isSimplicial X
A normal toric variety is simplicial if every cone in its fan is simplicial and a cone is simplicial if its minimal generators are linearly independent over $\QQ$. In fact, the following conditions on a normal toric variety $X$ are equivalent:
For more information, see Proposition 4.2.7 in Cox-Little-Schenck's Toric Varieties.
Projective spaces, weighted projective spaces, and Hirzebruch surfaces are simplicial.
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However, not all normal toric varieties are simplicial.
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To avoid repeating a computation, the package caches the result in the CacheTable of the normal toric variety.