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1
Content available remote

The F4-algorithm for Euclidean rings

100%
Sadiq A.
Open Mathematics
|
2010
|
tom 8
|
nr 6
1156-1159
EN
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.
2
Content available remote

An algorithm for primary decomposition in polynomial rings over the integers

80%
Pfister G., Sadiq A., Steidel S.
Open Mathematics
|
2011
|
tom 9
|
nr 4
897-904
EN
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.
3
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On reconstruction of polynomial automorphisms

80%
Gniadek P.
Annales Polonici Mathematici
|
1996
|
tom 64
|
nr 1
61-69
EN
We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.
4
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Equivalence and reduction of delay-differential systems

70%
Boudellioua M. S.
International Journal of Applied Mathematics and Computer Science
|
2007
|
tom 17
|
nr 1
15-22
EN
A new direct method is presented which reduces a given high-order representation of a control system with delays to a first-order form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann's strict system equivalence. This type of system equivalence leaves the transfer function and other relevant structural properties of the original system invariant.
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