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Solving large linear algebraic systems in the context of integrable non-abelian Laurent ODEs

Please always quote using this URN: urn:nbn:de:0297-zib-16102
  • 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.

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Author:Thomas Wolf, Eberhard Schrüfer, Kenneth Webster
Document Type:ZIB-Report
Tag:linear algebraic systems, integrability, Lax pairs, noncommutative ODE, Laurent ODE
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
Date of first Publication:2012/10/16
Series (Serial Number):ZIB-Report (12-32)
ISSN:1438-0064
Published in:Appeared in: Programming and Computer Software (2012), Volume 38, Number 2, pp. 73-83
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