An Algorithm which Transforms any Diophantine Equation into an Equivalent System ofEquations of the Forms x_i=1, x_i+x_j=x_k, x_i cdot x_j=x_k

Apoloniusz Tyszka , Krzysztof Molenda , Maciej Sporysz

Abstract

We describe an algorithm which transforms any Diophantine equation into an equivalent system of equations of the forms xi = 1, xi + xj = xk, xi · xj = xk. We apply the algorithm to the polynomial x1 · x2 − 1. This procedure is implemented in MuPAD, Sage, and Mathematica.
Author Apoloniusz Tyszka (FoPaPE)
Apoloniusz Tyszka,,
- Faculty of Production and Power Engineering
, Krzysztof Molenda (FoPaPE)
Krzysztof Molenda,,
- Faculty of Production and Power Engineering
, Maciej Sporysz (FoPaPE)
Maciej Sporysz,,
- Faculty of Production and Power Engineering
Journal seriesInternational Mathematical Forum , ISSN 1312-7594 , (0 pkt)
Issue year2013
Vol8
No1
Pages31-37
Publication size in sheets0.5
Keywords in EnglishDiophantine equation, reduction of degree, system of Diophantine equations
URL http://www.m-hikari.com/imf/imf-2013/1-4-2013/tyszkaIMF1-4-2013-1.pdf
Internal identifierWIPiE/2013/90
Languageen angielski
Score (nominal)5
ScoreMinisterial score = 0.0, 26-07-2017, ArticleFromJournal
Ministerial score (2013-2016) = 5.0, 26-07-2017, ArticleFromJournal
Citation count*
Cite
Share Share

Get link to the record


* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Back
Confirmation
Are you sure?