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
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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 -