# ApCoCoA-1:BBSGen.TraceSyzStep

## BBSGen.TraceSyzStep

This function computes the trace polynomial T_{Pi,X} with respect to a given term Pi and a variable from ring K[x_1,...,x_N].(see BBSGen.TraceSyzFull)

### Syntax

```BBSGen.TraceSyzStep(Pi,X,OO,BO,N);
BBSGen.TraceSyzStep(Pi:POLY,X:POLY,OO:LIST,BO:LIST,N:INTEGER):LIST
```

### Description

``` Note the following:
The chosen variable must be a divisor of the term Pi.
Pi must be a product of at least two different indeterminates otherwise the result is 0.

```
• @param The term Pi from K[x_1,...,x_N], the distinguished variable of choice from {x_1,...,x_N}, order ideal OO, border BO, the number of indeterminates of the polynomial ring K[x_1,...,x_N].

• @return Trace polynomial T_{Pi,X} with respect to a term Pi and a variable X.

#### Example

```Use R::=QQ[x[1..2]];

OO:=\$apcocoa/borderbasis.Box([1,1]);
BO:=\$apcocoa/borderbasis.Border(OO);
Mu:=Len(OO);
Nu:=Len(BO);
N:=Len(Indets());
Pi:=x[1]^2x[2];

X:=x[1];   ------------Choice of the Indeterminate

Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]];

BBSGen.TraceSyzStep(Pi,X,OO,BO,N);

c[1,2]t[1,2,3,1] + c[2,2]t[1,2,3,2] +
c[3,2]t[1,2,3,3] + c[4,2]t[1,2,3,4] +
c[1,4]t[1,2,4,1] + c[2,4]t[1,2,4,2] +
c[3,4]t[1,2,4,3] + c[4,4]t[1,2,4,4] +
t[1,2,1,3] + t[1,2,2,4]

-------------------------------
```