Homotopies, solutions of systems, scaling and reduction in PHCv2.3.23

The second release introduced the solution vectors with multiprecision.
The Creators in the package Homotopy allow more accessibility constants for
the Cheater's homotopy.  A multiprecision version of the homotopy package
was needed for the new release 2.1.  A multiprecision version of the
scaling routines is under development.  V2.3 has an improved Maple interface.
Utilities to build frequency tables for solutions were added in version 2.3,
which became part of the main phc -v validation module in release v2.3.07
and upgraded with quad trees in v2.3.10.

This library is organized in three parts:
1) Representation of solutions of families of systems.
2) Homotopy with homogenization 
3) Scaling and reduction of polynomial systems.

------------------------------------------------------------------------------
file name                          : short description
------------------------------------------------------------------------------
standard_complex_solutions         : standard solutions to families of systems
standard_complex_solutions_io      : input/output of standard solutions
multprec_complex_solutions         : multprec solutions to families of systems
multprec_complex_solutions_io      : input/output of multprec solutions
ts_sols                            : plain test on i/o of solutions
standard_solution_filters          : filters solutions subject to criteria
standard_solution_splitters        : splits solution lists in two
drivers_to_solution_filters        : drivers to filter solution lists
ts_solfilt                         : calls the solution filters
ts_grepsols                        : selects specific solutions
mainfilt                           : gives user of phc access to filtering
standard_maple_solutions_io        : output formats to Maple, standard floats
multprec_maple_solutions_io        : convert from/into Maple, multiprecision
ts_mapsols_io                      : test program on Maple output format
standard_solution_array_lists      : lists of solution arrays
ts_solar                           : test on lists of solution arrays
standard_solution_diagnostics      : diagnostics on stardard solutions
multprec_solution_diagnostics      : diagnostics on multprec solutions
standard_condition_tables          : frequency tables of standard solutions
multprec_condition_tables          : frequency tables of multprec solutions
drivers_for_condition_tables       : to make accessible to phc -v
ts_contab                          : test on frequency tables for solutions
standard_system_and_solutions_io   : get/put standard systems and solutions
multprec_system_and_solutions_io   : get/put multprec systems and solutions
standard_point_lists               : hashing solutions into the plane
standard_quad_trees                : processing hashed solutions via quadtree
standard_quad_trees_io             : output of cardinalities of quadtree
ts_quad                            : test on quadtree development
ts_selsol                          : select solutions from file
------------------------------------------------------------------------------
standard_embed_polynomials         : embedding polynomial in larger space
homogenization                     : making polynomials homogeneous
projective_transformations         : transform polynomials and solutions
standard_homotopy                  : homotopy for standard numbers
multprec_homotopy                  : homotopy for multiprecision numbers
drivers_for_homotopy_creation      : menu-driven homotopy construction
------------------------------------------------------------------------------
standard_scaling                   : scaling standard systems and solutions
multprec_scaling                   : scaling multprec systems
ts_scal                            : simple test program
drivers_for_scaling                : menu-driver for scaling routines
ts_drivscal                        : calls the driver
mainscal                           : scaling tool, as called by phc
reduction_of_polynomials           : S-polynomials and R-polynomials
reduction_of_polynomial_systems    : linear and nonlinear reduction
reduction_of_nonsquare_systems     : transform overconstrained into square
drivers_for_reduction              : menu-drivers for reducing systems
mainred                            : reduction tool, as called by phc
------------------------------------------------------------------------------
standard_linear_poly_solvers       : solve linear polynomial systems
ts_linsol                          : test on the linear poly solvers
------------------------------------------------------------------------------

The standard and multiprecision solutions lists are two separate packages,
not implemented by means of generics, because of the difficulties with
mixed real-complex numbers.

Note: some little tools have been added to manipulate lists of solutions.

mergesols : merge the list of solutions
