TY - GEN A1 - Tsarev, Sergey A1 - Wolf, Thomas T1 - Hyperdeterminants as integrable discrete systems N2 - We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A.~Cayley in 1845. We prove integrability (understood as $4d$-consistency) of a nonlinear difference equation defined by the $2 \times 2 \times 2$ - hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the $2\times 2\times 2\times 2$ - hyperdeterminant. T3 - ZIB-Report - 09-17 KW - hyper determinants KW - integrable systems KW - discrete equations KW - large polynomial systems KW - computer algebra KW - Form KW - Reduce KW - Singular Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11292 SN - 1438-0064 ER - TY - GEN A1 - Wolf, Thomas T1 - On solving large systems of polynomial equations appearing in Discrete Differential Geometry N2 - 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. T3 - ZIB-Report - 08-10 KW - integrable systems KW - discrete equations KW - large polynomial systems KW - computer algebra KW - REDUCE Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10646 SN - 1438-0064 ER -