| * This input file is an example for generating |
| * integral solutions to the following system of linear inequalities: |
| * 10 x1 + 7 x2 <= 70 |
| * 11 x1 + 5 x2 >= 55 |
| * x1 >= 0, x2 >= 0 |
| * By using the fact that 0<=x1<=7 and 0<=x2<=10, we apply |
| * the (binary representation) substitution: |
| x1 = 4 x13 + 2 x12 + x11 (all binary variables) |
| x2 = 8 x24 + 4 x23 + 2 x22 + x21 (all binary variables) |
| * The reduced system of linear inequalities is the input data. |
| * Since all integral (i.e. 0-1) solutions are extreme points, |
| * the integral extreme points are in one-to-one correspondence |
| * with the integral solutions to the original system. In this |
| * example, there are 194 extreme points among which 10 are |
| * integral (0-1) solutions. |
| |
| H-representation |
| begin |
| 16 8 integer |
| 0 1 0 0 0 0 0 0 |
| 0 0 1 0 0 0 0 0 |
| 0 0 0 1 0 0 0 0 |
| 0 0 0 0 1 0 0 0 |
| 0 0 0 0 0 1 0 0 |
| 0 0 0 0 0 0 1 0 |
| 0 0 0 0 0 0 0 1 |
| 1 -1 0 0 0 0 0 0 |
| 1 0 -1 0 0 0 0 0 |
| 1 0 0 -1 0 0 0 0 |
| 1 0 0 0 -1 0 0 0 |
| 1 0 0 0 0 -1 0 0 |
| 1 0 0 0 0 0 -1 0 |
| 1 0 0 0 0 0 0 -1 |
| 70 -40 -20 -10 -56 -28 -14 -7 |
| -55 44 22 11 40 20 10 5 |
| end |