# Construction of an SLP-Group and its Elements

## Structure Constructors

### `SLPGroup(n): RngIntElt -> GrpSLP`

Construct the free group $F$ of straight-line programs on $n$ generators, where $n$ is a non-negative integer. The $i$-th generator may be referenced by the expression `F.i`, $i = 1, \ldots, n$.

### `Example: SLP Group (ex-059102)`

The statement

```magma
> F := SLPGroup(2);

```

creates the free group on two generators. Here the generators may be referenced using the standard names, `F.1` and `F.2`. Group operations on the elements will be stored as part of the result.

## Construction of an Element

### `Identity(G): GrpSLP -> GrpSLPElt`

### `Id(G): GrpSLP -> GrpSLPElt`

### `G ! 1: GrpSLP, RngIntElt -> GrpSLPElt`

Construct the identity element (the straight-line program $[]$ of length 0) for the SLP-group $G$.