Given a Complex it returns the CoComplex of complement Faces and vice versa.
The complement (co)complex cC is remembered in C.complementComplex=cC and cC.complementComplex=C.
i1 : R=QQ[x_0..x_4] o1 = R o1 : PolynomialRing |
i2 : addCokerGrading R
o2 = | -1 -1 -1 -1 |
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
5 4
o2 : Matrix ZZ <--- ZZ
|
i3 : C=simplex R
o3 = 4: x x x x x
0 1 2 3 4
o3 : complex of dim 4 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 1}, Euler = 0
|
i4 : bC=boundaryOfPolytope C
o4 = 3: x x x x x x x x x x x x x x x x x x x x
0 1 2 3 0 1 2 4 0 1 3 4 0 2 3 4 1 2 3 4
o4 : complex of dim 3 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 0}, Euler = -1
|
i5 : cbC=complement bC
o5 = 0: x x x x x
4 3 2 1 0
o5 : co-complex of dim 0 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {0, 5, 10, 10, 5, 1}, Euler = 1
|
i6 : complement cbC == bC o6 = true |