# PHCmaple : A Maple Interface to the Numerical Homotopy Algorithms in PHCpack ∗

@inproceedings{Leykin2004PHCmapleA, title={PHCmaple : A Maple Interface to the Numerical Homotopy Algorithms in PHCpack ∗}, author={Anton Leykin and Jan Verschelde}, year={2004} }

Our Maple package PHCmaple provides a convenient interface to the functions of PHCpack, a collection of numeric algorithms for solving polynomial systems using polynomial homotopy continuation, which was recently extended with facilities to deal with positive dimensional solution sets. The interface illustrates the benefits of linking computer algebra with numerical software. PHCmaple serves as a first step in a larger project to integrate a numerical solver in a computer algebra system.

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## 18 Citations

Interfacing with the Numerical Homotopy Algorithms in PHCpack

- Computer ScienceICMS
- 2006

This paper describes two types of interfaces to PHCpack, the first of which was developed in conjunction with MPI (Message Passing Interface), needed to run the path trackers on parallel machines.

Polynomial homotopy continuation with PHCpack

- Computer ScienceACCA
- 2011

This document provides the outline for a software demonstration highlighting recent additions to the PHCpack software, such as accepting polynomials with negative exponents and sweeping for real points that lie isolated on complex solution curves.

PHClab: A MATLAB/Octave Interface to PHCpack

- Computer Science
- 2008

PHClab is a collection of scripts which call phc from within a MATLAB or Octave session that provides an interface to the blackbox solver for finding isolated solutions of polynomial equations.

Homotopy Methods for Solving Polynomial Systems tutorial at ISSAC'05, Beijing, China, 24 July 2005

- Computer Science, Mathematics
- 2007

This tutorial is on linking recent algorithms in numerical algebraic geometry to the software package PHCpack, a collection of algorithms to solve polynomial systems.

Parallel implementation of polyhedral homotopy methods

- Computer Science
- 2007

This thesis is the development of "parallel PHCpack", a project which started a couple of years ago developed by my advisor Jan Verschelde and his student Yusong Wang and which continues with Anton Leykin (parallel irreducible decomposition).

Symbolic-numeric completion of differential systems by homotopy continuation

- MathematicsISSAC
- 2005

A hybrid symbolic-numeric differential-elimination method for identifying and including missing constraints arising in differential systems is constructed, exploiting the fact that a system once differentiated becomes linear in its highest derivatives.

Factoring solution sets of polynomial systems in parallel

- Computer Science2005 International Conference on Parallel Processing Workshops (ICPPW'05)
- 2005

A probabilistic complexity study suggests modifications to the method, which will improve the serial version of the original algorithm and expose the limits of the master/servant parallel programming paradigm for this type of problem.

Evaluation of Jacobian Matrices for Newton’s Method with Deflation to Approximate Isolated Singular Solutions of Polynomial Systems

- Mathematics
- 2007

For isolated singular solutions of polynomial systems, we can restore the quadratic convergence of Newton’s method by deflation. The number of deflation stages is bounded by the multiplicity of the…

Newton's method with deflation for isolated singularities of polynomial systems

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2006

On approximate triangular decompositions in dimension zero

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2007

## References

SHOWING 1-10 OF 22 REFERENCES

Numerical Irreducible Decomposition Using PHCpack

- Computer Science, MathematicsAlgebra, Geometry, and Software Systems
- 2003

This paper indicates how the software package PHCpack can be used in conjunction with Maple and programs written in C and describes a numerically stable algorithm for decomposing positive dimensional solution sets of polynomial systems into irreducible components.

Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation

- Computer ScienceTOMS
- 1999

The structure and design of the software package PHC is described, which features great variety of root-counting methods among its tools and is ensured by the gnu-ada compiler.

Numerical Homotopies to Compute Generic Points on Positive Dimensional Algebraic Sets

- Mathematics, Computer ScienceJ. Complex.
- 2000

An embedding of the original polynomial system is presented, which leads to a sequence of homotopies, with solution paths leading to generic points of all components as the isolated solutions of an auxiliary system.

Using Monodromy to Decompose Solution Sets of Polynomial Systems into Irreducible Components

- Mathematics
- 2001

To decompose solution sets of polynomial systems into irreducible components, homotopy continuation methods generate the action of a natural monodromy group which partially classifles generic points…

Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems

- Computer Science, Mathematics
- 1987

This introduction to polynomial continuation remains a useful starting point for the reader interested in learning how to solve practical problems without advanced mathematics.

Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems

- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 2002

This paper proves theoretically and demonstrates in practice that linear traces suffice for this verification step, and shows how to do so more efficiently by building a structured grid of samples, using divided differences, and applying symmetric functions.

Towards factoring bivariate approximate polynomials

- MathematicsISSAC '01
- 2001

A new algorithm is presented for factoring bivariate approximate polynomials over C[x, y], which constructs a nearby composite polynomial, if one exists, and its irreducible factors.

Irreducible Decomposition of Curves

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2002

In this paper, we propose a fast semi-numerical algorithm for computing all irreducible branches of a curve in C?defined by polynomials with rational coefficients, we also treat the case of a…