Charles Wampler

Publications

AMS book jacket — Numerical Algebraic Geometry
by Silviana C. Amethyst, Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler
Student Mathematical Library, Vol. 110
American Mathematical Society, 2026.

This book is an accessible introduction to numerical algorithms for representing, locating, and manipulating nonlinear algebraic sets, i.e., the solutions of systems of polynomial equations. It is suitable for an upper-level undergraduate course, motivated undergraduate math majors seeking an independent project, and everyone interested in learning more about numerical algebraic geometry.

Bertini book jacket — Numerically Solving Polynomial Systems with Bertini
by Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler
SIAM Books, 2011.

This book is a user-oriented presentation of how to solve polynomial systems using the Bertini software package. It describes the algorithms in detail and includes a complete users manual.

Sommese-Wampler book jacket — *The Numerical Solution of Systems of Polynomials Arising in Engineering and Science*
by Andrew J. Sommese and Charles W. Wampler, II
World Scientific, 2005.

Our earlier book describes in detail the mathematics underlying numerical algebraic geometry as well as describing the state-of-the-art techniques as of 2005.

The exercises of the book refer to our HomLab suite of Matlab routines. That code is now outdated, but it is still available on the Software page of this website.