1610 eng reportzib 0 2012-10-16 2012-10-16 -- The paper reports on a computer algebra program {\sc 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 ODE introduced recently by M.\ Kontsevich. The computed symmetries confirmed that a Lax pair found for this system earlier generates all first integrals of degree at least up to 14. 1438-0064 urn:nbn:de:0297-zib-16102 Appeared in: Programming and Computer Software (2012), Volume 38, Number 2, pp. 73-83 Thomas Wolf Winfried Neun Eberhard Schrüfer Kenneth Webster 12-32 eng uncontrolled linear algebraic systems, integrability, Lax pairs, noncommutative ODE, Laurent ODE ORDINARY DIFFERENTIAL EQUATIONS DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] Digital Data and Information for Society, Science, and Culture https://opus4.kobv.de/opus4-zib/files/1610/ZR-12-32.pdf