06107902

j

06107902 Wolf, Thomas Schr\"ufer, Eberhard Webster, Kenneth Solving large linear algebraic systems in the context of integrable non-abelian Laurent ODEs. Program. Comput. Softw. 38, No. 2, 73-83 (2012). 2012 MAIK Nauka/Interperiodica Publishing, Moskva; Springer, New York EN numerical examples overdetermined systems computer algebra program Linear Selective Systems Solver linear algebraic systems rational coefficients large sparse systems symmetry investigation non-abelian Laurent ordinary differential equation Lax pair first integrals

doi:10.1134/S0361768812020065

arXiv:0706.2464

Summary: The paper reports on a computer algebra program LSSS (Linear Selective Systems Solver) for solving linear algebraic systems with rational coefficients. The program is especially efficient for very large sparse systems that have a solution in which many variables take the value zero. The program is applied to the symmetry investigation of a non-abelian Laurent ordinary differential equation (ODE) introduced recently by {\it M. Kontsevich} [private communication]. The computed symmetries confirmed that a Lax pair found for this system earlier generates all first integrals of degree at least up to 14.