Returns the dual grading of (i.e., a matrix whose row are) the dual polytope of C. The rows are sorted according to the polytopalFacets of C.
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
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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
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i4 : dA=dualGrading C
o4 = | -1 -1 -1 4 |
| -1 -1 4 -1 |
| -1 4 -1 -1 |
| 4 -1 -1 -1 |
| -1 -1 -1 -1 |
5 4
o4 : Matrix QQ <--- QQ
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i5 : dA===grading dualize C o5 = true |
i6 : dA===C.dualComplex.simplexRing.grading o6 = true |
i7 : pf=polytopalFacets C
o7 = {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
o7 : List
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i8 : coordinates pf#0
o8 = {{-1, -1, -1, -1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}}
o8 : List
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i9 : (dualGrading C)^{0}
o9 = | -1 -1 -1 4 |
1 4
o9 : Matrix QQ <--- QQ
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