Iterated Resultants in CAD
James H. Davenport, Matthew England
TL;DR
This paper explores the factorization of iterated resultants in Cylindrical Algebraic Decomposition (CAD) to optimize the projection phase, focusing on the SC-Square implementation.
Contribution
It investigates how factorization of resultants can be utilized to improve CAD efficiency, a novel approach not previously exploited.
Findings
Factorizations often occur in iterated resultants in CAD
Utilizing factorization can potentially optimize CAD computations
Focus on the SC-Square implementation for practical application
Abstract
Cylindrical Algebraic Decomposition (CAD) by projection and lifting requires many iterated univariate resultants. It has been observed that these often factor, but to date this has not been used to optimise implementations of CAD. We continue the investigation into such factorisations, writing in the specific context of SC-Square.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Manufacturing Process and Optimization · Robotic Mechanisms and Dynamics