Mixed-volume computation by dynamic lifting in PHCv2.4.85

The aim of dynamic lifting is to control the heights of the lifting values,
to obtain a stable evaluation of the polyhedral homotopy.

When all supports are equal, then the mixed volume is reduced to an
ordinary volume, which is computed by a regular triangulation.

1. Dynamic construction of regular triangulations :
2. The Cayley trick
3. Dynamic construction of mixed subdivision
4. The drivers and black-box computation

A 64-bit version of the dynamic lifting algorithm was provided
in version 2.3.71.

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

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file name                            : short descriptio
-------------------------------------------------------------------------------
standard_integer32_simplices         : simplices of integer polytopes
standard_integer64_simplices         : 64-bit version of simplices
standard_integer32_simplices_io      : input/output of simplices
standard_integer64_simplices_io      : input/output of 64-bit simplices
standard_integer32_triangulations    : triangulations of integer polytopes
standard_integer64_triangulations    : 64-bit version of triangulations
standard_integer64_triangulations_io : input/output of 64-bit triangulations
global_dynamic32_triangulation       : global aspects of dynamic lifting
global_dynamic64_triangulation       : 64-bit version of global dynamic lifting
dynamic32_lifting_functions          : dynamic lifting functions
dynamic64_lifting_functions          : 64-bit dynamic lifting functions
standard_dynamic32_triangulations    : construction of placing triangulation
standard_dynamic64_triangulations    : 64-bit placing triangulation algorithm
ts_dyntri                            : test on dynamic lifting
-------------------------------------------------------------------------------
cayley_embedding                 : embeds tuple in one support 
cayley_trick                     : computing mixed subdivisions
minkowski_polynomials            : volume polynomials
driver_for_minkowski_polynomials : driver to the volume polynomials
ts_drivmink                      : calls the driver for volume polynomials
-------------------------------------------------------------------------------
common_faces_of_polytope         : computation of neighboring faces
enumerate_faces_of_polytope      : extract faces of a triangulation
frequency_graph                  : computes occurencies of points in supports
initial_mixed_cell               : finds an initial mixed cell
flatten_mixed_subdivisions       : flattening of mixed subdivisions
unfolding_subdivisions           : re-lifting flattened parts of subdivisions
triangulations_and_subdivisions  : convert triangulations <> subdivisions
dynamic_mixed_subdivisions       : dynamic lifting in the mixed case
dynamic_polyhedral_continuation  : incremental polyhedral continuation
-------------------------------------------------------------------------------
drivers_for_dynamic_lifting      : menu driver for dynamic lifting
ts_drivdynl                      : calls the menu driver
black_mixed_volume_computations  : blackbox mixed volume computation
apply_induced_permutations       : applies induced permutations to systems
black_polyhedral_continuations   : blackbox polyhedral continuation
-------------------------------------------------------------------------------

The Cayley trick is an efficient way to construct all cells in a mixed
subdivision with the corresponding Minkowksi polynomial.
