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IsIdealHomogeneous -- specify whether an ideal is homogeneous


Whether the input ideal is homogeneous, if known. The value of this input is only used if CheckCM=>true.

If an ideal $I$ is homogeneous and has a geometric vertex decomposition with respect to an indeterminate $y$, which is to say that ${\rm in}_y(I) = C_{y, I} \cap (N_{y, I} + \langle y \rangle)$, then both $C_{y, I}$ and $N_{y, I}$ are also homogeneous. Also, an ideal that is both homogeneous and geometrically vertex decomposable is Cohen-Macaulay [KR, Corollary 4.5].


[KR] Patricia Klein and Jenna Rajchgot. Geometric vertex decomposition and liaison. Forum Math. Sigma, 9 (2021) e70:1-23.

See also

Functions with optional argument named IsIdealHomogeneous :

For the programmer

The object IsIdealHomogeneous is a symbol.