An algorithm which transforms any Diophantine equation into an equivalent system of equations of the forms x_i=1, x_i+x_j=x_k, x_i cdot x_j=x_k

A Tyszka; K Molenda; M Sporysz

doi:10.12988/imf.2013.13004

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An algorithm which transforms any Diophantine equation into an equivalent system of equations of the forms x_i=1, x_i+x_j=x_k, x_i cdot x_j=x_k

作者：A Tyszka; K Molenda; M Sporysz

来源：International Mathematical Forum, 2013, 8: 31-37.

DOI：10.12988/imf.2013.13004

摘要

We describe an algorithm which transforms any Diophantineequation into an equivalent system of equations of the forms mbox{$x_i=1$},mbox{$x_i+x_j=x_k$}, mbox{$x_i cdot x_j=x_k$}. We apply the algorithmto the polynomial mbox{$x_1 cdot x_2-1$}. This procedure is implementedin {sl MuPAD}, {sl Sage}, and {sl Mathematica}.