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.
The authors are partially supported by FEDER/Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación/MTM2017-88796-P (Symbolic Computation: new challenges in Algebra and Geometry together with its applications).J. R. Sendra and J. Caravantes are members of the research group ASYNACS (REF. CT-CE 2019/683).
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Caravantes, J., Sendra, J.R., Sendra, J. (2020). A Maple Package for the Symbolic Computation of Drazin Inverse Matrices with Multivariate Transcendental Functions Entries. In: Gerhard, J., Kotsireas, I. (eds) Maple in Mathematics Education and Research. MC 2019. Communications in Computer and Information Science, vol 1125. Springer, Cham. https://doi.org/10.1007/978-3-030-41258-6_12
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