Results 271 to 280 of about 2,413 (304)

Multivariate Polynomial Factorization

Journal of the ACM, 1975
Abstract : This paper describes algorithms for factoring a polynomial in one or more variables, with integer coefficients, into factors which are irreducible over the integers. These algorithms are based on the use of factorizations over finite fields and 'Hensel's Lemma construction'.
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On polynomial factorization

1982
These algorithms are probabilistic in the following sense. The time of computation depends on random choices, but the validity of the result does not depend on them. So, worst case complexity, being infinite, is meaningless and we compute average complexity.
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On Ritt's Factorization of Polynomials

Journal of the London Mathematical Society, 2000
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Ng, TW, Beardon, AF
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On the Factorization of Certain Polynomials

SIAM Review, 1960
THE STANDARD PROCEDURE of inverting Laplace Transforms which are rational functions involves locating the zeros of the denominators. There are many methods for locating the real zeros of polynomials,3 but the location of proper complex4 zeros can at times present a problem.
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Polynomial factorization

Proceedings of the 2003 international symposium on Symbolic and algebraic computation, 2003
The problem of factoring a polynomial in a single or several variables over a finite field, the rational numbers or the complex numbers is one of the success stories in the discipline of symbolic computation. In the early 1960s implementors investigated the constructive methods known from classical algebra books, but--with the exception of Gauss's ...
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A polynomial factorization challenge

ACM SIGSAM Bulletin, 1992
In the early 1970s, a major paradigm shift took place in algorithms research, away from experimental results to asymptotic analysis. Knuth popularized the "Big O" notation, and Hopcroft says in his 1986 ACM Turing Award (with Robert Tarjan) address: "During the 1960s, research on algorithms had been very unsatisfying.
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Equivalence of Polynomial Identity Testing and Polynomial Factorization

computational complexity, 2015
In this research paper it is demonstrated that the problem of deterministically factoring multivariate polynomials reduces to the problem of deterministic polynomial identity testing. More specifically, it is explored that, given an arithmetic circuit (either explicitly or via black-box access) that computes a multivariate polynomial \(f\), the task of
Swastik Kopparty, Shubhangi Saraf, Amir Shpilka   +2 more
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Factorization of Sums of Polynomials

Acta Applicandae Mathematica, 2002
Given monic polynomials (real or complex) \(A\) and \(B\) of the same degree. We seek the information about the factorization of the polynomial \(C=A+B\), under some information about the factorization of \(A\) and \(B\). The inverse problem is considered as well: given the polynomial \(C\), find polynomials \(A\) and \(B\) with prescribed ...
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Note on Factorable Polynomials

Canadian Mathematical Bulletin, 1969
Let X1, X2,…, Xk, denote k ≥ 2 indeterminates and let f(X1,…, Xk) be a homogeneous polynomial, in GF(pn) [X1,…, Xk], which is irreducible but not absolutely irreducible over GF(pn). Thus f is irreducible in GF(pn)[X1,…, Xk] but reducible in some GF(pnm) [X1,…, Xk], m > 1.
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Interval Partitions and Polynomial Factorization

Algorithmica, 2011
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Joachim von zur Gathen, Daniel Panario, L. Bruce Richmond   +2 more
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