Root refining and a modified Newton's method in PHCv2.3.18

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.

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file name                        : short description
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standard_root_refiners           : refining over standard complex numbers
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
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standard_numerical_rank          : numerical rank by SVD for standard numbers
multprec_numerical_rank          : numerical rank by SVD for multprec numbers
standard_newton_steps            : Newton step with SVD in standard arithmetic
multprec_newton_steps            : Newton step with SVD in multprec arithmetic
standard_aitken_extrapolation    : Aitken extrapolation in several variables
ts_newton                        : interactive testing routine
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
multprec_derivative_trees        : multiprecision version of derivative_trees
ts_dertrees                      : interactive test on derivative trees
standard_deflate_singularities   : adds new equations with standard coeff
multprec_deflate_singularities   : adds new equations with multprec coeff
standard_deflation_trees         : stores trees of standard deflated systems
multprec_deflation_trees         : stores trees of multprec deflated systems
standard_deflation_trees_io      : i/o of trees of standard deflated systems
multprec_deflation_trees_io      : i/o of trees of multprec deflated systems
ts_jactrees                      : test on trees of Jacobian matrices
standard_deflation_methods       : deflation algorithm with standard 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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monomial_hashing                 : hashing of Jacobian matrices via monomials
standard_jacobian_trees          : remember table for standard Jaco matrices
multprec_jacobian_trees          : remember table for multprec Jaco matrices
standard_deflation_matrices      : standard block assignment operations
multprec_deflation_matrices      : multprec block assignment operations
standard_evaluate_deflation      : evaluation of standard deflation matrices
multprec_evaluate_deflation      : evaluation of multprec deflation matrices
standard_evaluate_deflation_io   : output of directed acyclic graphs
multprec_evaluate_deflation_io   : output of directed acyclic graphs
standard_query_matrices          : to look into big standard matrices
multprec_query_matrices          : to look into big multprec matrices
ts_defmat                        : working with deflation matrices
standard_nullity_polynomials     : operations to create nullity matrices
multprec_nullity_polynomials     : multiprecision operations for nullity
standard_nullity_matrices        : creation and evaluation of nullity matrices
multprec_nullity_matrices        : multiprecision nullity matrices
standard_multiplicity_structure  : determination of dual space at singularity
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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