6 papers
Elimination Templates in Macaulay2
Manav Batavia, Cheng Chen, Anna Natalie Chlopecki +4
We introduce the package \texttt{EliminationTemplates} for the Macaulay2 computer algebra system, which provides tools for constructing automatic solvers for families of zero-dimen…
Certifying Galois/monodromy Actions via Homotopy Graphs
Timothy Duff, Kisun Lee
We develop a certified numerical algorithm for computing Galois/monodromy groups of parametrized polynomial systems. Our approach employs certified homotopy path tracking to guaran…
Universal Gröbner Bases of (Universal) Multiview Ideals
Timothy Duff, Jack Kendrick, Rekha R. Thomas
Multiview ideals arise from the geometry of image formation in pinhole cameras, and universal multiview ideals are their analogs for unknown cameras. We prove that a natural collec…
Numerically Computing Galois Groups of Minimal Problems
Timothy Duff
I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a param…
Brackets and Projective Geometry in Macaulay2
Dalton Bidleman, Timothy Duff, Jack Kendrick +1
We introduce the Brackets package for the computer algebra system Macaulay2, which provides convenient syntax for computations involving the classical invariants of the special lin…
A Galois-Theoretic Complexity Measure for Solving Systems of Algebraic Equations
Timothy Duff
Motivated by applications of algebraic geometry, we introduce the Galois width, a quantity characterizing the complexity of solving algebraic equations in a restricted model of com…