-- -*- M2-comint -*- {* hash: -1945377380 *}

i1 : R=QQ[x_0..x_4]

o1 = R

o1 : PolynomialRing

i2 : C=simplex(R)

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

o2 : complex of dim 4 embedded in dim 4 (printing facets)
     equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 1}, Euler = 0

i3 : grading C

o3 = | -1 -1 -1 -1 |
     | 1  0  0  0  |
     | 0  1  0  0  |
     | 0  0  1  0  |
     | 0  0  0  1  |

              5        4
o3 : Matrix ZZ  <--- ZZ

i4 : dC=C.dualComplex

o4 = 4: v v v v v  
         0 1 2 3 4

o4 : complex of dim 4 embedded in dim 4 (printing facets)
     equidimensional, simplicial

i5 : grading dC

o5 = | -1 -1 -1 4  |
     | -1 -1 4  -1 |
     | -1 4  -1 -1 |
     | 4  -1 -1 -1 |
     | -1 -1 -1 -1 |

              5        4
o5 : Matrix QQ  <--- QQ

i6 : fc(dC);

i7 : dC

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

o7 : complex of dim 4 embedded in dim 4 (printing facets)
     equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 1}, Euler = 0

i8 :