isSmooth giving unexpected results.

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Kumar Sannidhya Shukla

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May 26, 2025, 12:47:09 PMMay 26
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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.
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