rehomogenizeIdeal -- rehomogenization of a the dehomogenized slack ideal

i1 : V = {{0, 0, 0}, {1, 0, 0}, {1, 1, 0}, {0, 1, 0}, {0, 0, 1}, {0, 1, 1}};

i2 : X = symbolicSlackMatrix V

Order of vertices is 
{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}, {0, 0, 1}, {0, 1, 1}}

o2 = | 0   0    x_0 0    x_1 |
     | x_2 0    x_3 0    0   |
     | 0   x_4  0   0    x_5 |
     | x_6 x_7  0   0    0   |
     | 0   0    x_8 x_9  0   |
     | 0   x_10 0   x_11 0   |

                         6                   5
o2 : Matrix (QQ[x ..x  ])  <--- (QQ[x ..x  ])
                 0   11              0   11

i3 : H = rehomogenizeIdeal(3, X)

o3 = ideal (x x x x   - x x x x  , x x x x   - x x x x  , x x x x  -
             3 6 9 10    2 7 8 11   0 5 9 10    1 4 8 11   1 3 4 6  
     ------------------------------------------------------------------------
     x x x x )
      0 2 5 7

o3 : Ideal of QQ[x ..x  ]
                  0   11

i4 : R = QQ[x_0..x_11];

i5 : Y = matrix {{0, 0, 1, 0, 1}, {1, 0, 1, 0, 0}, {0, x_4, 0, 0, 1}, {1, 1, 0, 0, 0}, {0, 0, 1, 1, 0}, {0, x_10, 0, 1, 0}};

             6       5
o5 : Matrix R  <--- R

i6 : T = graph(QQ[y_0, y_1, y_2, y_3, y_4, y_5, y_6, y_7, y_8, y_9, y_10], {{y_1, y_6}, {y_3, y_6}, {y_3, y_7}, {y_0, y_8}, {y_1, y_8}, {y_4, y_8}, {y_4, y_9}, {y_5, y_9}, {y_0, y_10}, {y_2, y_10}});

i7 : rehomogenizeIdeal(3, Y, T)

o7 = ideal (x x x x   - x x x x  , x x x x   - x x x x  , x x x x  -
             3 6 9 10    2 7 8 11   0 5 9 10    1 4 8 11   1 3 4 6  
     ------------------------------------------------------------------------
     x x x x )
      0 2 5 7

o7 : Ideal of R