Data management and drivers for polynomial continuation in PHCv2.4.88

In version 2.3.75, this directory was simplified with the moving of specific
code for end games, sweeps, and path trackers to separate directories.
The paragraph below describes the historical development of the original
code in this Continuation directory.

The second release brought multiprecision 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
multiprecision 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.
The sweep became available via phc -p in v2.3.37 and went to significant
upgrades in v2.3.45.  In v2.3.46, multitasking was added to the blackbox 
polynomial continuation routines.  New in v2.3.58 is the introduction
of correctors with double double and quad double arithmetic.
In v2.3.59 we can run entire paths with double double arithmetic.
Overdetermined homotopies were added in version 2.4.13.

This library of continuation routines is organized in three layers:

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

Run "gprbuild continuation.gpr" to make all test programs.
On windows, type "gprbuild continuation.gpr -Xos=windows"
at the PowerShell prompt.
The "gprclean continuation.gpr" removes all files created by gprbuild.

------------------------------------------------------------------------------
file name                        : short description
------------------------------------------------------------------------------
standard_continuation_data       : data structures for continuation variables
dobldobl_continuation_data       : double double version of continuation data
quaddobl_continuation_data       : quad double version of continuation data
standard_continuation_data_io    : output routines on solution information
dobldobl_continuation_data_io    : output on double double solution info
quaddobl_continuation_data_io    : output on quad double 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_incfix_continuation     : increment-and-fix continuation
dobldobl_incfix_continuation     : increment-and-fix with double doubles
quaddobl_incfix_continuation     : increment-and-fix with quad doubles
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
standard_blackbox_refiners       : blackbox root refinement
dobldobl_blackbox_refiners       : blackbox refinement with double doubles
quaddobl_blackbox_refiners       : blackbox refinement with quad doubles
standard_blackbox_continuations  : blackbox polynomial continuation
dobldobl_blackbox_continuations  : blackbox continuation with double doubles
quaddobl_blackbox_continuations  : blackbox continuation with quad doubles
ts_bbpoco                        : calls the blackbox continuation 
main_homotopy_continuation       : defines phc -p
------------------------------------------------------------------------------

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.
