# Conversion Functions

## `IncidenceStructure(I): Inc -> Inc`

Given an incidence structure $I$ (of any type), return the same structure as a “true” incidence structure (i.e., belonging to the category Inc).

## `NearLinearSpace(I): Inc -> IncNsp`

Given an incidence structure $I$ (of any type), return the same structure as a near–linear space (i.e., belonging to the category `IncNsp`), if possible.

## `LinearSpace(I): Inc -> IncLsp`

Given an incidence structure $I$ (of any type), return the same structure as a linear space (i.e., belonging to the category `IncLsp`), if possible.

## `Design(I, t): Inc, RngIntElt -> Dsgn`

Given an incidence structure $I$ (of any type), return the same structure as a $t$–design (i.e., belonging to the category `Dsgn`), if possible.

## `Example: conv (ex-97a8b8)`

The following example illustrates some of the functions of the previous two sections.

```magma
> I := IncidenceStructure< 8 | {1, 2, 3, 4}, {1, 3, 5, 6}, {1, 4, 7, 8},
>   {2, 5, 6, 7}, {2, 5, 7, 8}, {3, 4, 6, 8} >;
> IsDesign(I, 1);
true 3
> IsDesign(I, 2);
false
> D := Design(I, 1);
> D;
1-(8, 4, 3) Design with 6 blocks
> IsSteiner(D, 1);
false
> IsNearLinearSpace(I);
false

```