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Articles 61 - 61 of 61
Full-Text Articles in Physical Sciences and Mathematics
Algorithmic Contributions To The Theory Of Regular Chains, Wei Pan
Algorithmic Contributions To The Theory Of Regular Chains, Wei Pan
Electronic Thesis and Dissertation Repository
Regular chains, introduced about twenty years ago, have emerged as one of the major
tools for solving polynomial systems symbolically. In this thesis, we focus on different
algorithmic aspects of the theory of regular chains, from theoretical questions to high-
performance implementation issues.
The inclusion test for saturated ideals is a fundamental problem in this theory.
By studying the primitivity of regular chains, we show that a regular chain generates
its saturated ideal if and only if it is primitive. As a result, a family of inclusion tests
can be detected very efficiently.
The algorithm to compute the regular GCDs …