On solving large systems of polynomial equations appearing in discrete differential geometry

The poster describes methods that combined find all solutions of a very large overdetermined polynomial algebraic system for only up to 22 unknowns but with billions of equations all homogeneous of degree 8 with on average millions of terms each. This problem resulted from the classification of all integrable 3-dimensional scalar discrete quasilinear equations Q3 = 0 on an elementary cubic cell of the lattice Z3.

[1]  Alexander I. Bobenko,et al.  Communications in Mathematical Physics Classification of Integrable Equations on Quad-Graphs. The Consistency Approach , 2003 .

[2]  A. Bobenko,et al.  Discrete nonlinear hyperbolic equations. Classification of integrable cases , 2007, 0705.1663.

[3]  Thomas Wolf.  Applications of CRACK in the Classification of Integrable Systems , 2003 .

[4]  B. Konopelchenko,et al.  Reciprocal Figures, Graphical Statics, and Inversive Geometry of the Schwarzian BKP Hierarchy , 2001, nlin/0107001.

[5]  Thomas Wolf,et al.  Some Symmetry Classifications of Hyperbolic Vector Evolution Equations , 2004, nlin/0412015.

[6]  Thomas Wolf.  Supersymmetric Representations and Integrable Super-extensions of the Burgers and Boussinesq Equations , 2022 .

[7]  A. V. Kiselev,et al.  Classification of integrable super-systems using the SsTools environment , 2007, Comput. Phys. Commun..

[8]  Thomas Wolf,et al.  Classification of Three-Dimensional Integrable Scalar Discrete Equations , 2007, 0706.2464.

[9]  S. P. Tsarev.  Classification of 3-dimensional integrable scalar discrete equations , 2007 .

[10]  T. Wolf.  On solving large systems of polynomial equations appearing in discrete differential geometry , 2008, Program. Comput. Softw..

[11]  Thomas Wolf,et al.  On weakly non-local, nilpotent, and super-recursion operators for N=1 homogeneous super-equations , 2005 .

[12]  J.A.M. Vermaseren,et al.  New features of FORM , 2000 .

[14]  J. Nimmo,et al.  An Integrable Discretization of a 2+1‐dimensional Sine‐Gordon Equation , 1998 .

[15]  T. Wolf,et al.  Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I , 2004, nlin/0412003.