### 5.1.132 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.

User manual for Singular version 4.4.1, 2025, generated by texi2html.