Sampling module for positive dimensional solution components with PHCv2.4.87

This directory is entirely new in release 2.1, with no changes in
release 2.2.  Intrinsic samplers were added in release 2.3.

There are four parts in this library:
  1) definition of witness sets as solutions to embedded systems;
  2) the sampling machine, sample points, lists, and grids;
  3) sampling of solution clusters for multiple components;
  4) sampling a hypersurface reduces to univariate solver: p(b+t*v) = 0.
Almost all sampling is done "extrinsically", using the explicit equations
of the linear hyperplanes instead of the generators of the linear spaces.
Intrinsic samplers which use these generators are still under development.
New since 2.3.53 are the use of local intrinsic coordinates, see ts_ilocal.
Samplers in double double and quad double arithmetic were added in
version 2.3.87 of PHCpack.

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

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file name                         : short description
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standard_plane_representations    : convert representations of planes
dobldobl_plane_representations    : dobldobl convert representations of planes
quaddobl_plane_representations    : quaddobl convert representations of planes
standard_point_coordinates        : coordinates of points in planes
dobldobl_point_coordinates        : dobldobl coordinates of points in planes
quaddobl_point_coordinates        : quaddobl coordinates of points in planes
standard_plane_operations         : utilities to work with planes
dobldobl_plane_operations         : work with planes in dobldobl precision
quaddobl_plane_operations         : work with planes in quaddobl precision
ts_planes                         : test on manipulating planes
standard_flag_representations     : intrinsic format of a flag
ts_flag                           : test on formats of flags
standard_intrinsic_solutions      : format conversions of witness points
dobldobl_intrinsic_solutions      : conversions of dobldobl witness points
quaddobl_intrinsic_solutions      : conversions of quaddobl witness points
ts_coords                         : test representations of witness points
standard_affine_solutions         : convert solutions in affine planes
planes_and_polynomials            : operations on planes and polynomials
witness_sets                      : main tools to create an embedding
witness_sets_io                   : utilities to read embedded systems
witness_sets_formats              : from intrinsic to extrinsic formats
intrinsic_witness_sets_io         : writes intrinsic sets to extrinsic format
ts_square                         : test on making polynomial systems square
ts_embed                          : test on embedding a polynomial system
ts_squemb                         : test on squaring and embedding
ts_locdim                         : attempt at a local dimension test
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standard_moving_planes            : define path of linear spaces
dobldobl_moving_planes            : path of planes with double doubles
quaddobl_moving_planes            : path of planes with quad doubles
standard_intrinsic_newton         : Newton's method for intrinsic coordinates
dobldobl_intrinsic_newton         : double double intrinsic Newton
quaddobl_intrinsic_newton         : quad double intrinsic Newton
ts_iddnewt                        : test {dobl,quad}dobl intrinsic Newton
standard_rescaling_coordinates    : local intrinsic coords, standard precision
dobldobl_rescaling_coordinates    : local intrinsic coords, dobldobl precision
quaddobl_rescaling_coordinates    : local intrinsic coords, quaddobl precision
standard_intrinsic_trackers       : tracking paths in intrinsic coordinates
dobldobl_intrinsic_trackers       : dobldobl tracking in intrinsic coordinates
quaddobl_intrinsic_trackers       : quaddobl tracking in intrinsic coordinates
standard_linear_span              : determine linear span of component
dobldobl_linear_span              : linear span in double double precision
quaddobl_linear_span              : linear span in quad double precision
ts_ispan                          : test on determining linear span
ts_iwset                          : convert to intrinsic witness sets
standard_intrinsic_continuation   : calls trackers on a list of solutions
dobldobl_intrinsic_continuation   : intrinsic tracking with double doubles
quaddobl_intrinsic_continuation   : intrinsic tracking with quad doubles
ts_inewt                          : test on intrinsic Newton's method
ts_itrack                         : test on intrinsic path trackers
standard_recentering_coordinates  : work with local intrinsic coordinates
ts_ilocal                         : test local intrinsic coordinates
affine_sampling_machine           : sampling using affine planes
sampling_machine                  : interface to homotopy continuation
sample_points                     : points sampled from a component
sample_points_io                  : input-output for sampled points
sample_point_lists                : lists of sampled points
sample_point_lists_io             : input-output for sampled point lists
sample_point_grids                : grids are lists of sampled point lists
sample_point_grids_io             : input-output for sampled point grids
ts_sample                         : interactive testing facility for sampler
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sampling_laurent_machine          : sampling on Laurent polynomial systems
dobldobl_sampling_machine         : sampling in double double precision
dobldobl_sampling_laurent_machine : sampling dobldobl Laurent systems
quaddobl_sampling_machine         : sampling in quad double precision
quaddobl_sampling_laurent_machine : sampling quaddobl Laurent systems
dobldobl_sample_points            : sampled points in double double precision
dobldobl_sample_grids             : grids of double double precision samples
dobldobl_sample_lists             : lists of double double sample points
quaddobl_sample_points            : sampled points in quad double precision
quaddobl_sample_lists             : lists of quad double sample points
quaddobl_sample_grids             : grids of quad double precision samples
ts_ddqdsam                        : test double double & quad double sampling
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rectangular_sample_grids          : sampling on parallel slices
dobldobl_rectangular_sample_grids : parallel sampling with double doubles
quaddobl_rectangular_sample_grids : parallel sampling with quad doubles
standard_stacked_sample_grids     : grids for general dimensions
dobldobl_stacked_sample_grids     : double double version of stacked grids
quaddobl_stacked_sample_grids     : quad double version of stacked grids
multprec_stacked_sample_grids     : multiprecision version of stacked grids
make_sample_grids                 : makes grids of sample points with tests
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standard_solution_clusters        : managing clusters of solutions
extrapolate_solution_clusters     : refining solutions by extrapolation
multiplicity_homotopies           : homotopy to sample multiple components
ts_mulhom                         : test on multiplicity samplers
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ts_unisam                         : test on the use of Weierstrass method
standard_lined_hypersurfaces      : generic points on hypersurfaces
dobldobl_lined_hypersurfaces      : generic points in double double precision
quaddobl_lined_hypersurfaces      : generic points in quad double precision
hypersurface_samplers             : sample points on hypersurface
hypersurface_sample_grids         : building grids for interpolation
dobldobl_gridded_hypersurfaces    : grids on hypersurfaces with double doubles
quaddobl_gridded_hypersurfaces    : grids on hypersurfaces with quad doubles
ts_hypsam                         : test on hypersurface sampler
polynomial_roots                  : homotopies to solve p(x) = 0
ts_roots                          : calls root finder
hypersurface_points               : homotopies to solve p(b+t*v) = 0
ts_hyppts                         : test on solving p(b+t*v) = 0
hypersurface_roots                : homotopies to solve p(t*v) = 0
ts_hyprts                         : test on solving p(t*v) = 0
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main_samplers                     : defines phc -y
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