Mon 20 Mar 2023 : removed ts_endgm.adb and ts_mulsam.adb.

Sun 19 Mar 2023 : removed multiplicity_homotopies, ts_mulhom.adb, and
  updated samplers.gpr.  Fixed ts_ilocal.adb for renaming of drivers package,
  updated samplers.gpr.  Fix also ts_inewt.adb and ts_itrack.adb similarly,
  updated samplers.gpr.  Removed intrinsic_sampling_machine and ts_sampar,
  updated samplers.gpr one last time.

Thu 10 Jun 2021 : defined samplers.gpr for the test procedures.

Thu 3 Dec 2020 : renamed drivers_to_grid_creators into make_sample_grids
  and moved code from mainsam into the package main_samplers.

Sun 8 Nov 2020 : updated mainsam.adb, sampling_machine.adb, {dobldobl,
  quaddobl}_sampling_machine.adb, sampling_laurent_machine,  and {dobldobl,
  quaddobl}_sampling_laurent_machine.adb for the renaming of drivers_for_poly_
  continuation into main_poly_continuation.

Sun 5 Jan 2019 : for compiler warnings, modified witness_sets_io.adb.

Fri 29 Dec 2017 : updated *dobl*sampling*machine.adb to avoid sharing
  in the initialization and the clearing.

Tue 26 Dec 2017 : changed initialize and clear in sampling_machine.adb
  to avoid a crash in phc -B.  Also fixed sampling_laurent_machine.adb.

Wed 26 Jul 2017 : extended intrinsic_witness_sets_io with procedures to
  write a witness set for a Laurent system with the solutions represented
  in intrinsic coordinates.

Thu 20 Jul 2017 : extended witness_sets with a complete function for
  Laurent polynomial systems.

Thu 13 Jul 2017 : added procedures to witness_sets_io which take the name
  of a file on input, with code taken from mainfac, and extended to read
  also witness sets defined by a Laurent polynomial system.

Tue 11 Jul 2017 : extended the *sample_points packages with an internal
  state to use the Laurent sampling machine, and also the *lists.a* packages.
  Extended the *sample_grids and the *rectangular_sample_grids packages
  in the same manner.

Sun 9 Jul 2017 : new packages {dobldobl,quaddobl}_sampling_laurent_machine
  to work with witness sets for Laurent polynomial systems in double double
  and quad double precision.  For Laurent systems, extended the packages
  planes_and_polynomials and witness_sets.

Sat 8 Jul 2017 : added function to planes_and_polynomials to represent a
  linear polynomial with multiprecision coefficients as a Laurent polynomial.
  Added package Sampling_Laurent_Machine to sample points on solution sets
  of Laurent polynomial systems.
  
Sun 25 Jun 2017 : extended witness_sets and witness_sets_io with operations
  to represent witness sets for Laurent systems.

Wed 21 Jun 2017 : to planes_and_polynomials added representations of
  hyperplanes as Laurent polynomial types.  The ts_embed.adb tests the
  embedding of Laurent systems, computed by the new operations specified
  in witness_sets.ads and implemented in witness_sets.adb.

Tue 20 Jun 2017 : extended witness_sets with operations on Laurent systems.

Fri 18 Mar 2016 : change in affine_sampling_machine.adb for changed interface
  in the drivers to the continuation procedures.

Mon 29 Feb 2016 : changes in {dobldobl,quaddobl}_sampling_machine for added
  parameter in dobldobl_incfix_continuation procedures.

Sat 27 Feb 2016 : changes in sampling_machine.adb for extra argument in the
  increment-and-fix continuation in standard double precision.

Wed 23 Dec 2015 : eased up on the restrictive settings in the samplers,
  changing {dobldobl,quaddobl}_sampling_machine.adb.

Tue 17 Nov 2015 : again more extensions in witness_sets for double double
  and quad double precision as needed in cascading homotopies.
  And then once again more extensions...

Mon 16 Nov 2015 : more versions in witness_sets and witness_sets_io
  of operations in double double and quad double precision.

Sun 15 Nov 2015 : updated intrinsic_witness_sets_io with write procedures
  for double double and quad double precision, needed for phc -l2 and -l4.

Wed 11 Nov 2015 : added operations for double double and quad double numbers
  to witness_sets_formats, as needed in the computation of a witness set
  for a hypersurface in double double and quad double precision.

Tue 10 Nov 2015 : more operations added to witness_sets for the double
  double and quad double versions of extrinsic diagonal homotopies.
  For the same reasons, provided Add_Dummy in witness_sets.

Mon 9 Nov 2015 : added operations to witness_sets as needed for the double
  double and quad double versions of extrinsic diagonal homotopies.

Thu 1 Oct 2015 : changed {dobldob,quaddobl}_sampling_machine.adb for
  changed type of tolerances in the root refiners.

Wed 16 Sep 2015 : new packages {dobldobl,quaddobl}_gridded_hypersurfaces for
  storing grids of points sampled from hypersurfaces in double double and
  quad double precision, compiled via a with clause in ts_hypsam.

Tue 15 Sep 2015 : new packages {dobldobl,quaddobl}_lined_hypersurfaces for
  sampling points on hypersurfaces in double double and quad double precision,
  with tests added to ts_hypsam.adb.

Mon 14 Sep 2015 : new package standard_lined_hypersurfaces with code refactored
  from hypersurface_samplers.  This refactoring changed also ts_hypsam.adb and
  hypersurface_sample_grids.

Sun 13 Sep 2015 : reformatted hypersurface_samplers to make room for versions
  in double double and quad double precision.

Thu 28 Aug 2014 : reformatting in witness_sets_formats.

Wed 27 Aug 2014 : extended mainsam.adb with routines to sample in
  double double and quad double precision, available in phc -y.

Tue 26 Aug 2014 : new packages {dobl,quad}dobl_intrinsic_continuation
  to run intrinsic path trackers in double double and quad double precision,
  for testing in ts_ilocal.  Extended witness_sets with operations to add
  embedded symbols to polynomials with double double and quad double
  coefficients.  Extended intrinsic_witness_sets_io with procedure to write
  witness sets in double double and quad double precision.
  The test program ts_ilocal works with double doubles and quad doubles.

Mon 25 Aug 2014 : added tests to ts_iwset for quad double precision,
  with changed tolerances for higher precision.

Sat 16 Aug 2014 : new packages {dobl,quad}dobl_linear_span, added tests
  to ts_iwset for double double precision.

Fri 15 Aug 2014 : new packages quaddobl_rescaling_coordinates and
  quaddobl_intrinsic_trackers, tested for compilation by ts_iwset.

Thu 14 Aug 2014 : new package quaddobl_intrinsic_newton for Newton's method
  with intrinsic coordinates in quad double precision, with extended testing
  in ts_iddnewt.  New packages dobldobl_rescaling_coordinates and
  dobldobl_intrinsic_trackers.

Wed 13 Aug 2014 : added make_square functions to witness_sets for systems
  of double double and quad double complex coefficients.
  New package dobldobl_intrinsic_newton tested by ts_iddnewt for Newton's
  method with intrinsic coordinates in double double precision.

Tue 12 Aug 2014 : extended witness_sets with routines to remove the embedding
  from systems with double double and quad double coefficients.
  New packages {dobl,quad}dobl_intrinsic_solutions, tested by ts_coords.
  Modified sample_point_grids_io.adb for a compiler warning.

Mon 11 Aug 2014 : new packages {dobl,quad}dobl_point_coordinates,
  {dobl,quad}dobl_plane_{operations, representations}, 
  {dobl,quad}dobl_moving_planes, tested by ts_planes.

Thu 31 Jul 2014 : new packages {dobl,quad}dobl_{stacked,rectangular}_
  sample_grids, called in drivers_to_grid_creators.

Fri 13 Jun 2014 : modified sample_point_lists.adb for compiler warning.
  Changed standard_intrinsic_newton.adb for changed QRLS.

Thu 29 May 2014 : changed sample_point_lists_io.adb for a compiler warning.

Wed 16 Apr 2014 : added exception handler to intrinsic_witness_sets_io.adb.

Tue 25 Mar 2014 : new packages {dobldobl,quaddobl}_sample_grids,
  to be tested in ts_ddqdsam.adb.

Mon 24 Mar 2014 : new packages {dobldobl,quaddobl}_sample_{points,lists},
  to be tested in ts_ddqdsam.adb.

Sun 23 Mar 2014 : extended witness_sets and planes_and_polynomials with
  methods in quad double arithmetic.  Updates in dobldobl_sampling_machine
  and new quaddobl_sampling_machine, tested by ts_ddqdsam, renamed from the
  former tester ts_ddsam.  Edited sampling_machine.adb to trace the correct
  way of calling the sample routine...  Extended planes_and_polynomials
  and witness_sets with dobldobl and quaddobl versions.

Sat 22 Mar 2014 : extended witness_sets_io for double double and quad double
  witness sets.  Extended planes_and_polynomials for double doubles.
  New package dobldobl_sampling_machine, tested by ts_ddsam.

Thu 27 Jun 2013 : updated witness_sets_formats for integer32.

Wed 26 Jun 2013 : updated mainsam.adb for natural32 and integer32 data types.

Mon 24 Jun 2013 : updated hypersurface_sample_grids,
  standard_stacked_sample_grids, multprec_stacked_sample_grids.adb,
  and rectangular_sample_grids.adb.

Fri 21 Jun 2013 : started rewriting because of integer32 and natural32 types.

Wed 19 Jun 2013 : planes_and_polynomials is needed in ../Schubert/Induction.

Thu 14 Feb 2013 : extended witness_sets_io with swap & sort embed symbols
  for double double and quad double systems.

Wed 13 Feb 2013 : extended witness_sets with remove slice for double double
  and quad double polynomial systems.

Mon 14 Jan 2013 : changed intrinsic_witness_sets_io.adb for the printing
  of empty witness sets.

Fri 12 Aug 2011 : changes in standard_intrinsic_trackers.adb, ts_ilocal.adb,
  and tuning in mainsam.adb.

Thu 11 Aug 2011 : cleaning up standard_intrinsic_trackers.adb.

Wed 10 Aug 2011 : fixed a bug in standard_intrinsic_trackers.adb.

Tue 9 Aug 2011 : updates in standard_intrinsic_{newton,trackers}.adb and
  standard_moving_planes.a*.

Mon 8 Aug 2011 : changes in standard_intrinsic_{trackers,continuation}.adb,
  ts_ilocal.adb and mainsam.adb.

Sun 7 Aug 2011 : moved One_Random_Direction from ts_ilocal to the package
  standard_moving_planes.  Moved Write_Witness_Set_to_File from ts_ilocal
  to intrinsic_witness_sets_io.  Created mainsam for phc -y.

Thu 4 Aug 2011 : added normalize to standard_moving_planes, updated
  standard_intrinsic_trackers, standard_intrinsic_continuation,
  and ts_ilocal.adb.

Sun 31 Jul 2011 : from Decomposition/standard_cascading_planes, moved
  intersect into standard_plane_operations, tested by ts_planes.adb.

Fri 29 Jul 2011 : fixed bug in witness_sets_io.adb when embedding was
  given with double numbering on the first line, e.g.: 4 4.

Wed 27 Jul 2011 : added recentered write to intrinsic_witness_sets_io.
  Modified standard_intrinsic_{trackers,continuation}.adb and ts_ilocal.adb.

Sun 24 Jul 2011 : fixed one bug in standard_intrinsic_trackers.adb.

Wed 20 Jul 2011 : more updates in standard_intrinsic_trackers.adb.

Tue 19 Jul 2011 : updates in standard_intrinsic_trackers.adb for bug...

Fri 15 Jul 2011 : new Orthogonalize procedure in standard_plane_representations
  and updates in standard_intrinsic_trackers.adb.

Mon 27 Jun 2011 : added routine to standard_moving_planes.

Sun 26 Jun 2011 : updated standard_intrinsic_trackers.adb and 
  standard_intrinsic_trackers, tested by ts_ilocal.adb.

Fri 24 Jun 2011 : added recentered to standard_intrinsic_trackers.

Thu 23 Jun 2011 : updated ts_ilocal.adb, standard_intrinsic_trackers.adb
  and standard_intrinsic_continuation.adb.

Wed 22 Jun 2011 : added use of Process_io in standard_intrinsic_newton.adb
  and standard_intrinsic_trackers.adb.

Sun 19 Jun 2011 : moved "check_orthonormality" from ts_ilocal.adb into
  standard_rescaling_coordinates.

Fri 17 Jun 2011 : modified standard_intrinsic_continuation.adb.

Thu 16 Jun 2011 : updated standard_intrinsic_continuation to track paths
  using local intrinsic coordinates.

Thu 2 Jun 2011 : changed witness_sets_formats.adb and hypersurface_roots.adb
  for warnings.

Wed 1 Jun 2011 : changed sample_point_grids.adb, sample_point_grids_io.adb,
  multprec_stacked_sample_grids.adb, and sample_point_lists_io.adb for warnings.

Sun 30 May 2011 : renamed standard_rescaling_coordinates into
  standard_recentering_coordinates.  Fixed ts_iwset.adb, ts_ispan.adb,
  ts_inewt.adb, ts_itrack.adb; modified ts_unisam.adb, ts_coords.adb,
  ts_embed.adb, ts_endgm.adb, ts_locdim.adb, ts_flag.adb,
  standard_solution_clusters.adb, standard_flag_representations.adb,
  intrinsic_witness_sets_io.adb, drivers_for_grid_creators.adb,
  standard_stacked_sample_grids.adb, sample_points.adb, 
  and sample_point_lists.adb for warnings.

Mon 25 Apr 2011 : updated ts_ilocal.adb for changed pred_pars/corr_pars
  in continuation_parameters.

Tue 14 Sep 2010 : updated headers of standard_intrinsic_trackers.ads
  and standard_intrinsic_continuation.ads.

Tue 23 Feb 2010 : small formatting changes in ts_sample.adb.

Wed 18 Nov 2009 : timers in ts_inewt.adb and ts_ilocal.adb.

Tue 17 Nov 2009 : evaluation of predictor in standard_intrinsic_trackers.adb.

Mon 16 Nov 2009 : updates in standard_intrinsic_trackers and ts_ilocal.adb.

Fri 13 Nov 2009 : updates in standard_rescaling_coordinates and ts_ilocal.adb,
  the idea seems to work.

Wed 11 Nov 2009 : updates in standard_intrinsic_newton.adb and ts_ilocal.adb.

Tue 10 Nov 2009 : updates in ts_ilocal.adb and new package
  standard_rescaling_coordinates.

Mon 9 Nov 2009 : updates in standard_moving_planes.a*, witness_sets.a*,
  ts_iwset, ts_ispan, ts_itrack, ts_inewt, new ts_ilocal.

Fri 6 Nov 2009 : for GNAT GPL warnings, update ts_inewt.adb,
  standard_intrinsic_newton.adb, standard_linear_span.adb,
  standard_moving_planes.adb, standard_plane_representations,
  standard_intrinsic_solutions.adb, standard_point_coordinates.adb,
  planes_and_polynomials, witness_sets_io.adb, standard_sampling_machine.adb,
  hypersurface_samplers.adb, standard_intrinsic_continuation.adb.

Wed 4 Nov 2009 : updated ts_unisam.adb, polynomial_roots.adb,
  standard_plane_operations, ts_iwset.adb did no longer compile.

Fri 19 Jun 2009 : updated ts_coords.adb, ts_itrack.adb, ts_ispan.adb,
  ts_inewt.adb, ts_mulsam.adb, ts_endgm.adb.

Fri 28 Nov 2008 : adjusted formatting in planes_and_polynomials.adb.

Sun 26 Oct 2008 : witness_sets_io.adb must scan for "THE SOLUTIONS"
  instead for "SOLUTIONS", otherwise checking for "START SOLUTIONS".

Thu 20 Dec 2007 : exported sort_embed_symbols in witness_sets_io, tested
  by ts_embed.adb as needed in lib_track for parallel diagonal homotopy.

Tue 27 Nov 2007 : improved witness_sets.adb without sharing when removing
  or adding a slice.

Mon 26 Nov 2007 : modified complete in witness_sets.adb so no sharing occurs,
  also remove_embedding was modified into remove_embedding1.

Mon 20 Aug 2007 : adding projective versions to standard_intrinsic_trackers
  and standard_intrinsic_continuation changed ts_inewt, ts_ispan, ts_iwset,
  and ts_itrack.

Tue 10 Jul 2007 : renamed the Add_Embedding of witness_sets to Add_Dummies
  and added an "Add_Dummy" operation to witness_sets.

Mon 9 Jul 2007 : added to witness_sets an Add_Embedding for zero polynomials.

Mon 8 Jan 2007 : added function to witness_sets_io.

Mon 18 Dec 2006 : moved "Swap_Symbols_to_End" to witness_sets_io.ads,
  for use in the jumpstarting of the diagonal homotopies.

Fri 15 Dec 2006 : changed witness_sets_io.ad* to jumpstart the diagonal
  homotopies.

Thu 14 Dec 2006 : renamed packages containing "witness_points" into
  "witness_sets".  Recompiled all ts_ programs, patched ts_multhom.adb, 
  but ts_sampar.adb failed to compile.  Also intrinsic_witness_sets_io.adb
  changed.

Wed 14 Jun 2006 : because of warnings on AIX, changed witness_points_io.adb
  and the package hypersurface_samplers.

Sat 10 Dec 2005 : reading an embedding recognizes extra "ss" slack variables,
  added to witness_points_io.ads, tested by ts_embed.adb.

Wed 7 Dec 2005 : added removal of embedding to ts_embed.adb; now we can
  find initial solutions to the simple staircase system automatically.

Tue 29 Nov 2005 : modified ts_embed.adb to fix bug in the embedding of
  overdetermined polynomial systems.

Mon 11 Jul 2005 : attempted a local dimension test in ts_locdim.adb

Thu 24 Mar 2005 : changed standard_intrinsic_trackers.adb, using process_io.
  removed extra output in standard_intrinsic_newton.adb.

Sun 16 Jan 2005 : changed stop conditions in standard_intrinsic_newton.adb

Thu 13 Jan 2005 : made some changes to standard_intrinsic_trackers.adb and
  standard_intrinsic_continuation.adb to look for a bug....

Sun 19 Dec 2004 : moved intrinsic_witness_sets_io from Solver to here.

Mon 19 Jul 2004 : reduced output in standard_intrinsic_continuation.

Wed 14 Jul 2004 : fixed the step_control in standard_intrinsic_trackers.

Tue 13 Jul 2004 : added one Affine_Expand to standard_point_coordinates.

Wed 16 Jun 2004 : splitted off the monodromy test from ts_inewt and
  created ts_ifactor.

Mon 14 Jun 2004 : added generic versions to standard_intrinsic_newton.

Wed 24 Mar 2004 : added "Transform" to standard_intrinsic_solutions.

Sun 14 Mar 2004 : updated witness_point_io with Sort_Embedded_Symbols

Mon 8 Mar 2004 : created the package standard_flag_representations,
  tested by ts_flag.

Mon 12 Jan 2004 : prepared for intrinsic Newton in projective coordinates

Tue 30 Dec 2003 : created ts_ispan and standard_linear_span to
  find the linear span of a solution component.

Tue 23 Dec 2003 : changed the intrinsic trackers to make room for
  more advanced predictors, more testing in ts_inewt.adb

Fri 19 Dec 2003 : created standard_moving_planes to define paths of
  linear spaces, as generic parameters to the intrinsic trackers;
  first experiments with monodromy

Thu 18 Dec 2003 : added validate to standard_intrinsic_continuation,
  updates in intrinsic newton, trackers, and massive test in ts_inewt.

Wed 17 Dec 2003 : created standard_intrinsic_trackers and
  standard_intrinsic_continuation, tested by ts_inewt.

Tue 16 Dec 2003 : splitted standard_affine_solutions into
  standard_intrinsic_solutions; created standard_intrinsic_newton,
  tested by ts_inewt.adb

Mon 15 Dec 2003 : splitted standard_affine_planes into
  standard_plane_representations, standard_point_coordinates, and
  standard_plane_operations.  Update of hypersurface_sample_grids.adb,
  ts_planes and a new ts_coords.

Mon 1 Sep 2003 : removed "Add_Variables" from Witness_Points package
  because now available in extra package in Homotopy library.

Tue 3 June 2003 : upgraded witness_points_io with "Add_Extra_Symbols"
  to deal with embedding of a cylinder

*** more adequate bookkeeping needed since release v2.2alpha on 5/30/03 ***
*** from now on, write the updates putting the most recent date first ****

Wed 31 May 2000 : due to modified Newton, changed component_scanners.adb

Sun 4 June 2000 : reorganization of cascade_of_homotopies, broken up into
  two separate modules: homotopy_cascade_filter and driver_for_cascade_filter.

Tue 19 June 2000 : new package "Standard_Classify_Points", split off
  from the "Standard_Irreducible_Decomp".  Did the same for multprec.
  Added the test facility ts_classify.

Wed 21 June 2000 : new package "Standard_Linear_Spaces" to compute spaces
  that contain the components.

Sat 9 Sep 2000 : restructuring component_scanners with more efficient
  homotopy continuation

Sun 10 Sep 2000 : refinement on the original generic points for a reliable
  membership test affects multprec_classify_points, component_scanners,
  and sample_generic_points.adb

Mon 11 Sep 2000 : fixed calls to dynamic interpolator in *Irred_Decomp.adb;
  limit on degree and #samples to prevent too huge memory usage;
  created new small program ts_nbterms to illustrate complexity growth.

Tue 12 Sep 2000 : preprocessor to membership test is container subspace
  inclusion, modified multprec_classify_points.

Sat 23 Sep 2000 : new sampling module, created the packages sampling_machine,
  sample_points, sample_points_io, sample_point_lists, sample_point_lists_io,
  and the testing facility ts_sample.
Sun 24 Sep 2000 : completed the sampling module as standalone unit
Mon 25 Sep 2000 : added sample_point_grids + io to the sampling module
Tue 26 Sep 2000 : added sampler to sample_point_grids, adjusted the
  standard_classify_points to use the new sampling module
Wed 27 Sep 2000 : adjusted multprec_classify_points to use new sampling
  so that now old component_scanners+sample_generic_points are obsolete
Thu 28 Sep 2000 : added diagnostics reporting to multprec_classify_points,
  central projections now also work in standard arithmetic, changed
  standard_classify_points.ads and its .adb
Fri 29 Sep 2000 : split off component tests from classify_points.

Sat 30 Sep 2000 : split off from drivers_to_breakup_components the
  routines to read in the embedding: drivers_to_embed_components.
  This causes ts_sample to change.
  Created "span module": span_of_component + io + ts_span.
Sun 1 Oct 2000 : new filtering module leads to the packages
  interpolation_points, interpolation_point_lists, interpolation_filters,
  and the testing facility ts_filter.
  To implement the homotopy membership test, changed sampling_machine
  and the sample_point_lists, tested this new feature in ts_sample.

Wed 4 Oct 2000 : created projection_operators, extended on Thu.
Fri 6 Oct 2000 : memory leaks fixed in sample_point_lists: Deep_Clear(sols)!
Tue 10 Oct 2000 : completion of the functionality of the filtering module:
  now it is possible to interactive and dynamically build up the filter
  using central projections.
Wed 11 Oct 2000 : started the creation of irreducible components

Wed 18 Oct 2000 : monodromy_group_actions (+io) to clean out ts_probdeco

Tue 24 Oct 2000 : added validation+rerun in samplers on two levels:
  sampling_machine and sample_points.
  Moved monodromy decomposition into drivers_to_breakup_components.

Thu 26 Oct 2000 : ts_irco runs now with subspace restriction,
  worked on On_Component tests in span_of_component, interpolation_filters,
  irreducible_components, and irreducible_component_lists.
Fri 27 Oct 2000 : ts_irco can now also do central projections.

Sat 4 Nov 2000 : fixed bug in Collapse_Equations in
  standard_subspace_restrictions.adb; taking samples in restricted subspace
  works now.

Sun 12 Nov 2000 : interpolation_filters "Sample_Update" puts invcond on file.

Sun 26 Nov 2000 : ts_divdif.adb contains now also comparison with the
  direct interpolation method on the test polynomial with all ones.
Mon 27 Nov 2000 : created rectangular_sample_grids

Sat 9 Dec 2000 : created divided_differences to shadow multi-precision
  calculations with standard arithmetic

Fri 15 Dec 2000 : created ts_dvdexp.adb to perform a structured experiment

Fri 29 Dec 2000 : replaced "Number_of_Terms" in the standard_ and multprec_
  polynomial_interpolators.adb.  Created "stacked_sample_grids".

Sun 28 Jan 2001 : standard_divided_differences works for k=3 !

Sat 3 Feb 2001 : finally got the Newton interpolation to run for any k

Sat 17 Feb 2001 : fixed loss of precision in Newton interpolation,
  updated interfaces in both standard and multprec divided differences.

Sat 21 Apr 2001 : started implementation of trace interpolation
  new .adb files : ts_traces, drivers_to_grid_creators, ts_unint,
  standard_univariate_interpolators.

Mon 7 May 2001 : modified standard_trace_interpolators.adb
Wed 9 May 2001 : fixed bug from standard_trace_interpolators to make it work;
  started multprec_* analogues

Wed 23 May 2001 : modifications in trace interpolation module

Fri 25 May 2001 : new package standard_nvariate_interpolators to implement
  the generalizations of trace forms for arbitrary dimensions.

Sun 27 May 2001 : ts_newint and standard_nvariate_interpolators work almost.

Sat 9 June 2001 : ts_elim implements numerical elimination tool;
  Expand works for the trace interpolators.

Fri 20 July 2001 : updated drivers_to_embed_components with new read
  for the embedding.

Sat 21 July 2001 : changed rectangular_sample_grids.adb so that only one
  constant term moves when applied to multi dimensional components.

Mon 23 July 2001 : updates ts_dvdexp.adb and ts_difdvi.adb.
Tue 24 July 2001 : changed rectangular_sample_grids,
  standard_trace_interpolators, and ts_powtrc.

Sun 29 July 2001 : changed rectangular_sample_grids,
  {standard,multprec}_trace_interpolators.adb, and ts_powtrc, to
  make interpolation with Newton identities work

Mon 30 July 2001 : created the package "multivariate_factorization" with
  test routine ts_mulfac, starting with taking out code from ts_unisam.

Thu 2 Aug 2001 : created package "drivers_to_polynomial_factorization" to
  link the factorization of polynomials with phc.  Monodromy runs but has
  problems, because of poor hypersurface_samplers.

Fri 21 Dec 2001 : added Extract_Samples to standard_stacked_sample_grids
  to enable plain multivariate interpolation

Fri 28 Dec 2001 : polished version of ts_embed.adb required modification
  in slice_and_embed_components.ads and .adb.

Sun 30 Dec 2001 : create ts_squemb.adb to combine squaring and embedding.

Thu 21 Mar 2002 : slice_and_embed_components contains now the routine
  embed_with_dummies, also ts_embed.adb is changed

Mon 27 May 2002 : changed slice_and_embed_components into witness_points,
  this caused the headers of many files to change.

Tue 28 May 2002 : created standard_affine_planes and ts_planes as tester.

Thu 21 Nov 2002 : added witness_points_formats, as needed in Decomposition.

