|  |  5.1.130 regularity 
See
 fres;
 list;
 minres;
 mres;
 option;
 res;
 resolution;
 sres.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
 ![$0 \rightarrow\ \bigoplus_a K[x]e_{a,n}\ \rightarrow\ \dots
\rightarrow\ \bigoplus_a K[x]e_{a,0}\ \rightarrow\
I\ \rightarrow\ 0$](sing_175.png) 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
 resandmresis homogeneous
the regularity is computed and used as a degree bound during
the computation unlessoption(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
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