Why is the Quintic Unsolvable?

It is intuitive that removing even a single point from a line disconnects it, but removing a finite set of points from a plane leaves it connected. A line disconnected by a single point. A plane remaining connected even with a few points removed. However, this basic fact leads to a non-trivial property of real and complex polynomials: not all...

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KaTeXMacros = { "\\clplus": "\\oplus", "\\clminus": "\\ominus", "\\clmul": "\\otimes", "\\cldiv": "\\oslash", "\\bclmod": "\\mathbin{\\mathrm{clmod}}", }; 1. Overview This article explains Reed-Solomon erasure codes and the problems they solve in gory detail, with the aim of providing enough background to understand how the PAR1 ...

KaTeXMacros = { "\\iroot": "\\operatorname{iroot}", "\\Bits": "\\operatorname{Bits}", "\\Err": "\\operatorname{Err}", "\\NewtonRoot": "\\mathrm{N{\\small EWTON}\\text{-}I{\\small ROOT}}", }; 1. The algorithm Today I’m going to talk about the generalization of the integer square root algorithm to higher roots. That is, given \(n\) and...

(Note: this article is a summary of this thread on ompf2.) The usual method for sampling a sphere from a point outside the sphere is to calculate the angle of the cone of the visible portion and uniformly sample within that cone, as described in Shirley/Wang. However, one detail that is glossed over is that you still need to map from the sampled...