Root refining and a modified Newton's method in PHCv2.4.88

This directory is entirely new in release 2.3.  It contains the
older root refiners, which were extended in the second release with
multiprecision arithmetic.  Release 2.2 contained the start of
a Newton's method based on numerical differentiation routines.
New in release 2.3 is Newton's method with deflation for singularities.
Most recently added in release 2.3.18 is Aitken extrapolation.
Root refiners with double double and quad double complex arithmetic
were added in v2.3.55.

Run "gprbuild newton.gpr" to make all test programs.
On windows, type "gprbuild newton.gpr -Xos=windows"
at the PowerShell prompt.
The "gprclean newton.gpr" removes all files created by gprbuild.

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file name                        : short description
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handle_underflow_gracefully      : exception handlers for underflow
standard_root_refiners           : refining over standard complex numbers
dobldobl_root_refiners           : Newton in double double complex arithmetic
ts_ddnewt                        : test on dobldobl_root_refiners
quaddobl_root_refiners           : Newton in quad double complex arithmetic
ts_qdnewt                        : test on quaddobl_root_refiners
multprec_root_refiners           : refining up to arbitrary precision
ts_rootrefi                      : calls the root refiners
multprec_residual_evaluations    : computing residuals with multprec numbers
ts_mreseva                       : multiprecision residual computation
root_refining_parameters         : sets the parameters of root refiners
black_box_root_refiners          : basic versions of the root refiners
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standard_numerical_rank          : numerical rank by SVD for standard numbers
dobldobl_numerical_rank          : numerical rank by SVD for dobldobl numbers
quaddobl_numerical_rank          : numerical rank by SVD for quaddobl numbers
multprec_numerical_rank          : numerical rank by SVD for multprec numbers
standard_complex_newton_steps    : Newton/SVD in standard complex arithmetic
dobldobl_complex_newton_steps    : Newton/SVD in dobldobl complex arithmetic
quaddobl_complex_newton_steps    : Newton/SVD in quaddobl complex arithmetic
multprec_complex_newton_steps    : Newton/SVD in multprec complex arithmetic
standard_aitken_extrapolation    : Aitken extrapolation in several variables
ts_newton                        : interactive testing routine
ts_realnewt                      : development of Newton for real numbers
standard_numerical_derivatives   : numerical differentiation
standard_evaluation_machine      : defines functions to differentiate
ts_numdif                        : test on numerical differentiation
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standard_derivative_trees        : trees of partial derivatives
dobldobl_derivative_trees        : dobldobl version of derivative_trees
quaddobl_derivative_trees        : quaddobl version of derivative_trees
multprec_derivative_trees        : multiprecision version of derivative_trees
monomial_hashing                 : hashing of Jacobian matrices via monomials
standard_jacobian_trees          : remember table for standard Jaco matrices
dobldobl_jacobian_trees          : remember table for dobldobl Jaco matrices
quaddobl_jacobian_trees          : remember table for quaddobl Jaco matrices
multprec_jacobian_trees          : remember table for multprec Jaco matrices
ts_jactrees                      : test on trees of Jacobian matrices
standard_deflate_singularities   : adds new equations with standard coeff
dobldobl_deflate_singularities   : adds new equations with dobldobl coeff
quaddobl_deflate_singularities   : adds new equations with quaddobl coeff
multprec_deflate_singularities   : adds new equations with multprec coeff
ts_deflop                        : to make systems to look for singularities
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standard_deflation_trees         : stores trees of standard deflated systems
dobldobl_deflation_trees         : stores trees of dobldobl deflated systems
quaddobl_deflation_trees         : stores trees of quaddobl deflated systems
multprec_deflation_trees         : stores trees of multprec deflated systems
standard_deflation_trees_io      : i/o of trees of standard deflated systems
dobldobl_deflation_trees_io      : i/o of trees of dobldobl deflated systems
quaddobl_deflation_trees_io      : i/o of trees of quaddobl deflated systems
multprec_deflation_trees_io      : i/o of trees of multprec deflated systems
ts_deftrees                      : interactive test on derivative trees
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standard_deflation_matrices      : standard block assignment operations
dobldobl_deflation_matrices      : dobldobl block assignment operations
quaddobl_deflation_matrices      : quaddobl block assignment operations
multprec_deflation_matrices      : multprec block assignment operations
standard_evaluate_deflation      : evaluation of standard deflation matrices
dobldobl_evaluate_deflation      : evaluation of dobldobl deflation matrices
quaddobl_evaluate_deflation      : evaluation of quaddobl deflation matrices
multprec_evaluate_deflation      : evaluation of multprec deflation matrices
standard_evaluate_deflation_io   : output standard directed acyclic graphs
dobldobl_evaluate_deflation_io   : output dobldobl directed acyclic graphs
quaddobl_evaluate_deflation_io   : output quaddobl directed acyclic graphs
multprec_evaluate_deflation_io   : output multprec directed acyclic graphs
standard_query_matrices          : to look into big standard matrices
dobldobl_query_matrices          : to examine large dobldobl matrices
quaddobl_query_matrices          : to examine large quaddobl matrices
multprec_query_matrices          : to look into big multprec matrices
ts_defmat                        : working with deflation matrices
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standard_multiple_solutions      : group standard solutions after deflation
dobldobl_multiple_solutions      : group dobldobl solutions after deflation
quaddobl_multiple_solutions      : group quaddobl solutions after deflation
standard_deflation_methods       : deflation algorithm with standard numbers
dobldobl_deflation_methods       : deflation algorithm with dobldobl numbers
quaddobl_deflation_methods       : deflation algorithm with quaddobl numbers
multprec_deflation_methods       : deflation algorithm with multprec numbers
drivers_to_deflate_singularities : drivers to the deflation method
ts_deflate                       : interactive test
ts_straight                      : test on straight-line programs
ts_stair                         : test examples from the staircase
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standard_nullity_polynomials     : operations to create nullity matrices
dobldobl_nullity_polynomials     : double double operations for nullity
quaddobl_nullity_polynomials     : quad double operations for nullity
multprec_nullity_polynomials     : multiprecision operations for nullity
standard_nullity_matrices        : creation and evaluation of nullity matrices
dobldobl_nullity_matrices        : double double nullity matrices
quaddobl_nullity_matrices        : quad double nullity matrices
multprec_nullity_matrices        : multiprecision nullity matrices
standard_multiplicity_structure  : determination of dual space at singularity
dobldobl_multiplicity_structure  : multiplicity in double double precision
quaddobl_multiplicity_structure  : multiplicity in quad double precision
ts_multip                        : computation of multiplicity structure
standard_multiple_deflation      : implementation of higher-order deflation
multprec_multiple_deflation      : multiprecision higher-order deflation
standard_probe_kernel            : utilities to determine order of deflation
multprec_probe_kernel            : multiprecision version of probe_kernel
ts_muldef                        : test on higher-order deflation
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varbprec_complex_newton_steps    : variable precision Newton steps
random_conditioned_root_problems : generate and test random root problems
verification_of_solutions        : run sequences of varbprec Newton steps
ts_vmpnewt                       : test on variable precision Newton
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standard_newton_circuits         : run Newton on coefficient circuits
standard_inlined_newton_circuits : on coeff circs with inlined linear solver
standard_refiner_circuits        : condition tables and cluster report
ts_newcirc                       : test Newton on coefficient circuits
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