 '10 at 19:42
1  
I think you do this for curves but not for general varieties. –  Felipe Voloch Jan 7 '10 at 19:56
    
Thank you very much! –  David Speyer Jan 7 '10 at 20:29

There is a package for doing this in Macaulay 2 also: http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.3.1/share/doc/Macaulay2/RationalPoints/html/index.html

You might have to download the file and load it.

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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.