Publications (24)
Solving Decomposable Sparse Systems
Taylor Brysiewicz, Jose Israel Rodriguez, Frank Sottile +1
Amendola et al. proposed a method for solving systems of polynomial equations lying in a family which exploits a recursive decomposition into smaller systems. A family of systems a…
Polyhedral Geometry in OSCAR
Taylor Brysiewicz, Michael Joswig
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geomet…
Newton polytopes and numerical algebraic geometry
Taylor Brysiewicz
We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle…
Numerical Software to Compute Newton Polytopes and Tropical Membership
Taylor Brysiewicz
We present our implementation of an algorithm which functions as a numerical oracle for the Newton polytope of a hypersurface in the Macaulay2 package NumericalNP.m2. We propose a…
Max-convolution through numerics and tropical geometry
Taylor Brysiewicz, Jonathan D. Hauenstein, Caroline Hills
The maximum function, on vectors of real numbers, is not differentiable. Consequently, several differentiable approximations of this function are popular substitutes. We survey thr…
A counterexample to Fermi isospectral rigidity for two dimensional discrete periodic Schrödinger operators
Taylor Brysiewicz, Matthew Faust, Wencai Liu
Using numerical certification, we prove the existence of a nontrivial real-valued two dimensional periodic potential whose associated discrete Schrödinger operator is Fermi isospe…