Multivariable Polynomial Division

[Raiden]

Hi, after a lot of searching, I can't figure out the command that is
used to perform a multivariable polynomial division. For example, I'm
looking for a command that would let me choose a monimal order (e.g.
deglex) and a variable order (e.g. x>y) and then perform a polynomial
division (e.g. [x^3y^2-3x^2y+xy-y]/[2x^2y+x]). I know this is probably
a really dumb thing to ask, but I really can't figure out the command
that does this.

[Douglas Leonard]

Have you looked at all the examples in the pages related to / // and %?

>>> Raiden <sjh...@mail.missouri.edu> 05/18/11 3:10 PM >>>

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[Federico Galetto]

Hi!

You can specify a monomial order in the declaration of the ring. For
example:

R=QQ[x,y,MonomialOrder=>GRevLex]

GRevLex is actually the default option. Other popular choices include
Lex and GLex (check the help page on monomial orderings for more).

Multivariate polynomial division is performed with //. In your case

(x^3*y^2-3*x^2*y+x*y-y)//(2*x^2*y+x)

The remainder is obtained with %. If you need to divide by more than
one polynomial, then put all your polynomials in a matrix and divide
by that.

Hope this helps,
Federico.