Proceedings Article10.1109/SFCS.1985.17
Computing with polynomials given by straight-line programs II sparse factorization
Erich Kaltofen
- 21 Oct 1985
- pp 450-458
28
TL;DR: An algorithm for the factorization of a multivariate polynomial represented by a straight-line program into its irreducible factors represented as sparse polynomials is developed with controllably high probability the correct factorization.
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Abstract: We develop an algorithm for the factorization of a multivariate polynomial represented by a straight-line program into its irreducible factors represented as sparse polynomials. Our algorithm is in random polynomial-time for the usual coefficient fields and outputs with controllably high probability the correct factorization. It only requires an a priori bound for the total degree of the input and over rational numbers a bound on the size of the polynomial coefficients.
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References
Factoring Polynomials with Rational Coefficients
TL;DR: This paper presents a polynomial-time algorithm to solve the following problem: given a non-zeroPolynomial fe Q(X) in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q (X).
Factoring polynomials with rational coeficients
H.W. Lenstra,A.K. Lenstra,L. Lovfiasz +2 more
- 01 Jan 1982
TL;DR: In this paper, a polynomial-time algorithm was proposed to decompose a primitive polynomials into irreducible factors in Z(X) if the greatest common divisor of its coefficients is 1.
Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization
TL;DR: An algorithm is presented 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 polynomials, which implies the following theorem.
151
Factoring multivariate polynomials over finite fields
TL;DR: An algorithm for the factorization of multivariate polynomials with coefficients in a finite field that is polynomial-time in the degrees of the polynometric to be factored is described.
124
Factoring multivariate polynomials over finite fields
Arjen K. Lenstra
- 01 Jan 1983
TL;DR: An algorithm for the factorization of multivariate polynomials with coefficients in a finite field that is polynomial-time in the degrees of the polynometric to be factored is described.
113