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Maximal Volume Ideal Polyhedra and the Arithmetic Angle Phenomenon
Igor Rivin
We present a software suite for the analysis and optimization of ideal convex polyhedra in hyperbolic 3-space . Using Rivin's variational characterization of ideal po…
From Euler to Today: Universal Mathematical Fallibility A Large-Scale Computational Analysis of Errors in ArXiv Papers
Igor Rivin
We present the results of a large-scale computational analysis of mathematical papers from the ArXiv repository, demonstrating a comprehensive system that not only detects mathemat…
Computational Resolution of Hadamard Product Factorization for Matrices
Igor Rivin
We computationally resolve an open problem concerning the expressibility of full-rank matrices as Hadamard products of two rank-2 matrices. Through exhaustive search o…
Computing Periodic Billiard Orbits in Balls via Newton's Method and Smale's -Criterion
Igor Rivin
We present a computational method for finding and verifying periodic billiard orbits in balls () using Newton's method applied to a variational formulation. The orbits…
Counting Matrices in SL3(Z) with Fixed Completely Split Character Polynomial: Preliminary Upper Bounds
Igor Rivin
We count matrices in the special linear group SL(n, Z) whose characteristic polynomials split completely over Q.