division of multivariate polynomials

Hello,

I am in the process of writing a small program that divides two
multivariate polynomials (both over the integers), but I have read
that there is a problem with dividing multivariates as you can often
get different answers depending upon the monomial ordering used?

I have thought of a scheme however of approaching this problem
numerically. That is to choose a variable common to both the dividend
polynomial and the divisor and to choose random values for the other
variables so as to convert them both into univariates. Then univariate
division is carried out, and this process repeated for other values,
enough times so that interpolation may be used over the coefficients
so as to 'build in' the other variables into the coefficients of the
univariates.

Is there any forseeable problem with using this sort of scheme?

Thanks
Jeremy Watts
.

Relevant Pages

  • Re: division of multivariate polynomials
    ... I am in the process of writing a small program that divides two ... multivariate polynomials, ... you should decide if you want exact division or division ... extra details (like monomial order) to _define_ it. ...
    (sci.math.symbolic)
  • Re: division of multivariate polynomials
    ... I am in the process of writing a small program that divides two ... multivariate polynomials, ... you should decide if you want exact division or division ... extra details (like monomial order) to _define_ it. ...
    (sci.math.symbolic)