| dc.description.abstract | We investigate algorithms for decomposing a module $M$ over a finite-dimensional path algebra $\Lambda$. The algorithms first have to construct the endomorphism ring
\[
\End(M) = \Hom(M, M).
\]
\noindent Consequently, we look at three different algorithms for constructing the set of homomorphisms $\HomMN$ between two modules $M$ and $N$. By extension we get $\End_\Lambda(M) = \Hom_\Lambda(M, M)$. After calculating $\End_\Lambda(M)$ we investigate in detail a method for decomposing the module $M$, using a probabilistic approach by iteratively applying Fitting\textquotesingle s Lemma.
Finally, we provide asymptotic bounds for the runtime of all the algorithms. We then categorise them into complexity classes. Constructing the set of homomorphisms $\HomMN$ is shown to be in the complexity class \textbf{P} of polynomial-time functions. | |
