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GB.GetNthSyzShifts

Syntax

GB.GetNthSyzShifts(M:IDEAL or MODULE,N:INT):TAGGED("shifts")
    

Summary

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
-------------------------------
        
    

See Also