Three new algorithms for multivariate polynomial GCD

Authors:
Tateaki Sasaki;Masayuki Suzuki
Affiliations:
The Institute of Physical and Chemical Research, Wako-shi, Saitama 351-01, Japan;The Institute of Physical and Chemical Research, Wako-shi, Saitama 351-01, Japan
Venue:
Journal of Symbolic Computation
Year:
1992

Citing 10
Cited 5

Subresultants and Reduced Polynomial Remainder Sequences

Journal of the ACM (JACM)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors

Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants

Journal of the ACM (JACM)
The Subresultant PRS Algorithm

ACM Transactions on Mathematical Software (TOMS)
Probabilistic algorithms for sparse polynomials

EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
GCDHEU: Heuristic Polynomial GCD Algorithm Based on Integer GCD Computation

EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
Some algebraic algorithms based on head term elimination over polynomial rings

EUROCAL '87 Proceedings of the European Conference on Computer Algebra
Non-modular computation of polynomial GCD's using trial division

EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
The EZ GCD algorithm

ACM '73 Proceedings of the ACM annual conference
The EEZ-GCD algorithm

ACM SIGSAM Bulletin

Multivariate quotient by power-series division

ACM SIGSAM Bulletin
Computing Approximate GCDs in Ill-conditioned Cases

Proceedings of the 2007 international workshop on Symbolic-numeric computation
An improved EZ-GCD algorithm for multivariate polynomials

Journal of Symbolic Computation
Computing multivariate approximate GCD based on Barnett's theorem

Proceedings of the 2009 conference on Symbolic numeric computation
Sparse implicitization by interpolation: Characterizing non-exactness and an application to computing discriminants

Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

Three new algorithms for multivariate polynomial GCD (greatest common divisor) are given. The first is to calculate a Grobner basis with a certain term ordering. The second is to calculate the subresultant by treating the coefficients w.r.t. the main variable as truncated power series. The third is to calculate a PRS (polynomial remainder sequence) by treating the coefficients as truncated power series. The first algorithm is not important practically, but the second and third ones are efficient and seem to be useful practically. The third algorithm has been implemented naively and compared with the trial-division PRS algorithm and the EZGCD algorithm. Although it is too early to derive a definite conclusion, the PRS method with power series coefficients is very efficient for calculating low degree GCD of high degree non-sparse polynomials.