# 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
```

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