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GB.GetNthSyz

returns the part of the Nth syzygy module computed so far
Syntax 

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

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 Syz always determines the complete syzygy module even from within the Interactive Groebner Framework.

Example 
  Use R ::= QQ[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])
-------------------------------


See Also