Solving polynomial systems. Algorithms and Applications. - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2001

Solving polynomial systems. Algorithms and Applications.

Abstract

This talk presents new algorithms for solving polynomial systems and in particular two new efficient algorithms for computing Gröbner bases. To avoid as much as possible intermediate computation, the F4 algorithm computes successive truncated Gröbner bases and replaces the classical polynomial reduction found in the Buchberger algorithm by the simultaneous reduction of several polynomials. This powerful reduction mechanism is achieved by means of a symbolic precomputation and by extensive use of sparse linear algebra methods. A second algorithm, called F5, eliminate the Buchberger criteria so that there is no reduction to zero during the computation when the input system is a regular sequence. In a second part of the talk we review different applications solved by these algorithms/programs (Robotic, Cryptography, N body problem, Coding theory, ...).

Keywords

Domains

Other [cs.OH]
Not file

Dates and versions

inria-00100675 , version 1 (26-09-2006)

Identifiers

  • HAL Id : inria-00100675 , version 1

Cite

Jean-Charles Faugère. Solving polynomial systems. Algorithms and Applications.. Computer Algebra in Applications to Integrable Systems, 2001, Cambridge, England. ⟨inria-00100675⟩
59 View
0 Download

Share

Gmail Facebook Twitter LinkedIn More