Computing Sparse Representations of Systems of Rational Fractions

François Lemaire (1) , Alexandre Temperville (1)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

We present new algorithms for computing sparse representations of systems of parametric rational fractions by means of change of coordinates. Our algorithms are based on computing sparse matrices encoding the degrees of the parameters occurring in the fractions. Our methods facilitate further qualitative analysis of systems involving rational fractions. Contrary to symmetry based approaches which reduce the number of parameters, our methods only increase the sparsity, and are thus complementary. Previously hand made computations can now be fully automated by our methods.

Mots clés: parametric systems; simplification of rational fractions; sparse basis of vector spaces

Domaines: Algorithme et structure de données [cs.DS]

François Lemaire, Alexandre Temperville. Computing Sparse Representations of Systems of Rational Fractions. Computer Algebra in Scientific Computing, Sep 2016, Bucharest, Romania. pp.349 - 366, ⟨10.1007/978-3-319-45641-6_23⟩. ⟨hal-01407919⟩