Abstract
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 Q 3 = 0 on an elementary cubic cell of the lattice Z 3 .
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