# regularity(...,Weights=>...)

## Synopsis

• Usage:
regularity(..., Weights => w)
• Inputs:
• w, a list, a list of integers

## Description

The module or chain complex provided should be over a ring whose degree length (see degreeLength) is the same as the length of the list w. The dot products of w with the multi-degrees occurring will be used in the resulting computation.

## Further information

• Default value: null
• Function: regularity -- compute the Castelnuovo-Mumford regularity
• Option key: Weights -- assigning weights to the variables

## Functions with optional argument named Weights :

• betti(...,Weights=>...)
• "minimalBetti(Ideal,Weights=>...)" -- see minimalBetti(Ideal) -- minimal betti numbers of (the mininimal free resolution of) a homogeneous ideal or module
• "minimalBetti(Module,Weights=>...)" -- see minimalBetti(Ideal) -- minimal betti numbers of (the mininimal free resolution of) a homogeneous ideal or module
• "monoid(...,Weights=>...)" -- see monoid -- make or retrieve a monoid
• "newRing(...,Weights=>...)" -- see newRing -- make a copy of a ring, with some features changed
• regularity(...,Weights=>...)
• "symmetricAlgebra(...,Weights=>...)" -- see symmetricAlgebra -- the symmetric algebra of a module
• "tensor(...,Weights=>...)" -- see tensor(Ring,Ring) -- tensor product