SAGBI and SAGBI-Gröbner Bases over Principal Ideal Domains
نویسندگان
چکیده
منابع مشابه
SAGBI Bases Under Composition
Our interest in the subject of this paper is inspired by Hong (1998), where Hoon Hong addresses the problem of the behavior of Gröbner bases under composition of polynomials. More precisely, let Θ be a set of polynomials, as many as the variables in our polynomial ring. The question then is under which conditions on these polynomials it is true that for an arbitrary Gröbner basis G (with respec...
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We degenerate Cox–Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev–Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective n-space at n + 3 points, sagbi bases of Cox–Nagata rings establish a link between the Verlinde formul...
متن کاملSignature-based Criteria for Möller's Algorithm for Computing Gröbner Bases over Principal Ideal Domains
Signature-based algorithms have become a standard approach for Gröbner basis computations for polynomial systems over fields, but how to extend these techniques to coefficients in general rings is not yet as well understood. In this paper, we present a signature-based algorithm for computing Gröbner bases over principal ideal domains (e.g. the ring of integers or the ring of univariate polynomi...
متن کاملApplications of SAGBI-bases in dynamics
The classical reduction techniques of bifurcation theory, Liapunov–Schmidt reduction and centre manifold reduction, are investigated where symmetry is present. The symmetry is given by the action of a finite or continuous group. The symmetry is exploited systematically by using the algebraic structure of the module of equivariant polynomial tuples. We generalize the concept of SAGBI-bases to mo...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1999
ISSN: 0747-7171
DOI: 10.1006/jsco.1998.0243