A Polynomial-Time Reduction from Bivariate to Univariate Integral Polynomial Factorization

n algorithm is presented which reduces the probm lem of finding the irreducible factors of a bivariate polynoial with integer coefficients in polynomial time in the total i degree and the coefficient lengths to factoring a univariate nteger polynomial. Together with A. Lenstra's, H. Lenstra's u and L. Lovasz' polynomial-time factorization algorithm for nivariate integer polynomials and the author's multivariate - i to bivariate reduction the new algorithm implies the follow ng theorem. Factoring a polynomial with a fixed number of n b variables into irreducibles, except for the constant factors, ca e accomplished in time polynomial in the total degree and - e the size of its coefficients. The new algorithm can be gen ralized to reducing multivariate factorization directly to - m univariate factorization and to factoring multivariate polyno ials with coefficients in algebraic number fields and finite fields in polynomial time. - 2 - B 1. Introduction oth the classical Kronecker alg..

Reconstruction of two-dimensional signals from the Fourier transform magnitude

Originally presented as author's thesis (Sc. D.--Massachusetts Institute of Technology), 1986.Bibliography: p. 155-158.Supported in part by the Advanced Research Projects Agency monitored by ONR under contract no. N00014-81-K-0742 Supported in part by the National Science Foundation under grant ECS-8407285David Izraelevitz