CoCoA:GB.GetNthSyzShifts

GB.GetNthSyzShifts

shifts of the Nth syzygy module computed so far

Description

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

for 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 shifts of the part of the Nth syzygy module computed so far.

Example

  Use R ::= Q[t,x,y,z];
  I := Ideal(x^2-yt,xy-zt,xy);
  $gb.Start_Res(I);
  $gb.Steps(I,6);
  $gb.GetNthSyzShifts(I,2);
Shifts([x^2yz])
-------------------------------
  $gb.Complete(I);
  $gb.GetNthSyzShifts(I,2);
Shifts([x^2yz, txyz, tx^2z, x^3y])
-------------------------------
  J := Ideal(t,x)^3;
  Res(J);
0 --> R^3(-4) --> R^4(-3)
-------------------------------
  $gb.GetNthSyzShifts(J,1);
Shifts([x^3, tx^2, t^2x, t^3])
-------------------------------
  $gb.GetNthSyzShifts(J,2);
Shifts([tx^3, t^2x^2, t^3x])
-------------------------------
  SS := It;
  SS[1];
tx^3
-------------------------------

Syntax

$gb.GetNthSyzShifts(M:IDEAL or MODULE,N:INT):TAGGED(<quotes>shifts</quotes>)

GB.GetNthSyz

GB.GetRes

Res

Shifts

The Interactive Groebner Framework

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