3 citations · 3 across the 6 of their papers we have counts for
7 papers
Restricted monodromy containing transpositions
Julianne Barnhart, Taylor Brysiewicz, Michael Burr +1
We relate the monodromy group of a branched cover to the monodromy groups of its restrictions. We show that the presence of a transposition in a restricted monodromy group signific…
Subalgebra and Khovanskii bases equivalence
Colin Alstad, Michael Burr, Oliver Clarke +1
The main results of this paper establish a partial correspondence between two previously-studied analogues of Groebner bases in the setting of algebras: namely, subalgebra (aka SAG…
Isolating clusters of zeros of analytic systems using arbitrary-degree inflation
Michael Burr, Kisun Lee, Anton Leykin
Given a system of analytic functions and an approximation to a cluster of zeros, we wish to construct two regions containing the cluster and no other zeros of the system. The small…
SubalgebraBases in Macaulay2
Michael Burr, Oliver Clarke, Timothy Duff +3
We describe a recently revived version of the software package SubalgberaBases, which is distributed in the Macaulay2 computer algebra system. The package allows the user to comput…
Sparse trace tests
Taylor Brysiewicz, Michael Burr
We establish how the coefficients of a sparse polynomial system influence the sum (or the trace) of its zeros. As an application, we develop numerical tests for verifying whether a…
Inflation of poorly conditioned zeros of systems of analytic functions
Michael Burr, Anton Leykin
Given a system of analytic functions and an approximate zero, we introduce inflation to transform this system into one with a regular quadratic zero. This leads to a method for iso…
Effective certification of approximate solutions to systems of equations involving analytic functions
Michael Burr, Kisun Lee, Anton Leykin
We develop algorithms for certifying an approximation to a nonsingular solution of a square system of equations built from univariate analytic functions. These algorithms are based…