5.1.107 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 list expression.


\noindent
Let $0 \rightarrow\ \bigoplus_a K[x]e_{a,n}\ \rightarrow\ \dots
  \rightarrow\ \bigoplus_a K[x]e_{a,0}\ \rightarrow\
  I\ \rightarrow\ 0$
be a minimal resolution of I considered with homogeneous maps of degree 0.
The regularity is the smallest number $s$ with the property deg($e_{a,i})
 \leq s+i$ for all $i$.
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 behavior:
  list jj=jr;
  regularity(jj);
==> 25
  jj=nres(j,0);
  regularity(jj);
==> 27
  jj=minres(jj);
  regularity(jj);
==> 25
See
list;
minres;
mres;
option;
res;
resolution;
sres.
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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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