When does (T) equal sat(T)?

Authors:
Francois Lemaire;Marc Moreno Maza;Wei Pan;Yuzhen Xie
Affiliations:
University of Lille 1, Lille, France;University of Western Ontario, London, ON, Canada;University of Western Ontario, London, ON, Canada;University of Western Ontario, London, ON, Canada
Venue:
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Year:
2008

Citing 9
Cited 6

A generalized Euclidean algorithm for computing triangular representations of algebraic varieties

Journal of Symbolic Computation
Algorithmic properties of polynomial rings

Journal of Symbolic Computation
On the theories of triangular sets

Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Triangular sets for solving polynomial systems: a comparative implementation of four methods

Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Computing triangular systems and regular systems

Journal of Symbolic Computation
Polynomial Gcd Computations over Towers of Algebraic Extensions

AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Rational simplification modulo a polynomial ideal

Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Notes on triangular sets and triangulation-decomposition algorithms I: polynomial systems

SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
Comprehensive triangular decomposition

CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing

Computations modulo regular chains

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Some notes upon "When does equal sat(T)?"

AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
An algorithm for computing set-theoretic generators of an algebraic variety

Proceedings of the 36th international symposium on Symbolic and algebraic computation
On the regularity property of differential polynomials modulo regular differential chains

CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
When does equal sat(T)?

Journal of Symbolic Computation
On Fulton's algorithm for computing intersection multiplicities

CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a regular chain T, we aim at finding an efficient way for computing a system of generators of Sat(T), the saturated ideal of T. A natural idea is to test whether the equality {T}=Sat(T) holds, that is, whether T generates its saturated ideal. By generalizing the notion of primitivity from univariate polynomials to regular chains, we establish a necessary and sufficient condition, together with a Grobner basis free algorithm, for testing this equality. Our experimental results illustrate the efficiency of this approach in practice.