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Program Systems: Theory and Applications, 2017, Volume 8, Issue 1, Pages 3–46
DOI: https://doi.org/10.25209/2079-3316-2017-8-1-3-46 (Mi ps247) 		 
Mathematical Foundations of Programming

Programming computer algebra with basing on constructive mathematics. Domains with factorization

S. D. Meshveliani

Ailamazyan Program Systems Institute of Russian Academy of Sciences
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DOI: https://doi.org/10.25209/2079-3316-2017-8-1-3-46
Abstract: The paper continues prevoius author publications on a constructive mathematics approach in computational algebra using a language with dependent types.
A constructive expression for the notion of a domain with factorization to primes for a monoid and for a ring possessing certain additionnal properties is obtained. A way to achieve constructed machine-checked proofs for theorems that relate the factorization notion for domains of different kinds is discussed.
All the described methods and proofs are completely implemented as a working program written in the Agda functional language. (In Russian).
Key words and phrases: constructive mathematics, computer algebra, dependent types, functional programming, Agda.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations AAAA-A16-116021760039-0
Received: 26.11.2016
Accepted: 23.01.2017
Document Type: Article
UDC: 510.252, 004.432.42
Language: Russian
Citation: S. D. Meshveliani, “Programming computer algebra with basing on constructive mathematics. Domains with factorization”, Program Systems: Theory and Applications, 8:1 (2017), 3–46
Citation in format AMSBIB
\Bibitem{Mec17}
\by S.~D.~Meshveliani
\paper Programming computer algebra with basing on constructive mathematics. Domains with factorization
\jour Program Systems: Theory and Applications
\yr 2017
\vol 8
\issue 1
\pages 3--46
\mathnet{http://mi.mathnet.ru/ps247}
\crossref{https://doi.org/10.25209/2079-3316-2017-8-1-3-46}
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