Date of Award
Master of Science (MS)
School of Mathematical and Statistical Sciences
We investigate how the coefficients of a sparse polynomial system influence the sum, or the trace, of its solutions. We discuss an extension of the classical trace test in numerical algebraic geometry to sparse polynomial systems. Two known methods for identifying a trace affine linear subset of the support of a sparse polynomial system use sparse resultants and polyhedral geometry, respectively. We introduce a new approach which provides more precise classifications of trace affine linear sets than was previously known. For this new approach, we developed software in Macaulay2.
McKay, Julianne, "Identifying Trace Affine Linear Sets Using Homotopy Continuation" (2022). All Theses. 3831.