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An algorithm to compute the set of characteristics of a system of polynomial equations over the integers

✍ Scribed by Rosemary Baines; Peter Vámos

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
135 KB
Volume
35
Category
Article
ISSN
0747-7171

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✦ Synopsis

We describe a (finite) algorithm to determine the set of characteristics of a system of polynomial equations with integer coefficients by using the theory of Gröbner bases. This gives us a proof that the set of characteristics must be either finite and not containing zero, or containing zero and cofinite. Another, algebraic, proof of this is given in the appendix. These results carry over to systems of polynomial equations over a principal ideal domain and also yields an algorithm for finding the characteristic set of a matroid.

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