A note on solutions of the cuboid factor equations

2012/09/04 by Руслан Шарипов, Ruslan Sharipov, Sharipov, Ruslan · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math.NT #msc:11D25 #msc:11D72 #msc:12E05 #msc:14G05

paper · pdf · doi:10.48550/arxiv.1209.0723

AmSTeX, 15 pages, amsppt style, 3 ancillary files

arxiv created 2012/09/04 · arxiv updated 2012/09/05

Abstract

A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. It is described by a system of four quadratic equations with respect to six variables. The cuboid factor equations were derived from these four equations by symmetrization procedure. They constitute a system of eight polynomial equations. Recently two sets of formulas were derived providing two solutions for the cuboid factor equations. These two solutions are studied in the present paper. They are proved to coincide with each other up to a change of parameters in them.

Citations

• The surface parametrizing cuboids

Cited by

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• A fast modulo primes algorithm for searching perfect cuboids and its implementation
• A note on rational and elliptic curves associated with the cuboid factor equations
• A note on invertible quadratic transformations of the real plane

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