# Obtaining the reduced incidence algebra as a matrix algebra

I want to use Sage to give me the reduced incidence algebra of a poset P as a finite dimensional algebra generated by matrices, that I can use to input this algebra into GAP.

Question: How can I obtain a list of matrices that generate a finite dimensional algebra using Sage? A multiplication table would also be helpful and might be used to obtain the algebra in GAP.

Here how to use GAP to get an algebra generated by matrices:

```
A:=Algebra(Rationals,[[[1,0],[0,1]],[[0,1],[0,0]]]);
```

Here an example how to get the reduced incidence algebra using Sage:

```
n=5
P = posets.TamariLattice(n)
I = P.incidence_algebra(QQ)
T=I.reduced_subalgebra()
display(T.dimension())
```

I found the command "table()" (see http://sporadic.stanford.edu/referenc... ) but it seems to not work to give me the matrices that generated the reduced incidence algebra here.