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Solving large linear algebraic systems in the context of integrable non-abelian Laurent ODEs. (English) Zbl 1256.65074
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 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.

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F50 Computational methods for sparse matrices
65F05 Direct numerical methods for linear systems and matrix inversion
68W30 Symbolic computation and algebraic computation
65Y15 Packaged methods for numerical algorithms
Full Text: DOI arXiv
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