Singular 2-0-4 Manual: 5.1.107 regularity

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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.
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 with the property deg( $e_{a,i}) \leq s+i$ 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 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.

User manual for Singular version 2-0-4, October 2002, generated by texi2html.