Sun 5 Oct 2025 : removed excluded_source_files from newton.gpr.

Tue 13 Feb 2024 : to {dobldobl,quaddobl}_root_refiners, added verbose level.
  Added verbose level to standard_root_refiners.

Thu 8 Feb 2024 : in {standard,dobldobl,quaddobl}_root_refiners.adb fixed bug
  in application of deflation: do not report a failure if deflation fails.

Mon 25 Dec 2023 : {standard,dobldobl,quaddobl}_root_refiners.a*,
  added the verbose level.  Fixed {dobldobl,quaddobl}_root_refiners.adb,
  reinstating after deflation only if tolerances are not reached.

Thu 17 Jun 2021 : removed the obsolete standard_floating_newton_steps.

Tue 15 Jun 2021 : fixed ts_muldef.adb and {standard,multprec}_probe_kernel,
   {standard,multprec}_multiple_deflation, multprec_nullity_polynomials,
   and multprec_nullity_matrices.adb.  Updated newton.gpr.

Thu 10 Jun 2021 : added the exec_dir attribute to newton.gpr.

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

Sun 22 Nov 2020 : moved bablvali, bablvali2, bablvali4 into the package
  black_box_root_refiners.

Sun 23 Aug 2020 : added verbose level to drivers_to_deflate_singularities.

Thu 16 Jul 2020 : in standard_inlined_newton_circuits.adb ,added check 
  on divergence to the LU_Newton_Steps procedures.

Fri 10 Jul 2020 : in standard_refiner_circuits.adb, placed "if verbose"
  condition in case of a failed solution path.

Thu 2 Jul 2020 : eliminated the rcols, icols parameters from the procedures
  in standard_inlined_newton_circuits, with updated ts_newcirc, and
  updated calls in standard_refiner_circuits.adb.

Tue 30 Jun 2020 : toggled off the verbose mode when making a circuit from
  a polynomial system in standard_newton_refiners.adb.
  Refactored Run procedures in standard_refiner_circuits.

Wed 24 Jun 2020 : new package standard_inlined_newton_circuits with
  inlined linear solving, tested in ts_newcirc; added Inlined_Run
  procedures to standard_refiner_circuits.

Fri 19 Jun 2020 : added an additional parameter to the procedures to run
  many steps in standard_newton_circuits to allow for extra iterations.

Wed 17 Jun 2020 : to standard_newton_circuits added procedures to write
  to file when in verbose mode, tested by ts_newcirc, and with updates to
  the procedure calls in standard_refiner_circuits.adb.

Tue 16 Jun 2020 : extended standard_newton_circuits with mixed residuals,
  tested by ts_newcirc.

Thu 11 Jun 2020 : new package standard_refiner_circuits with code taken
  from ts_newcirc.  Added Main procedures to standard_refiner_circuits.

Wed 10 Jun 2020 : developed better cluster report in ts_newcirc.
  Moved buckets and heap data structures from ts_newcirc into a new
  package standard_solutions_heap in the folder ../Solutions.

Tue 9 Jun 2020 : extra procedures in drivers_to_dd_qd_root_refiners for
  compilation errors with ts_ddnewt and ts_qdnewt.  Extended the package
  standard_newton_circuits, with extra test procedures in ts_newcirc.
  Updated procedures standard_newton_circuits to report the first residual
  and added condition tables to ts_newcirc.

Mon 8 Jun 2020 : new ts_newcirc to develop Newton's method on coefficient
  circuits for better performing root refiners.  Move procedure from
  ts_newcirc to a new package standard_newton_circuits.

Mon 27 Apr 2020 : extended drivers_to_dd_qd_root_refiners.adb with
  multitasking for square systems that are not Laurent.

Thu 23 Apr 2020 : updated drivers_to_dd_qd_root_refiners so the input and
  output file names can be passed from the command line.

Mon 25 Mar 2019 : completed addition of mixed residual computations in the
  root refiners, in dobldobl_root_refiners.adb and quaddobl_root_refiners.a*.

Sun 24 Mar 2019 : added mixed residual computations to the root refiners
  in the {standard,dobldobl,quaddobl}_root_refiners packages.

Fri 31 Aug 2018 : reinstated the application of Newton's method after
  deflation in standard_root_refiners.adb.  Reinstated also Gauss-Newton
  in standard_root_refiners.adb after deflation, also fixed the
  {dobldobl,quaddobl}_root_refiners.adb in a similar fashion.

Mon 20 Aug 2018 : bug fix in dobldobl_root_refiners.adb, forgotten
  Tail_Of(solsptr) caused phc -b2 to run forever.

Thu 7 Jun 2018 : in *dobl_root_refiners, removed all solution arrays and
  removed the application of Newton's method after deflation.
  Bug fix in standard_root_refiners.adb, forgotten Tail_Of(solsptr).

Wed 6 Jun 2018 : removed the solution array from a reporting version of
  the root refiner in standard_root_refiners.adb.  Also changed the other
  refiners in standard_root_refiners.adb.

Wed 25 Apr 2018 : added new packages dobldobl_query_matrices,
  dobldobl_nullity_matrices, dobldobl_nullity_polynomials,
  and dobldobl_multiplicity_structure to compute the multiplicity structure
  in double double precision, tested by ts_multip.adb.
  Adjusted standard_query_matrices.adb for compiler warnings.
  Added similar new quaddobl packages, tested by ts_multip.adb.

Wed 4 Apr 2018 : something is not right with Reporting_Deflate(), replaced
  it in standard_root_refiners.adb by Silent_Deflate().

Tue 3 Apr 2018 : in standard_root_refiners.adb, avoided the application of
  Newton's method after deflation, re-initialized nit in each run.

Sat 8 Jul 2017 : extended multprec_root_refiners with procedures for
  Laurent systems.

Fri 23 Jun 2017 : to standard_root_refiners, added procedures to refine
  solutions of Laurent systems, without a separate list of refined solutions.

Wed 21 Jun 2017 : to the package black_box_root_refiners, added versions
  for Laurent polynomial systems, for use in phc -v.

Thu 5 Jan 2017 : added double double and quad double versions to
  the black_box_root_refiners.

Wed 4 Jan 2017 : new package black_box_root_refiners with code refactored
  from bablvali.adb.

Sat 22 Oct 2016 : in standard_root_refiners.adb used independent sequences
  of random numbers for the point lists in the frequency tables.
  Did the same for dobldobl_root_refiners.adb and quaddobl_root_refiners.adb.

Sat 26 Mar 2016 : moved documentations of the specifications from adb to ads
  in drivers_to_deflate_singularities.

Thu 24 Mar 2016 : in {dobldobl,quaddobl}_root_refiners.adb, better reporting
  of the deflations.  Adjusted defaults in root_refining_parameters.adb

Wed 23 Mar 2016 : updated standard_complex_newton_steps with function to
  guard against all singular values equal to zero.
  Did the same in {dobldobl,quaddobl,multprec}_complex_newton_steps.
  Extended handle_underflow_gracefully with procedures in double double
  and quad double precision.  To {dobldobl,quaddobl}_root_refiners,
  added deflation, updated drivers_to_dd_qd_root_refiners.adb.

Tue 22 Mar 2016 : upgraded standard_root_refiners to deflate overdetermined
  polynomial systems.

Mon 21 Mar 2016 : improved drivers_to_dd_qd_root_refiners.adb by refactoring,
  allowing for interacting parameter tuning and more checks.
  Added extra procedures to the root_refining_parameters.

Thu 10 Mar 2016 : drivers_to_dd_qd_root_refiners.adb modified so that the
  system given to phc -v is also written to the output file.

Mon 7 Mar 2016 : bug fix in the application of circuits to overdetermined
  systems in Gauss-Newton in {dobldobl,quaddobl}_root_refiners.

Sun 6 Mar 2016 : added SVD Gauss-Newton to dobldobl_root_refiners
  and also to the quaddobl_root_refiners, and to standard_root_refiners.

Thu 1 Oct 2015 : changed type of tolerance parameters in the root refiners in
  {dobldobl,quaddobl}_root_refiners to double_float.

Wed 30 Sep 2015 : minor documentation edits in standard_root_refiners.
  Extended {dobldobl,quaddobl}_root_refiners with root accounting procedures.
  The reporting root refiners write a condition report on the solutions
  computed in double double and quad double precision.
  Added versions to dobldobl_root_refiners to return only the true solutions.

Fri 25 Sep 2015 : extended {dobldobl,quaddobl}_root_refiners with versions
  for Laurent polynomial systems.

Wed 23 Sep 2015 : extended quaddobl_root_refiners with a reporting version.

Fri 11 Sep 2015 : added reporting Newton to {dobldobl,quaddobl}_root_refiners.

Fri 26 Jun 2015 : suppress 'exception raised in reporting deflate'
  in standard_root_refiners.adb.

Mon 22 Jun 2015 : added procedures in {dobldobl,quaddobl}_root_refiners to
  use circuits for the Jacobian matrices, changed ts_ddnewt and ts_qdnewt;
  upgraded drivers_to_dd_qd_root_refiners.adb.

Sun 30 Nov 2014 : changes to random_conditioned_root_problems and ts_vmpnewt
  because of compiler warnings.

Sat 29 Nov 2014 : new package random_conditioned_root_problems, refactored
  from ts_vmpnewt.adb.

Mon 24 Nov 2014 : guarded log10(0.0) in varbprec_complex_newton_steps.adb.

Sat 22 Nov 2014 : changes in varbprec_complex_newton_steps.adb for compiler
  warnings and added exception handlers (now commented out), with similar
  changes in verification_of_solutions.adb.

Fri 21 Nov 2014 : updated varbprec_complex_newton_steps with improved
  condition numbers for the evaluation problem for small residuals.
  Added to varbprec_complex_newton_steps versions for Laurent polynomial
  systems, which caused changes in verification_of_solutions.adb and
  the test program ts_vmpnewt.adb.  To verification_of_solutions, added
  procedure to work on Laurent polynomial systems, tested by ts_vmpnewt.

Thu 20 Nov 2014 : new package verification_of_solutions, tested by
  ts_vmpnewt.adb to run sequences of variable precision Newton steps.
  Added fourth tester to ts_vmpnewt.adb to develop a driver routine.

Wed 19 Nov 2014 : ts_vmpnewt.adb tests estimator of condition number based
  on random conditioned problem generated at arbitrary multiprecision.
  Added variable precision Newton steps to varbprec_complex_newton_steps,
  tested by ts_vmpnewt.adb.  The 4th part of varbprec_complex_newton_steps
  are procedures to run a sequence of Newton steps, tested by ts_vmpnewt.adb.

Tue 18 Nov 2014 : extended varbprec_complex_newton_steps with multiprecision
  procedure to estimate the loss of accuracy in a Newton step.

Mon 17 Nov 2014 : extended varbprec_complex_newton_steps with procedures
  to estimate the loss of accurate decimal places at various precisions.

Sun 16 Nov 2014 : prompts user for wanted number of accurate decimal places
  in test procedure ts_vmpnewt.adb.  To varbprec_complex_newton_steps,
  procedures were added to do a Newton step to a wanted accuracy.

Sat 15 Nov 2014 : added tests on random conditioned root problems at
  various precision levels in ts_vmpnewt.adb.

Thu 13 Nov 2014 : multprecision versions in varbprec_complex_newton_steps,
  tested by ts_vmpnewt.adb.

Wed 12 Nov 2014 : new package varbprec_complex_newton_steps, with basic
  testing in ts_vmpnewt.adb.

Thu 7 Aug 2014 : to drivers_to_deflate_singularities added drivers to
  deflate in double double and quad double precision.

Wed 6 Aug 2014 : new packages {dobl,quad}dobl_deflation_matrices and
  {dobl,quad}dobl_evaluate_deflation{_io}, tested by ts_defmat.
  New packages {dobl,quad}dobl_multiple_solutions and
  {dobl,quad}dobl_deflation_methods, tested by ts_deflate.
  Updates in drivers_to_deflate_singularities and ts_deflate.

Tue 5 Aug 2014 : new packages {dobl,quad}dobl_{derivative,jacobian}_trees,
  tested by ts_jactrees.adb.  Definition of the deflation operator for
  systems with double double and quad double coefficients in 
  {dobl,quad}dobl_deflate_singularities, and {dobl,quad}dobl_deflation_trees
  with _io, tested by ts_deftrees.  Upgraded ts_deflop to apply the
  deflation operator to systems with double double and quad double
  complex coefficients.

Mon 4 Aug 2014 : new packages {dobl,quad}dobl_numerical_rank and 
  {dobl,quad}dobl_complex_newton_steps, tested in ts_newton.

Sat 2 Aug 2014 : added Standard_Newton_Step to standard_root_refiners for
  consistency with root refiners at other precision levels.

Mon 28 Jul 2014 : extended multprec_root_refiners with a procedure to compute
  one Newton step on a Laurent polynomial system.

Fri 20 Jun 2014 : upgraded standard_root_refiners.adb with an improved
  cluster detection and multiplicity calculation.

Thu 19 Jun 2014 : new version of is_clustered in standard_root_refiners.adb.

Wed 18 Jun 2014 : added extra flag "merge" to standard_root_refiners.adb
  to avoid merging clusters when no multiplicity was raised.

Tue 17 Jun 2014 : messages in standard_root_refiners.adb to find out
  an inefficiency in case the deflate flag is turned on.

Fri 13 Jun 2014 : updated standard_deflation_methods.adb 
  and standard_deflate_singularities.adb for changed QRLS.
  Formatting changes in standard_root_refiners.adb.

Wed 11 Jun 2014 : initialization of nbdef in standard_root_refiners.adb
  for when underflow is handled gracefully in deflation.

Tue 26 Nov 2013 : updated multprec_root_refiners with one Newton step.

Thu 27 Jun 2013 : updated drivers_to_dd_qd_root_refiners.adb for warning.

Wed 26 Jun 2013 : updated root_refining_parameters for use in mainvali.adb.

Thu 20 Jun 2013 : updated multprec_complex_newton_steps.adb because of
  compiler warnings.

Mon 10 - Tue 11 Jun 2013 : almost all files changed because of the new
  natural32 and integer32 data types.

Tue 14 May 2013 : added new interfaces to the double double and quad double
  root refiners in {dobldobl,quaddobl}_root_refiners.

Wed 8 May 2013 : new package root_refining_parameters and exported members
  of standard_root_refiners for use in the multitasking version.

Thu 25 Apr 2013 : some edits in standard_root_refiners.adb.

Sun 10 Feb 2013 : some editing in ts_deflate.adb, added silent driver
  to drivers_to_deflate_singularities and standard_deflate_singularities.

Tue 1 Jan 2013 : fixed ts_defmat.adb, because it no longer compiled.

Sun 30 Dec 2012 : ts_deflate.adb, ts_rootrefi.adb no longer compiled, fixed.

Thu 9 Jun 2011 : changed standard_root_refiners to gracefully handle an
  exception when the system is too large to deflate.
  Commented out stuff in exception handler of monomial_hashing.adb.

Wed 1 Jun 2011 : changed multprec_evalate_deflation_io.adb,
  {standard,multprec}_numerical_rank.adb, standard_deflate_singularities.adb,
  standard_multiple_solutions.add, multprec_jacobian_trees.adb,
  standard_nullity_polynomials.adb and dobldobl_root_refiners.ads for warnings.

Sun 29 May 2011 : changed {standard,multprec}_root_refiners.adb and
  standard_multiplicity_structure.adb for warnings.

Fri 20 May 2011 : for warnings, changed ts_deftrees and {standard,
  multprec}_derivative_trees.adb, also modified {standard,multprec}_
  multiple_deflation.adb, multprec_nullity_polynomials.adb, and
  multprec_nullity_matrices.adb.

Mon 27 Sep 2010 : updated drivers_to_dd_qd_root_refiners.adb to use
  multiprecision convertors with proper working precision set.

Mon 6 Sep 2010 : adjustment in MENU of drivers_to_dd_qd_root_refiners.adb.

Sun 6 Jun 2010 : extended {dobldobl,quaddobl}_root_refiners.ad* for
  ts_mtddref and ts_mtqdref.

Fri 28 May 2010 : {dobldobl,quaddobl}_root_refiners are tested by
  ts_ddnewt and ts_qdnewt.

Wed 28 Oct 2009 : added "sharpeners" to standard_root_refiners
  to deal with overdetermined polynomial systems.
  Added also Gauss-Newton and sharpeners to multprec_root_refiners.

Sun 11 Oct 2009 : experimented with toggling off root accounting in
  multprec_root_refiners.adb, but to no avail.

Fri 9 Oct 2009 : update {standard,multprec}_root_refiners.adb with new
  Write_Tables that omit the distance tables.  Solutions of Laurent systems
  can now be refined with standard_root_refiners.

Thu 8 Oct 2009 : formatting in multprec_root_refiners.adb and removal
  of Distances_Tables, also in standard_root_refiners.adb.

Wed 30 Sep 2009 : added storage threshold to standard_deflation_matrices,
  removed tracing output from standard_root_refiners.adb, 
  standard_deflation_methods.adb, standard_evaluate_deflation.adb,
  and standard_complex_newton_steps.adb.

Tue 29 Sep 2009 : changes in standard_root_refiners.adb to fix bug with
  deflation, also changes in standard_deflation_methods.adb and
  standard_complex_newton_steps.adb to track the infinite loop...

Mon 21 Sep 2009 : added exception handler to monomial_hashing.adb
  to track a bug.  Introduced 64-bit arithmetic to monomial_hashing,
  changing {standard,multprec}_deflation_matrices.a*,
  {standard,multprec}_evaluate_deflation.a*,
  {standard,multprec}_deflation_methods.a*, and standard_root_refiners.adb.

Fri 11 Sep 2009 : added exception handlers to standard_root_refiners.adb
  because of crash with unoptimized phc -0 -b cyclic7 /tmp/out.

Fri 19 Jun 2009 : changed standard_multiple_deflation.adb because of bug
  when recompiling ts_muldef.adb.

Mon 27 Oct 2008 : created ts_deflop.adb to make systems to seek singularities.

Thu 14 Aug 2008 : fixed bug in standard_deflation_methods.adb, discovered
  while looking for infinite loop with random trinomials.

Fri 1 Aug 2008 : changed standard_root_refiners.adb to handle underflow
  gracefully also in the deflate routines, like in Newton.
  The crash occurred when dealing with monomial equations.

Wed 23 Apr 2008 : to fix a crash in deflation, standard_root_refiners.adb,
  handle_underflow_gracefully.adb, and standard_deflation_methods.a*
  all changed.  Crash followed wrong multiplier computations.

Mon 21 Jan 2008 : underflow causes problems in standard_root_refiners.adb,
  commented out the ineffective exception handlers.

Sun 20 Jan 2008 : created package handle_underflow_gracefully to deal
  with underflow in root refiners, modified standard_root_refiners.adb.
  Note that underflow only occurs when -gnatp is not an option.

Thu 19 Jan 2008 : when constraint_error happens it might be underflow,
  therefore: changed standard_root_refiners.adb to check residual in
  the exception handlers.

Mon 7 Jan 2008 : changed standard_deflation_methods.adb and
  standard_root_refiners.adb, to find the cause of a crash originating
  in standard_complex_newton_steps.adb.

Thu 3 Jan 2008 : warnings in GNAT GPL 2006 caused changes in
  standard_root_refines.adb, standard_complex_newton_steps.adb,
  standard_deflation_methods.a*, and standard_deflate_singularities.adb,
  standard_deflation_matrices.adb, standard_evaluate_deflation_io.adb.

Wed 2 Jan 2008 : changed standard_jacobian_trees.adb
  standard_evaluate_deflation.adb, and drivers_to_deflate_singularities.a*,
  for warnings in GNAT GPL 2006.

Wed 25 Dec 2007 : fixed memory leak with clearing of Jacobi matrices,
  standard_jacobian_trees.adb and standard_root_refiners.adb changed.

Sat 8 Dec 2007 : clearing the evaluation tree of Jacobian matrices
  in standard_root_refiners.adb did not work... oops: could be source
  of a huge memory leak and many problems...

Fri 13 Jul 2007 : if the multiplicity field of a solution on input is > 1,
  then root accounting standard_root_refiners.adb will not change it.

Tue 26 Jun 2007 : initialization of nbdef in standard_root_refiners.adb
  so it makes for a more accurate accounting.

Fri 22 Jun 2007 : another fix to standard_root_refiners.adb.

Thu 21 Jun 2007 : backup before deflation in standard_root_refiners.adb
  to be able to restore in case deflation fails.

Fri 1 Jun 2007 : modifications to standard_root_refiners.adb for correct
  root accounting when deflation is applied.

Sat 26 May 2007 : one Newton iteration after the deflation in
  standard_root_refiners.adb shows the condition number.

Mon 19 May 2007 : updated drivers_to_deflate_singularities.adb so that
  Algorithm_Deflation_and_Clustering is now called (better #6 in phc -v).
  Modified standard_root_refiners.adb.

Fri 18 May 2007 : added clear in {standard,multprec}_jacobian_trees for
  Jacobian remember tables, used in {standard,multprec}_evaluate_deflation.
  Updated {standard,multprec}_deflation_methods.adb and ts_deflate.adb
  Created new package standard_multiple_solutions.

Thu 17 May 2007 : continued modification of standard_deflation_methods.a*,
  ts_deflate.adb now works fine with automatic algorithmic deflation.
  Added some memory management to standard_evaluate_deflation.a*...

Wed 16 May 2007 : updated standard_deflation_methods.a* with routines for
  automatic algorithmic deflation, tested by ts_deflate.adb.

Sat 12 May 2007 : prepared standard_root_refiners.adb for deflation.

Wed 28 Mar 2007 : ts_realnewt.adb does one Newton step fine for systems
  with standard floating-point coefficients.

Tue 27 Mar 2007 : ts_realnewt.adb develops Newton for real systems.

Sun 4 Feb 2007 : because of change in naming of "newton_steps", 
  changed drivers_to_deflate_singularities.adb and
  {standard,multprec}_deflation_methods.adb.

Sat 3 Feb 2007 : inserted "complex" in {standard,multprec}_newton_steps to
  create {standard,multprec}_floating_newton_steps, tested by ts_newton.adb.

Tue 12 Dec 2006 : modifications to *aitken* and ts_newton.adb.

Mon 11 Dec 2006 : removed "classify" from ts_newton.adb to make room for
  Aitken extrapolation: "standard_aitken_extrpolation" is new package.

Wed 14 Jun 2006 : because of warnings on AIX, changed standard_ and
  multprec_evaluate_deflation.adb.

Wed 3 May 2006 : created {standard,multprec}_solution_diagnostics,
  relieving {standard,multprec}_root_refiners.adb from auxiliary code.

Mon 6 Feb 2006 : because of renamings in standard_condition_tables,
  {standard,multprec}_root_refiners.adb changed.

Mon 26 Dec 2005 : created {standard,multprec}_probe_kernel to determine
  minimal order for multiple_deflation.  Changed *multiple_deflation.a*
  and ts_muldef.adb.

Thu 22 Dec 2005 : inserted exception handlers in standard_newton_steps.adb
  and standard_deflation_methods.adb; updated standard_multiple_deflation
  and ts_muldef.adb.

Wed 21 Dec 2005 : created multprec_nullity* and *multiple_deflation*,
  all tested by ts_muldef.adb. 

Tue 20 Dec 2005 : standard_nullity_matrices and standard_nullity_polynomials
  are new packages, originating from standard_multiplicity_structure.

Mon 19 Dec 2005 : updated ts_multip.adb to use get from the new package
  standard_system_and_solutions_io; new ts_muldef for higher-order deflation.

Fri 16 Dec 2005 : fixed output in standard_multiplicity_structure.adb.

Sun 11 Dec 2005 : added diagnostics to standard_deflation_matrices.adb
  and standard_evaluate_deflation.adb to start working on A(4);
  patched bugs in standard_deflation_matrices.adb to avoid crashes.

Sun 13 Nov 2005 : changed standard_deflate_singularities.a* for corank 1,
  also modified standard_deflation_methods.a*.

Sun 29 Oct 2005 : changed standard_deflation_methods.adb for corank one.

Thu 27 Oct 2005 : for corank one, changed standard_deflate_singularities.*
  and standard_deflation_methods.adb.

Sat 6 Aug 2005 : added a special corank one deflation case in
  {standard,multprec}_deflate_singularities and *_deflation_methods.adb.

Mon 11 Jul 2005 : changed standard_deflation_methods for one solution.

Sat 9 Jul 2005 : fixed bug in standard_deflation_methods.adb
  and multprec_deflation_methods.adb.

Sun 3 Jul 2005 : added driver to standard_multiplicity_structure,
  tested in ts_multip.adb.

Fri 1 Jul 2005 : interactive algorithmic deflation works up to k = 3,
  changed *evaluate_deflation.a* and *deflation_methods.a*.

Thu 30 Jun 2005 : created {standard,multprec}_deflation_methods with the
  code from drivers_to_deflate_singularities.adb, changed ts_deflate.adb.

Mon 27 Jun 2005 : added multprec_ to _derivative_trees, _jacobian_trees
  (see ts_jactrees), to _deflation_matrices, _evaluate_deflation (+i/o),
  _query_matrices, tested by ts_defmat.adb.

Sun 26 Jun 2005 : "Two_Right_Multiply*" is out of standard_deflation_matrices,
  A(3) works! cleaned up standard_evaluation_matrices, autotest in ts_defmat.

Fri 24 Jun 2005 : patched standard_deflation_matrices so A(3) works
  for all two dimensional systems

Sun 19 Jun 2005 : prepared standard_deflation_matrices for higher order
  right multiplications, changed standard_evaluate_deflation.adb too.

Sat 18 Jun 2005 : standard_deflation_matrices.adb works for A(3), for all
  second degrees systems, changed standard_evaluate_deflation.adb a little.

Fri 10 Jun 2005 : simplified standard_deflation_matrices, fixed bug
  in ts_jactrees.adb.

Mon 6 Jun 2005 : messed with Right_Multiply_Deflation and added one
  routine to standard_query_matrices.

Sun 5 Jun 2005 : fixed Right_Multiply_Jacobian with B-matrix and changed
  standard_deflation_matrices

Thu 2 Jun 2005 : bug in Number_of_Columns changed ts_defmat.adb and
  standard_deflation_matrices.adb.

Wed 1 Jun 2005 : bugs changed standard_deflation_matrices and ts_defmat.adb.

Mon 30 May 2005 : added strip_multipliers to standard_deflate_singularities
  and multprec_deflate_singularities, changed ts_deflate.adb, ts_multip.adb.

Sun 29 May 2005 : fixed indexing bug in standard_deflation_matrices.adb.

Fri 27 May 2005 : trying "Right_Multiply" in standard_deflation_matrices
  and standard_evaluate_deflation.adb.

Wed 25 May 2005 : changed standard_deflation_matrices.adb: A(2) is okay.

Tue 24 May 2005 : created "Right_Multiply" in standard_deflation_matrices.adb,
  also changed .ads and standard_evaluate_deflation.adb.

Sat 21 May 2005 : work on structural flaw in standard_deflation_matrices.adb
  reduces number of errors in A(2).

Fri 20 May 2005 : fixed one more bug and discovered structural flaw in
  standard_deflation_matrices.adb.

Thu 19 May 2005 : changed standard_evaluation_deflation.ads, .adb, and
  standard_deflation_matrices.adb to discover a new bug.

Wed 18 May 2005 : fixed one bug in standard_evaluate_deflation.adb.

Wed 11 May 2005 : package standard_multiplicity_structure tested by ts_multip.
  Moved numerical_rank out of standard_newton_steps into a new package,
  standard_numerical_rank, similarly for multiprecision version;
  fixed compilation error in ts_newton.adb.

Tue 10 May 2005 : created standard_query_matrices, for sharing between
  ts_defmat.adb and ts_multip.adb.

Mon 25 Apr 2005 : stored assignments in standard_deflation_matrices,
  changed standard_jacobian_trees, deflation_matrices(+io) and ts_defmat.

Wed 20 Apr 2005 : added "monkeys" or monomial keys to ts_defmat.adb and
  standard_evaluate_deflation.ads.

Tue 19 Apr 2005 : added "Number_of_Columns" to count dimensions properly
  to the standard_evaluate_deflation.ads, also ts_defmat.adb changed.

Sat 16 Apr 2005 : updated standard_evaluate_deflation.adb and ts_defmat.adb.

Thu 14 Apr 2005 : eval in standard_evaluate_deflation.adb shows numbers;
  also changed ts_defmat.adb.

Sun 10 Apr 2005 : put evaluation of symbolic deflation matrix in ts_defmat.

Sat 9 Apr 2005 : created standard_evaluate_deflation_io and developed
  the eval in standard_evaluate_deflation, tested by ts_defmat.adb.

Fri 8 Apr 2005 : minor changes in ts_defmat.adb

Thu 7 Apr 2005 : added dimension to enumeration of tree in ts_defmat.adb.

Tue 5 Apr 2005 : removed bug from standard_evaluate_deflation.adb.

Wed 23 Feb 2005 : changed *root_refiners.adb to give reciprocal negative
  field with clustered solutions.

Sun 20 Feb 2005 : changed *root_refiners.adb to report clustered solutions
  with a negative multiplicity field.

Sun 9 Jan 2005 : Eval_Tree from ts_defmat in standard_evaluate_deflation,
  data structure is as efficient as enumeration.

Tue 4 Jan 2005 : introduced "Eval" in standard_evaluate_deflation,
  adjusted ts_defmat

Mon 3 Jan 2005 : created the package standard_evaluate_deflation,
  to be tested by ts_defmat

Sat 1 Jan 2005 : updated standard_jacobian_trees with Eval_Node.

Fri 31 Dec 2004 : renamed ts_dertrees into ts_jactrees and updated.

Tue 28 Dec 2004 : create ts_defmat.adb to work with deflation matrices.

Fri 27 Aug 2004 : fixed bug of 2nd deflation in ts_straight.adb.

Tue 24 Aug 2004 : created ts_straight.adb to experiment with straight-line
  version of the evaluation and differentiation of deflated systems

Tue 10 Aug 2004 : added timer in drivers_to_deflate_singularities.adb and
  created standard_jacobian_trees, tested by ts_dertrees.

Mon 9 Aug 2004 : create standard_derivative_trees, tested by ts_dertrees,
  which replaces ts_allder, also renamed ts_dtrees into ts_deftrees.
