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Polynomial Division
As with integers, operations related to division are key to many computations with polynomials. Mathematica includes not only highly optimized univariate polynomial-division algorithms, but also state-of-the-art multivariate generalizations.
Cancel cancel factors in a ratio of polynomials
    
PolynomialReduce represent one polynomial as a sum of others
GroebnerBasis find a reduced Groebner basis for a list of polynomials
    
PolynomialMod reduce polynomial coefficients modulo m
Modulus specify the modulus for a finite field
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