Returns the cone which is the hull of lattice vectors in L. The output has C.isPolytope==true.
If applied to the string fn the result of a previous computation stored via the option file is read from the file fn.
The hull of L has to be strictly convex.
i1 : L= {{0,1,1,0,0},{0,1,0,1,0},{0,1,0,0,0},{1,0,0,0,1},{1,0,-1,-1,-1},{1,0,0,0,0}};
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i2 : L=apply(L,vector)
o2 = {| 0 |, | 0 |, | 0 |, | 1 |, | 1 |, | 1 |}
| 1 | | 1 | | 1 | | 0 | | 0 | | 0 |
| 1 | | 0 | | 0 | | 0 | | -1 | | 0 |
| 0 | | 1 | | 0 | | 0 | | -1 | | 0 |
| 0 | | 0 | | 0 | | 1 | | -1 | | 0 |
o2 : List
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i3 : C=hull L
o3 = 4: y y y y y y
0 1 2 3 4 5
o3 : complex of dim 4 embedded in dim 4 (printing facets)
equidimensional, non-simplicial, F-vector {1, 6, 14, 16, 8, 1}, Euler = 0
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i4 : C.grading
o4 = | 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 1 1 0 0 |
| 0 1 0 1 0 |
| 1 0 -1 -1 -1 |
| 1 0 0 0 1 |
6 5
o4 : Matrix ZZ <--- ZZ
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i5 : dC=dualize C
o5 = 4: v v v v v v v v
0 1 2 3 4 5 6 7
o5 : complex of dim 4 embedded in dim 4 (printing facets)
equidimensional, non-simplicial, F-vector {1, 8, 16, 14, 6, 1}, Euler = 0
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i6 : dC.grading
o6 = | 0 1 -1 -1 0 |
| 0 1 1 -1 0 |
| 0 1 -1 1 0 |
| 1 0 0 0 -1 |
| 1 0 2 0 -1 |
| 1 0 0 2 -1 |
| 1 0 0 0 1 |
| 0 1 -1 -1 2 |
8 5
o6 : Matrix ZZ <--- ZZ
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The cone is represented as a complex on its rays, hence if dim(Face) is applied to a Face it will return the dimension of the corresponding cone minus one.
This uses the package OldPolyhedra.m2 to compute the facets. Too slow compared to Maple/convex.
If the package ConvexInterface is loaded, then this command calls Maple/Convex. See the corresponding option explained at SRdeformations.
The object hull is a method function with options.