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On solving large systems of polynomial equations appearing in Discrete Differential Geometry

Please always quote using this URN: urn:nbn:de:0297-zib-10646
  • The paper describes a method for solution of very large overdetermined algebraic polynomial systems on an example that appears from a classification of all integrable 3-dimensional scalar discrete quasilinear equations $Q_3=0$ on an elementary cubic cell of the lattice ${\mathbb Z}^3$. The overdetermined polynomial algebraic system that has to be solved is far too large to be formulated. A probing' technique which replaces independent variables by random integers or zero allows to formulate subsets of this system. An automatic alteration of equation formulating steps and equation solving steps leads to an iteration process that solves the computational problem.

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Metadaten
Author:Thomas Wolf
Document Type:ZIB-Report
Tag:REDUCE; computer algebra; discrete equations; integrable systems; large polynomial systems
MSC-Classification:37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Kxx Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] / 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
52-XX CONVEX AND DISCRETE GEOMETRY / 52-04 Explicit machine computation and programs (not the theory of computation or programming)
52-XX CONVEX AND DISCRETE GEOMETRY / 52Cxx Discrete geometry / 52C99 None of the above, but in this section
PACS-Classification:00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.30.-f Function theory, analysis / 02.30.Ik Integrable systems
00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.70.-c Computational techniques; simulations (for quantum computation, see 03.67.Lx; for computational techniques extensively used in subdivisions of physics, see the appropriate section; for example, see 47.11.-j Computational methods in fluid dynamics) / 02.70.Wz Symbolic computation (computer algebra)
Date of first Publication:2008/03/03
Series (Serial Number):ZIB-Report (08-10)
ISSN:1438-0064
ZIB-Reportnumber:08-10
Published in:Appeared in: Programming and Computer Software, 34 (2008), no 2, p 75-83
DOI:https://doi.org/10.1134/S0361768808020047
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