I am new to Polymake and I'm trying to use it for computations in toric geometry.

I have tried the following example to test if a toric divisor is Cartier, but got an error that I don't understand:

Code: Select all

```
polytope > application "fulton";
fulton > $tv = new NormalToricVariety(new PolyhedralFan(INPUT_RAYS=>[[-1,-1,0],[-1,-1,-2],[3,0,2],[0,3,2]], INPUT_CONES=>[[0,1],[0,2,3],[1,2,3]]));
fulton > print $tv->PROJECTIVE;
polymake: used package cdd
cddlib
Implementation of the double description method of Motzkin et al.
Copyright by Komei Fukuda.
http://www-oldurls.inf.ethz.ch/personal/fukudak/cdd_home/
false
fulton > $td = $tv->DIVISOR(COEFFICIENTS=>[1,1,1,1]);
fulton > print $td->Q_CARTIER;
polymake: WARNING: rule DIVISOR.Q_CARTIER, DIVISOR.CARTIER_DATA : RAYS, DIVISOR.COEFFICIENTS, MAXIMAL_CONES, LINEAL
ITY_SPACE ( applied to parent ) failed: too many solutions for Cartier data
true
fulton > print $td->CARTIER;
polymake: WARNING: could not compute 'CARTIER' probably because of unsatisfied preconditions:
precondition : PRINCIPAL ( CARTIER : )
precondition : SMOOTH_FAN ( DIVISOR.CARTIER : ) ( applied to parent )
precondition : DIVISOR.Q_CARTIER ( DIVISOR.CARTIER : ) ( applied to parent )
```

Are these types of toric varieties (non-complete, some maximal cones are not of maximal dimension) not fully supported in polymake?

I'm grateful for any explanation.