# Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization

@article{Kaltofen1985PolynomialTimeRF, title={Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization}, author={Erich L. Kaltofen}, journal={SIAM J. Comput.}, year={1985}, volume={14}, pages={469-489} }

Consider a polynomial f with an arbitrary but fixed number of variables and with integral coefficients. We present an algorithm which reduces the problem of finding the irreducible factors of f in polynomial-time in the total degree of f and the coefficient lengths of f to factoring a univariate integral polynomial. Together with A. Lenstra’s,.H. Lenstra’s and L. Lovasz’ polynomial-time factorization algorithm for univariate integral polynomials [Math. Ann., 261 (1982), pp. 515–534] this…

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