3 papers
math.AG2026
Numerical Irreducible Decomposition in Julia
Paul Breiding
This article introduces a new implementation for computing a numerical irreducible decomposition for a system of polynomial equations. The implementation is part of the software pa…
math.NA2026
Low-Memory Numerical Certification
Paul Breiding, Taylor Brysiewicz, David K. Johnson
We introduce a low-memory framework for certifying numerical solutions to polynomial systems which uses solution iterators and spatial partitioning trees to reduce memory requireme…
math.AG2026
Elimination Without Eliminating: Computing Complements of Real Hypersurfaces Using Pseudo-Witness Sets
Paul Breiding, John Cobb, Aviva K. Englander +6
Many hypersurfaces in algebraic geometry, such as discriminants, arise as the projection of another variety. The real complement of such a hypersurface partitions its ambient space…