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 - TY - GEN A1 - Tsarev, Sergey A1 - Wolf, Thomas T1 - Classification of 3-dimensional integrable scalar discrete equations N2 - We classify all integrable 3-dimensional scalar discrete affine linear equations $Q_3=0$ on an elementary cubic cell of the lattice ${\mathbb Z}^3$. An equation $Q_3=0$ %of such form is called integrable if it may be consistently imposed on all $3$-dimensional elementary faces of the lattice ${\mathbb Z}^4$. Under the natural requirement of invariance of the equation under the action of the complete group of symmetries of the cube we prove that the only ontrivial(non-linearizable) integrable equation from this class is the well-known dBKP-system. T3 - ZIB-Report - 08-13 KW - integrable systems KW - discrete equations KW - large polynomial systems KW - computer algebra KW - REDUCE KW - FORM KW - Crack Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10667 SN - 1438-0064 ER -