Echelon Form

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

ISSN: 2150-914X

Año de publicación: 2015

Volumen: 2015

Páginas: 1-171

Tipo: Artículo

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Otras publicaciones en: Archive of Formal Proofs

Proyectos relacionados

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

2015/00074/001

Resumen

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