Abstract: |
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.
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BibTeX: |
@article{Echelon_Form-AFP,
author = {Jose Divasón and Jesús Aransay},
title = {Echelon Form},
journal = {Archive of Formal Proofs},
month = feb,
year = 2015,
note = {\url{http://isa-afp.org/entries/Echelon_Form.shtml},
Formal proof development},
ISSN = {2150-914x},
}
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