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Import the second public release of PHCpack.

OKed by Jan Verschelde.

Mixed-volume computation and polyhedral homotopies by implicit lifting in PHCv2.

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.

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file name                          : short description
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power_lists                        : manipulating support sets of polynomials
ts_powlis                          : 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
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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  : transformations on lists of integer vectors
transforming_laurent_systems       : transformations on Laurent systems
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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
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binomial_system_solvers            : solvers of systems of two monomials
fewnomial_system_solvers           : solvers of fewnomial systems
durand_kerner                      : solve polynomial equation in one variable
ts_binsolve                        : test binomial system solvers
ts_fewnom                          : test fewnomial system solvers
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
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This is the first implementation of polyhedral homotopy continuation.
Everytime PHC is reorganized, I go through a deep pain struggling through
packages as Volumes and Mixed_Homotopy_Continuation.  There are far too
many dynamic structures and pointers to make it efficient.

About half of this library is needed in the other polyhedral methods.
Vertices and fewnomial system solvers are fundamental and deserve a
thorough reorganization.

wc *adb counts 6658 lines of Ada code