The International Obfuscated C Code Contest was a programming contest for the most creatively obfuscated yet succinct C code. By contrast, an interest herein is in programs which are, in a sense, easily seen to be correct, but which cannot be proved correct in pre-assigned, computably axiomatized, powerful, true theories T. A point made by our first theorem, then, is that, then, unverifiable pr...

We give an efficient algorithm for solving resultant form equations over number fields. This is the first time that such equations are completely solved by reducing them to unit equations in two variables.

Earlier results expressing multivariate subresultants as ratios of two subdeterminants of the Macaulay matrix are extended to Jouanolou’s resultant matrices. These matrix constructions are generalizations of the classical Macaulay matrices and involve matrices of significantly smaller size. Equivalence of the various subresultant constructions is proved. The resulting subresultant method improv...

The first step in the generalization of the classical theory of homogeneous equations to the case of arbitrary support is to consider algebraic systems with multihomogeneous structure. We propose constructive methods for resultant matrices in the entire spectrum of resultant formulae, ranging from pure Sylvester to pure Bézout types, and including matrices of hybrid type of these two. Our appro...

In this paper we report on the recent progress in computing bivariate polynomial resultants on Graphics Processing Units (GPU). Given two polynomials in Z[x, y], our algorithm first maps the polynomials to a prime field. Then, each modular image is processed individually. The GPU evaluates the polynomials at a number of points and computes univariate modular resultants in parallel. The remainin...