Computer Algebra Challenges from Integrable non-abelian Laurent ODEs

Computer Algebra Challenges from Integrable non-abelian Laurent ODEs

Thomas Wolf and Eberhard Schruefer

With examples of integrable matrix homogeneous ODE-systems, Dr. Wolf and Dr. Schruefer will discuss non-abelian Laurent polynomials and an ODE-system of Kontsevich which they study for integrability.

Further studies towards the classification of such ODE systems and the investigation of Lax pairs of a given system lead to challenging bi-linear algebraic systems for undetermined coefficients to solve. To compute symmetries of order up to 15 for the Kontsevich sytem, linear algebraic systems with over 330 million equations for 60 million undetermined coefficients had to be solved.

Dr. Wolf and Dr. Schruefer will discuss the new algorithms that have made these computations possible, the necessary extensions of the computer algebra system with comparisons to other computer algebra systems, and the SHARCNET hardware that was used in the process.

Contact: Thomas Wolf

Poster

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