Polynomial homotopy continuation with PHCpack

Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation

Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and reflect on the application of polynomial homotopy continuation methods to solve polynomial systems in the cloud. Via the graph isomorphism problem we organize...

Interfacing with the Numerical Homotopy Algorithms in PHCpack

Our Maple package PHCmaple came to existence in 2004 when it provided a convenient interface to the basic functionality of phc, a program which is a part of PHCpack and implements numeric algorithms for solving polynomial systems using polynomial homotopy continuation. Following the recent development of PHCpack the package has been extended with functions that deal with singular polynomial sys...

Quality Up in Polynomial Homotopy Continuation by Multithreaded Path Tracking

Speedup measures how much faster we can solve the same problem using many cores. If we can afford to keep the execution time fixed, then quality up measures how much better the solution will be computed using many cores. In this paper we describe our multithreaded implementation to track one solution path defined by a polynomial homotopy. Limiting quality to accuracy and confusing accuracy with...

Solving polynomial systems via homotopy continuation and monodromy

We develop an algorithm to find all solutions of a generic system in a family of polynomial systems with parametric coefficients using numerical homotopy continuation and the action of the monodromy group. We argue that the expected number of homotopy paths that this algorithm needs to follow is roughly linear in the number of solutions. We demonstrate that our software implementation is compet...

A review on Homotopy Continuation Methods for Polynomial Systems