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.