Echelon Form

  1. Divasón Mallagaray, José
  2. Aransay Azofra, Jesús María
Revue:
Archive of Formal Proofs

ISSN: 2150-914X

Année de publication: 2015

Volumen: 2015

Pages: 1-171

Type: Article

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D'autres publications dans: Archive of Formal Proofs

Projets liés

Formalización de las matemáticas: aplicaciones en cálculo simbólico y álgebra computacional. Formalization of mathematics. applications to symbolic computation and computer algebra.

2015/00074/001

Résumé

We formalize an algorithm to compute the Echelon Form of a matrix. We have proved its existence over Bézout domains and made it executable over Euclidean domains, such as the integer ring and the univariate polynomials over a field. This allows us to compute determinants, inverses and characteristic polynomials of matrices. The work is based on the HOL-Multivariate Analysis library, and on both the Gauss-Jordan and Cayley-Hamilton AFP entries. As a by-product, some algebraic structures have been implemented (principal ideal domains, Bézout domains...). The algorithm has been refined to immutable arrays and code can be generated to functional languages as well