TY - GEN

T1 - Gcd modulo a primary triangular set of dimension zero

AU - Dahan, Xavier

N1 - Publisher Copyright:
© 2017 ACM.

PY - 2017/7/23

Y1 - 2017/7/23

N2 - Computing gcd over a triangular set T is the core routine of the machinery of some triangular decomposition methods, in the realm of polynomial ideal theory. As such it has been studied intensively and is well-understood and implemented in several situations, especially in the case where coefficients are over a radical triangular set; It is not the case over a non-radical one. This paper introduces a gcd notion in this case, when additionally for simplicity 〈T〉 is assumed to be primary. It is built upon the Henselian property of the coefficient ring, and is natural in that it is linked with the subresultant sequence of a and b modulo T. A general algorithm still relies on some assumptions, except for the case of a triangular set T = (T1)x1)) of one variable.

AB - Computing gcd over a triangular set T is the core routine of the machinery of some triangular decomposition methods, in the realm of polynomial ideal theory. As such it has been studied intensively and is well-understood and implemented in several situations, especially in the case where coefficients are over a radical triangular set; It is not the case over a non-radical one. This paper introduces a gcd notion in this case, when additionally for simplicity 〈T〉 is assumed to be primary. It is built upon the Henselian property of the coefficient ring, and is natural in that it is linked with the subresultant sequence of a and b modulo T. A general algorithm still relies on some assumptions, except for the case of a triangular set T = (T1)x1)) of one variable.

KW - Gcd, primary ideal

KW - Henselian ring

KW - Subresultant

KW - Triangular set

UR - http://www.scopus.com/inward/record.url?scp=85027728254&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027728254&partnerID=8YFLogxK

U2 - 10.1145/3087604.3087612

DO - 10.1145/3087604.3087612

M3 - Conference contribution

AN - SCOPUS:85027728254

T3 - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

SP - 109

EP - 116

BT - ISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation

A2 - Burr, Michael

PB - Association for Computing Machinery

T2 - 42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017

Y2 - 25 July 2017 through 28 July 2017

ER -