# An algorithm for primary decomposition in polynomial rings over the integers

Gerhard Pfister; Afshan Sadiq; Stefan Steidel

Open Mathematics (2011)

- Volume: 9, Issue: 4, page 897-904
- ISSN: 2391-5455

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topGerhard Pfister, Afshan Sadiq, and Stefan Steidel. "An algorithm for primary decomposition in polynomial rings over the integers." Open Mathematics 9.4 (2011): 897-904. <http://eudml.org/doc/269723>.

@article{GerhardPfister2011,

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.},

author = {Gerhard Pfister, Afshan Sadiq, Stefan Steidel},

journal = {Open Mathematics},

keywords = {Gröbner bases; Primary decomposition; Modular computation; Parallel computation; primary decomposition; modular computation; parallel computation},

language = {eng},

number = {4},

pages = {897-904},

title = {An algorithm for primary decomposition in polynomial rings over the integers},

url = {http://eudml.org/doc/269723},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Gerhard Pfister

AU - Afshan Sadiq

AU - Stefan Steidel

TI - An algorithm for primary decomposition in polynomial rings over the integers

JO - Open Mathematics

PY - 2011

VL - 9

IS - 4

SP - 897

EP - 904

AB - 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.

LA - eng

KW - Gröbner bases; Primary decomposition; Modular computation; Parallel computation; primary decomposition; modular computation; parallel computation

UR - http://eudml.org/doc/269723

ER -

## References

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