Sun 27 Jun 2021 : removed the obsolete evaluate_schubert_conditions package.

Thu 10 Jun 2021 : defined the exec_dir attribute in induction.gpr.

Wed 9 Jun 2021 : defined induction.gpr to build the test procedures.

Mon 14 Dec 2020 : commented out message in setup_flag_homotopies.adb.

Sat 12 Dec 2020 : updated the messages in main_schubert_induction when the
  verbose level is positive.

Sun 29 Nov 2020 : drivers_for_schubert_induction is main_schubert_induction;
  and moved mainenum into main_schubert_induction as its main procedure.
  Updated main_schubert_induction for the name changes of the drivers_
  into make_ and main_ packages.  Updated test_checker_games.adb,
  test_schubert_conditions.adb and test_lr_homotopies.adb.

Sun 8 Nov 2020 : updated wrapped_path_trackers.adb for the renaming of
  drivers_for_poly_continuation into main_poly_continuation.

Wed 2 Sep 2020 : moved all test procedures in ts_checkers, ts_flagcond,
  ts_induce, and ts_lrhom into separate packages test_checker_games,
  test_schubert_condition, test_homotopy_definitions, and test_lr_homotopies.

Tue 18 Aug 2020 : modified flag_transformations.adb for compiler warnings.
  Modified also setup_flag_homotopies for compiler warnings.

Mon 17 Aug 2020 : updated drivers_for_schubert_induction.adb with the
  final message that no more input is needed.

Mon 10 Aug 2020 : in moving_flag_continuation.adb, fixed calling the wrapped
  pade trackers.  Added new_line to drivers_for_schubert_induction.adb.

Sun 9 Aug 2020 : modifications in moving_flag_continuation
  and checker_poset_deformations.adb for compiler warnings.

Sat 8 Aug 2020 : simplified names in wrapped_path_trackers, and then
  updated moving_flag_continuation.adb.  Added the rpt flag to apply the
  robust path tracker in moving_flag_continuation, with caused updates in
  checker_poset_deformations, resolve_schubert_problems, and
  drivers_for_schubert_induction.adb.

Thu 6 Aug 2020 : moved functions and procedure to wrap solution vectors
  from wrapped_path_trackers into a new package wrapped_solution_vectors,
  updated moving_flag_continuation.adb.  Modifications to ts_flagcond.adb,
  ts_induce.adb, and ts_lrhom.adb for compiler warnings.

Wed 5 Aug 2020 : modified moving_flag_continuation.adb to pass the verbose
  level to the calls of the wrapped path trackers.

Tue 4 Aug 2020 : updates in drivers_for_schubert_induction and mainenum
  to pass the number of tasks, given at the command line prompt.

Mon 3 Aug 2020 : modifications in resolve_schubert_problems.adb,
  checker_poset_deformations, and moving_flag_continuation to pass
  the verbose level.  Modified moving_flag_continuation and procedures
  in wrapped_path_trackers to pass the verbose level.

Sun 2 Aug 2020 : in mainenum.adb, passed the verbose level to the
  main procedures in drivers_for_schubert_condition, and then to
  resolve_schubert_problems, and then to check_poset_deformations.

Thu 29 Aug 2019 : updated drivers_for_schubert_induction.adb for compiler
  warnings.

Thu 13 Jun 2019 : added the verbose level option to mainenum.

Thu 5 Jan 2017 : in drivers_for_schubert_induction, applied the root refiners
  for double double and quad double precision.

Wed 4 Jan 2017 : in drivers_for_schubert_induction, called the root refiners
  on the end solutions.

Mon 2 Jan 2017 : writing of the sequence of flags in the stack to file
  in resolve_schubert_problems.adb.  A random flag should be orthogonal,
  fixed this in setup_flag_homotopies.adb.

Fri 30 Dec 2016 : added Append procedure to setup_flag_homotopies.
  Refactored Is_Zone_A_Empty in checker_homotopies.
  Added remove_one_variable procedures to recondition_swap_homotopies.
  Position procedure added to checker_localization_patterns.
  The recondition and scaling procedures in recondition_swap_homotopies
  need more arguments, adjusted calls in moving_flag_continuation.adb.
  Double double and quad double versions in recondition_swap_homotopies.
  Silent and dd/qd versions in moving_flag_continuation.

Thu 29 Dec 2016 : added reconditioning of solution vectors to
  recondition_swap_homotopies, moved the test out of checker_homotopies.adb
  and into moving_flag_continuation.adb, added a procedure to add an extra
  symbol in setup_flag_homotopies.  The last equation in the reconditioned
  homotopy must move, changed again also moving_flag_continuation.adb.
  Added rescaling solutions to recondition_swap_homotopies.

Wed 28 Dec 2016 : added helper function to checker_localization_patterns.
  New package recondition_swap_homotopies, with a test in First_Swap_Plane
  in checker_homotopies.adb.  Added the construction of a random linear
  equation to recondition_swap_homotopies, tested in checker_homotopies.adb.

Thu 22 Dec 2016 : made progress in the bug fix in checker_homotopies.adb.
  Applied the patch to the other procedures in checker_homotopies.adb
  which define the first swap plane.

Wed 21 Dec 2016 : fixed spelling error in checker_homotopies.ads and
  added extra print statement for debugging in checker_homotopies.adb.
  Improved Rank definition in checker_localization_patterns.adb.

Wed 30 Nov 2016 : added nt parameter in call to resolve in ts_lrhom.adb.

Wed 2 Nov 2016 : to resolve_schubert_problems, added multitasking,
  with adjusted calls in the drivers_for_schubert_induction.adb.
  Prompted for the number of tasks in driver_for_schubert_induction.adb.

Tue 1 Nov 2016 : upgraded moving_flag_continuation to use multitasking,
  added stubs to checker_poset_deformations.adb.  Then replaced the stubs
  in checker_poset_deformations and placed stubs in the package bodies
  drivers_for_schubert_induction.adb and resolve_schubert_problems.adb.

Sun 30 Oct 2016 : added multitasking to wrapped_path_trackers.

Mon 24 Oct 2016 : fixed call to Resolve in ts_lrhom.adb to include the
  option of squaring overdetermined homotopies.

Fri 21 Oct 2016 : fixed Flag_Conditions in moving_flag_homotopies.adb,
  which caused a crash in the Cheater's homotopy.
  Added the moved_flag to the setting up of cheater's homotopy in
  moving_flag_homotopies.adb

Thu 20 Oct 2016 : renamed menu option in mainenum.adb and added checks on
  the brackers in drivers_for_schubert_induction.
  Added extra output to drivers_for_schubert_induction.adb to isolated the
  crash when running the Cheater's homotopy.

Tue 18 Oct 2016 : removed some unnecessary with clauses from
  moving_flag_continuation.adb.

Mon 17 Oct 2016 : reshuffled with/use clauses in moving_flag_homotopies.
  Fixed type error in moving_flag_continuation.adb.

Thu 26 May 2016 : refactored code in wrapped_path_trackers.adb.

Fri 20 May 2016 : refactored computation of the solved system into
  separate functions in drivers_for_schubert_induction.
  Added silent root count to resolve_schubert_problems.

Thu 19 May 2016 : added question in drivers_for_schubert_induction.adb
  to ask whether to square the overdetermined homotopies, this also then
  changed its specification and the packages resolve_schubert_problems
  and checker_poset_deformations.  Used the boolean flag in the trackers
  in moving_flag_continuation, called in checker_poset_deformations.adb.
  Bug fix in moving_flag_continuation.adb, update in the writing to file
  in drivers_for_schubert_induction.adb.

Wed 18 May 2016 : improved documentation of moving_flag_homotopies.ads
  and the output in moving_flag_continuation.adb.  Added root refinement
  on the original overdetermined problem in moving_flag_continuation.adb.
  Added extra flag to trackers in moving_flag_continuation to indicate
  whether overdetermined homotopies need squaring or not.

Tue 17 May 2016 : prepared wrapped_path_trackers.adb for overdetermined
  homotopies.

Wed 11 May 2016 : in wrapped_path_trackers.adb numbered exception handlers.

Mon 29 Feb 2016 : updated in wrapped_path_trackers for changes in 
  {dobldobl,quaddobl}_incfix_continuation.adb.

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

Fri 11 Dec 2015 : fixed ts_lrhom.adb, for the Resolve was missing an option.

Thu 22 Oct 2015 : adding standard_ in front of bracket_polynomials changed
  symbolic_schubert_conditions.ads and numeric_schubert_conditions
  Silent version of resolve in resolve_schubert_problems, with adjusted
  prompting for level of output in drivers_for_schubert_induction.
  Added extra boolean parameter in moving_flag_continuation, which
  changed checker_poset_deformations, resolve_schubert_problems,
  and drivers_for_schubert_induction.

Wed 21 Oct 2015 : updated ts_flagcond.adb with tests in double double
  and quad double precision.

Tue 20 Oct 2015 : new package checker_poset_deformations with code out of
  moving_flag_continuation, which changed resolve_schubert_problems.adb
  and drivers_for_schubert_induction.adb.  Added procedues for double
  double and quad double precision to checker_poset_deformations.
  Renamed intersection_solution_posets into standard_solution_posets
  for the new packages {dobldobl,quaddobl}_solution_posets.
  This led to changes in checker_poset_deformations.ads,
  resolve_schubert_problems, and drivers_for_schubert_induction.ads.
  Also ts_lrhom.adb changed.  Added versions for double doubles and
  quad double in resolve_schubert_problems and flag_transformations.
  Changed drivers_for_schubert_induction, ready to start runs in
  double double and quad double precision ...

Mon 19 Oct 2015 : upgraded moving_flag_homotopies with procedures to make
  equations for homotopies in double double and quad double precision.
  Extensions in moving_flag_continuation for double double and quad doubles.

Sun 18 Oct 2015 : numeric_schubert_conditions supports the expansion of
  minors in double double and quad double precision.
  Moved code from moving_flag_homotopies.adb to setup_flag_homotopies.

Sat 17 Oct 2015 : mapping in double double and quad double precision added
  to checker_localization_patterns.  In checker_homotopies, added procedures
  in double double and quad double precision.

Fri 16 Oct 2015 : symbolic_schubert_conditions and remember_symbolic_minors
  are extended to return matrices of polynomials with coefficients in
  double double and quad double precision.  Prepared the numerical versions
  in numeric_schubert_conditions for similar extensions.  The refactoring
  changed the test programs ts_induce, ts_lrhom, and ts_flagcond.
  Extended remember_numeric_minors with remember tables for minors in
  double double and quad double precision, used in numeric_schubert_conditions
  and in moving_flag_homotopies.  The specifications for the procedures in
  wrapped_path_trackers.ads were incomplete.  Tracking of paths in double
  double and quad double precision called in moving_flag_continuation.

Thu 15 Oct 2015 : moving_flag_continuation and resolve_schubrt_problems
  have the option of using a more efficient problem formulation, deterimined
  in drivers_for_schubert_induction.adb.  Improved driver procedures in
  drivers_for_schubert_induction.adb.  In ts_flagcond.adb, the generic
  point test for the efficient problem formulation is harder to compute...
  Update in ts_lrhom.adb for the extra option in resolve.
  Extended flag_transformations for double doubles and quad doubles,
  which required changes in moving_flag_homotopies, tested by ts_induce.
  New package wrapped_path_trackers with code factored out of the package
  moving_flag_continuation, for extension to double doubles and quad doubles.
  This refactoring changed moving_flag_continuation and the body of
  drivers_for_schubert_induction.  New packages start_flag_homotopies
  and setup_flag_homotopies, factored from moving_flag_homotopies.
  This changed resolve_schubert_problems.adb and
  drivers_for_schubert_induction.adb.  Updated numeric_schubert_conditions.adb
  to prepare for double double and quad double precision.

Wed 14 Oct 2015 : extended symbolic_schubert_conditions with a procedure
  and a function to enumerate and count all brackets not above a bracket,
  tested in ts_checkers and ts_flagcond.  Added a minimal_expand to
  numeric_schubert_conditions, for use in moving_flag_homotopies, and
  tested by ts_flagcond.adb.

Tue 13 Oct 2015 : drivers_for_schubert_condition changed so the user can
  enter values for the generic flags.

Mon 12 Oct 2015 : updated checker_posets_io and intersection_posets_io
  with procedures to write to file, in addition to standard output.
  Added Write_Expansion in drivers_for_schubert_induction.adb when
  resolving a general Schubert problem.  Separated generation of the random
  flags off into a separate procedure in drivers_for_schubert_induction.

Sun 11 Oct 2015 : the random seed is written at the end of the output file
  in drivers_for_schubert_induction.adb.  Improved the documentation of
  Set_Parameters in moving_flag_continuation.ads.  An extra parameter in the
  Resolve in resolve_schubert_problems to make the path trackers reporting,
  which then also changed ts_lrhom.  In drivers_for_schubert_induction.adb,
  written the random flags at the start as well as the fixed flags at the end.

Fri 31 Oct 2014 : used Random_Flags in the Resolve_Schubert_Problem
  in drivers_for_schubert_induction.adb.

Thu 30 Oct 2014 : improved output in drivers_for_schubert_induction.adb.

Wed 29 Oct 2014 : constant tol moved to specifications of the procedures
  in drivers_for_schubert_induction.  Added a verbose option to the resolve
  in resolve_schubert_problems and adjusted ts_lrhom.adb.
  Changed checker_moves.adb and checker_homotopies.adb for silent versions.
  Moved driver routines from ts_lrhom to drivers_for_schubert_induction
  so phc -e can now handle any number of Schubert intersection conditions.

Tue 28 Oct 2014 : constant tol moved from the body of the procedures in
  moving_flag_continuation into the specification parameters.
  This caused changes in drivers_for_schubert_induction.adb
  and resolve_schubert_problems.adb.

Mon 27 Oct 2014 : resolve_schubert_problems uses stack_of_flags.
  Bug fix in flag_transformations.adb and increased tolerance 'tolsing'
  in moving_flag_continuation from 1.0E-8 to 1.0E-6.
  Added tol parameter to the procedures in moving_flag_continuation.

Sun 26 Oct 2014 : silent versions of connect to track procedures in
  resolve_schubert_problems.  Added stack_of_flags in flag_transformations
  and made the call in resolve_schubert_problems.adb.

Sat 25 Oct 2014 : cleaned up flag_transformations and upgraded 
  resolve_schubert_problems.adb with use of the new transformation procedure.
  Silent stay and swap homotopy in moving_flag_continuation,
  track_all_paths_in_poset in moving_flag_continuation has silent version.

Fri 24 Oct 2014 : added procedure to flag_transformations, to transform
  using only the current flag in a sequence of flags.
  Added condition in track_all_paths_in_poset of moving_flag_continuation
  to ensure that leaves of parents are lined up with roots of children.
  Instead of concatenation, new solutions are pushed to the lists in
  resolve_schubert_problems.adb.

Thu 23 Oct 2014 : changed Random_Flag in moving_flag_homotopies.adb,
  so the matrix is now a random dense matrix.  Fixed matching of localization
  patterns when lining up the solutions from one level to the next in
  resolve_schubert_problems.adb.  In moving_flag_continuation.ads,
  exported the utility copy_flags, and in moving_flag_continuation.adb,
  set the unhappy to true if path tracking is aborted.  The resolution
  of Schubert problems seems to work now for four conditions.
  Updated ts_lrhom.adb with writing of the results at the end.

Wed 22 Oct 2014 : added procedure to transform a sequence of flags in
  flag_transformations.  Applied the transformations to the start solutions
  in resolve_schubert_problems.  Linked up nodes at the leaves of the parent
  correctly to the nodes at the roots of the children.

Tue 21 Oct 2014 : bug fix in moving_flag_continuation.adb with extra output
  diagnostics in checker_homotopies.adb.  Abort track path in poset in
  moving_flag_continuation.adb if there are no start solutions, so no crash.

Mon 20 Oct 2014 : extended checker_homotopies with inverse transformations
  on solution lists after the 3 types of Littlewood-Richardson homotopies.
  Extended moving_flag_continuation to work with lists of solutions,
  small change in resolve_schubert_problems.adb.
  Bug fix in moving_flag_continuation.adb.

Sun 19 Oct 2014 : added more checks in moving_flag_continuation and changes
  in resolve_schubert_problems.adb.  Number of flags given on input to a
  checker game depends on the level in the intersection poset.

Sat 18 Oct 2014 : added routines in moving_flag_continuation to take the
  solution nodes at the previous level into account, as called in 
  resolve_schubert_problems.adb.

Fri 17 Oct 2014 : called Littlewood-Richardson homotopies on one checker
  game in the resolve_schubert_problems.

Thu 16 Oct 2014 : Debugged procedure to compute solutions at leaves in
  resolve_schubert_problems, tested by ts_lrhom.adb.

Wed 15 Oct 2014 : extended intersection_solution_posets with retrieval
  function used in resolve_schubert_problems.adb.
  Added a procedure to compute start solutions at the leaves and augmented
  parameter list of the resolve, tested by ts_lrhom.adb.

Tue 14 Oct 2014 : new package intersection_solution_posets, tested by
  ts_lrhom.  Used the intersection_solution_posets in the resolve
  of resolve_schubert_problems, also tested by ts_lrhom.

Mon 13 Oct 2014 : removed dead code in moving_flag_continuation with changed
  specs caused change in drivers_for_schubert_induction.adb.
  Extended checker_posets_io with an extra write procedure.
  New package resolve_schubert_conditions, based on the stubbing code from
  ts_lrhom.adb.

Sun 12 Oct 2014 : added silent versions of the coordinate transformations
  in checker_homotopies.  Memory management in moving_flag_continuation.adb.
  Silent path tracker added to moving_flag_continuation.

Sat 11 Oct 2014 : must multiply forgotten variables by x(r+1,s+1) as well
  in the first_swap_plane of checker_homotopies.adb.

Fri 10 Oct 2014 : clean up unused code in checker_homotopies, removed
  commented out lines in moving_flag_homotopies.adb.

Thu 9 Oct 2014 : bug fix in checker_homotopies.adb, first_swap_plane.
  The same bug existed in the second_swap_plane of checker_homotopies.adb.

Wed 8 Oct 2014 : improved transformation of solutions after a swap homotopy
  in checker_homotopies with new Update_Swap_Column procedure.

Tue 7 Oct 2014 : swap type II homotopies work after changes in 
  checker_homotopies and moving_flag_continuation.
  After more updates in checker homotopies and moving_flag_continuation.adb,
  the case [2 4 6]^3 appears to be solved again correctly.
  Fixed call to flag_conditions in drivers_for_schubert_induction.adb,
  after updating moving_flag_homotopies.adb.

Mon 6 Oct 2014 : printing of the moving flag in moving_flag_homotopies and
  bug fixes in moving_flag_continuation.adb.  Better documentation about
  the flag transitions in moving_flag_continuation.  In checker_homotopies.adb
  we must evaluate the computer coordinates to transform the planes,
  furthermore, matrix inversion is needed in checker_homotopies.
  Also for swap homotopies, localization maps are multiplied with the
  current moving flag.

Sun 5 Oct 2014 : improved coordinate transformation in checker_homotopies
  and changes in moving_flag_continuation.adb for the stay homotopies.

Sat 4 Oct 2014 : cleaning up in checker_homotopies.adb, modifications in
  moving_flag_{homotopies,continuation}.adb for the stay homotopies.

Fri 3 Oct 2014 : updated moving_flag_{continuation,homotopies} and
  drivers_for_schubert_induction.adb to get the trivial stay case to work.

Thu 2 Oct 2014 : bug fixes and completed code in checker_homotopies
  and changes in moving_flag_continuation.adb.

Wed 1 Oct 2014 : updated checker_homotopies with coordinate transformations
  on the solutions in the cases where there is no homotopy.
  Applied the coordinate transformation in the Trivial_Stay case.

Tue 30 Sep 2014 : wrapper for the many conditions imposed by many flags
  for use in a cheater homotopy.

Mon 29 Sep 2014 : updated moving_flag_homotopies with the correct numeric
  transformation, tested by the first option of ts_induce.

Sun 28 Sep 2014 : stubbing Littlewood-Richardson homotopies in ts_lrhom.adb.

Sat 27 Sep 2014 : extended ts_lrhom.adb with a walk from leaves to root in
  the intersection poset to resolve intersection conditions.
  Made the connections between checker posets between root of child and
  the leaves of the parents in the intersection poset.
  Extended checker_posets with procedure to add the coefficients from
  the leaves to the root in the poset, called in ts_lrhom.

Fri 26 Sep 2014 : improved documentation of intersection_posets_io.ads.
  Changed interface in checker_posets_io.  New ts_lrhom.adb to interactively
  develop the resolution of general Schubert problems.

Sun 21 Sep 2014 : every procedure in ts_checkers is now documented.
  Improved interfaces in the package flag_transformations.

Fri 19 Sep 2014 : refactored code from ts_flagcond.adb into the package
  flag_transformations, with better verification of the solutions.
  Refactored code from ts_flagcond into numeric_schubert_conditions.

Thu 18 Sep 2014 : moved code for the function "moved_flag" from ts_induce
  to the package moving_flag_homotopies.  Extended the numerical testing
  in ts_flagcond.adb.  Upgrades in flag_transformations, tested by ts_induce.
  Applied the transformations in the numerical test in ts_flagcond.adb.

Wed 17 Sep 2014 : added test on rank on the solutions with respect to the
  flag and the intersection condition to ts_flagcond.adb.

Sun 15 Jun 2014 : refactored ts_induce.adb into the new package 
  flag_transformations to transform pair of flags.

Thu 5 Jun 2014 : adjusted drivers_for_schubert_induction to pass the 
  coefficients of the fixed flags.

Wed 4 Jun 2014 : more changes to drivers_for_schubert_induction, now for
  the Python interface.

Mon 2 Jun 2014 : changed drivers_for_schubert_induction.

Sun 1 Jun 2014 : updated drivers_for_schubert_induction to prepare for the
  C interface.

Wed 28 May 2014 : put_line to write of "= 0" in intersection_posets_io.adb
  and added random_triplet to ts_checkers.adb.

Tue 27 May 2014 : fix in ts_induce.adb for extra "silent" parameter in
  the intersect of intersection_posets.

Fri 23 May 2014 : updates in drivers_for_schubert_induction for the
  resolution of a general Schubert problem, with code from ts_checkers.adb.
  Modifications in intersection_posets to make it silent.

Sat 17 May 2014 : code to transform a pair of flags added to ts_induce.

Wed 14 May 2014 : extra function in ts_checkers.adb to generate a random
  intersection condition, extra Final_Sum in intersection_posets.

Tue 13 May 2014 : small changes to ts_induce.adb for compiler warnings.

Tue 25 Jun 2012 : updated mainenum.adb for natural32 and integer32.

Wed 19 Jun 2012 : Almost all files changes because of natural32 & integer32.

Thu 9 Jun 2011 : changed moving_flag_continuation.adb for changed
  specifications of standard_root_refiners.

Wed 1 Jun 2011 : for warnings, changed drivers_for_schubert_induction.adb.

Sun 29 May 2011 : for GNAT GPL 2010 warnings, modified checker_moves.adb
  and moving_flag_continuation.adb; only 2 warnings left 
  with moving_flag_homotopies.adb and checker_posets.adb...

Wed 6 Jan 2010 : for GNAT GPL 2009 warnings, modified intersection_posets.adb
  and intersection_posets_io.adb.  Extended schubert_posets.a*.

Tue 5 Jan 2010 : minor modifications in schubert_posets and ts_flagcond.adb.

Mon 4 Jan 2010 : created schubert_posets, tested by ts_flagcond.adb.

Fri 1 Jan 2010 : updated in ts_flagcond.adb.

Thu 31 Dec 2009 : updates in ts_checkers.adb and ts_flagcond.adb.

Tue 29 Dec 2009 : for GNAT GPL 2009 warnings: change in ts_checkers.adb,
  numeric_schubert_conditions.a*.  Fixed ts_flagcond.adb, extending
  drivers_for_schubert_conditions.adb.

Fri 30 Oct 2009 : updates in numeric_schubert_conditions for bug chases,
  moving_flag_homotopies and drivers_for_schubert_induction to make
  cheater's homotopy between Schubert problems work.
  Last minute change to drivers_for_schubert_induction.adb.

Thu 29 Oct 2009 : the fixed flags are written in full by
  drivers_for_schubert_induction.adb

Wed 28 Oct 2009 : phc -e runs what was in ts_flagcond #5, updated
  drivers_for_schubert_induction.

Tue 27 Oct 2009 : updated moving_flag_continuation to return also solutions,
  tested by ts_flagcond.adb.  Added fifth option to mainenum.adb, moved code
  from ts_flagcond.adb to drivers_for_schubert_induction.

Fri 19 Jun 2009 : updated ts_induce.adb.

Tue 16 Jun 2009 : updated checker_homotopies.a*, ts_flagcond.adb, and
  moving_flag_continuation.adb.

Mon 15 Jun 2009 : updates in checker_boards_io.a*, checker_posets_io.adb,
  checker_localization_patterns.adb, moving_flag_homotopies.adb,
  checker_homotopies.a* and moving_flag_continuation.a*.

Sun 14 Jun 2009 : changes in moving_flag_continuation.adb and
  checker_homotopies.adb.

Fri 12 Jun 2009 : updates in checker_homotopies.a* and
  moving_flag_continuation.a*, so finally [2 4]^4 works in ts_flagcond!

Thu 11 Jun 2009 : updates in checker_homotopies.a* and
  moving_flag_continuation.a* and moving_flag_homotopies.adb.

Wed 10 Jun 2009 : updates in checker_homotopies.a* and
  moving_flag_continuation.adb.

Tue 9 Jun 2009 : updates in checker_boards.a*, checker_posets_io.adb,
  checker_localization_patterns.a*, checker_homotopies.a*, ts_checkers.adb,
  and moving_flag_continuation.adb.

Mon 8 Jun 2009 : updates in checker_homotopies.a*,
  moving_flag_homotopies.a*, and moving_flag_continuation.adb

Fri 5 Jun 2009 : upgrades in checker_homtopies.a*, moving_flag_homotopie.a*,
  checker_localization_patterns.a*, moving_flag_continuation.a*.

Thu 4 Jun 2009 : updates in moving_flag_continuation.adb and
  checker_homotopies.a*

Wed 3 Jun 2009 : updates in moving_flag_homotopies.a*
  and moving_flag_continuation.a*

Tue 2 Jun 2009 : updates in moving_flag_homotopies.a*
  and moving_flag_continuation.a*

Mon 1 Jun 2009 : updated ts_induce.adb, moving_flag_homotopies.a*,
  and moving_flag_continuation.adb.

Thu 28 May 2009 : changes in checker_homotopies.a*, ts_flagcond.adb,
  moving_flag_homotopies.adb and moving_flag_continuation.a*

Tue 26 May 2009 : changes in moving_flag_continuation.adb and ts_flagcond.adb.

Mon 25 May 2009 : updated moving_flag_{continuation,homotopies},
  for multiple intersection conditions in ts_flagcond.adb.
  
Thu 21 May 2009 : changed moving_flag_homotopies.a*, ts_flagcond.adb,
  and moving_flag_continuation.adb.

Wed 20 May 2009 : changed moving_flag_homotopies.a*, ts_flagcond.adb,
  and moving_flag_continuation.adb.

Tue 19 May 2009 : updates in checker_homotopies.a*, ts_induce.adb,
  and moving_flag_continuation.adb

Mon 18 May 2009 : removed from symbolic_schubert_conditions.adb redundant
  with/use clauses.  Code from ts_induce.adb into checker_homotopies.
  Updated checker_moves.a* and moving_flag_continuation.adb.

Tue 31 Mar 2009 : replaced standard_natural_vectors.io.get from the
  checker_boards_io, changes in ts_flagcond.adb.

Mon 30 Mar 2009 : extended ts_flagcond.adb with previous transformation
  and localization patterns in option #6.

Thu 26 Mar 2009 : extended checker_boards_io with procedure to write
  along the localization pattern, used in ts_flagcond.adb.  Also changed
  are moving_flag_continuation.adb and moving_flag_homotopies.
  Added inverse symbolic transformation to moving_flag_homotopies.

Wed 25 Mar 2009 : extra function in checker_localization_patterns,
  updates in moving_flag_homotopies.adb and moving_flag_continuation.adb,
  tested by ts_flagcond.adb, which has one extra test function.

Tue 24 Mar 2009 : new procedure in moving_flag_continuation.adb,
  ts_flagcond.adb change documents Random_Flag versus One_Flag.

Tue 27 Jan 2009 : moved code from ts_induce.adb into checker_posets_io,
  updates in moving_flag_homotopies.adb and moving_flag_continuation,
  tested by ts_flagcond: now ready to track all moves in a path...

Mon 26 Jan 2009 : added enumeration of all paths to checker_posets,
  tested by new option #8 in ts_checkers.  The new #6 in ts_induce
  writes all localizations for all paths in a checker poset.

Tue 13 Jan 2009 : added root refiners and more diagnostics to
  moving_flag_homotopies.adb and moving_flag_continuation.adb now
  contains a working path tracker to start the [2 4 6]^3 condition.

Thu 8 Jan 2009 : made moving_flag_continuation.track_game interactive
  and added function to moving_flag_homotopies.

Thu 11 Dec 2008 : added path trackers to moving_flag_continuation.

Tue 2 Dec 2008 : updates of moving_flag_homotopies, moving_flag_continuation,
  tested by ts_flagcond.adb, also code from ts_induce.adb is moved.

Fri 28 Nov 2008 : moving_flag_homotopies now contains start_solution,
  new package moving_flag_continuation, tested by ts_flagcond.adb.
  Added writing to file routines to checker_boards_io.

Wed 26 Nov 2008 : bug fix in one_flag_homotopy in moving_flag_homotopies.adb,
  tested by ts_flagcond.adb.

Tue 25 Nov 2008 : added one_flag_homotopy to moving_flag_homotopies.

Mon 24 Nov 2008 : created package moving_flag_homotopies, moving code
  from ts_induce.adb and ts_flagcond.adb.

Sun 23 Nov 2008 : ts_flagcond.adb shows the effect of transformations
  on a generalizing moving flag in symbolic form.  The numeric form of
  the transformations is in ts_induce.adb.

Fri 21 Nov 2008 : update of ts_flagcond.adb with symbolic form of flag.

Thu 20 Nov 2008 : moved pattern for moving flag from checker_boards
  to checker_localization_patterns and added a transformation routine.
  Updated checker_boards_io, checker_posets_io.adb, and ts_checkers.adb.
  Also ts_induce.adb changed and ts_flagcond.adb is updated.

Wed 19 Nov 2008 : started definition of a moving flag homotopy
  in ts_flagcond.adb.  Updated ts_checkers.adb after additions to
  checker_moves.a* and checker_posets.a* to see generalizing moves.

Tue 18 Nov 2008 : fixed reporting error in ts_induce.adb.
  Added to checker_boards* and ts_induced.adb to see pattern of the
  moving flag in the specializing and generalizing homotopies.
  Also changed ts_checkers.adb so the moving flag patterns shows.

Thu 13 Nov 2008 : formatting in checker_localization_patterns.adb,
  checker_moves.adb, checker_posets.adb, checker_posets_io.adb,
  intersection_posets.adb, intersection_posets_io.adb,
  symbolic_schubert_conditions.adb, ts_checkers.adb

Fri 14 Dec 2007 : mainenum.ads got copied over from ../Pieri.

Fri 8 Jun 2007 : more updates in numeric_schubert_conditions.a*,
  so ts_flagcond.adb is now doing the point test on the equations.

Thu 7 Jun 2007 : debugged numeric_schubert_conditions.adb, removed output
  from remember_symbolic_minors.adb, and now ts_flagcond.adb writes system.

Wed 6 Jun 2007 : updated remember* and {symbolic,numeric}_schubert*,
  tested by ts_flagcond.adb.

Tue 5 Jun 2007 : created remember_numeric_minors and added "symbolic_"
  to the minor_table data type in remember_symbolic_minors.
  Adjusted {symbolic,numeric}_schubert_conditions and ts_flagcond.adb.

Mon 4 Jun 2007 : adjusted (symbolic,numeric}_schubert_conditions and
  created new remember_symbolic_minors, tested by ts_flagcond.adb.

Thu 24 May 2007 : mv numeric_schubert_conditions evaluate_schubert_conditions
  and started the specifications of numeric_schubert_conditions.

Tue 3 Apr 2007 : changed checker_posets.a* and checker_posets_io.adb,
  intersection_posets.adb and intersection_posets_io.adb to work with
  coefficients of arbitrary length; also fixed ungraceful exit.

Thu 29 mar 2007 : fixed another bug in checker_posets.adb, minor change
  in ts_checkers.adb.

Tue 27 Mar 2007 : fixed bug in checker_posets, adding new Add_Multiplicity
  procedure, and a 7th option in ts_checkers.

Mon 26 Mar 2007 : fixed bug in intersection_posets.adb, the .ads changed
  in the testing process as well.

Fri 23 Mar 2007 : flag_minor_system added to symbolic_schubert_conditions,
  tested by ts_flagcond.

Tue 20 Mar 2007 : computed the #equations in symbolic_schubert_conditions
  and also the enumeration of the minors, tested by ts_flagcond.adb.

Fri 9 Mar 2007 : made a modest start at numeric_schubert_conditions.ad*,
  tested by ts_flagcond.adb.

Thu 8 Mar 2007 : created ts_flagcond.adb to test the operations in
  {symbolic,numeric}_schubert_conditions.

Fri 17 Nov 2006 : modified Add_Multiplicity in checker_posets, which 
  fixed a bug in intersection_posets.adb, reported by Frank.
 
Mon 2 Oct 2006 : ts_induce allows to create an intersection poset,
  fixed typo in intersection_posets.adb.  New operations in checker_posets
  and intersection_posets_io to allow homotopy navigation in ts_induce.

Thu 28 Sep 2006 : extra procedure "Add_Multiplicity" in checker_posets,
  changed checker_posets_io.adb and intersection_posets.adb.

Wed 27 Sep 2006 : intersection_posets (+io) replaces checker_poset_trees
  (+io), ts_chekcers now prints out the complete expansion.
  Altered the package description in checker_posets.ads.

Tue 26 Sep 2006 : except for checker_boards and its io, every file got
  changed.  Debugged checker_localization_patterns and created
  checker_poset_trees + io to combine several intersection conditions.

Mon 25 Sep 2006 : updated checker_moves with debugging option for happiness,
  added one function to checker_localization_patterns.adb, ts_checkers is
  modified so that it allows only happy checkers on input.

Fri 15 Sep 2006 : extra parenting functions to checker_posets to make
  walk in ts_induce.adb with generalizing_homotopies more complete.

Thu 14 Sep 2006 : changed checker_posets and _io, for ts_checkers.adb and
  ts_induce.adb which now traverses the poset from the leaves to the root.

Wed 13 Sep 2006 : tweaked checker_boards_io.ads and .adb, modified
  checker_posets.ads and its .adb, also checker_posets_io.adb, and
  the test program ts_checkers.adb, so posets are now also printed
  with their interconnectivity information.

Tue 12 Sep 2006 : added comments to "Number_of_Moves" in checker_moves.ads,
  minor change in checker_moves.adb; extra info in ts_checkers.adb, nicer 
  output by checker_boards_io, added explanations in checker_boards.ads.
  New "checker_localization_patterns" package, split off from ts_checkers.
  Updated ts_induce.
