-- -*- M2-comint -*- {* hash: 1379031189 *} 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 : 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 : 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 : R=QQ[x_0..x_5] o9 = R o9 : PolynomialRing i10 : C=simplex R o10 = 5: x x x x x x 0 1 2 3 4 5 o10 : complex of dim 5 embedded in dim 5 (printing facets) equidimensional, simplicial, F-vector {1, 6, 15, 20, 15, 6, 1}, Euler = 0 i11 : C.isPolytope o11 = true i12 : C.polytopalFacets o12 = {x 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 3 4 0 1 2 3 5 0 1 2 4 5 0 1 3 4 5 0 2 3 4 5 ----------------------------------------------------------------------- x x x x x } 1 2 3 4 5 o12 : List i13 :