Numerical Irreducible Decomposition in Julia

2026/08/03 by Paul Breiding
Mathematics · #math.AG

paper · pdf

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

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 package HomotopyContinuation.jl written in the programming language Julia.

Citations

• u-generation: solving systems of polynomials equation-by-equation
• Linear PDE with Constant Coefficients
• Noetherian operators and primary decomposition
• Trace test
• Numerical algorithms on the affine Grassmannian
• Julia: A Fresh Approach to Numerical Computing
• Julia: A Fresh Approach to Numerical Computing
• Numerical primary decomposition
• The Geometry of Algorithms with Orthogonality Constraints