Tyszka, Apoloniusz; Molenda, Krzysztof; Sporysz, Maciej An algorithm which transforms any Diophantine equation into an equivalent system of equations of the forms \(x_i=1\), \(x_i+x_j=x_k\), \(x_i \cdot x_j=x_k\). (English) Zbl 1285.11150 Int. Math. Forum 8, No. 1-4, 31-37 (2013). Summary: We describe an algorithm which transforms any Diophantine equation into an equivalent system of equations of the forms \(x_i=1\), \(x_i+x_j=x_k\), \(x_i \cdot x_j=x_k\). We apply the algorithm to the polynomial \(x_1\cdot x_2-1\). This procedure is implemented in MuPAD, Sage, and Mathematica. Cited in 1 Document MSC: 11Y50 Computer solution of Diophantine equations 11D72 Diophantine equations in many variables Keywords:reduction of degree; system of Diophantine equations Software:MuPAD; Mathematica; SageMath PDFBibTeX XMLCite \textit{A. Tyszka} et al., Int. Math. Forum 8, No. 1--4, 31--37 (2013; Zbl 1285.11150) Full Text: DOI Link