# Singular

### 5.1.128 regularity

Syntax:
regularity ( list_expression )
regularity ( resolution_expression )
Type:
int
Purpose:
computes the regularity of a homogeneous ideal, resp. module, from a minimal resolution given by the argument.
Let be a minimal resolution of I considered with homogeneous maps of degree 0. The regularity is the smallest number with the property deg( for all .
Note:
If applied to a non minimal resolution only an upper bound is returned.
If the input to the commands res and mres is homogeneous the regularity is computed and used as a degree bound during the computation unless option(notRegularity); is given.
Example:
  ring rh3=32003,(w,x,y,z),(dp,C); poly f=x11+y10+z9+x5y2+x2y2z3+xy3*(y2+x)^2; ideal j=homog(jacob(f),w); def jr=res(j,0); regularity(jr); ==> 25 // example for upper bound behaviour: list jj=jr; regularity(jj); ==> 25 jj=nres(j,0); regularity(jj); ==> 27 jj=minres(jj); regularity(jj); ==> 25 
See fres; list; minres; mres; option; res; resolution; sres.