Fri 18 Jun 2021 : extended main_pade_trackers, to prompt the user for the
  Laurent series option to run Newton's method at a series.
  Updated the documentation in main_pade_trackers.ads for the extended
  precision levels: triple, penta, octo, and deca double precision.

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

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

Tue 15 Dec 2020 : in {trip,pent,octo,deca}dobl_newton_matrix_series.adb,
  applied the echelon solvers for linear systems.

Thu 10 Dec 2020 : to fabry_on_homotopy_helpers.adb, *_fabry_on_homotopy.adb,
  for * in {standard, *dobl}, applied the procedures in numbers_io,
  to make the prompting of input parameters more robust.

Wed 9 Dec 2020 : added a procedure to fabry_homotopy_on_helpers and
  rearranged code in standard_fabry_on_homotopy to ask for all input
  of the user before the time consuming creation of the homotopy.
  Updated {dobl,trip,quad}dobl_fabry_on_homotopy similarly.
  Updated {pent,octo,deca}dobl_fabry_on_homotopy similarly.

Tue 8 Dec 2020 : extended *dobl_fabry_on_homotopy.adb with multitasked runs.
  Updated standard_fabry_on_homotopy.ads and its body in the .adb file.
  Added a test to newton_fabry_on_homotopy to generate a test homotopy,
  which can be called from ts_fabryhom.
  Updated all *_fabry_on_homotopy packages to pass the number of tasks
  and updated main_pade_trackers.

Mon 7 Dec 2020 : fixed *_newton_convolution_steps.adb so the output is
  properly written to file in verbose mode.  Extended to write to output
  file the procedures in decadobl_fabry_on_homotopy.  New package
  fabry_on_homotopy_helpers, used in all *_fabry_on_homotopy.adb files.
  Extended all *_fabry_on_homotopy packages to procedures that write to file.

Sat 5 Dec 2020 : extended main_pade_trackers.adb to run Newton's method
  starting at a constant term in triple double precision, using the new
  package tripdobl_newton_matrix_series, the extended series_and_solutions,
  power_series_methods, and run_power_series_methods.
  New {pent,octo,deca}dobl_newton_matrix_series, with extensions in
  series_and_solutions, power_series_methods, run_power_series_methods,
  and main_pade_trackers to penta, octo, and deca double precision.

Tue 1 Dec 2020 : eliminated the procedure mainseries, as it only calls the
  Main of the main_pade_trackers.  New package test_series_solutions with
  code taken from ts_sersol.adb.

Fri 23 Oct 2020 : new packages {tripdobl,pentdobl,octodobl,decadobl}_
  rational_approximations, test_rational_approximations, called by ts_ratapp.

Tue 29 Sep 2020 : new package run_power_series_methods with code taken
  from mainseries.adb.  Moved the code from the test procedure ts_serpade
  into the packages test_{standard,dobldobl,quaddobl}_pade_approximants.
  Moved code from mainseries.adb to main_pade_trackers.

Fri 25 Sep 2020 : new {standard,dobldobl,tripdobl,quaddobl}_convolution_steps,
  with code taken from newton_power_convolutions (which will be removed),
  and test_{standard,dobldobl,tripdobl,quaddobl}_newtconvsteps, with code
  from ts_sernewcnv.  The removal of newton_power_convolutions leads to
  updates in {standard,dobldobl,quaddobl}_predictor_convolutions.adb
  and {dobl,trip,quad}dobl_fabry_on_homotopy.  Extended ts_sernewcnv
  to penta, octo, and deca double precision with the new packages
  {pent,octo,deca}dobl_newton_convolution_steps and
  test_{pent,octo,deca}dobl_newtconvsteps.
  To series_and_homotopies, series_path_trackers, test_series_predictors,
  homotopy_series_readers added operations with penta, octo, and deca doubles.
  New packages {pent,octo,deca}dobl_homotopy_convolutions_io and
  {pent,octo,deca}dobl_fabry_on_homotopy, called in ts_fabryhom.

Wed 23 Sep 2020 : bug fix in mainseries.adb so menus options 1 and 2
  of phc -u are again accessible for proper choices of precision levels.
  New packages {standard,dobldobl,quaddobl}_fabry_on_homotopy with code
  from ts_fabryhom.  For triple double precision, extended 
  newton_power_convolutions, series_and_homotopies, series_path_trackers,
  homotopy_series_readers, test_series_predictors, with new packages
  tripdobl_homotopy_convolutions_io and tripdobl_fabry_on_homotopy,
  called by ts_fabryhom.

Tue 22 Sep 2020 : because of split of newton_convolutions package,
  updated {standard,dobldobl,quaddobl}_predictor_convolutions.adb,
  newton_power_convolutions.adb, staggered_newton_convolutions.adb,
  ts_sernewcnv.adb, and ts_fabryhom.adb.

Wed 12 Aug 2020 : extended ts_fabryhom with test procedures in double double
  and quad double precision.

Tue 11 Aug 2020 : new test procedure ts_fabryhom on the application of
  Fabry's theorem to a homotopy defined as a coefficient convolution system.
  Added the convergence radius estimates to ts_fabryhom.

Mon 10 Aug 2020 : the "n" as the parameter in the Run procedures of
  wrapped_pade_trackers is changed into "idxpar", as this better indicates
  that it is the index of the continuation parameter.

Fri 7 Aug 2020 : added mhom := 0 for the natural parameter homotopies in
  {standard,dobldobl,quaddobl}_homotopy_convolutions_io.adb.
  Corrected call to the Run in ts_wrappade.adb to p'last+1 = #variables.
  Extended wrapped_pade_trackers with procedures on lists of solutions,
  with more tests in ts_wrappade.  Fixed a test in ts_wrappade and
  simplified code for the run on one pathin wrapped_pade_trackers.adb.

Thu 6 Aug 2020 : new package wrapped_pade_trackers, tested by ts_wrappade.

Thu 30 Jul 2020 : in track_path_convolutions.adb, set the default to 
  coefficient convolution circuits.

Thu 23 Jul 2020 : applied the inlined singular value computation in
  standard_predictor_convolutions.

Thu 16 Jul 2020 : minor improvement in the menu for the settings of the
  parameters in homotopy_continuation_parameters_io.adb.

Tue 14 Jul 2020 : to staggered_newton_convolutions, added indexed LU Newton
  procedures, tested by ts_sernewcnv.  In standard_predictor_convolutions.adb,
  replaced the Inlined_LU_Newton_Steps by Indexed_LU_Newton_Steps.
  Added verbose level to the main procedures in track_path_convolutions,
  predictor_corrector_trackers, predictor_corrector_loops, and
  standard_predictor_convolutions.

Sun 12 Jul 2020 : updated standard_predictor_convolutions.adb so that for
  lower degree polynomials the Hessians are computed only once.

Sat 11 Jul 2020 : to standard_predictor_convolutions, added procedure to
  compute the singular values of Hessians only once for low degree polynomials.

Thu 9 Jul 2020 : bug fix in predictor_corrector_loops.adb, added the case
  for when the predictor is of LU type.

Wed 8 Jul 2020 : to staggered_newton_convolutions, added inlined procedures,
  added tests to ts_sernewcnv.  In predictor_corrector_trackers.adb,
  changed the predictor type to LU for coefficient convolutions,
  in predictor_corrector_loops.adb, added the call to the LU_Predictor
  procedure in case the predictor is of type LU, and changed the
  LU_Newton_Steps to staggered ones in standard_predictor_convolutions,
  for homotopies given as coefficient convolution systems.
  To standard_predictor_convolutions, added the 8 parameters for the
  staggered inlined LU Newton steps to the LU_Predictor type and
  applied the inlined LU in the Newton_Fabry procedures.

Fri 3 Jul 2020 : updated predictor_corrector_trackers for the new
  package standard_floating_vecvecvecs, updated ts_pcscnv.

Thu 2 Jul 2020 : in predictor_corrector_{loops,trackers}.adb replaced
  the Newton steps on coefficient circuits by inlined versions.

Tue 30 Jun 2020 : updated track_path_convolutions.adb to reflect that
  homogeneous coordinates are not yet supported for coefficient circuits.
  Adjusted mainseries to pass the number of tasks at the command line.

Mon 29 Jun 2020 : in track_path_convolutions.adb, started wall clock
  timer after the interactions with the user, just before the track.

Sun 28 Jun 2020 : modified homotopy_series_readers setting tpow to 1,
  updated test_series_predictors.adb and ts_serpade.adb.
  Added extra procedures to track_path_convolutions, for use in the
  multitasked versions.

Sat 27 Jun 2020 : updated newton_power_convolutions.adb, for the new
  package newton_coefficient_convolutions.  Added new package
  staggered_newton_convolutions, tested by ts_sernewconv.
  In predictor_corrector_loops.adb, passed the verbose flag correctly
  when applied on coefficient convolutions circuits.
  In standard_predictor_convolutions.adb, set newton's method to the
  staggered degree versions.  In staggered_newton_convolutions.adb,
  for homotopies that are quadratic in t, check convergence only after
  the second degree -- this is a patch!

Thu 25 Jun 2020 : improved step_by_step track in ts_pcscnv.
  Reset all higher order coefficients of the series when assigning the
  lead coefficient in {standard,dobldobl,quaddobl}_predictor_convolutions.
  Called the Set_Lead_Coefficients in the predictor_corrector_loops.adb,
  when coefficient convolution circuits are applied.

Mon 22 Jun 2020 : updated the shift in predictor_corrector_trackers, to
  shift with the accumulated t value, instead of accumulating the steps,
  updated ts_pcscnv for change procedure prototypes.

Sat 20 Jun 2020 : added extra procedures to predictor_corrector_trackers,
  modified ts_pcscnv.  To predictor_corrector_trackers.adb, added assignment
  of solution at the end of the path.  To track_path_convolutions, added
  a procedure to track all paths, tested by ts_pcscnv.

Fri 19 Jun 2020 : updates in predictor_corrector_loops.adb, added procedures
  to track one path in predictor_corrector_trackers, tested by ts_pcscnv.
  Tracking one path with the new coefficient circuits seems to work now.

Wed 17 Jun 2020 : new package predictor_corrector_trackers, with code from
  predictor_corrector_loops.  This changed track_path_convolutions.adb and
  ts_pcscnv.  Fixed ts_corcnv.adb.  To predictor_corrector_loops, added
  procedures for coefficient circuits, with EvalCffRad procedure added to
  standard_predictor_convolutions, tested by ts_pcscnv.

Tue 16 Jun 2020 : fixed bug in standard_predictor_convolutions, in the eta
  computation on coefficient circuits, added test to ts_padepcnv.

Mon 15 Jun 2020 : defined Predictor_Feedback procedures on coefficient
  convolution circuits in standard_predictor_convolutions.
  Added the main predictor procedures on coefficient convolution circuits
  to standard_predictor_convolutions.

Sat 13 Jun 2020 : in standard_predictor_convolutions, added the computation
  of the Hesse-Pade step on coefficient circuits.

Wed 3 Jun 2020 : in *_predictor_convolutions.adb, replaced the 11 by 0
  in the calls to SVD.

Sun 10 May 2020 : added Newton_Fabry procedures on coefficient convolutions,
  to the package standard_predictor_convolutions.

Sat 9 May 2020 : added procedures to newton_power_convolutions, to apply
  the faster coefficient convolution circuits when running Newton's method.
  Tested new Newton procedures in ts_sernewcnv.

Fri 1 May 2020 : updated track_path_convolutions so it writes the seed
  number at the end of a run for reproducibility.

Thu 30 Apr 2020 : in corrector_convolutions.adb, applied extra Newton steps,
  added one extra corrector step value in the predictor_corrector_loops.adb.
  At the end of each path trackers, in predictor_corrector_loops.adb, also
  applied the extra corrector steps.

Mon 27 Apr 2020 : updated mainseries.adb with the question for multitasking,
  so the multitasked Newton-Fabry-Pade-Hesse tracker can be called in phc -u.

Sat 25 Apr 2020 : added procedures to hyperplane_convolution_scaling
  for m-homogenization, applied in predictor_corrector_loops.adb, 
  and tested in ts_pcscnv.  In ts_pcscnv, transformed the solutions into
  affine coordinates after a multi-homogeneous run.
  New package track_path_convolutions, with code from ts_pcscnv.
  Updated mainseries.adb to call the main procedures in of track_path_
  convolutions so phc -u has the faster Newton-Fabry-Pade-Hesse tracker.

Fri 24 Apr 2020 : added tests for ts_scalecnv for m-homogenization.
  Added the multi-homogenization parameters from ts_pcscnv to the
  procedures in predictor_corrector_loops.

Wed 22 Apr 2020 : fixed the adjustments of the coefficient vector for
  multi-homogeneous coordinates in hyperplane_convolution_scaling,
  tested by ts_scalecnv.

Tue 21 Apr 2020 : in predictor_corrector_loops.adb, changed the 1 into
  pars.corsteps in the final corrector steps, after running a path.
  Added affine transformations on the solutions to ts_pcscnv.

Sun 19 Apr 2020 : in corrector_convolutions, added the max |dx| into the
  stop criterion of the LU Newton steps, changed predictor_corrector_loop.adb.

Sat 18 Apr 2020 : added a parameter to the correctors for some extra steps,
  updates in corrector_convolutions changed predictor_corrector_loops.adb.

Thu 16 Apr 2020 : started the development of multi-homogeneous scaling,
  with updates in hyperplane_convolution_scaling and ts_scalecnv.

Wed 15 Apr 2020 : new package hyperplane_convolution_scaling with code
  from ts_scalecnv.  Made additions to hyperplane_convolution_scaling,
  applied scaling in predictor_corrector_loops and tested in the 
  step-by-step trackers in ts_pcscnv.adb.  Adjusted the path trackers
  in predictor_corrector_loops for scaling in homogeneous coordinates,
  tested in ts_pcscnv.

Tue 14 Apr 2020 : added scaling of the solutions and adjusting of the
  coefficients of the last equation in the circuit to ts_scalecnv.

Mon 13 Apr 2020 : extended series_path_trackers with procedures that take
  in the gamma constant directly (instead of via pars.gamma) and added on
  procedure to standard_homotopy_convolutions_io for the new ts_scalecnv.
  Extended {dobldobl,quaddobl}_homotopy_convolutions_io and added tests
  to ts_scalecnv.

Sat 11 Apr 2020 : modified ts_pcscnv so it also writes start system and
  start solution to the output file and predictor_corrector_loops.adb,
  so the end solution at each path is written before the path statistics.
  Adjusted ts_pcscnv.adb for a square natural-parameter homotopy.

Fri 10 Apr 2020 : added computation of the average ratio of step sizes
  and timers to predictor_corrector_loops, updated ts_pcscnv.
  Added computation of smallest and largest step sizes and number of steps
  to predictor_corrector_loops, updated ts_pcscnv.
  Fixed setting of the number of corrector iterations in the procedures
  of corrector_convolutions.adb.  Added counters to predictor_corrector_loops
  for the corrector iterations, updated ts_pcscnv.

Thu 9 Apr 2020 : extended corrector_convolutions with LU Newton methods that
  estimate inverse condition numbers, called in predictor_corrector_loops.adb.
  Added writing of some counters to file in predictor_corrector_loops,
  with minor addition to ts_pcscnv.adb.

Wed 8 Apr 2020 : added printing of target system and timers to ts_pcscnv,
  with extra procedures towards future packaging of path trackers.
  Updated procedures in predictor_corrector_loops with the mixed residual
  on output, with updated calls in ts_pcscnv.

Tue 7 Apr 2020 : fixed the application of the corrector by storing the
  leading coefficients before evaluation of the step size in the
  procedures of predictor_corrector_loops.adb.

Mon 6 Apr 2020 : updated predictor_corrector_loops.adb, setting the number
  of the iterations relative to the degree of Pade approximants.

Sun 5 Apr 2020 : updated {standard,dobldobl,quaddobl}_predictor_convolutions,
  so the SVD procedures are called with work space vectors.

Sat 4 Apr 2020 : fixed bug in predictor_corrector_loops: must use the
  accumulated value for t instead of the step in Step_Coefficient.
  Updated homotopy_continuation_parameters_io.adb to allow for a zero
  value for the number of corrector steps.  In predictor_corrector_loops,
  added a test on this zero value to toggle off the corrector.

Fri 3 Apr 2020 : added procedures without output to the packages
  *predictor_convolutions, corrector_convolutions, predictor_corrector_loops,
  and ts_pcscnv.  Add printing of solution list to ts_pcscnv.

Thu 2 Apr 2020 : added array types to the predictor convolutions packages
  {standard,dobldobl,quaddobl}_predictor_convolutions.

Wed 1 Apr 2020 : added a create procedure to wrap the allocation of a
  pointer to the data for the Hessians in *predictor_convolutions,
  with updates and improvements in ts_pcscnv.  New package with code
  from ts_pcscnv, predictor_corrector_loops to track a path.
  Corrected output to file mistake in corrector_convolutions.adb.
  Added procedures to predictor_corrector_loops to track all paths,
  tested by ts_pcscnv.

Tue 31 Mar 2020 : added end value for homotopy continuation parameter t
  to *predictor_convolutions, tested by ts_padepcnv and ts_pcscnv;
  added Bounded_Update procedures to three_way_minima.
  Applied the new update of radii of constants for the computation
  of the mixed residuals in ts_pcscnv.  Extended corrector_convolutions
  with procedures to allocate, store, and restore all coefficients of
  convolution systems, tested by ts_pcscnv.

Mon 30 Mar 2020 : added minimum step size to *predictor_convolutions with
  an explicit setting of the fail, tested by ts_padepcnv and ts_pcscnv.
  Added cutting of step size to predictor-corrector loop in ts_pcscnv.

Sun 29 Mar 2020 : added store and restore procedures for the leading
  coefficients to corrector_convolutions, tested by ts_pcscnv.
  Added mixed residuals to corrector_convolutions, tested by ts_corcnv
  and ts_pcscnv.  Simplified procedures in ts_pcscnv, the sol parameter
  can be elinated because of the predictor vectors in psv.

Sat 28 Mar 2020 : new predictor_corrector_loop procedures in ts_pcscnv.
  Added application of corrector in ts_pcscnv.

Fri 27 Mar 2020 : moved step_coefficients functions and procedures from
  the ts_corcnv test procedure into the corrector_convolutions package.
  New test procedure ts_pcscnv for one predictor-corrector-shift step.

Thu 26 Mar 2020 : basic version of one Newton step in ts_corcnv.
  New package corrector_convolutions with LU correctors, with code from
  the text procedure ts_corcnv.  Added procedures to ts_corcnv to evaluate
  the coefficients of the homotopy at a positive step size.

Mon 23 Mar 2020 : new {standard,dobldobl_quaddobl}_homotopy_convolutions_io,
  packages for prompting homotopies represented by convolution circuits,
  tested by ts_padepcnv and ts_hesspcnv.  Skeleton for a new test procedure
  ts_corcnv to test corrector convolutions.

Sun 22 Mar 2020 : new packages test_predictor_convolutions, with code
  taken from ts_padepcnv and ts_hesspcnv.  Updated 14 other test procedures
  ts_jacrabin, ts_serhom, ts_sernew, ts_sernewcnv, ts_sersol, ts_serpade,
  ts_serpath, ts_serpred, ts_predstep, ts_hesscrit, ts_hesspred, ts_ratapp,
  ts_padepred, ts_nxtpadsol to use the prompt for the precision.

Sat 21 Mar 2020 : moved predictor procedures from ts_padepcnv to the
  {standard,dobldobl,quaddobl}_predictor_convolutions packages.
  Added array types to all predictor_convolutions packages.
  New procedure in ts_padepcnv to check all start solutions.

Fri 20 Mar 2020 : used discriminant records for a new predictor type in
  {standard,dobldobl,quaddobl}_predictor_convolutions, tested by ts_padepcnv.
  Added frequency counters to ts_padepcnv.  Add type Predictor_Vectors to
  {standard,dobldobl,quaddobl}_predictor_convolutions, tested by ts_padepcnv.

Thu 19 Mar 2020 : eliminated a superfluous vector variable in the Prediction
  procedures of ts_padepcnv, added a prompt for checking all start solutions.

Wed 18 Mar 2020 : new package three_way_minima, tested by ts_padepcnv,
  moved output procedures from ts_padepcnv to the predictor convolutions,
  to {standard,dobldobl,quaddobl}_predictor_convolutions, and added file
  type parameters to write output to file.  New Hesse_Pade procedures in
  *_predictor_convolutions, with code from ts_padepcnv.

Tue 17 Mar 2020 : added reporting procedure to ts_padepcnv.
  Added verbose option to the predictor test procedures in ts_padepcnv.

Mon 16 Mar 2020 : moved functions for the mixed residual computations from
  ts_padepcnv to {standard,dobldobl,quaddobl}_mixed_residuals.
  Moved the predictor feedback loop from ts_padepcnv to the packages
  {standard,dobldobl,quaddobl}_predictor_convolutions.

Sun 15 Mar 2020 : added computation of mixed residuals to ts_padepcnv.

Fri 13 Mar 2020 : added functions to series_and_predictors to evaluate
  a formula for the distance in double double and quad double precision.
  Added functions to ts_padepcnv to compute the minimum step size.

Thu 12 Mar 2020 : extended and improved ts_padepcnv.  In the specifications
  of the Predictor Convolution packages, documented the requirement on the
  degree of the power series, relative to the degrees of the approximants.
  Small update in ts_padepred.adb for the verbose flag.
  Applied the offset index in *_predictor_convolutions.adb, tested by
  ts_padepcnv, with also some modifications in ts_padepred.

Wed 11 Mar 2020 : moved the distance functions from ts_padepcnv into
  the *_predictor_convolution packages.  Computed the SVD for the Jacobian
  in the LU predictor in ts_padepcnv and applied the pole step.
  Added functions and procedures to homotopy_pade_approximants to compute
  the solution error estimates directly on coefficients vectors.

Tue 10 Mar 2020 : added comparison checks to ts_hesspcnv.
  Extended *_predictor_convolutions with the singular values of Hessians,
  tested by ts_padepcnv.  Added the distance computation to ts_padepcnv.

Mon 9 Mar 2020 : added SVD predictor types to the packages on convolution
  homotopies: *_predictor_convolutions, tested by ts_padepcnv.
  Add Predict procedures to *_predictor_convolutions, tested by ts_padepcnv.
  Started new test procedure ts_hesspcnv to apply the Hessian criterion
  on homotopies represented by convolutions.

Sun 8 Mar 2020 : better control of output in ts_padepcnv.
  Added SVD to ts_padepcnv.

Sat 7 Mar 2020 : new package standard_predictor_convolutions, tested
  by ts_padepcnv.  Added {dobldobl,quaddobl}_predictor_convolutions,
  with tests in ts_padepcnv.

Fri 6 Mar 2020 : updates to the ts_padepcnv to develop a predictor
  for homotopies given by convolution circuits.

Thu 5 Mar 2020 : updated homotopy_series_readers.adb to use the get
  procedures of the new package artificial_parameter_homotopy_io.

Wed 4 Mar 2020 : modifications to ts_padepred.adb for compiler warnings.
  New test procedures ts_padepcnv to develop the Pade predictor based
  on convolution circuits.

Sun 23 Feb 2020 : fixed dimensions for the SVD in ts_sernewcnv.adb.

Sat 22 Feb 2020 : fixed stop criterion in newton_power_convolutions.adb.

Fri 21 Feb 2020 : improved ts_sernewcnv for overdetermined problems.
  Fixed the passing of the proper dim parameter in the creation of
  the systems of convolution circuits in ts_sernewcnv.
  Improved stop criterion in newton_power_convolutions.adb,
  fixed dimension of work space vectors in ts_sernewcnv for QRLS.

Sat 15 Feb 2020 : new test procedure ts_ratapp to test the new thread safe
  procedures to construct rational approximations.  Added extra evaluation
  operations to {standard,dobldobl,quaddobl}_rational_approximations.

Fri 14 Feb 2020 : improved organization of tests in ts_sernewcnv.
  Added procedures to standard_rational_approximations for thread safety.
  Added similar procedures to the double double and quad double versions,
  to {dobldobl,quaddobl}_rational_approximations.

Mon 27 Jan 2020 : to newton_power_convolutions, added a verbose flag to
  print the progress index.

Sat 25 Jan 2020 : updated ts_sernewcnv for Convolution_Circuit name change.

Mon 20 Jan 2020 : added a scale option to newton_power_convolutions,
  with ts_sernewcnv prompting the user for the value of this flag.

Mon 13 Jan 2020 : extracted code from ts_sernewcnv into the new package
  homotopy_convolution_circuits, in the ../../Math_Lib/Circuits folder.

Sat 11 Jan 2020 : new package newton_power_convolutions to run several
  Newton steps on power series, with convolution circuits and linearization,
  tested by ts_sernewcnv.  Extended newton_power_convolutions with versions
  for double double and quad double precision, tested by ts_sernewcnv.
  Completed newton_power_convolutions with QR and SVD procedures,
  with tests added to ts_sernewcnv.

Thu 2 Jan 2020 : added verbose level to power_series_methods, modified
  series_and_predictors, {standard,dobldobl,quaddobl}_pade_trackers.adb.
  Added verbose level in {standard,dobldobl,quaddobl}_newton_matrix_series,
  modified power_series_methods.adb.  For compiler warnings, modified
  {standard,dobldobl,quaddobl}_newton_series.adb.

Wed 1 Jan 2020 : for compiler warnings, modified test_pade_predictors,
  ts_padepred.adb, ts_sernew.adb, ts_serpade.adb, ts_serpred.adb,
  ts_sersol.adb, ts_serhom.adb, ts_jacrabin.adb, ts_durker.adb.

Wed 28 Aug 2019 : updated homotopy_pade_approximants with the computation
  of a threshold index and zero checks on the solution error norm estimate.

Tue 27 Aug 2019 : added verbose level to the step_control procedures in
  {standard,dobldobl,quaddobl}_pade_trackers.  If the step-by-step tracker
  runs in the verbose mode, then all Newton iterations are shown,
  updated *_seriespade_tracker.adb.

Mon 26 Aug 2019 : initialized mhom to zero in series_path_trackers.adb.

Wed 21 Aug 2019 : to series_path_trackers, added a procedure to write the 
  partition of the variables to file.

Tue 20 Aug 2019 : in series_and_trackers, used the coefficient homotopy also
  when no output to file and passed the (mhom,idz) parameters through,
  which changed drivers_to_series_trackers.  Removal of the series step 
  counter and ratio modified also series_path_trackers.adb.
  Updated series_and_trackers and drivers_to_series_trackers for double
  double and quad double versions, for passing mhom and idz.

Mon 19 Aug 2019 : added on extra iteration on Newton's method for power
  series in standard_pade_trackers.adb, also in the silent version.

Sun 18 Aug 2019 : to homotopy_coefficient_scalling, added a procedure to
  verify the coefficients of the last m equations for m-homogenization,
  tested in {standard,dobldobl,quaddobl}_pade_trackers.adb.
  Completed the scaling of the m-homogeneous solutions and coefficients
  and homotopy_coefficient_scaling, applied in the procedures in
  in {standard,dobldobl,quaddobl}_pade_trackers.adb.

Sat 17 Aug 2019 : added the multihomogeneous parameters to *_pade_trackers,
  which changed series_path_trackers, series_and_trackers, and
  drivers_to_series_trackers.  Initialized the coefficient homotopy,
  also for multi-homogenization, updating series_path_trackers, and
  {standard,dobldobl,quaddobl}_pade_trackers.adb.  In the root refiners 
  in driver_to_series_trackers, transformed from multihomogeneous to affine
  coordinates, which also updated series_path_trackers.adb.

Fri 16 Aug 2019 : improved internal structure of series_path_trackers,
  with better entering of the partition of the set of unknowns.

Thu 15 Aug 2019 : updated series_path_trackers, interactive_pade_trackers.adb,
  replacing the homogeneous boolean by a natural number of m-homogenization.
  Added multi-homogeneous transformations to homotopy_series_readers and
  applied them in series_path_trackers, with extra procedures.

Mon 12 Aug 2019 : ignoring corrector failure, disabled the corrector
  feedback loop in {standard,dobldobl,quaddobl}_pade_trackers.adb.
  Separated projective transformation of solutions and systems in
  homotopy_series_readers, adjusted interactive_pade_readers and
  the *_seriespade_trackers for homogeneous coordinates.
  Updated dobldobl_seriespade_tracker.adb and quaddobl_seriespade_tracker.adb
  so the step-by-step tracker works in homogeneous coordinates also in
  double double and quad double precision.

Fri 9 Aug 2019 : double double and quad double extensions to the procedures
  in homotopy_coefficient_scaling, updates in standard_pade_trackers.adb,
  dobldobl_pade_trackers.adb and quaddobl_pade_trackes.adb.
  In drivers_to_series_trackers, transformed back to affine coordinates,
  updated series_path_trackers.adb to pass the verbose level.
  Moved code to transform a system into affine coordinates from
  drivers_to_series_trackers.adb to a new package affine_coordinates.

Wed 7 Aug 2019 : extended homotopy_coefficient_scaling with a silent version
  of the scaling procedure, updated standard_pade_trackers.adb.
  Changed the defaults for the degrees in homotopy_continuation_parameters,
  elimination of sbeta changed homotopy_continuation_parameters_io.adb.

Tue 6 Aug 2019 : fixed the scaling of the last coefficients in the homotopies
  in standard_pade_trackers.adb so tracking in homogeneous coordinates works.
  Moved two procedures out of standard_pade_trackers into a new package
  homotopy_coefficient_scaling.

Mon 5 Aug 2019 : adjusted homotopy_mixed_residuals so that, when the
  coefficient homotopy is defined, then it is used to compute the residual.
  Managed to get the scaling of solutions and the last coefficients to work for
  t = 0.0 in standard_pade_trackers.adb.  Improved standard_pade_trackers.adb.

Sat 3 Aug 2019 : printing of coefficients of the last equation in the
  homotopies shows the correspondence between the coefficient homotopy
  and homotopy with series coefficients in standard_pade_trackers.adb.

Fri 2 Aug 2019 : forgot to enlarge the symbol table when adding the extra
  symbol Z0 for the homogenization of the homotopy.

Thu 1 Aug 2019 : adjusted double double and quad double versions in 
  homotopy_series_readers.adb and homotopy_newton_steps.adb.
  Set the value for tpow to one in homotopy_series_readers.adb if homcrd.

Wed 31 Jul 2019 : made coefficient homotopy in homotopy_series_readers.adb,
  called in homotopy_newton_steps.adb for homogeneous coordinates, and
  added diagnostic prints in standard_pade_trackers.adb.

Tue 30 Jul 2019 : updated homotopy_series_readers.adb with versions for
  double double and quad double precision of the projective transformations.

Mon 29 Jul 2019 : added prompts for homogeneous coordinates in 
  interactive_pade_trackers.adb and series_path_trackers; with projective
  transformations done in homotopy_series_readers.

Thu 25 Jul 2019 : in series_and_trackers.adb, commented out the reporting
  on the counts and ratios for the series step.

Fri 19 Jul 2019 : disabled the series step in *_pade_trackers.adb and also
  in *_seriespade_tracker.adb.

Fri 5 Jul 2019 : removed "Testing ..." line in homotopy_series_readers.adb.
  New package interactive_pade_trackers with code from ts_nxtpadsol.
  Added verbose level to the main procedues in interactive_pade_trackers
  and updated mainseries.adb, so step-by-step is possible with phc -u.

Wed 3 Jul 2019 : refactored code in standard_seriespade_tracker and added
  the curvature bound with better output statistics, tested by ts_nxtpadsol.
  Updated also the double double and quad double versions in the files
  *_seriespade_tracker.*, with extra output written by ts_nxtpadsol.
  Exported the value for eta in the *_seriespade_tracker.* files.

Tue 2 Jul 2019 : improve the output in series_and_trackers.adb and in
  the standard_pade_trackers.adb.  Bug fixed in standard_pade_trackers.adb,
  forgot to extend the solution vector with t for the eta computation.
  Improved the output in *dobl_pade_trackers.adb.
  Added ratio of times which step sizes were minimal to the output,
  modified series_and_trackers and series_path_trackers.adb.

Mon 1 Jul 2019 : modified {standard,*dobl}_pade_approximants.adb for a 
  compiler warning.  Modified test_series_predictors.adb for compiler warning.
  Fixed the number of iterations in Newton's method for power series
  in the test procedures in ts_hesspred.adb.
  Added initialization, construction, and destruction of the Jacobian
  and Hessians to *_seriespade_tracker.adb.

Sun 30 Jun 2019 : added a 3-way minimum to standard_pade_trackers,
  updated series_path_trackers.adb and series_and_trackers.adb.
  Fixed some errors in standard_pade_trackers.adb, updated the double double
  and quad double versions in *dobl_pade_trackers, with updates in
  series_path_trackers.adb and series_and_trackers.adb.
  Updated writing of the path statistics in series_and_trackers
  and in series_path_trackers.adb.

Sat 29 Jun 2019 : the number of iterations in the Newton method for power
  series should depend on the degree of the series, updated the packages
  standard_pade_trackers, and *dobl_pade_trackers.adb.
  Fixed the extra corrector steps in homotopy_newton_steps.adb.

Fri 28 Jun 2019 : added the verbose level parameter to the main procedures
  in drivers_to_series_trackers.

Thu 27 Jun 2019 : refactored quaddobl_pade_trackers, updated the packages
  series_path_trackers.adb and series_and_trackers.adb.
  Some minor changes in dobldobl_pade_trackers.  Forgot to update 
  the smallest and largest step sizes in quaddobl_pade_trackers.adb.
  Exported the minimum function in standard_pade_trackers, updated
  dobldobl_pade_trackers.adb and quaddobl_pade_trackers.adb.

Wed 26 Jun 2019 : moved the predictor-corrector feedback loop in separate
  procedures in standard_pade_trackers, updated series_and_trackers,
  and series_path_trackers.adb.  Moved the step control in the
  standard_pade_trackers into separate procedures.  Did this too for
  double double precision, changed dobldobl_pade_trackers, 
  updated series_and_trackers.adb and series_path_trackers.adb.

Tue 25 Jun 2019 : removed superfluous with/use clauses from the
  headers of the package dobldobl_pade_trackers.
  Added the curvature beta parameter to homotopy_continuation_parameters,
  updated homotopy_continuation_parameters_io, and used the cbeta in
  the {standard,dobldobl,quaddobl}_pade_trackers.

Mon 24 Jun 2019 : refactored series_and_trackers into the new package
  standard_pade_trackers, which changed series_path_trackers.adb and
  {standard,dobldobl,quaddobl}_seriespade_tracker.adb.
  New package dobldobl_pade_trackers, with code from series_and_trackers,
  which changed series_path_trackers.adb.
  Removed residual prediction from series_and_trackers in double double
  precision, updated dobldobl_seriespade_tracker.adb.
  New package quaddobl_pade_trackers, with code from series_and_trackers,
  which changed series_path_trackers.adb and quaddobl_seriespade_tracker.adb.

Sun 23 Jun 2019 : updated mainseries.adb to pass the verbose level.
  Applied the verbose level in the procedures of series_and_trackers.adb.

Sat 15 Jun 2019 : added the verbose level to mainseries.
  Added the verbose level to the procedures in mainseries.adb,
  to series_path_trackers and series_and_trackers, tested by ts_serpath.

Sat 1 Jun 2019 : updates in power_series_methods.adb for compiler warnings.
 
Tue 14 May 2019 : fixed bug with the value of extra in the stop criterion
  in homotopy_newton_steps.adb.

Sat 6 Apr 2019 : in black_box_univariate_solvers.adb, set the t-value in
  the returned solutions to 0.0 instead of to 1.0.

Sat 20 Mar 2019 : to the correctors in homotopy_newton_steps, added the 
  extra parameter, to allow for possible extra corrector steps.
  This changed series_and_trackers.adb and *seriespade_tracker.adb.

Thu 28 Mar 2019 : fixed a bug in series_and_trackers.adb, allowing for
  smaller step sizes than alpha, ignored corrector failures, and toggled
  off the Hessian step size, for path 155 of cyclic 11-roots which takes
  large values for some specific gamma value.

Tue 26 Mar 2019 : toggled of the series step size also for double double
  and quad double precision in series_and_trackers.adb.
  Added Newton step with SVD to homotopy_newton_steps and made numerous
  small changes to series_and_trackers, in search for a bug.

Mon 25 Mar 2019 : modified the homotopy_newton_steps.adb to have the stop
  criterion for the convergence to involve the err as well.

Sun 24 Mar 2019 : added mixed residuals corrector to the step-by-step run
  of the series-Pade tracker in *seriespade_tracker.adb.
  Updated the drivers_to_series_trackers and series_path_trackers.adb
  to pass the absolute coefficient homotopy polynomials to the refiners.

Wed 20 Mar 2019 : cleared abh in series_path_trackers.adb at the end of a run.
  In series_and_trackers, added functions to compute the predictor residual
  with mixed residuals.  More output in series_and_predictors.adb for
  information about the series step size criterion.
  Turned off the series step in series_and_trackers.adb for doubles.

Tue 19 Mar 2019 : added application to the 'abh' parameter in the body of
  series_and_trackers.adb.

Mon 18 Mar 2019 : added homotopies with absolute value coefficients to the
  input parameters of series_and_trackers, and then series_path_trackers.adb
  had to be modified as well.
  
Sat 16 Mar 2019 : added making of the absolute value coefficients of the
  homotopy polynomials to series_path_trackers.adb.

Wed 13 Mar 2019 : to homotopy_newton_steps, added correctors which compute
  the mixed residuals for the stored homotopy polynomials.

Mon 11 Mar 2019 : added newton step with mixed residuals to the 
  package homotopy_newton_steps.

Sun 10 Mar 2019 : added the making of the absolute value coefficients
  polynomials of the homotopy system to homotopy_mixed_residuals.

Sat 9 Mar 2019 : new package homotopy_mixed_residuals to compute the mixed
  residuals for stored homotopies.

Thu 28 Feb 2019 : added to homotopy_newton_steps.adb the calculation of the
  max norm of the solution vector in the stop criterion.
  Relaxed criterion for divergence in homotopy_newton_steps.adb and
  increased the maximum number of corrector steps in series_and_trackers.adb.

Wed 27 Feb 2019 : applied step_distance also to double double and quad double
  versions in series_and_trackers.adb.  Instead of residual, used the size
  of the update in homotopy_newton_steps.adb and checked the predres against
  alpha instead of minstep in series_and_trackers.adb.

Tue 26 Feb 2019 : added extra interface functions for the "step_distance"
  to series_and_predictors, for use in the series_and_trackers.adb.

Mon 25 Feb 2019 : added functions to series_and_predictors, to wrap the
  computation of the step size based on the distance to the nearest solution.

Sun 24 Feb 2019 : removed redundant clauses from test_pade_predictors.adb.

Sat 23 Feb 2019 : added extra parameters for the Hessian step size criterium
  to series_and_trackers, series_path_trackers.adb, with updates in
  drivers_to_series_trackers.

Fri 22 Feb 2019 : new test procedure ts_predstep.adb sets the step based
  on both the closest pole and the nearest solution estimate.

Thu 21 Feb 2019 : new test procedure ts_hesspred.adb to test the setting
  the step size based on the estimate for the nearest solution vector.

Wed 20 Feb 2019 : added the candidate step size based on the estimate
  of the distance to the nearest solution.

Tue 19 Feb 2019 : to singular_values_of_hessians, added the making of the
  Jacobian and Hessians, with code extracted from ts_hesscrit.adb.
  Added wrapper for the distance estimate for solution data types to
  the singular_values_of_hessians, extracting code from ts_hesscrit.
  Fixed closest_pole name in test_pade_predictors.adb and ts_padepred.adb.
  To homotopy_pade_approximants, added functions to estimate the error
  on the solution vector.

Mon 18 Feb 2019 : in singular_values_of_hessians.adb, multiplied the
  sigma1 for the evaluation Jacobian with the factor 2.0.

Sun 17 Feb 2019 : extracted Jacobian and Hessian computation in separate
  procedures in ts_hesscrit.

Sat 16 Feb 2019 : extended singular_values_of_hessians with a function
  to return the estimate of the distance to the nearest solution,
  tested by ts_hesscrit.  Extended ts_hesscrit for dd & qd precision.

Fri 15 Feb 2019 : introduced real vectors in singular_values_of_hessians
  with extensions to arrays of Hessians.  Also ts_hesscrit.adb changed.
  Exposed wrappers in singular_values_of_hessians, used to compute the
  singular values of the Jacobian matrix in ts_hesscrit.adb.

Thu 14 Feb 2019 : new package singular_values_of_hessians wraps the SVD,
  called in ts_hesscrit.adb.

Wed 13 Feb 2019 : new file ts_hesscrit to develop the Hessian criterion.

Tue 12 Feb 2019 : reset the degree of the power series (adding one)
  and in homotopy_pade_approximants, compute the radius of the closest pole,
  among all poles, not just the poles with positive real part.
  Updated *_seriespade_tracker.adb, series_and_predictors, and
  the series_and_trackers.adb.

Mon 4 Feb 2019 : decreased the degree of the power series by one and added
  one to the number of iterations in series_and_trackers.adb and in the
  {standard,dobldobl,quaddobl}_seriespade_tracker.adb files.

Mon 21 Jan 2019 : added range check on order in series_and_predictors.adb.
  Removed some with clauses from series_and_predictors.ads.
  In *_rational_approximations.adb, ensured that the returned denominator
  coefficients are never zero.  Updates in series_and_trackers for warnings.
  Added writing of the Pade vector (if verbose) in *_seriespade_tracker.adb.

Sun 20 Jan 2019 : added natural parameter homotopy modifications to
  standard_seriespade_tracker and ts_nxtpadsol.adb.

Sat 19 Jan 2019 : adjusted the writing of the homotopy for natural parameter
  homotopies in series_path_trackers.  Dropped value for the natural parameter
  from the solutions in series_path_trackers.adb, but only when idxpar /= 0!
  Fixed setting dimension in series_path_trackers.adb, toggled off the
  root refinement for natural parameter homotopies.

Thu 10 Jan 2019 : modified series_path_trackers for runs with natural
  parameter homotopies.

Wed 9 Jan 2019 : modified drivers_to_series_trackers.adb to take into 
  account the monitor flag, in addition to the verbose parameter.

Sat 5 Jan 2019 : extended series_path_trackers.adb with double double and
  quad double versions of coefficient-parameter evaluation.

Fri 4 Jan 2019 : from standard_newton_matrix_series, power_series_methods,
  series_and_predictors.adb, removed superfluous parameters.
  Improved the residual prediction in series_and_trackers, which changed
  {standard,dobldobl,quaddobl}_seriespade_tracker.adb.
  In standard_newton_matrix_series, added coefficient-parameter homotopies 
  to the QR methods, improved power_series_methods, series_and_predictors,
  series_and_trackers, updated series_path_trackers.adb.
  Completed definitions in standard_newton_matrix_series.adb and made
  extensions in {dobldobl,quaddobl}_newton_matrix_series, applied in
  power_series_methods, series_and_predictors, and series_and_trackers.

Thu 3 Jan 2019 : added tests on coefficient-parameter homotopies 
  to ts_serhom.adb.  Added coefficient-parameter evaluation to
  standard_newton_matrix_series, power_series_methods, series_and_predictors,
  series_and_trackers, and series_path_trackers.adb.

Tue 1 Jan 2019 : added consistently the max norm computation to
  {standard,dobldobl,quaddobl}_newton_matrix_series.adb.
  Improved the shift procedures in series_and_homotopies.adb.
  Applied the improved shift procedures in series_and_trackers.adb.

Fri 28 Dec 2018 : modified series_path_trackers.adb so target system,
  start system, and start solutions are written to the output file.
  Added function to *seriespade_tracker.a* to return all poles.

Thu 27 Dec 2018 : added functions to return the current step size and
  t value in the *tracker.a* packages.

Wed 26 Dec 2018 : in *seriespade_tracker.adb, output of all poles.
  In homotopy_pade_approximants.adb, simplified the computation of
  the smallest forward pole radius.  Fixed bug in the allocation of a
  Pade approximant in {standard,dobldobl,quaddobl}_pade_approximants.adb.
  Fixed yet another bug in homotopy_pade_approximants.adb, with the
  computation of the smallest forward pole radius.
  Extended the *tracker.a* packages with functions to return the
  smallest forward pole radius and the closest pole, after extending
  series_and_predictors, and updating series_and_trackers.adb.
  Improved the name of a function in *seriespade_tracker.a*.

Mon 24 Dec 2018 : bug fix in *seriespade_tracker.adb, must reset the
  cseries homotopy with each new start solution.  Updated the test
  procedure ts_nxtpadsol.adb with a loop for all start solutions.

Sat 22 Dec 2018 : added more selectors to the *seriespade_predictors.a*
  and extended the verbose option for the Newton predictor and step size.

Fri 14 Dec 2018 : added procedures to homotopy_pade_approximants to
  compute the poles without memory allocation, adjusted the corresponding
  procedures in series_and_predictors, applied in series_and_trackers.adb.
  Added procedures to {standard,dobldobl,quaddobl}_pade_approximants
  to define the Pade vector in place, without extra allocations,
  updated series_and_predictors, and applied the new procedures 
  in series_and_trackers.adb.  Adjusted the calls to the new procedures
  in the bodies of the packages *_seriespade_tracker.adb.

Thu 13 Dec 2018 : new package homotopy_newton_steps contains the correct
  procedures from series_and_trackers, with memory improvements.
  Relaxed alpha and tolres defaults in homotopy_continuation_parameters.adb.
  The Correct in *seriespade_tracker works, tested in ts_nxtpadsol 
  on the first given start solution.
  Fixed bug in resetting gamma in series_path_trackers.adb,
  changed drivers_to_series_trackers, exposing the tpow value.
  Basic version of the get_next() works for standard double precision,
  in standard_seriespade_trackers.adb, tested by ts_nxtpadsol.adb.

Wed 12 Dec 2018 : started writing of standard_seriespade_tracker, with
  a test in ts_nxtpadsol, for a get_next() method for tracking curves.
  Defined the init in standard_seriespade_tracker, and added new packages
  dobldobl_seriespade_tracker and quaddobl_seriespade_tracker, with
  test procedures in ts_nxtpadsol.

Tue 11 Dec 2018 : added a corrector feedback loop to the package
  series_and_trackers, relaxed the default corrector residual tolerance
  in homotopy_continuation_parameters.adb.  To series_and_trackers, added
  a counter for the corrector failures, changed series_path_trackers.adb.

Mon 10 Dec 2018 : added time stamp writing to drivers_to_series_trackers,
  updated series_and_trackers, and series_path_trackers.adb.

Fri 7 Dec 2018 : only drop out with too small step size if the predictor
  residual is larger than alpha, modified series_and_trackers.adb.

Wed 5 Dec 2018 : flipped the sign of the t when assigning to the solution
  data structure at the end of tracking a path in series_and_trackers.adb.

Tue 4 Dec 2018 : added new_line(file); after printing solutions
  in series_and_trackers.adb.

Mon 3 Dec 2018 : extended drivers_to_series_trackers with procedures to
  launch the path trackers.  Added to drivers_to_series_trackers the
  procedures which take values of the homotopy continuation parameters.

Sat 1 Dec 2018 : added an access type to homotopy_continuation_parameters,
  plus operations for the storage of an instance of the parameters.
  Adjusted the output in the tune of homotopy_continuation_parameters_io.adb.

Thu 29 Nov 2018 : added a parameter for the tolerance on the corrector
  residual to homotopy_continuation_parameters and updated the tuning
  in homotopy_continuation_parameters_io.adb and updated the trackers
  in series_and_trackers.adb.  To series_and_trackers, computed the
  smallest and largest step sizes on a path, tested by ts_serpath.
  Corrected wrong initialization in series_and_trackers.adb and
  in ts_serpath.  Refactored the Main procedures in mainseries.adb.
  Moved code from ts_serpath into series_path_trackers, for use in
  mainseries.adb.  Remove superfluous new_line in series_and_trackers.adb.

Wed 28 Nov 2018 : renamed the beta in homotopy_continuation_parameters
  into pbeta and added the sbeta parameter, which then changed the put
  and tune in homotopy_continuation_parameters_io.adb, and also changed
  series_and_trackers.adb.  Added parameters to the Correct procedures
  in series_and_trackers.  Updated path tracking statistics to
  series_and_trackers and ts_serpath.adb.

Tue 27 Nov 2018 : set the default number of steps on a path to 1000
  in homotopy_continuation_parameters.adb and flipped the sign of the
  argument of the shift() in series_and_trackers.adb.

Mon 26 Nov 2018 : in series_and_trackers.adb, set the verbose option to
  false when calling the Series_and_Predictors.Newton_Prediction().
  In series_and_trackers.adb, swapped the correct() before the shift
  and added an extra round of corrections at the end of the tracking.
  Added stop condition also in the reporting version of the correct()
  in series_and_trackers.adb.

Sun 25 Nov 2018 : added residual computation on prediction solution to
  series_and_trackers.adb, with a step reduction.  Adjusted the default
  values in homotopy_continuation_parameters.adb.

Sat 24 Nov 2018 : improved the output in series_and_trackers.adb and
  ts_serpath.adb.

Fri 23 Nov 2018 : in Tune() of homotopy_continuation_parameters_io,
  changed the out into an in out type and did not reset the pars to
  the default values.  In ts_serpath, reset the gamma constant to
  the accessibility constant from the homotopy packages.
  Reset the gamma constant in ts_serpath, for repeatable runs.
  New package drivers_to_series_trackers, with code from ts_serpath.

Thu 22 Nov 2018 : made the prompting for the Jacobian Rabinowitsch trick
  optional in homotopy_series_readers.  New packages to manage the values
  of parameters: homotopy_continuation_parameters, and its *_io,
  used in series_and_trackers, tested by ts_serpath.
  Added root refiners to ts_serpath.

Wed 21 Nov 2018 : fixed another memory leak in series_and_homotopies.adb.

Tue 20 Nov 2018 : cleared the Jacobian series matrices in
  {standard,dobldobl,quaddobl}_newton_matrix_series.adb.
  Added timers to series_and_trackers.adb and ts_serpath.adb.

Mon 19 Nov 2018 : added clear() of Pade approximants vector after use in
  series_and_trackers.adb.  Fixed memory leak in series_and_homotopies.adb.
  In the verbose methods in power_series_methods.adb, clear(eva) added.

Sat 17 Nov 2018 : added degrees of numerator and denominator to the
  procedures in series_and_trackers, tested by ts_serpath.

Fri 16 Nov 2018 : added clear()'s to standard_newton_matrix_series.adb.

Thu 15 Nov 2018 : added clear() calls in series_and_trackers.adb in an
  attempt to stop the memory leak.  To series_and_trackers.adb, added
  the application of the Pade approximants in the predictors.

Wed 14 Nov 2018 : added the construction of Pade approximants to
  series_and_predictors.  Factored the setting of the step size into
  a separate procedure in series_and_trackers.  Added a function to
  cap the step size with the smallest forward pole radius in
  series_and_predictors.

Tue 13 Nov 2018 : made double double and quad double version like the
  double versions, updated *dobl_rational_approximations and
  *dobl_pade_approximants, wrapped smallest_forward_pole procedure into
  a function in homotopy_pade_approximants, better tests in ts_padepred.
  Documented a verbose option in standard_rational_approximations.ads.

Sat 10 Nov 2018 : added value for the maximal degree of the series 
  in series_and_trackers.adb, improved ts_serpath.adb.

Fri 9 Nov 2018 : prompt for the maximal degree bound in mainseries.adb.

Thu 8 Nov 2018 : added bound on the degrees of the series in
  {standard,dobldobl,quaddobl}_newton_series and adjusted ts_sernew.adb.
  Did the same for the *_newton_matrix_series packages.
  Because of this added degree bound, adjusted power_series_methods,
  ts_sersol, series_and_predictors, homotopy_series_readers.adb,
  series_and_trackers.adb, and ts_padepred.adb.

Wed 7 Nov 2018 : adjusted all *newton* and *pade_approximants.a*
  files for the new series definitions.  Adjusted power_series_methods,
  series_and_solutions, series_and_predictors, series_and_homotopies,
  and homotopy_series_readers, ts_sernew, ts_sersol, and mainseries.adb.
  Modified test_series_predictors, ts_serpred, ts_serhom, ts_serpath,
  series_and_trackers, test_pade_predictors, ts_serpade, ts_padepred.

Fri 26 Oct 2018 : moved test procedures into test_pade_predictors, code
  taken from ts_padepred.adb.  Added procedures and functions to
  test_pade_predictors to compute the forward pole radius and tested
  the computation of the forward pole radius in ts_padepred.

Thu 25 Oct 2018 : extended jacobian_rabinowitsch trick to extend solutions
  with extra coordinates introduced by the trick, tested in ts_jacrabin.adb.
  Updated homotopy_series_readers.adb to prompt the user if the Rabinowitsch
  trick needs to be applied.  Also updated homotopy_series_readers.adb
  for the trick in double double and quad double precision.

Wed 24 Oct 2018 : new test procedure to develop the application of
  the trick of Rabinowitsch.  Moved code out of ts_jacrabin.adb into
  the new package jacobian_rabinowitsch_trick, with new versions for
  double double and quad double precision.

Tue 23 Oct 2018 : fixed the computation of the poles for denominators with
  leading zero coefficients, modifying homotopy_pade_approximants
  and ts_padepred.adb.

Mon 22 Oct 2018 : wrapped reading of natural parameter homotopies into
  homotopy_series_readers, adjusted test_series_predictors, tested by
  ts_serpred.adb.  Also updated ts_padepred.adb for natural homotopies.

Sat 20 Oct 2018 : added the computation to the smallest forward pole to
  homotopy_pade_approximants, tested in ts_padepred.adb.

Fri 19 Oct 2018 : test_series_predictors and test_pade_predictors are two
  new packages with code taken from ts_serpred.adb, with new ts_padepred
  to develop the Pade predictors.

Thu 18 Oct 2018 : to *_pade_approximants, added Eval functions which take
  double, double double, or quad double arguments.  Extended the test
  procedures in ts_serpred.adb to evaluate the Pade approximant predictor.

Wed 17 Oct 2018 : the homotopy in ts_serpred.adb needs to be constructed
  with tpow = 1.  To black_box_univariate_solvers, added procedures which
  take coefficient vectors on input, extended homotopy_pade_approximants.adb
  with procedures to copute all poles, tested by ts_serpred.adb.

Tue 16 Oct 2018 : added computation of poles to homotopy_pade_approximants,
  tested by ts_serpred.adb.  Added verbose options to ts_serpred.adb,
  standard_rational_approximations, standard_pade_approximants, and
  homotopy_pade_approximants.

Mon 15 Oct 2018 : in ts_serpade.adb, wrapped test code into procedures.

Tue 27 Feb 2018 : added exception handlers to some procedures in
  standard_newton_matrix_series.adb and power_series_methods.adb
  to track down the cause of a crash.

Sun 4 Jun 2017 : added index parameter in homotopy_series_readers and
  homotopy_pade_approximants, fixed bug in example Pade test in ts_serpade.

Fri 2 Jun 2017 : prompted for random gamma or not in the artificial parameter
  homotopy in ts_serpade.  Patched the computation of the denominator of the
  Pade approximant in case of a singular coefficient matrix with a zero right
  hand size in the *_rational_approximations.adb bodies, tested by ts_serpade.
  The homotopy system should not be cleared in homotopy_series_readers.adb.

Wed 31 May 2017 : added the conversion of a Pade vector to a system of
  polynomials in the *_pade_approximants_io packages.

Mon 29 May 2017 : exposed the info parameter in the construction of the Pade
  approximants in *_rational_approximations, which altered the body of the
  *_pade_approximants packages, tested by ts_serpade.
  To homotopy_series_readers, added an interface to take complex vectors
  on input to construct a power series solution.
  Added default symbol 't' to the *_pade_approximants_io packages.
  New package homotopy_pade_approximants, tested in ts_serpade,
  to wrap series Newton and the Pade approximant creators.

Sun 28 May 2017 : new package standard_pade_approximants_io to compute the
  string representation of a Pade approximant, called in ts_serpade.adb.
  Similarly, made the packages {dobldobl,quaddobl}_pade_approximants_io.

Sat 27 May 2017 : added vector of vector of Pade approximant types to the
  *_pade_approximants packages.

Thu 25 May 2017 : for the example test case, extended the range so it shows
  a converging Pade approximant versus a diverging series.
  For the general homotopy test, prompt for the number of steps to set
  the range of evaluation of the series and Pade approximations.

Wed 24 May 2017 : added an example test case to ts_serpade.

Tue 23 May 2017 : new package standard_pade_approximations to encapsulate
  a Pade approximant and a vector of Pade approximants, tested by ts_serpade.
  Added {dobldobl,quaddobl}_pade_approximants packages.
  Comparison with power series approximation added to ts_serpade.

Mon 22 May 2017 : added coefficients function to ts_serpade and constructed
  a rational pade approximation for the solution in the homotopy.
  Added loop to test the Pade approximations at 5 points.

Sun 21 May 2017 : the package homotopy_series_readers collects code of the
  test procedures ts_serpred and ts_serpath.  Added default value for the
  power of the continuation parameter in homotopy_series_readers.
  Extra procedures in homotopy_series_readers for the given gamma constant.
  Added series Newton to homotopy_series_readers, tested in ts_serpade.

Sat 20 May 2017 : new package dobldobl_rational_approximations, tested by
  ts_serpade, to compute Pade approximations with double doubles.
  Added new package quaddobl_rational_approximations, for quad doubles.
  Fixed call to proper double double and quad double functions to
  evaluate the exp() and the log() function.

Fri 19 May 2017 : new ts_serpade.adb to develop a rational approximation,
  given a power series.  Added more tests: exp(x), sin(x), cos(x).
  Refactored code in ts_serpade into standard_rational_approximations,
  a new package.

Tue 20 Dec 2016 : refactored mainseries.adb, with better questions to
  select the options of phc -u and make room for echelon Newton.
  To phc -u added the option of starting Newton at a series which
  has several leading terms.

Sat 17 Dec 2016 : refactored ts_sersol, to allow to start Newton's method
  at series with more than just the leading term.

Fri 16 Dec 2016 : in ts_sernew, fixed the call to echelon Newton.
  In *newton_matrix_series.adb, fixed an error in the output. 
  Started adding the echelon Newton methods to power_series_methods,
  added more with tests in ts_sersol.

Thu 15 Dec 2016 : added echelon Newton methods to more precision levels in 
  the {standard,dobldobl,quaddobl}_newton_matrix_series.
  Added tests to ts_sernew on the echelon Newton matrix series methods.

Wed 14 Dec 2016 : extended standard_newton_matrix_series with the echelon
  form of the linear solvers.

Wed 30 Nov 2016 : fixed compilation error in series_and_predictors.adb.

Sun 9 Oct 2016 : edits in series_and_trackers.adb for compiler warnings.

Sat 8 Oct 2016 : to mainseries.adb added call to Newton-Puiseux method
  for regular solution series.

Mon 8 Aug 2016 : added a put_vector to power_series_methods.adb,
  also for the dobldobl and quaddobl versions, and not only for SVD.

Sun 31 Jul 2016 : extended power_series_methods to return rcond with LU.
  Modified mainseries.adb so SVD_Newton is always applied.

Sat 30 Jul 2016 : added test procedures to ts_sernew to test the SVD
  Newton methods on matrix series.  To power_series_methods, added SVD Newton.

Fri 29 Jul 2016 : extended *newton_matrix_series* with SVD_newton methods.

Thu 28 Jul 2016 : cleaned up ts_serpath.adb, for compiler warnings,
  and printing of the solution list at the end of the paths.
  Added condition number estimate to standard_newton_matrix_series,
  and the double double and quad double versions.

Wed 27 Jul 2016 : used *newton_matrix_series in power_series_methods.adb,
  which seems to work much better in the path trackers ts_serpath.adb.

Mon 25 Jul 2016 : new package standard_newton_matrix_series which applies
  linearization for the update in Newton's method, tested by ts_sernew.
  For double double and quad double precision, Newton with linearization 
  is defined in the packages {dobldobl,quaddobl}_newton_matrix_series.
  Added test procedures in ts_sernew for double double and quad doubles.

Sat 16 Jul 2016 : added track_many_paths procedures to series_and_trackers.

Thu 14 Jul 2016 : changed series_and_predictors.adb so output is written
  to file when in verbose mode.  Refactored code in ts_serpath to procedure.

Wed 13 Jul 2016 : added prompting for file to ts_serpath.

Tue 12 Jul 2016 : added double double and quad double versions to the
  series_and_trackers, tested by ts_serpath.  Provided silent and verbose
  versions in series_and_trackers, for testing by ts_serpath.
  Added file to the arguments in series_and_predictors, which changed
  ts_serpred and series_and_trackers.adb.

Mon 11 Jul 2016 : new package series_and_trackers, with code from ts_serpath.

Sun 10 Jul 2016 : ts_serpath contains a very simple path tracker.

Sat 9 Jul 2016 : new test procedure ts_serpath to develop the path tracking
  with power series.

Thu 7 Jul 2016 : replacing order by degree changed *newton_series*,
  ts_sernew, and series_and_predictors.  In series_and_predictors,
  renamed Least_Order() to Order().

Wed 6 Jul 2016 : extra functions in series_and_solutions to work directly
  with the coordinate vectors of solutions.  Refactored code from ts_serpred
  to series_and_predictors, for the first stage of the series predictor.
  Tested the setting of step size in ts_serpred, also for dd/qd.

Tue 5 Jul 2016 : bug fix in series_and_solutions.adb with the create
  in case idx = 0; this special case must have a separate loop.
  Made not verbose versions in power_series_methods.adb silent.
  New package series_and_predictors, tested by ts_serpred.
  Added setting of the step size to series_and_predictors.

Mon 4 Jul 2016 : added eval function to series_and_homotopies, tested
  by ts_serhom.  Added shift operations to series_and_homotopies,
  with added test in ts_serhom.  DoblDobl and QuadDobl versions of
  the functions and procedures are added to series_and_homotopies,
  with corresponding tests in ts_serhom.

Sun 3 Jul 2016 : new package series_and_homotopies, tested by ts_serhom.

Wed 29 Jun 2016 : new package series_and_solutions, tested by ts_sersol.
  Added tests in double double and quad double precision to ts_sersol.
  New package power_series_methods with code factored out of ts_sersol.
  Added mainseries to define the phc -u.

Tue 28 Jun 2016 : in _newton_series.adb, for QR_Newton, also write the
  result of the polynomial evaluation at the start.
  Applied set_order() to the polynomial systems and its Jacobian matrix
  in standard_newton_series.adb.

Mon 27 Jun 2016 : new packages {dobldobl,quaddobl}_newton_series for double
  double and quad double Newton on series, tested by ts_sernew.

Fri 24 Jun 2016 : added QR Newton to standard_newton_series,
  with added tests in ts_sernew.

Tue 21 Jun 2016 : updated standard_newton_series with many steps,
  tested by ts_sernew.

Mon 20 Jun 2016 : new packages standard_newton_series, tested by ts_sernew.

Wed 7 Oct 2015 : fixed call to silent root refiners in ts_extrapts for
  double double and quad double precisin.

Mon 21 Sep 2015 : extended black_box_univariate_solvers with routines in
  double double and quad double precision.

Thu 28 Aug 2013 : extended black_box_univariate_solvers with routines to
  solving univariate Laurent polynomials with multiprecision arithmetic.
  Exported more routines for the C to PHCpack interface.

Sat 30 Nov 2013 : updated black_box_univariate_solvers.a*,
  sample_plane_curves.a*, ts_extrapol.adb and ts_extrapts for multiprecision.

Fri 29 Nov 2013 : changed sample_plane_curves.adb and ts_extrapol.adb
  in search for a bug that turned out to be in the copy of lists in
  multprec_complex_solutions.adb.

Thu 28 Nov 2013 : higher-order predictors in multiprecision arithmetic
  in a new package multprec_extrapolators, and for testing purposes,
  updated sample_plane_curves, multprec_durand_kerner, ts_extrapol, and
  black_box_univariate_solvers.

Mon 10 Jun 2013 : all files in this directory changed because of the
  new types natural32 and integer32.

Tue 14 May 2013 : new directory with code from Root_Counts/Implift 
  and ../Trackers.  New package sample_plane_curves, with updates in
  ts_extrapol and a new ts_extrapts.
