  A standard method for finding a rational number from its values modulo a
collection of primes is to determine its value modulo the product of the primes
via Chinese remaindering, and then use Farey sequences for rational
reconstruction. Successively enlarging the set of primes if needed, this method
is guaranteed to work if we restrict ourselves to good primes. Depending on the
particular application, however, there may be no efficient way of identifying
good primes.
  In the algebraic and geometric applications we have in mind, the final result
consists of an a priori unknown ideal (or module) which is found via a
construction yielding the (reduced) Groebner basis of the ideal. In this
context, we discuss a general setup for modular and, thus, potentially parallel
algorithms which can handle bad primes. A key new ingredient is an error
tolerant algorithm for rational reconstruction via Gaussian reduction.
