# Modernizing PHCpack through phcpy

@article{Verschelde2013ModernizingPT, title={Modernizing PHCpack through phcpy}, author={Jan Verschelde}, journal={ArXiv}, year={2013}, volume={abs/1310.0056} }

PHCpack is a large software package for solving systems of polynomial equations. The executable phc is menu driven and file oriented. This paper describes the development of phcpy, a Python interface to PHCpack. Instead of navigating through menus, users of phcpy solve systems in the Python shell or via scripts. Persistent objects replace intermediate files.

## 17 Citations

### Solving Polynomial Systems with phcpy

- Computer ScienceProceedings of the 18th Python in Science Conference
- 2019

This paper explores new developments in phcpy, a scripting interface for PHCpack, over the past five years, and finds certain classes of polynomial system frequently arise, to whichphcpy is well-suited.

### Polynomial homotopy continuation on GPUs

- Computer ScienceACCA
- 2016

A library to track many solution paths defined by a polynomial homotopy on a Graphics Processing Unit (GPU) developed on NVIDIA graphics cards with CUDA SDKs and released under the GNU GPL license.

### Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation

- Mathematics, Computer ScienceCASC
- 2015

The design and implementation of the web interface for polynomial homotopy continuation methods is described and the graph isomorphism problem is organized and classified, identifying newly submitted systems with systems that have already been solved.

### Tracking Many Solution Paths of a Polynomial Homotopy on a Graphics Processing Unit in Double Double and Quad Double Arithmetic

- Computer Science, Mathematics2015 IEEE 17th International Conference on High Performance Computing and Communications, 2015 IEEE 7th International Symposium on Cyberspace Safety and Security, and 2015 IEEE 12th International Conference on Embedded Software and Systems
- 2015

The authors' massively parallel predictor-corrector algorithms to track many solution paths of a polynomial homotopy are described, which combines the reverse mode of algorithmic differentiation with double double and quad double arithmetic to compute more accurate results faster.

### Accelerating polynomial homotopy continuation on a graphics processing unit with double double and quad double arithmetic

- Mathematics, Computer SciencePASCO
- 2015

This work describes the implementation of numerical continuation methods for double double and quad double arithmetic, and reports on computational results on benchmark polynomial systems defined by polynomials in several variables with complex coefficients.

### Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm

- MathematicsMath. Comput.
- 2021

We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric…

### A Polyhedral Method to Compute All Affine Solution Sets of Sparse Polynomial Systems

- Mathematics, Computer ScienceArXiv
- 2013

This work presents a polyhedral method to compute all affine solution sets of a polynomial system, which enumerates all factors contributing to a generalized permanent.

### The Method of Gauss-Newton to Compute Power Series Solutions of Polynomial Homotopies

- MathematicsArXiv
- 2016

### The m-Bézout Bound and Distance Geometry

- Computer Science, MathematicsCASC
- 2021

A closed-form bound on the m-Bezout bound is offered for multi-homogeneous systems whose equations include two variable subsets of the same degree, which applies only to systems characterized by further structure.

### On the Maximal Number of Real Embeddings of Spatial Minimally Rigid Graphs

- MathematicsISSAC
- 2018

This work modify a commonly used parametric semi-algebraic formulation that exploits the Cayley-Menger determinant to minimize the a priori number of complex embeddings, where the parameters correspond to edge lengths, and introduces a method based on coupler curves that makes the sampling feasible for spatial minimally rigid graphs.

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