Automating elementary number-theoretic proofs using Gröbner bases

by John Harrison

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4 - 0 self

Datum	Value	Source
TITLE	Automating elementary number-theoretic proofs using Gröbner bases	SVM HeaderParse 0.2
AUTHOR NAME	John Harrison	SVM HeaderParse 0.2
AUTHOR AFFIL	Intel Corporation, JF1-13; 2111 NE 25th Avenue	SVM HeaderParse 0.2
AUTHOR ADDR	Hillsboro OR 97124, USA	SVM HeaderParse 0.2
ABSTRACT	Abstract. We present a uniform algorithm for proving automatically a fairly wide class of elementary facts connected with integer divisibility. The assertions that can be handled are those with a limited quantifier structure involving addition, multiplication and certain number-theoretic predicates such as ‘divisible by’, ‘congruent ’ and ‘coprime’; one notable example in this class is the Chinese Remainder Theorem (for a specific number of moduli). The method is based on a reduction to ideal membership assertions that are then solved using Gröbner bases. As well as illustrating the usefulness of the procedure on examples, and considering some extensions, we prove a limited form of completeness for properties that hold in all rings. 1	SVM HeaderParse 0.2
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