Computing singular elements modulo squares

08/24/2020

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by   Przemysław Koprowski, et al.

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The group of singular elements was first introduced by Helmut Hasse and later it has been studied by numerous authors including such well known mathematicians as: Cassels, Furtwängler, Hecke, Knebusch, Takagi and of course Hasse himself; to name just a few. The aim of the present paper is to present algorithms that explicitly construct groups of singular and S-singular elements (modulo squares) in a global function field.