Interpolation module for solution components with PHCv2.4.87

The interpolation routines constitute a separate module.
Three approaches have been studied and implemented :
  1) the direct method solves a linear system, (elimination or QR);
  2) bootstrapping technique to set up generalized divided differences;
  3) the trace form leads to direct application of Newton interpolation.

This directory is entirely new in release 2.1, there are no updates
to report in release 2.2.  The span was elaborated in v2.3.08.

The filtering module encapsulates projectors and interpolators :
  a) span of a component;
  b) projection operator : sample point -> interpolation point;
  c) interpolators and management of filtering polynomials.
The span of a component is needed to ensure the number of central points
in the projector, but is otherwise not an essential part of the filter.

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

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file name                          : short description
------------------------------------------------------------------------------
standard_linear_spaces             : standard spaces containing components
standard_subspace_restrictions     : restrict to container subspaces
multprec_linear_spaces             : multprec spaces containing components
multprec_subspace_restrictions     : restrict to container subspaces
span_of_component                  : data abstraction for span of component
span_of_component_io               : input/output for span of component
span_of_witness_set                : enumerate spans for all witness points
ts_span                            : interactive testing facility for span
------------------------------------------------------------------------------
standard_polynomial_interpolators  : interpolating with machine precision
multprec_polynomial_interpolators  : interpolating with multi-precision
ts_nbterms                         : number of terms of dense polynomials
ts_stpolin                         : test on standard arithmetic interpolation
ts_mupolin                         : test on multi-precision interpolation
ts_adpolin                         : interpolation with adaptive precision
divided_differences                : shadow calculations for debugging
standard_divided_differences       : Newton interpolation with standard doubles
dobldobl_divided_differences       : Newton interpolation with double doubles
quaddobl_divided_differences       : Newton interpolation with quad doubles
multprec_divided_differences       : multi-precision Newton interpolation
ts_divdif                          : interactive test on Newton interpolation
ts_dvdexp                          : experiment on conditioning/stability
standard_univariate_interpolators  : basic Newton interpolation for functions
dobldobl_univariate_interpolators  : Newton interpolation with double doubles
quaddobl_univariate_interpolators  : Newton interpolation with quad doubles
multprec_univariate_interpolators  : multi-precision 1-D Newton interpolation
standard_power_traces              : Newton identities with standard precision
dobldobl_power_traces              : Newton identities with double doubles
quaddobl_power_traces              : Newton identities with quad doubles
multprec_power_traces              : Newton identities with multi-precision
ts_powtrc                          : interactive test on Newton identities
standard_nvariate_interpolators    : Newton interpolation for n-dim functions
dobldobl_nvariate_interpolators    : double double n-D Newton interpolation
quaddobl_nvariate_interpolators    : quad double n-D Newton interpolation
multprec_nvariate_interpolators    : multiprecision n-D Newton interpolation
ts_newint                          : test on the direct Newton interpolators
standard_trace_interpolators       : standard trace form of interpolator
dobldobl_trace_interpolators       : double double interpolator with traces
quaddobl_trace_interpolators       : quad double interpolator with traces
multprec_trace_interpolators       : multiprecision interpolator with traces
ts_traces                          : interactive test on trace interpolation
ts_trapol                          : test on trace interpolators for one poly
ts_elim                            : tests numerical elimination
------------------------------------------------------------------------------
standard_linear_projections        : standard projectors to hypersurface case
standard_central_projections       : project from standard base points
multprec_linear_projections        : multprec projectors to hypersurface case
multprec_central_projections       : project from multi-precision base points
ts_project                         : test linear and central projectors
interpolation_points               : projected sample points
interpolation_point_lists          : lists of projected sample points
projection_operators               : turns samples into interpolation points
interpolation_filters              : filtering polynomials
interpolation_filters_io           : input-output for filters
ts_filter                          : interactive testing facility for filter
------------------------------------------------------------------------------
