PHCpack in Macaulay2

Details PHCpack in Macaulay2 PHCpack in Macaulay2

2011-05-24

arxiv.org/abs/1105.4881v1

Mathematics

Algebraic Geometry

5 pages, appendix: 6 pages (example Macaulay2 code included)

Scientific paper

The Macaulay2 package PHCpack.m2 provides an interface to some of the functionality of PHCpack, a general-purpose solver for polynomial systems by homotopy continuation. The main function of the package interfaces PHCpack's numerical solver phc, published as Algorithm 795 in ACM Trans. Math. Softw. (TOMS). The blackbox solver computes mixed volumes using mixedvol, ACM TOMS Algorithm 846, and then applies polyhedral homotopy methods to solve a polynomial system. As numerical algebraic geometry plays an important role in applications, we illustrate the package on an example from algebraic statistics. In particular, we verify the Gaussian cycle conjecture for the undirected 8-cycle by numerically solving a square system in 36 variables and obtaining 321 solutions after filtering.

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