Trace test
Anton Leykin, Jose Israel Rodriguez, Frank Sottile

TL;DR
This paper discusses the trace test in numerical algebraic geometry, extending it to subvarieties of product spaces with a practical dimension reduction approach for efficient verification.
Contribution
It introduces a new method for applying the trace test to subvarieties of product spaces using multihomogeneous witness sets and dimension reduction techniques.
Findings
Effective trace test for subvarieties in product spaces
Dimension reduction simplifies the trace test process
Practical approach for verifying witness sets in affine space
Abstract
The trace test in numerical algebraic geometry verifies the completeness of a witness set of an irreducible variety in affine or projective space. We give a brief derivation of the trace test and then consider it for subvarieties of products of projective spaces using multihomogeneous witness sets. We show how a dimension reduction leads to a practical trace test in this case involving a curve in a low-dimensional affine space.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Computational Geometry and Mesh Generation
