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Given an arbitrary but fixed integer r -&-ge; 3. We show that testing r-variate polynomials with integer coefficients for irreducibility is m-reducible in polynomial time of the total degree and the largest coefficient length to testing bivariate polynomials for irreducibility. Factoring r-variate polynomials into irreducibles is polynomial time Turing-reducible to completely factoring bivariate polynomials.

A polynomial reduction from multivariate to bivariate integral polynomial factorization.