Date: Dec 31, 2012 7:45 PM
Author: Roman Pearce
Subject: PolynomialQuotient slow
Something seems wrong here with the performance of PolynomialQuotient. Is there blowup because the leading coefficient in x is a polynomial? Also it seems slower in Mathematica 9 versus v8.

d = 5

f = Expand[ ((1+x)*(1+y)*(1+z))^d + 1 ];

g = Expand[ ((1-x)*(1-y)*(1-z))^d + 1 ];

AbsoluteTiming[ p = Expand[ f g ]; ]

AbsoluteTiming[ q = PolynomialQuotient[p, f, x]; ]

AbsoluteTiming[ P = Factor[ p ]; ]

What is the preferred method for (exact) division of polynomials? On this example I tried Cancel[ p/f ] and it works fine, but on other problems it is faster to use PolynomialQuotient. Suggestions?