PolynomialQuotient slow

*To*: mathgroup at smc.vnet.net*Subject*: [mg129307] PolynomialQuotient slow*From*: Roman Pearce <rpearcea at gmail.com>*Date*: Mon, 31 Dec 2012 19:45:11 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

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?