CoCoA:GB.GetNthSyz

GB.GetNthSyz

returns the part of the Nth syzygy module computed so far

Description

This function, if used after executing Res(M), returns the Nth

syzygy module for M. Within the Interactive Groebner Framework, in

which resolutions may be computed one step at a time, the function returns the part of the Nth syzygy module computed so far. In contrast, the function <ttref>Syz</ttref> always determines the complete syzygy module even from within the Interactive Groebner Framework.

Example

  Use R ::= Q[t,x,y,z];
  I := Ideal(x^2-yt,xy-zt,xy);
  $gb.Start_Res(I);
  $gb.Step(I);
  $gb.GetNthSyz(I,1);  $gb.GetNthSyz(I,2);
Module([[0]])
-------------------------------
Module([[0]])
-------------------------------
  $gb.Step(I);
  $gb.GetNthSyz(I,1);  $gb.GetNthSyz(I,2);
Module([0, 0])
-------------------------------
Module([[0]])
-------------------------------
  $gb.Steps(I,5);
  $gb.GetNthSyz(I,1);  $gb.GetNthSyz(I,2);
Module([-xz, -y^2, yz])
-------------------------------
Module([[0]])
-------------------------------
  $gb.Complete(I);
  $gb.GetNthSyz(I,1);  $gb.GetNthSyz(I,2);
Module([-xz, -y^2, yz], [tz, xy, 0], [0, -x^2 + ty, -tz], [-x^2 + ty, 0, xy])
-------------------------------
Module([-x, -y, 0, z], [-t, -x, -y, 0])
-------------------------------

Syntax

$gb.GetNthSyz(M:IDEAL or MODULE,N:INT):MODULE

GB.GetNthSyzShifts

GB.GetRes

Res

Syz

The Interactive Groebner Framework

   <type>groebner</type>
   <type>groebner-interactive</type>
   <type>ideal</type>
   <type>module</type>