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A Maple Package for the Symbolic Computation of Drazin Inverse Matrices with Multivariate Transcendental Functions Entries

  • Jorge CaravantesEmail author
  • J. Rafael Sendra
  • Juana Sendra
Conference paper
  • 54 Downloads
Part of the Communications in Computer and Information Science book series (CCIS, volume 1125)

Abstract

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.

Keywords

Maple Drazin inverse Gröbner bases Symbolic Computation Meromorphic functions 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Jorge Caravantes
    • 1
    Email author
  • J. Rafael Sendra
    • 1
  • Juana Sendra
    • 2
  1. 1.Dpto. de Física y MatemáticasUniversidad de AlcaláAlcalá de HenaresSpain
  2. 2.Dpto. de Matemática Aplicada a las TICUniversidad Politécnica de MadridMadridSpain

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