Computes the global sections of a toric Weil divisor D with coefficients v with respect to the coker grading by A. In the same way as v they are represented by vectors (exponent vectors of Laurent monomials in rank target A variables).
If a list of indices L in {0..rank target A -1} is specified, then those Laurent monomial exponents are computed, which induce a linear equivalence of D to an effective divisor with support precisely on L.
i1 : A=matrix {{1, 0}, {0, 1}, {-1, -1}}
o1 = | 1 0 |
| 0 1 |
| -1 -1 |
3 2
o1 : Matrix ZZ <--- ZZ
|
i2 : b=vector {2,0,0}
o2 = | 2 |
| 0 |
| 0 |
3
o2 : ZZ
|
i3 : globalSections(A,b)
o3 = {| -2 |, | -2 |, | -2 |, | -1 |, | -1 |, 0}
| 0 | | 1 | | 2 | | 0 | | 1 |
| 2 | | 1 | | 0 | | 1 | | 0 |
o3 : List
|
i4 : A=matrix {{1, 0}, {0, 1}, {-1, -1},{1,1}}
o4 = | 1 0 |
| 0 1 |
| -1 -1 |
| 1 1 |
4 2
o4 : Matrix ZZ <--- ZZ
|
i5 : b=vector {2,0,0,0}
o5 = | 2 |
| 0 |
| 0 |
| 0 |
4
o5 : ZZ
|
i6 : globalSections(A,b)
o6 = {| -2 |, | -1 |, 0}
| 2 | | 1 |
| 0 | | 0 |
| 0 | | 0 |
o6 : List
|
i7 : globalSections(A,b,{1})
o7 = {| -2 |}
| 2 |
| 0 |
| 0 |
o7 : List
|
This uses the package OldPolyhedra.m2 (if ConvexInterface.m2 is not present) to compute the lattice points of a convex hull. constructHilbertBasis of the package OldPolyhedra.m2 used by latticePoints overwrites global variable C. Fixed this in my local version.
The object globalSections is a method function.