Compute Castelnuovo-Mumford regularity

asked 2026-01-26 16:50:31 +0100

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updated 2026-01-26 16:50:59 +0100

Is there a command to compute the Castelnuovo--Mumford regularity of a homogeneous ideal?

Definition. If $\beta_{i,j}(I)$ denotes the graded Betti numbers of a minimal graded free resolution of $I$, then $$ \operatorname{reg}(I) = \max \{{ j -i :\beta_{i,j}(I) \neq 0 \}} $$

I have checked the documentation, but I did not find such a command under Graded free resolution.

If such a command exists, do you know whether it is more efficient than the one provided in Macaulay2?

Thanks a lot in advance!

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