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Multiprojective witness sets and a trace test
Abstract In the field of numerical algebraic geometry, positive-dimensional solution sets of systems of polynomial equations are described by witness sets. In this paper, we define multiprojective…
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…
The maximum likelihood degree of toric varieties
Maximum likelihood geometry in the presence of data zeros
Focusing on sampling and model zeros, it is shown that, in these cases, the solutions to the likelihood equations are contained in a previously studied variety, the likelihood correspondence, which gives a lower bound on the ML degree.
Maximum Likelihood Duality for Determinantal Varieties
In a recent paper, Hauenstein, Sturmfels, and the second author discovered a conjectural bijection between critical points of the likelihood func- tion on the complex variety of matrices of rank r…
Numerical irreducible decomposition of multiprojective varieties
In the field of numerical algebraic geometry, positive-dimensional solution sets of systems of polynomial equations are described by witness sets. In this paper, we define multiprojective witness…
Combinatorial excess intersection
- J. Rodriguez
- Mathematics, Computer ScienceJ. Symb. Comput.
- 10 December 2012
Defect of Euclidean distance degree
Bertini for Macaulay2
Bertini, a popular software package for computational applications of this field, includes implementations of a variety of algorithms based on polynomial homotopy continuation, and the Macaulay2 package Bertini.m2 provides an interface to Bertini, making it possible to access the core run modes of Bertini in MacPaulay2.
Euclidean Distance Degree of the Multiview Variety
Non-proper Morse theory is used to give a topological interpretation of the Euclidean distance degree of an affine variety in terms of Euler characteristics.