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arXiv · 1008.2074

An algorithm for primary decomposition in polynomial rings over the integers

Gerhard Pfister·Afshan Sadiq·Stefan Steidel
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Abstract

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.

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Gerhard Pfister, Afshan Sadiq, Stefan Steidel. 2010-08-12. An algorithm for primary decomposition in polynomial rings over the integers. https://doi.org/10.2478/s11533-011-0037-8

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