Sampling module for positive dimensional solution components with PHCv2.3.20

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.

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file name                        : short description
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standard_plane_representations   : convert representations of planes
standard_point_coordinates       : coordinates of points in planes
standard_plane_operations        : utilities to work with planes
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
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_coords                        : test representations of witness points
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_intrinsic_newton        : Newton's method for intrinsic coordinates
standard_intrinsic_trackers      : tracking paths in intrinsic coordinates
standard_intrinsic_continuation  : calls trackers on a list of solutions
standard_moving_planes           : define path of linear spaces
ts_iwset                         : convert to intrinsic witness sets
ts_inewt                         : test on intrinsic Newton's method
ts_itrack                        : test on intrinsic path trackers
standard_linear_span             : determine linear span of component
ts_ispan                         : test on determining linear span
affine_sampling_machine          : sampling using affine planes
ts_sampar                        : interactive testing of affine sampler
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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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
hypersurface_samplers            : sample points on hypersurface
hypersurface_sample_grids        : building grids for interpolation
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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