Tracking of solution paths of polynomial homotopies in PHCv2.3.24

The second release brought multi-precision root refiners and the usage
of QR and Least Squares in the correctors at the end of the paths.
In version 2.1, this is extended to tracking solution paths with
multi-precision arithmetic.  Release 2.2 contains the start of
a Newton's method based on numerical differentiation routines and
supports coefficient parameter homotopy continuation.
New in release 2.3 is Newton's method with deflation for singularities
and improved endgame routines based on extrapolation methods.
Newton's method and root refiners are now in a separate directory.
Compact representation of continuation parameters and path tracking
with incremental read/write were introduced in v2.3.05.

This library of continuation routines is organized in three layers:

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

------------------------------------------------------------------------------
file name                        : short description
------------------------------------------------------------------------------
standard_continuation_data       : data structures for parameters/variables
standard_continuation_data_io    : output routines on solution information
continuation_parameters          : management of tuning of parameters
continuation_parameters_io       : interactive setting of parameters
process_io                       : output during path tracking
pack_continuation_parameters     : compact representation of parameters
ts_pactun                        : tuning parameters via compact format
------------------------------------------------------------------------------
standard_predictors              : increment t, predict solutions
multprec_predictors              : predictors with multi-precision numbers 
standard_dispatch_predictors     : selection of standard predictor
multprec_dispatch_predictors     : selection of multprec predictor
standard_correctors              : Newton's method as corrector
multprec_correctors              : correctors with multi-precision numbers
ts_preco                         : test on predictor and corrector
standard_vlprs_tables            : extrapolation tables with standard numbers
standard_vlprs_algorithm         : extrapolation in standard arithmetic
multprec_vlprs_tables            : extrapolation tables with multprec numbers
multprec_vlprs_algorithm         : extrapolation in multiprecision arithmetic
standard_winding_numbers         : standard extrapolate for winding numbers
multprec_winding_numbers         : multprec extrapolate for winding numbers
ts_vlprs                         : test extrapolation on generated series
directions_of_solution_paths     : routines for polyhedral end game
standard_path_trackers           : path trackers with standard numbers
multprec_path_trackers           : path trackers with multi-precision numbers
ts_path                          : test facility for path trackers
ts_track                         : path tracking with increment read/write
increment_and_fix_continuation   : increment-and-fix continuation
multprec_incfix_continuation     : multi-precision increment-and-fix
drivers_for_poly_continuation    : menu-driver for polynomial continuation
ts_poco                          : calls the polynomial continuation driver
------------------------------------------------------------------------------
scanners_for_continuation        : scans the continuation parameters
black_box_poly_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
------------------------------------------------------------------------------
solutions_with_parameters        : selecting and joining variables
systems_with_parameters          : definition of parameter homotopy + i/o
parameter_homotopy_continuation  : drivers to path tracking
ts_parcon                        : stand-alone calling program
------------------------------------------------------------------------------

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.
