We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals, resp. over finite fields, and the idea of Shimoyama-Yokoyama, resp. Eisenbud-Hunecke-Vasconcelos, to extract primary ideals from pseudo-primary ideals. A parallelized version of the algorithm is implemented in Singular. Examples and timings are given at the end of the article.
@article{bwmeta1.element.doi-10_2478_s11533-011-0037-8,
author = {Gerhard Pfister and Afshan Sadiq and Stefan Steidel},
title = {An algorithm for primary decomposition in polynomial rings over the integers},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {897-904},
zbl = {1246.13028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0037-8}
}
Gerhard Pfister; Afshan Sadiq; Stefan Steidel. An algorithm for primary decomposition in polynomial rings over the integers. Open Mathematics, Tome 9 (2011) pp. 897-904. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0037-8/
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