# hull -- The positive hull complex.

## Synopsis

• Usage:
hull(L)
hull(fn)
• Inputs:
• L, a list, of Vectors lying all in the same space.
• fn, ,
• Optional inputs:
• file => ..., default value null, Store result of a computation in a file.
• Outputs:
• C, ,

## Description

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}}; 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 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 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 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 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

## Caveat

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.