# Difference between revisions of "ApCoCoA-1:BBSGen.TraceSyzLinStep"

## BBSGen.TraceSyzLinStep

This function computes the K[c]-linear summand of 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.TraceSyzLinStep(Pi,X,OO,BO,N);
BBSGen.TraceSyzLinStep(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 other wise the result is 0.
Pi must be a product of at least two different indeterminates.

```

• @param The term Pi, the distinguished variable of choice that divides Pi, order ideal OO, border BO, the number of Indeterminates of the polynomial ring K[x_1,...,x_N].

• @return K[c]-linear summand of the trace polynomial with respect to Pi and the 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^2x;

X:=x;   ------------Choice of the Variable

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

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

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

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