Features of PHCpack

version 2.4:

• path trackers on graphics processing units (GPUs), with Xiangcheng Yu
• functioning prototype of a cloud service, with Nathan Bliss, Jeff Sommars, and Xiangcheng Yu
• Python scripting interface: phcpy

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 (some milestones) of Releases:

v2.3.79 on 16 May 2013.

Better support for multicore architectures (run phc as phc -t) and higher order predictors.

v2.3.70 on 8 November 2012.

An irreducible decomposition for solution sets defined by binomial systems. Version 2.3.68 on 14 June 2012 contains an improved black box solver for toric components of general binomial systems, based on new polyhedral algorithms developed jointly with Danko Adrovic.

v2.3.55 on 28 May 2010.

Newton's method with complex quad double arithmetic (developed in collaboration with Genady Yoffe) based on QD-2.3.9.

v2.3.52 on 30 October 2009.

Cheater homotopies for triple intersection conditions solved by Littlewood-Richardson homotopies were introduced in v2.3.52, along with improved multiprecision refinement of roots. Release v2.3.51 has better multiprecision (for phc -v), and the blackbox solver accepts now also Laurent polynomial systems, i.e.: negative values for exponents.

Release v2.3.45 introduced multitasking: with phc -p -t8 the path trackers will use 8 threads. This was extended to the blackbox solver in v2.3.46, i.e.: phc -b -t8 uses 8 threads for path tracking.

v2.3.41 on 16 May 2008.

The Python module phcpy (developed in collaboration with Kathy Piret) exports the blackbox solver of PHCpack, adding another programmers interface to the software.

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.