Applied and Computational Mathematics and Statistics
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 Creator(s):
 Jonathan Hauenstein, Margaret Regan
 Description:
Polynomials which arise via elimination can be difficult to compute explicitly. By using a pseudowitness set, we develop an algorithm to explicitly compute the restriction of a polynomial to a given line. The resulting polynomial can then be used to evaluate the original polynomial and directional derivatives along the line at any point on the given line. Several examples are used to demonstrate this new algorithm including examples of computing the critical points of the discriminant locu…
 Date Created:
 20200327
 Record Visibility:
 Public

 Creator(s):
 Margaret Regan, Jonathan Hauenstein
 Description:
A common computational problem is to compute topological information about a real surface defined by a system of polynomial equations. Our software, called polyTop, leverages numerical algebraic geometry computations from Bertini and Bertini_real with topological computations in javaPlex to compute the Euler characteristic, genus, Betti numbers, and generators of the fundamental group of a real surface. Several examples are used to demonstrate this new software.
 Date Created:
 20180302
 Record Visibility:
 Public

 Creator(s):
 Margaret Regan, Jonathan Hauenstein
 Description:
Three key aspects of applying homotopy continuation to parameterized systems of polynomial equations are investigated. First, for parameterized systems which are homogenized with solutions in projective space, we investigate options for selecting the affine patch where computations are performed. Second, for parameterized systems which are overdetermined, we investigate options for randomizing the system for improving the numerically stability of the computations. Finally, since one is typica…
 Date Created:
 20170706
 Record Visibility:
 Public