Fixing unexpected behaviour in ToricHigherDirectImages

[sashahbc]

There was unexpected behaviour from the output of HDI, which ultimately came from an incorrect lattice point computation in a polyhedron. I added an internal method for the correct computation idealFromPolyhedron which uses rawHilbertBasis to compute the appropriate lattice points. I also added the example which demonstrated the incorrect behaviour as a test.

The example in question is

X=normalToricVariety({{1,2},{2,3},{1,1},{1,0},{-1,-1},{0,1}}, {{0,1},{1,2},{2,3},{3,4},{4,5},{5,0}});
Y=normalToricVariety({{-1,-1},{1,0},{0,1}},{{0,1},{1,2},{2,0}});
M = matrix {{1,0},{0,1}};
phi = map(Y,X,M);
D={-3,-6,-3,0,0,0};
prune HDI(phi,0,D)
                 2
o6 = (QQ[x ..x ])
          0   2
o6 : QQ[x ..x ]-module, free, degrees {3..4}
         0   2

The source is an interated blowup of PP^2, and this is computing the pushforward of a line bundle via the composition of blowdowns, a birational map. The output turns out to be of rank two, which doesn't make sense---the fibres should generically be rank one. The corrected version appropriately outputs a presentation of the ideal m^3, where m is the blown up point.

o8 = cokernel {3} | x_1  0    0    |
              {3} | -x_2 x_1  0    |
              {3} | 0    -x_2 x_1  |
              {3} | 0    0    -x_2 |
                                                4
o8 : QQ[x ..x ]-module, quotient of (QQ[x ..x ])
         0   2                           0   2

[mahrud]

You seem to have accidentally added some spaces here.

[mahrud]

If the name includes "ideal", I think the output should also include an ideal, no?