Reference

Markiyan Hirnyk — Sun, 03 Mar 2013 16:46:48 Z

It is not so simple. See Divisibility in http://en.wikipedia.org/wiki/Multivariate_polynomial#Number_of_variables .

Maple uses the ?divide and ?PolynomialIdeals/Quotient commands to this end.

exact division

roman_pearce — Mon, 04 Mar 2013 10:27:17 Z

For exact division, Maple's divide command uses this algorithm:

http://www.cecm.sfu.ca/~rpearcea/sdmp/sdmp_div.pdf

For division with remainder (rem and quo) Maple uses the division algorithm for univariate polynomials, where the coefficients are polynomials in the remaining variables. You can see the code:

interface(verboseproc=3): eval(sprem);

For reference, try "Algorithms for Computer Algebra" by Geddes, Czapor, and Labahn.

MaplePrimes - answers and comments on Question, Algorithme de division en plusieurs variable?

Reference

exact division