Symposium on Symbolic and Algebraic Manipulation 

About: Symposium on Symbolic and Algebraic Manipulation is an academic conference. The conference publishes majorly in the area(s): Symbolic computation & Finite field. Over the lifetime, 120 publications have been published by the conference receiving 3973 citations.

Probabilistic algorithms for sparse polynomials

Abstract: In this paper we have tried to demonstrate how sparse techniques can be used to increase the effectiveness of the modular algorithms of Brown and Collins. These techniques can be used for an extremely wide class of problems and can applied to a number of different algorithms including Hensel's lemma. We believe this work has finally laid to rest the bad zero problem.

A criterion for detecting unnecessary reductions in the construction of Groebner bases

Abstract: We present a new criterion that may be applied in an algorithm for constructing Grobner-bases of polynomial ideals. The application of the criterion may drastically reduce the number of reductions of polynomials in the course of the algorithm. Incidentally, the new criterion allows to derive a realistic upper bound for the degrees of the polynomials in the Grobner-bases computed by the algorithm in the case of polynomials in two variables.

Factoring polynomials over large finite fields

Abstract: This paper reviews some of the known algorithms for factoring polynomials over finite fields and presents a new deterministic procedure for reducing the problem of factoring an arbitrary polynomial over the Galois field GF(p m) to the problem of finding the roots in GF(p) of certain other polynomials over GF(p). The amount of computation and the storage space required by these algorithms are algebraic in both the degree of the polynomial to be factored and the logarithm of the order of the finite field. Certain observations on the application of these methods to the factorization of polynomials over the rational integers are also included.

On Euclid's algorithm and the computation of polynomial greatest common divisors

Abstract: This paper examines the computation of polynomial greatest common divisors by various generalizations of Euclid's algorithm. The phenomenon of coefficient growth is described, and the history of successful efforts first to control it and then to eliminate it is related. The recently developed modular algorithm is presented in careful detail, with special attention to the case of multivariate polynomials. The computing times for the subresultant PRS algorithm, which is essentially the best of its kind, and for the modular algorithm are analyzed, and it is shown that the modular algorithm is markedly superior. In fact, the modular algorithm can obtain a GCD in less time than is required to verify it by classical division.

Computation with permutation groups

Abstract: The purpose of this paper is to provide an introduction to some computational techniques which have proved useful in the study of large permutation groups. In particular they have been used to study the Suzuki simple group of degree 1782 and order 448,345,497,600 and the simple group G2(5) of order 5,859,000,000 in a representation of degree 3906. Many of the algorithms discussed here are still in a developmental state and no claim is made that the most efficient solutions have been found.