Displaying similar documents to “Reduction of Power Series in a Polydisc with Respect to a Gröbner Basis”

Border bases and kernels of homomorphisms and of derivations

Janusz Zieliński (2010)

Open Mathematics

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Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations. ...

Multidimensional residues and ideal membership.

Alessandro Perotti (1998)

Publicacions Matemàtiques

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Let I(f) be a zero-dimensional ideal in C[z1, ..., zn] defined by a mapping f. We compute the logarithmic residue of a polynomial g with respect to f. We adapt an idea introduced by Aizenberg to reduce the computation to a special case by means of a limiting process. We then consider the total sum of local residues of g w.r.t. f. If the zeroes of f are simple, this sum can be computed from a finite number of logarithmic residues. In...

Bipartition Polynomials, the Ising Model, and Domination in Graphs

Markus Dod, Tomer Kotek, James Preen, Peter Tittmann (2015)

Discussiones Mathematicae Graph Theory

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This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting representations, for instance as a sum ranging over all spanning forests. As a consequence, the bipartition polynomial is a powerful tool for proving properties of other graph polynomials and graph...

Mean value for the matching and dominating polynomial

Jorge Luis Arocha, Bernardo Llano (2000)

Discussiones Mathematicae Graph Theory

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The mean value of the matching polynomial is computed in the family of all labeled graphs with n vertices. We introduce the dominating polynomial of a graph whose coefficients enumerate the dominating sets for a graph and study some properties of the polynomial. The mean value of this polynomial is determined in a certain special family of bipartite digraphs.

Solving linear systems of equations over integers with Gröbner bases

Amir Hashemi (2014)

Acta Arithmetica

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We introduce a novel application of Gröbner bases to solve (non-homogeneous) systems of integer linear equations over integers. For this purpose, we present a new algorithm which ascertains whether a linear system of equations has an integer solution or not; in the affirmative case, the general integer solution of the system is determined.