The study of Drazin inverses is an active research area that is developed, among others, in three directions: theory, applications and computation. This paper is framed in the computational part.
Many authors have addressed the problem of computing Drazin inverses of matrices whose entries belong to different domains: complex numbers, polynomial entries, rational functions, formal Laurent series, meromorphic functions. Furthermore, symbolic techniques have proven to be a suitable tools for this goal.
In general terms, the main contribution of this paper is the implementation, in a package, of the algorithmic ideas presented in [10, 11]. Therefore, the package computes Drazin inverses of matrices whose entries are elements of a finite transcendental field extension of a computable field. The computation strategy consists in reducing the problem to the computation of Drazin inverses, via Gröbner bases, of matrices with rational functions entries.
More precisely, this paper presents a Maple computer algebra package, named DrazinInverse, that computes Drazin inverses of matrices whose entries are elements of a finite transcendental field extension of a computable field. In particular, the implemented algorithm can be applied to matrices over the field of meromorphic functions, in several complex variables, on a connected domain.
Maple Drazin inverse Gröbner bases Symbolic Computation Meromorphic functions
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Avrachenkov, K.E., Filar, J.A., Howlett, P.G.: Analytic Perturbation Theory and Its Applications. SIAM (2013)Google Scholar