  This document serves as an arXiv entry point for the appendix to the paper
[13] (the ancillary file e6_proof.pdf -- ``Proof of the tree module property
for exceptional representations of the quiver $\widetilde{\mathbb{E}}_6$'') and
the appendix to the paper [12] (the ancillary file d6_proof.pdf -- ``Proof of
the tree module property for exceptional representations of the quiver
$\widetilde{\mathbb{D}}_6$''). The ancillary files contain the computer
generated part of the proofs of the main results in [13] respectively [12],
giving a complete and general list of tree representations corresponding to
exceptional modules over the path algebra of the canonically oriented Euclidean
quiver $\widetilde{\mathbb{E}}_6$, respectively $\widetilde{\mathbb{D}}_6$. The
proofs (involving induction and symbolic computation with block matrices) were
partially generated by a purposefully developed computer software, outputting
in a detailed step-by-step fashion as if written ``by hand''.
  We also give here a short theoretical introduction and an overview of the
computational method used to prove the formulas given in the papers [13] and
[12].
