Publication: On Solving Large Systems of Polynomial Equations Appearing in Discrete Differential Geometry

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Title	On Solving Large Systems of Polynomial Equations Appearing in Discrete Differential Geometry
Authors/Editors*	T Wolf
Where published*	Programming and Computer Software
How published*	Journal
Year*	2008
Volume	34
Number	2
Pages	75-83
Publisher	Pleiades Publishing Ltd.
Keywords	integrable systems, discrete equations, large polynomial systems, computer algebra, REDUCE, FORM, CRACK
Link	http://lie.math.brocku.ca/twolf/papers/PCS75.pdf
Abstract	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 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.