On singularities of the inverse problems associated with perfect cuboids

Abstract

Two cubic equations and three auxiliary equations for edges and face diagonals of a rational perfect cuboid have been recently derived. They constitute a background for two inverse problems. The coefficients of cubic equations and the right hand sides of auxiliary equations are rational functions of two rational parameters, i. e. they have denominators. Hence the inverse problems have singular points. These singular points are studied in the present paper.

AmSTeX, 6 pages, amsppt style

References in corpus (7)

• A note on the third cuboid conjecture. Part I
• On an ideal of multisymmetric polynomials associated with perfect cuboids
• Perfect cuboids and multisymmetric polynomials
• A biquadratic Diophantine equation associated with perfect cuboids
• On the equivalence of cuboid equations and their factor equations
• A general rational solution of an equation associated with perfect cuboids
• Inverse problems associated with perfect cuboids

Cited by in corpus (5)

• A note on rational and elliptic curves associated with the cuboid factor equations
• On two algebraic parametrizations for rational solutions of the cuboid equations
• A note on solutions of the cuboid factor equations
• Asymptotic estimates for roots of the cuboid characteristic equation in the linear region
• Reverse asymptotic estimates for roots of the cuboid characteristic equation in the case of the second cuboid conjecture