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The F4-algorithm for Euclidean rings

100%

Sadiq A.

Open Mathematics

2010

tom 8

nr 6

1156-1159

In this short note, we extend Faugére’s F4-algorithm for computing Gröbner bases to polynomial rings with coefficients in an Euclidean ring. Instead of successively reducing single S-polynomials as in Buchberger’s algorithm, the F4-algorithm is based on the simultaneous reduction of several polynomials.

An algorithm for primary decomposition in polynomial rings over the integers

51%

Pfister G., Sadiq A., Steidel S.

Open Mathematics

2011

tom 9

nr 4

897-904

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.

Ograniczanie wyników

2 Open Mathematics

2 Sadiq A.

1 Pfister G.

1 Steidel S.

1 2011

1 2010

Wyniki wyszukiwania

The F4-algorithm for Euclidean rings

An algorithm for primary decomposition in polynomial rings over the integers