Symbolic Computation Group

The monomials involved in a polynomial system encode a large amount of information about its solutions. This fact has motivated the development of algorithms which take advantage of sparsity for polynomial system solving. In this talk I will discuss how hybrid symbolic-numeric algorithms like the polyhedral homotopy, sparse system decomposition, and the sparse trace test, help us reliably solve sparse polynomial systems. Along the way, I will discuss the basics of homotopy continuation, monodromy, and polyhedral geometry.

Aspects of this talk are joint work with Burr, Rodriguez, Sottile, and Yahl.