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Import the second public release of PHCpack.

OKed by Jan Verschelde.

Increment-and-fix tracking of solution paths of polynomial homotopies in PHCv2.

New in this release are the multi-precision root refiners and the usage
of QR and Least Squares in the correctors at the end of the paths.

This library of continuation routines is organized in three layers:

  0. The basic data structures
  1. Increment-and-Fix continuation
  2. Driver routines

Hierarchical organization :

  conpar_io                        : 0.0. Continuation_Parameters_io
    |-- conpar                     : 0.0.0. Continuation_Parameters
    |-- cont_data                  : 0.0.1. Continuation_Data
  process_io                       : 0.1. Process_io

  continue                         : 1.0. Increment_and_Fix_Continuation
    |-- pathtrac                   : 1.0.1. Path_Trackers
          |-- dispred              : 1.0.2. Dispatch_Predictors
          |-----|-- predictors     : 1.0.3. Predictors
          |-- correctors           : 1.0.4. Correctors
          |-- dirpaths             : 1.0.5. Directions_of_Solution_Paths
                |-- vlprsalg       : 1.0.5.0. vLpRs_Algorithm
                      |-- vlrpstab : 1.0.5.0.0. vLpRs_Tables
  rootrefi                         : 1.1. Root_Refiners

  drivwind                         : 2.0. Driver_for_Winding_Numbers
    |-- drivpoco                   : 2.0.0. Drivers_for_Polynomial_Continuation
          |-- drivpadi             : 2.0.0.0. Drivers_for_Path_Directions

--------------------------------------------------------------------------------
file name                         : short description
--------------------------------------------------------------------------------
continuation_data                 : data structures for parameters/variables
continuation_parameters           : management of tuning of parameters
continuation_parameters_io        : interactive setting of parameters
process_io                        : output during path tracking
--------------------------------------------------------------------------------
predictors                        : increment t, predict solutions
dispatch_predictors               : selection of predictor
correctors                        : Newton's method as corrector
vlprs_tables                      : data management for extrapolation
vlprs_algorithm                   : extrapolation algorithm
directions_of_solution_paths      : routines for polyhedral end game
path_trackers                     : path following routines
increment_and_fix_continuation    : increment-and-fix continuation
drivers_for_poly_continuation     : menu-driver for polynomial continuation
ts_poco                           : calls the polynomial continuation driver
--------------------------------------------------------------------------------
standard_root_refiners            : refining over standard complex numbers
multprec_root_refiners            : refining up to arbitrary precision
ts_rootrefi                       : calls the root refiners
--------------------------------------------------------------------------------
scanners_for_continuation         : scans the continuation parameters
black_polynomial_continuations    : black-box polynomial continuation
mainpoco                          : poco as called by the main program
bablpoco                          : calls black-box polynomial continuation
valipoco                          : validation of computed path directions
postpoco                          : stand-alone routine for polyhedral end game
--------------------------------------------------------------------------------

An important feature is that much of the routines in this library are
independent of how polynomials are represented.

The basic data structures allow the management of data that is generated
during the path-following.  Tuning of parameters is menu-driven.

Increment-and-Fix continuation is typical for polynomial continuation,
since paths do not turn back, when working over the complex numbers.
There is a rich variety of predictors available.
Increment-and-fix continuation with a polyhedral end game for the
computation of the directions of the solution paths.

wc *adb counts 8844 lines of Ada code