I am using the QPA package with GAP and have the following problem:
I want to, given a path $p$, obtain a list (preferably ordered) of the arrows which make up $p$.
For example, if I have arrows $a,b,c$ in a path algebra $kQ$ and I have the path $p=ab$, I want the list $[a,b]$ to be returned from some function where I only have to input the path (and maybe the path algebra).
I did some digging and only found such a function for the quiver but not the path algebra: 3.7-4 in https://folk.ntnu.no/oyvinso/QPA/qpa/doc/chap3_mj.html#X7C8294338676C80E is a "WalkOfPath" function which returns such a list, but this only works for paths seen as paths in the quiver instead of paths seen as elements of a path algebra. There also does not appear to be a way to take a path of a path algebra and convert it back to a path in the quiver.
Any feedback is appreciated, cheers.
Edit: I have made a function which produces an unordered list of the arrows in a path, however this does not display them in the order in which they appear in the path (the latter would be better, so I am leaving the question open to answering). Also, my function does not include arrow multiplicities, which is something I really want out of it. Here is my function:
patharrows := function(pathalg, path) local i, arrows, output, rels, ideal; if path=Zero(path) then return ; fi; arrows := NthPowerOfArrowIdeal(pathalg, 1); output := ; for i in [1..Length(arrows)] do rels := [arrows[i]]; ideal := Ideal(pathalg, rels); if \in(path, ideal) then Add(output, arrows[i]); fi; od; return output; end;