Paper Info
Title
Bad Primes in Computational Algebraic Geometry.
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.
Year
DOI
Venue
2017
10.1007/978-3-319-42433-3_12
Lecture Notes in Computer Science
Keywords
DocType
Volume
Modular computations,Algebraic curves,Adjoint ideal
Journal
9725
ISSN
Citations 
PageRank 
0302-9743
0
0.34
References 
Authors
3
5
Name
Order
Citations
PageRank
Janko Boehm152.36
Wolfram Decker2268.41
Claus Fieker37314.37
Santiago Laplagne4132.84
Gerhard Pfister58312.74