Solutions of systems and homotopies in PHCv2.4.87

The second release introduced the solution vectors with multiprecision.
Version 2.3 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.
Double double and quad double solutions were introduced in v2.3.55.
Solutions in triple, penta, octo, and deca double precision were added
in version 2.4.80.  Version 2.4.87 adds support for hexa double precision.

There are three parts in this library:
(1) definition of solutions with standard, double double, quad double,
    general multiprecision, their input/output, and string conversions;
(2) solution filters, as available in option #0 of phc -f;
(3) various utilities to manipulate solutions.

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

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file name                          : short description
------------------------------------------------------------------------------
symbols_io                         : utilities for i/o of symbols
standard_complex_solutions         : standard solutions to families of systems
standard_complex_solutions_io      : input/output of standard solutions
dobldobl_complex_solutions         : solutions with double double complex
dobldobl_complex_solutions_io      : i/o for double double complex solutions
tripdobl_complex_solutions         : solutions with triple double complex
tripdobl_complex_solutions_io      : i/o for triple double complex solutions
quaddobl_complex_solutions         : solutions with quad double complex
quaddobl_complex_solutions_io      : i/o for quad double complex solutions
pentdobl_complex_solutions         : solutions with penta double complex
pentdobl_complex_solutions_io      : i/o for penta double complex solutions
octodobl_complex_solutions         : solutions with octo double complex
octodobl_complex_solutions_io      : i/o for octo double complex solutions
decadobl_complex_solutions         : solutions with deca double complex
decadobl_complex_solutions_io      : i/o for deca double complex solutions
hexadobl_complex_solutions         : solutions with hexa double complex
hexadobl_complex_solutions_io      : i/o for hexa double complex solutions
multprec_complex_solutions         : multprec solutions to families of systems
multprec_complex_solutions_io      : input/output of multprec solutions
ts_sols                            : test precision conversions of solutions
test_solutions_io                  : tests input/output of solution lists
ts_sols_io                         : main test on i/o of solution lists
standard_solution_strings          : write solutions to strings and parse
dobldobl_solution_strings          : double double solutions and strings
quaddobl_solution_strings          : quad double solutions and strings
multprec_solution_strings          : multprecision solutions and strings
solution_string_splitters          : split coordinates of a solution string
test_solution_strings              : test string representations
ts_solstr                          : main test string representations
------------------------------------------------------------------------------
standard_system_and_solutions_io   : i/o of double systems and solutions
dobldobl_system_and_solutions_io   : i/o of dobldobl system and solutions
tripdobl_system_and_solutions_io   : i/o of tripdobl system and solutions
quaddobl_system_and_solutions_io   : i/o of quaddobl system and solutions
pentdobl_system_and_solutions_io   : i/o of pentdobl system and solutions
octodobl_system_and_solutions_io   : i/o of octodobl system and solutions
decadobl_system_and_solutions_io   : i/o of decadobl system and solutions
hexadobl_system_and_solutions_io   : i/o of hexadobl system and solutions
multprec_system_and_solutions_io   : i/o of multprec systems and solutions
test_system_and_solutions_io       : test on reading systems with solutions
ts_syssols_io                      : main test on i/o of systems and solutions
prompt_for_systems                 : scan, read, and prompt for system
prompt_for_solutions               : scan, read, and prompt for solutions
ts_getstart                        : test to extract the start system
------------------------------------------------------------------------------
standard_solution_filters          : filters solutions subject to criteria
dobldobl_solution_filters          : filters of double double solutions
quaddobl_solution_filters          : filters of quad double solutions
standard_solution_splitters        : splits solution lists in two
dobldobl_solution_splitters        : double double version of solution splitters
quaddobl_solution_splitters        : quad double version of solution splitters
standard_solution_manipulators     : removing imaginary part of target
dobldobl_solution_manipulators     : dobldobl version of solution manipulators
quaddobl_solution_manipulators     : quaddobl version of solution manipulators
main_solution_filters              : main procedures to filter solution lists
ts_solfilt                         : calls the solution filters
ts_grepsols                        : selects specific solutions
------------------------------------------------------------------------------
lists_of_symbols                   : manages lists of symbols
standard_maple_solutions_io        : output formats to Maple, standard floats
multprec_maple_solutions_io        : convert from/into Maple, multiprecision
test_maple_solutions               : tests on Maple output format
ts_mapsols_io                      : main test on Maple output format
standard_dictionary_solutions_io   : convert solutions into Python dictionaries
test_dictionary_solutions          : test on Python dictionary conversion
ts_dicsols_io                      : main test on dictionary solutions
standard_solution_array_lists      : lists of solution arrays
ts_solar                           : test on lists of solution arrays
------------------------------------------------------------------------------
standard_point_lists               : hashing standard solutions into the plane
dobldobl_point_lists               : hashing dobldobl solutions into the plane
quaddobl_point_lists               : hashing quaddobl solutions into the plane
ts_ptlists                         : test on sorting point lists
standard_quad_trees                : processing hashed solutions via quad tree
standard_quad_trees_io             : output of cardinalities of quad tree
dobldobl_quad_trees                : quad trees for double double points
quaddobl_quad_trees                : quad trees for quad double points
ts_quadpart                        : test on the partitioning with quad tree
ts_quad                            : test on quad tree development
standard_select_solutions          : tools to select standard solutions
dobldobl_select_solutions          : tools to select dobldobl solutions
quaddobl_select_solutions          : tools to select quaddobl solutions
ts_selsol                          : select solutions from file
------------------------------------------------------------------------------
standard_tracked_solutions_io      : reading tracked data in double precision
dobldobl_tracked_solutions_io      : reading tracked data with double doubles
quaddobl_tracked_solutions_io      : reading tracked data with quad doubles
drivers_for_failed_paths           : i/o and driver procedures
ts_trasols_io                      : processing output files of trackers
------------------------------------------------------------------------------
standard_solution_diagnostics      : diagnostics on standard solutions
dobldobl_solution_diagnostics      : diagnostics on dobldobl solutions
quaddobl_solution_diagnostics      : diagnostics on quaddobl solutions
multprec_solution_diagnostics      : diagnostics on multprec solutions
standard_condition_tables          : frequency tables of standard solutions
dobldobl_condition_tables          : frequency tables of dobldobl solutions
quaddobl_condition_tables          : frequency tables of quaddobl solutions
multprec_condition_tables          : frequency tables of multprec solutions
standard_condition_report          : report on standard double solutions
dobldobl_condition_report          : report on double double solutions
quaddobl_condition_report          : report on quad double solutions
drivers_for_condition_tables       : to make accessible to phc -v
ts_contab                          : test on frequency tables for solutions
------------------------------------------------------------------------------
solution_drops                     : drop a coordinate of a solution
ts_soldrop                         : interactive tests on solution drops
varbprec_complex_solutions         : variable precision solutions
------------------------------------------------------------------------------
standard_mixed_residuals           : residuals in standard double precision
dobldobl_mixed_residuals           : residuals in double double precision
quaddobl_mixed_residuals           : residuals in quad double precision
ts_mixres                          : test on computing residuals
------------------------------------------------------------------------------
standard_solutions_heap            : make cluster report efficiently
------------------------------------------------------------------------------

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.
