regularity C
Given a free complex $C$ over a standard graded polynomial ring, the regularity $r$ of $C$ is the smallest integer such that each basis element of $C_i$ has degree at most $i + r$.
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The regularity is the label of the last row of the Betti table of $C$.
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Here is a slightly more complicated example.
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Although Castelnuovo-Mumford regularity is defined in more general settings (e.g. toric varieties with multi-degrees) this method does not currently handle these extensions. Similarly, Castelnuovo-Mumford regularity can be defined for non-free complexes, but this method doesn't handle that case either.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/Complexes/ChainComplexDoc.m2:4370:0.