     MGBI (Minimised Geometric Buchberger algorithm for Integer programming)

  This software is a solving IP based on Groebner Bases. It includes four
files: README, Makefile, mgbi.c, samples.tex.
  
User manual:

 1. Compile the program:
   %make

 2. Run the program:

   %mgbi
    run mgbi, there are following messages:
   
   ********************************************
   *                                          *
   *                IP Solver                 *
   *               version 1.0                *
   *                                          *
   *                 Qiang  Li                *
   *            University of Tsukuba         *
   *                                          *
   ********************************************

   (1)."Input equations:" 

      you can input equations in special form, for example:

         3 x 1 + x 2 + x 3 = 7 ,
         2 x 1 + 3 x 2 + x 4 = 10 .

   (2)."Input function cx" 
     you can input object function in special form, for example:
    
         2 x 1 + x 2 .

   (3). "Reduced Grobner basis:" 
      the system will display the reduced GB and the size of the set of GB:

       reduced Grobner basis :
       [(1,0,0,0,)->(0,0,3,2,)]
       [(0,1,0,0,)->(0,0,1,3,)]

       RGB size=2

   (4). "Input a feasible solution:" 
      you can input any feasible solution of IP, for example:

      x1=1
      x2=1
      x3=3
      x4=5

   (5). "the optimal solution:"
      the system will display the optimal solution of the IP:

      x1=0, x2=0, x3=7, x4=10.


