### Obtaining admissible relations for acyclic tree quivers with Sage for QPA

Let $Q$ be a finite acyclic quiver which is a tree as an undirected graph.

Question: Is there a way to use Sage to obtain all admissible ideals $I$ in the quiver algebra $KQ$ (those are simply the ideals generated by paths of lenghts at least two)?

The output should be so that it can be read by the GAP-package QPA.

Here an example:

The input is the quiver $Q$ given by

```
Quiver( ["v1","v2","v3","v4"], [["v1","v2","a1"],["v2","v3","a2"],["v3","v4","a3"]] )
```

The output is the 5 admissible ideals given as follows:

`[ [],[ `~~(1)*a1*a2, (1)*a2*a3 ~~a1*a2, a2*a3 ], [ ~~(1)*a2*a3 ~~a2*a3 ], [ ~~(1)*a1*a2 ~~a1*a2 ], [ ~~(1)*a1*a2*a3 ~~a1*a2*a3 ] ]

(more generally the number of admissible ideals for a linear oriented line quiver is given by the Catalan numbers)