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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?



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