Features of PHCpack

version 2.3:

parallel Pieri homotopies, in collaboration with Yusong Wang

Newton's method with deflation, developed with Anton Leykin and Ailing Zhao

intrinsic versions of diagonal homotopies

three new options: phc -k (feedback), phc -w (witness set intersection), and phc -a (preliminary version of a new solver)

version 2.2:

diagonal homotopies to intersect solution sets

bindings with MPI with dynamic and static distribution of paths, developed in collaboration with Yusong Wang

improved interface to C uses phc as a state machine

phc -b extended with univariate polynomials, simplicial systems, and factorization algorithms of one single multivariate polynomial

general code for coefficient-parameter homotopy continuation

version 2.1:

tools for numerical irreducible decomposition

simple interface to C and Maple

collection of C software added by Yusong Wang to realize feedback laws computed by homotopies of numerical Schubert calculus

version 2.0:

multi-precision facilities, developed in Ada 95

numerical Schubert calculus

version 1.0:

blackbox added on top of the toolboxes

automatic solving thanks to polyhedral homotopies

tested on large collection of polynomial systems

version 0.0:

toolbox approach, operation in four stages

only executable versions needed to run

menu driven, file oriented programs

History of Releases:

v2.3.34 on 29 November 2007.

This version brings stable mixed volumes into the blackbox solver. Release v2.3.31 allowed the computation of stable mixed volumes. MixedVol, a faster mixed volume computation was included since v2.3.13. Deflation as applied within phc -b was introduced in v2.3.27. Jumpstarting homotopies (developed in collaboration with Yan Zhuang) was first introduced as phc -q in v2.3.05.

v2.3: Independence Day 2005 (4 July 2005).

Release of source code for parallel Pieri homotopies (in collaboration with Yusong Wang), Newton's method for isolated singularities with deflation (developed with Anton Leykin and Ailing Zhao), intrinsic versions of the diagonal homotopies, and a preliminary version of an equation-by-equation solver. This release was presented at FoCM 2005.

v2.2: Veterans' day 2003 (11 November 2003).

Release of source code for diagonal homotopies to intersect positive dimensional solution sets of polynomial systems, as an extra tool. An improved blackbox solver and above all bindings with MPI provide a parallel path tracker, developed in collaboration with Yusong Wang. This main new feature is described in an extended abstract presented at the SIAM conference on parallel processing, February 2004.

v2.1: Halloween 2002 (31 October 2002).

Release of source code for tools for a numerical irreducible decomposition: cascade of homotopies for witness sets and routines to factor solution sets into irreducible components. The tools are available in the options phc -c and phc -f. This release is described in a proceedings volume of a Dagstuhl meeting (Fall 2001), and was presented at FoCM 2002, and at exercise sessions at the RAAG summer school in Rennes (summer 2003).

v2.0: August 1999.

Release of rewritten Ada 95 source code, extended with multi-precision arithmetic and homotopies (SAGBI and Pieri) in the numerical Schubert calculus. Executables for SUN, SGI, Linux and Windows PCs. PHCpack becomes Algorithm 795 of ACM TOMS (archived v1.0).

v1.0: August 1997.

Release of the full Ada 83 source code and executable versions for SUN, IBM AIX, and DEC workstations; and a demonstration database of test polynomial systems. The documentation paper was submitted to ACM Transactions on Mathematical Software.

v0.0: March 1995.

Pre-release of PHC and MVC, executable versions of the software, made publicly available on the occasion of the PoSSo Workshop on Software (Paris, 1-4 March 1995), and documented in the proceedings of this workshop.