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arXiv · 1702.06920

Bad Primes in Computational Algebraic Geometry

Janko Boehm·Wolfram Decker·Claus Fieker·Santiago Laplagne·Gerhard Pfister
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Abstract

Computations over the rational numbers often suffer from intermediate coefficient swell. One solution to this problem is to apply the given algorithm modulo a number of primes and then lift the modular results to the rationals. This method is guaranteed to work if we use a sufficiently large set of good primes. In many applications, however, there is no efficient way of excluding bad primes. In this note, we describe a technique for rational reconstruction which will nevertheless return the correct result, provided the number of good primes in the selected set of primes is large enough. We give a number of illustrating examples which are implemented using the computer algebra system Singular and the programming language Julia. We discuss applications of our technique in computational algebraic geometry.

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Janko Boehm, Wolfram Decker, Claus Fieker, Santiago Laplagne, Gerhard Pfister. 2017-02-22. Bad Primes in Computational Algebraic Geometry. https://doi.org/10.1007/978-3-319-42432-3_12

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