Journal
JOURNAL OF LOGIC AND ALGEBRAIC PROGRAMMING
Volume 64, Issue 1, Pages 13-39Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.jlap.2004.07.003
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We describe: here a representation of computable real numbers and a set of algorithms for the elementary functions associated to this representation. A real number is represented as a sequence of finite B-adic numbers and for each classical function (rational, algebraic or transcendental), we describe how to produce a sequence representing the result of the application of this function to its arguments, according to the sequences representing these arguments. For each algorithm we prove that the resulting sequence is a valid representation of the exact real result.. This arithmetic is the first real arithmetic with mathematically proved algorithms. (c) 2004 Elsevier Inc. All rights reserved.
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