Polyhedral homotopies by implicit lifting in PHCpack version 2.3.21

This directory contains software for the computation of mixed volumes,
according to the recursive formula Bershtein used in his proof.
Also the homotopy method of Bernshtein has been implemented.

The minor modification in release 2.2 is the addition of a black-box
routine to solve polynomials in one variable, using Durand-Kerner
(a.k.a. the method of Weierstrass), and a black-box solver for systems
with few monomials.  Since 2.3.06 a new fewnomial system solver exists,
and in release 2.3.11, the old fewnomial solvers were removed.

-------------------------------------------------------------------------------
file name                          : short description
-------------------------------------------------------------------------------
supports_of_polynomial_systems     : manipulating support sets of polynomials
ts_supports                        : test the power lists
vertices                           : extracting vertices from supports
drivers_for_vertex_points          : drivers to the vertex extraction
ts_drivpts                         : calls the driver to vertices
-------------------------------------------------------------------------------
transformations                    : unimodular transformations on monomials
transformations_io                 : input/output of unimodular transformations
integer_vectors_utilities          : utilities to manipulate integer vectors
transforming_solutions             : transformations on solution lists
transforming_integer_vector_lists  : transforming lists of integer vectors
transforming_laurent_systems       : transformations on Laurent systems
-------------------------------------------------------------------------------
trees_of_vectors                   : data structure to hold outer normals
trees_of_vectors_io                : input/output of trees of vectors
lists_of_vectors_utilities         : utilities to manipulate lists of vectors
arrays_of_lists_utilities          : utilities to manipulate arrays of lists
volumes                            : compute volumes and mixed volumes
ts_impvol                          : test on mixed-volume computation
-------------------------------------------------------------------------------
standard_durand_kerner             : solve polynomial equation in one variable
multprec_durand_kerner             : multi-precision Durand-Kerner method
hybrid_durand_kerner               : hybrid standard/multi-precision version
ts_durker                          : test polynomial equation solver
mixed_homotopy_continuation        : polyhedral continuation 
set_structures_and_volumes         : combines product and polyhedral methods
generic_position                   : test on genericity of system
driver_for_polyhedral_continuation : set-up for continuation
drivers_for_implicit_lifting       : menu-driver for implicit lifting
ts_drivimpl                        : calls the menu-driver for implicit lifting
black_box_univariate_solvers       : called by the black-box solver (phc -b)
-------------------------------------------------------------------------------

This is the first implementation of polyhedral homotopy continuation.
Some design mistakes make it inefficient and hard to maintain, although
there is progress: fewnomial system solvers are revised and out.
