Hello Macaulay2 users,
Calling isSmooth on a toric variety is giving unexpected result. Consider the following affine toric variety:
rayList = {{1, 0, 3/5}, {0, 1, 2}, {5, 0, 1}}
coneList = {{0, 1, 2}}
X = normalToricVariety (rayList, coneList)
Clearly the vectors generating the maximal cone do not form a lattice basis (det matrix rayList == -2). So isSmooth X should return false, but it returns returns true. In fact, if I use the isSmooth provided by the Polyhedra package and call it with the maximal cone above as an argument, it returns false.
i101 : isSmooth coneFromVData matrix rayList
o101 = false
Am I misunderstanding what isSmooth (NormalToricVariety) is supposed to do?
Best regards,
Kumar.