Given a finite dimensional local commutative algebra over a finite field $K$ and a finite dimensional module $M$. What is the fastest/best way to obtain all submodule from $M$ using a Computer algebra system
 like GAP/QPA? It might be also interesting to hear how you might do that by hand.



Finding all submodules
Here is how you can do it with QPA:



```
gap> A := NakayamaAlgebra(GF(3), [4]);
<GF(3)[<quiver with 1 vertices and 1 arrows>]/<two-sided ideal in <GF(3)[<quiver with 1 vertices and 1 arrows>]>, (1 generators)>>
gap> M := IndecProjectiveModules(A)[1];
<[ 4 ]>
gap> subs := AllSubmodulesOfModule(M);
[ [ <<[ 0 ]> ---> <[ 4 ]>> ], [ <<[ 1 ]> ---> <[ 4 ]>> ], [ <<[ 2 ]> ---> <[ 4 ]>> ], [ <<[ 3 ]> ---> <[ 4 ]>> ], 
  [ <<[ 4 ]> ---> <[ 4 ]>> ] ]

```

I hope that this is helpful.


Best regards, the QPA-team.


