Make a co-complex from a list of faces and/or facets.
This is mostly used internally but may be occasionally useful for the end user.
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 : grading R
o3 = | -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
o3 : Matrix ZZ <--- ZZ
|
i4 : dC=dualize C
o4 = 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
o4 : co-complex of dim 2 embedded in dim 5 (printing facets)
equidimensional, simplicial, F-vector {0, 0, 0, 8, 12, 6, 1}, Euler = 1
|
i5 : fdC=fc dC
o5 = {{}, {}, {}, {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
------------------------------------------------------------------------
v v v }, {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 0 1 2 3 0 1 2 4 0 1 2 5 0 1 3 4 0 1 4 5 0 2 3 4
------------------------------------------------------------------------
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 3 4 5 1 2 3 4 1 2 3 5 1 2 4 5 1 3 4 5 2 3 4 5
------------------------------------------------------------------------
{v 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 3 4 0 1 2 3 5 0 1 2 4 5 0 1 3 4 5 0 2 3 4 5
------------------------------------------------------------------------
v v v v v }, {v v v v v v }}
1 2 3 4 5 0 1 2 3 4 5
o5 : List
|
i6 : Rdual=simplexRing dC o6 = Rdual o6 : PolynomialRing |
i7 : grading Rdual
o7 = | -1 -1 -1 -1 5 |
| -1 -1 -1 5 -1 |
| -1 -1 5 -1 -1 |
| -1 5 -1 -1 -1 |
| 5 -1 -1 -1 -1 |
| -1 -1 -1 -1 -1 |
6 5
o7 : Matrix QQ <--- QQ
|
i8 : dC1=coComplex(Rdual,fdC)
o8 = 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
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 : dC==dC1 o9 = true |