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• Содержание выпуска •
• Mathematical Foundations of Programming •
• Software and Hardware for Distributed Systems and Supercomputers •
• Artificial Intelligence, Intelligence Systems, Neural Networks •
• Supercomputing Software and Hardware •
• Software and Hardware for Distributed Systems and Supercomputers •
Mathematical Foundations of Programming
Responsible for the Section: doctor of physico-mathematical Sciences
Nikolay Nepeivoda
On the left: assigned number of the paper, submission date, the number
of A5 pages contained in the paper, and the reference to the full-text
PDF
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Article #
1_2017
44
p.
/r2/pdf.jpg)
PDF |
submitted on 26th
Nov 2016 displayed on
website on 23th
Jan
2017
Sergei
Meshveliani
Programming computer algebra with basing on constructive
mathematics. Domains with factorization
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: constructive mathematics, computer algebra,
dependent types, functional programming, Agda.
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article citation |
http://psta.psiras.ru/read/psta2017_1_3-46.pdf |
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DOI
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https://doi.org/10.25209/2079-3316-2017-8-1-3-46 |
• Содержание выпуска •
• Mathematical Foundations of Programming •
• Software and Hardware for Distributed Systems and Supercomputers •
• Artificial Intelligence, Intelligence Systems, Neural Networks •
• Supercomputing Software and Hardware •
• Software and Hardware for Distributed Systems and Supercomputers •
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