-- -*- M2-comint -*- {* hash: 1851268728 *}

i1 : R=QQ[x_0..x_5]

o1 = R

o1 : PolynomialRing

i2 : C=boundaryCyclicPolytope(3,R)

o2 = 2: x x x  x x x  x x x  x x x  x x x  x x x  x x x  x x x  
         0 1 2  0 2 3  0 3 4  0 1 5  1 2 5  2 3 5  0 4 5  3 4 5

o2 : complex of dim 2 embedded in dim 5 (printing facets)
     equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1

i3 : C.simplexRing

o3 = R

o3 : PolynomialRing

i4 : C.grading

o4 = | -1 -1 -1 -1 -1 |
     | 1  0  0  0  0  |
     | 0  1  0  0  0  |
     | 0  0  1  0  0  |
     | 0  0  0  1  0  |
     | 0  0  0  0  1  |

              6        5
o4 : Matrix ZZ  <--- ZZ

i5 : C.fc_2

o5 = {x x x , x x x , x x x , x x x , x x x , x x x , x x x , x x x }
       0 1 2   0 2 3   0 3 4   0 1 5   1 2 5   2 3 5   0 4 5   3 4 5

o5 : List

i6 : C.facets

o6 = {{}, {}, {}, {x x x , x x x , x x x , x x x , x x x , x x x , x x x ,
                    0 1 2   0 2 3   0 3 4   0 1 5   1 2 5   2 3 5   0 4 5 
     ------------------------------------------------------------------------
     x x x }, {}, {}, {}}
      3 4 5

o6 : List

i7 : dC=dualize C

o7 = 2: v v v  v v v  v v v  v v v  v v v  v v v  v v v  v v v  
         0 1 2  0 1 4  0 3 4  1 2 3  1 2 5  1 4 5  2 3 4  3 4 5

o7 : co-complex of dim 2 embedded in dim 5 (printing facets)
     equidimensional, simplicial, F-vector {0, 0, 0, 8, 12, 6, 1}, Euler = 1

i8 : cC=complement C

o8 = 2: x x x  x x x  x x x  x x x  x x x  x x x  x x x  x x x  
         3 4 5  1 4 5  2 1 5  2 3 4  0 3 4  1 0 4  2 1 3  2 1 0

o8 : co-complex of dim 2 embedded in dim 5 (printing facets)
     equidimensional, simplicial, F-vector {0, 0, 0, 8, 12, 6, 1}, Euler = 1

i9 : dualize cC

o9 = 2: v v v  v v v  v v v  v v v  v v v  v v v  v v v  v v v  
         3 4 5  2 3 5  1 2 5  0 4 5  0 3 4  0 2 3  0 1 5  0 1 2

o9 : complex of dim 2 embedded in dim 5 (printing facets)
     equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1

i10 :