MaplePrimes - answers and comments on Question, Rem and Quo for multivariate polynomials

Quo/Rem of multivariate polynomials over a finite field

laurent — Fri, 22 Jul 2011 21:37:37 Z

Do you mean K(y,z)[x] or K[y,z][x] ? If the latter (i.e. you have multivariate polynomials in x,y and z) and your finite field is a prime field, have a look at ?PRem.

If you really are looking at rational functions in y and z as your coefficient field or K is a more general field, you'll want to use ?Domains.

I hope this helps

-Laurent

I am looking for q and r as rational functions

Istarion — Thu, 28 Jul 2011 20:09:21 Z

I am looking for q and r as rational functions of y and z, and I am implementing the code for any finite field. I was told earlier on this site, though, that ?Domains was left unfinished, and is sort of a skeleton.

Basically, I am working with elements of F[x.y.z], and I have constructed them using alias(a = RootOf('irreducible polynomial mod p, of degree n')), and then using Expand() mod p and collect() to perform basic operations. For this part of the code, though, I want to treat them as being polynomials in x, and perform polynomial division. Is there an easier way to do this using Domains? I've been trying PRem, and it doesn't seem to be doing what I would like in most situations.

Thanks for your help!

Found answer - thanks!

Istarion — Thu, 04 Aug 2011 21:11:32 Z

So, after fighting it with a bit, I realized that the reason Prem wasn't working properly was because sometimes I would write xy instead of x*y or x y, which I'm assuming it interpreted as a whole new variable. It was really weird, because it kept saying things like r was 0, when my program was ensuring a gcd of 1 the line before.

tl;dr version: Prem is working for me now, and it was my own error that prevented it from working properly before. Thank you very much for your help!