The algebraic eigenvalue problem
The algebraic eigenvalue problem
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Nilpotent normal form via Carleman linearization (for systems of ordinary differential equations)
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Rational normal form for dynamical systems by Carleman linearization
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
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We consider in this paper an algorithm for the exact computation of the Frobenius, Jordan and Arnold's form of matrices depending holomorphically on parameters. The problem originates from the problem of formal resolution of a first order system of differential equations depending on parameter. We have implemented this algorithm in Macsyma.