Sun 27 Jun 2021 : deleted multprec_lattice_facets and its io package.

Sat 12 Jun 2021 : defined tropical.gpr to build the test procedures.

Wed 2 Jan 2019 : fixed compiler error in ts_tropawit.adb because of
  changed specification in standard_blackbox_continuations.

Fri 11 Dec 2015 : updated ts_tropawit.adb for standard_blackbox_continuations,
  a package name change from black_box_poly_continuations.

Thu 26 Mar 2015 : extended point_lists_and_strings with parse operation
  of a string representation of a Python tuple into an integer vector.

Wed 25 Mar 2015 : added writing of string representation of support
  when given as a list of points in point_lists_and_strings.

Wed 10 Sep 2014 : fixed another bug in multprec_lattice_3d_facets.adb
  and commented out printing statements in multprec_lattice_4d_facets.adb,
  standard_lattice_{3d,4d}_facets.adb.

Tue 9 Sep 2014 : standard_lattice_3d_facets.adb contains more commented out
  diagnostic prints for a bug fix in multprec_lattice_{3d,4d}_facets.adb.
  Added Normalize operation to multprec_lattice_polytopes for the -0 problem.

Fri 5 Sep 2014 : in multprec_lattice_3d_facets.adb, commented out some
  diagnostic output during the construction of the initial facet normal
  and commented out output in multprec_lattice_polytopes.adb.
  Moved the convert_to_string from point_lists_and_strings.adb to
  the multprec_integer_numbers_io package.  Added a function to compute
  the support value of a facet in multprec_lattice_{3d, 4d}_facets.
  New package facets_and_strings for the string representation of facets.

Tue 2 Sep 2014 : updated point_lists_and_strings and the test ts_ptlstr.

Mon 1 Sep 2014 : new package point_lists_and_strings, tested by ts_ptlstr
  meant for interfacing with Python.

Tue 19 Nov 2013 : updated ts_inform.adb and about half of all files in
  this directory to get ts_convhull.adb compiling again after the
  natural32 and integer32 types introduced in summer.

Sun 30 Jun 2013 : updated ts_inform.adb, standard_pretropical_facets,
  and ts_pretrop.adb, also ts_tropisms.adb and ts_tropawit.adb.

Sat 29 Jun 2013 : updated ts_intorto.adb.

Fri 28 Jun 2013 : modified ts_convhull.adb and almost all of its dependencies
  for the new 32-bit integer data types.

Thu 27 Jun 2013 : to get ts_comfac.adb compiled again, modified
  driver_for_common_factor.adb, standard_lattice_polygones,
  standard_initial_forms, standard_binomial_factors,
  standard_binomial_factors_io.adb, standard_puiseux_certifications.adb,
  and standard_puiseux_certificates_io.adb.

Wed 26 Jun 2013 : updated driver_for_common_factor for integer32, natural32
  and standard_puiseux_certificates.

Mon 29 Apr 2013 : extended ts_inform.adb with elimination function.

Thu 28 Mar 2013 : ts_inform.adb writes system at end.

Wed 27 Mar 2013 : extended ts_inform.adb to read matrix of tropisms from file.

Fri 22 Mar 2013 : extended ts_inform.adb to compute initial form for surfaces.

Mon 3 Jan 2011 : experiments added in ts_inform.adb.

Sun 2 Jan 2011 : moved code from ts_inform into standard_initial_forms.

Sat 1 Jan 2011 : bug fix in standard_lattice_3d_facets.adb, changed also
  standard_lattice_4d_facets.ad*, standard_lattice_polytopes.adb,
  convex_hull_methods.adb and standard_lattice_3d_facets_io.a*; 
  added fvector function in standard_lattice_facets.

Tue 28 Dec 2010 : updates in standard_lattice_{3d,4d,}_facets.adb for bugs,
  also in {standard,multprec}_lattice_polytopes.adb, and in
  multprec_lattice_3d_facets.adb, and in ts_convhull.adb. 

Mon 27 Dec 2010 : on more bug fix: {standard,multprec}_lattice_3d_facets.adb,
  {standard,multprec}_lattice_polytopes.adb, and ts_convhull.adb.
  Also changed multprec_lattice_supports.adb, added cyclic d-polytopes
  to convex_hull_methods, tested by ts_convhull.adb.
  New package standard_lattice_facets with its _io for general case.

Sun 26 Dec 2010 : changed {standard,multprec}_lattice_polytopes.adb and
  {standard,multprec}_lattice_4d_facets.adb, multprec_lattice_supports.adb,
  and multprec_lattice_4d_facets_io.adb.

Sat 25 Dec 2010 : bug fixes in standard_lattice_{3d,4d}_facets.a*,
  with change in {standard,multprec}_lattice_4d_facets_io.adb, 
  tried to fix multprec_lattice_{3d,4d}_facets.a*...
  changed convex_hull_methods.adb.

Thu 23 Dec 2010 : bug fix in {standard,multprec}_lattice_4d_facets.ad*,
  changes in standard_lattice_3d_facets.adb, convex_hull_methods.adb

Wed 22 Dec 2010 : bug fix in multprec_lattice_3d_facets.adb,
  changes in {standard,multprec}_lattice_4d_facets.adb and its _io.adb;
  new package convex_hull_methods, splitted off from ts_convhull.adb.

Tue 21 Dec 2010 : fixed bug in check_edge in ts_convhull.adb and in
  multprec_lattice_4d_facets.adb (no clear of shared facet normal).

Thu 3 Dec 2009 : introducing *_3d_facets_* broke ts_pretrop.adb and
  standard_pretropical_facets.a*.

Sat 17 Oct 2009 : added procedure to multprec_lattice_3d_facets_io,
  updated {standard,multprec}_lattice_polytopes.adb, added functions to
  test Euler characteristic to {standard,multprec}_lattice_4d_facets,
  tested by ts_convhull.adb.

Fri 16 Oct 2009 : to make room for the general implementation, renamed
  standard_lattice_facets* into standard_lattice_3d_facets* which caused
  changes in standard_lattice_edges, standard_lattice_4d_facets,
  and standard_lattice_polytopes.  Did the same for multprec_*_facets + _io,
  changing multprec_lattice_edges*, multprec_lattice_polytopes.adb, and
  also ts_convhull.adb.  Created multprec_lattice_4d_facets and changed
  multprec_lattice_polytopes, taking rank from multprec_*3d_facets.

Thu 15 Oct 2009 : updates in standard_lattice_4d_facets and ts_convhull.

Wed 14 Oct 2009 : moved Rank out standard_lattice_facets and into
  standard_lattice_polytopes, extended standard_lattice_4d_facets,
  tested by ts_convhull.adb.

Fri 9 Oct 2009 : all multprec_* files changes because of backshifting from
  multprec_integer64 to multprec_integer arithmetic.  Also ts_intorto.adb
  and ts_convhull.adb changed.

Wed 16 Sep 2009 : created package standard_lattice_4d_facets, tested by
  ts_convhull.adb.  Made change in standard_lattice_facets.adb.

Tue 15 Sep 2009 : fixed bug in standard_lattice_edges.adb, minor changes
  in standard_lattice_facets.a* and ts_convhull.adb.  Also checked the
  multiprecision version with multprec_lattice_edges.a*.

Mon 14 Sep 2009 : new package standard_lattice_edges shows bug detected by
  ts_convhull.adb.

Fri 4 Sep 2009 : renaming of standard_power_transformations caused changes
  in standard_binomial_factors.adb, standard_binomial_factors_io.adb,
  standard_puiseux_certificates.adb, standard_puiseux_certificates_io.adb,
  and standard_lattice_facets.adb.  New package standard_integer_orthogonals
  tested by ts_intorto.  Also new is the package standard_lattice_polytopes, 
  tested by ts_convhull.

Wed 2 Sep 2009 : bug fixes in standard_pretropical_facets, modifications
  in ts_pretrop.adb.

Tue 1 Sep 2009 : fixed bug in multprec_lattice_facets.adb,
  seems to run fine but not tested for memory leaks.

Mon 31 Aug 2009 : fixed multprec_lattice_polygons.adb, modified ts_convhull,
  change in documentation in standard_lattice_supports.ads,
  created multprec_lattice_supports.  Moved code from ts_pretrop.adb
  to ts_convhull.adb.  New packages: multprec_lattice_facets + io.

Sun 30 Aug 2009 : started multprec_lattice_polygons, new ts_convhull.

Wed 26 Aug 2009 : updates in standard_{lattice,pretropical}_facets.a*,
  extended ts_pretrop.adb, we are almost there...

Thu 27 Aug 2009 : ts_pretrop.adb allows the computation of tropisms to
  a space curve, updated standard_{lattice,pretropical}_facets, and also
  standard_lattice_supports.a*.

Wed 26 Aug 2009 : updates in standard_{lattice,pretropical}_facets.a*,
  extended ts_pretrop.adb.

Tue 25 Aug 2009 : created standard_pretropical_facets, tested by ts_pretrop.

Mon 24 Aug 2009 : extended ts_pretrop.adb, adding array type to
  standard_lattice_facets.ads.

Fri 21 Aug 2009 : fixed last bug from standard_lattice_facets.adb,
  minor change in ts_pretrop.adb.

Thu 20 Aug 2009 : updated standard_lattice_polygons with 64-bit arithmetic,
  which changed standard_binomial_factors.  Also used 64-bit arithmetic in
  standard_lattice_supports, standard_lattice_facets + i/o and ts_pretrop.
  There is still a bug ...

Wed 19 Aug 2009 : updates in standard_lattice_facets + i/o, ts_pretrop.adb.

Tue 18 Aug 2009 : updates in standard_lattice_supports, ts_pretrop.adb.

Mon 17 Aug 2009 : new package standard_lattice_supports, updates in
  standard_lattice_facets, tested by ts_pretrop.adb.

Sun 16 Aug 2009 : fixed bugs in standard_lattice_facets, ts_pretrop.adb,
  so initial facet is computed correctly for 3d polytope.

Fri 14 Aug 2009 : updates in standard_lattice_facets and ts_pretrop.adb.

Thu 13 Aug 2009 : new package standard_lattice_facets develops the giftwrapping
  algorithm in 3 dimensions.

Tue 11 Aug 2009 : new ts_pretrop.adb for tropisms in 3 dimensions.

Wed 29 Jul 2009 : changes in driver_for_common_factor.adb for output.

Tue 28 Jul 2009 : added driver_for_common_factor, for use in mainfac.

Tue 21 Jul 2009 : fixed standard_puiseux_certificates.adb, and modified
  ts_comfac.adb, so the evaluate confirms the order of evaluation.

Mon 20 Jul 2009 : output error in standard_binomial_factors.adb
  and fixes in standard_puiseux_certificates, tested by ts_comfac.adb.

Fri 17 Jul 2009 : bug fix in standard_binomial_factors.adb and its _io.adb
  to deal with zero first component in tropism, modified ts_comfac,
  new package standard_puiseux_certificates, with its _io.

Thu 16 Jul 2009 : updates in standard_binomial_factors and ts_comfac.
  Also changed standad_binomial_factors_io.

Wed 15 Jul 2009 : added wrapper function to standard_lattice_polygons
  fixed bug in standard_binomial_factors.adb and its _io.adb,
  tested by ts_comfac.adb.

Tue 14 Jul 2009 : new packages standard_binomial_factors and _io,
  updates in standard_lattice_polygons and standard_initial_forms,
  tested by ts_comfac.adb.

Mon 13 Jul 2009 : new package standard_lattice_polygons, separated from
  ts_comfac.adb.  New package standard_initial_forms, from ts_inform.adb.

Fri 10 Jul 2009 : ts_comfac.adb develops code to find a common factor of
  two multivariate polynomials, using polyhedral methods.

Tue 14 Oct 2008 : ts_inform.adb selects initial form systems.
