The MixedVol Algorithm for fast mixed volume computation in PHCv2.3.16

This directory is the main feature in release v2.3.13 of PHCpack.

This directory contains a translation of the C software "MixedVol" to 
compute mixed volumes fast, derived from the code "MixedVol", described in

  Tangan Gao, T. Y. Li, Mengnien Wu:
  "Algorithm 846: MixedVol: a software package for mixed-volume computation"
  ACM Transactions on Mathematical Software (TOMS), 31(4):555-560, 2005.

Their "ReadMe" file in the distribution of the software contains the following
lines (showing that Xing Li contributed as well):
"MixedVol: Polynomial system mixed volume calculation program.
 version 1.0 Copyright (C) 2003  Tangan Gao, T. Y. Li, Xing Li, and Mengnien Wu.
 This program is free software; you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation; either version 2 of the License, or
 (at your option) any later version."

The conversion of the source code from C++ down to C was done by Yan Zhuang.

The program "ts_mv2c.adb" calls the C software "MixedVol" via
the intermediate interface program mv.c.

------------------------------------------------------------------------------
file name                        : short description
------------------------------------------------------------------------------
convsub.adb                      : converting output into phc format
------------------------------------------------------------------------------
simplex_pivoting                 : pivoting operations in simplex algorithm
prepare_for_mv                   : preprocessing for mixed-volume computation
cell_stack                       : stack of mixed cells
mixed_volume                     : main routine to compute the mixed volume
relation_table                   : edges on lower hull of Minkowski sums
one_level_lp                     : performs LP tests at one level
form_lp                          : defines the LP problems at all levels
index_tree_lp                    : data + operations on trees of LP problems
zero_index_tree                  : case of level 0 at tree of LP problems
------------------------------------------------------------------------------
mv.h and mv.c                    : C program to compute mixed volume
mv.ads and mv.adb                : Ada tranlation of the program mv
ts_mv2c.adb                      : calls the C program mv
ts_mv.adb                        : calls the Ada translation of mv
------------------------------------------------------------------------------
MixedVol_Algorithm               : interface to MixedVol for use in phc
ts_mva                           : standalone test on MixedVol_Algorithm
------------------------------------------------------------------------------
