A $d$-dimensional normal toric variety is degenerate if its rays do not span $\QQ^d$. For example, projective spaces and Hirzebruch surfaces are not degenerate.
i1 : assert not isDegenerate toricProjectiveSpace 3 |
i2 : assert not isDegenerate hirzebruchSurface 7 |
Although one typically works with non-degenerate toric varieties, not all normal toric varieties are non-degenerate.
i3 : U = normalToricVariety ({{4,-1,0},{0,1,0}},{{0,1}}); |
i4 : isDegenerate U o4 = true |
Many routines in this package, such as the total coordinate ring, require the normal toric variety to be non-degenerate.