Computations on Quasi Algebraic Set

William Sit
Department of Mathematics
The City College of New York
New York, NY 10031


The decomposition of a constructible set into a union of quasi-algebraic sets is often a first step to solve many problems and it is sometimes desirable to have as few cases to consider as possible. We derive decision criteria and algorithms for testing inclusion and equality relations between two unions of quasi-algebraic sets and between rational functions defined on them. We emphasize flexibility in practical representations of these geometry objects and in implementation of the criteria. The algorithms are implemented in Axiom and used to refine Sit's algorithm for parametric linear systems. Our main result can be applied to obtain an irredundant decomposition of a constructible set.

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IMACS ACA'98 Electronic Proceedings