Many important problems in the exact sciences can be solved using exact computation. The use of exact arithmetic, however, often leads to large operands and unacceptable computing times. We propose to introduce rounded computation steps in a controlled way. The accuracy of intermediate results can be guaranteed by mathematical theorems, by self-validation, or by a posteriori verification. Results can be rounded in a number of ways among them floating point arithmetic. While retaining the mathematical integrity of our methods we obtain dramatic reductions in average computing times.
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