  We introduce a pentagon equation solver, available as part of SageMath, and
use it to construct braid group representations associated to certain anyon
systems. We recall the category-theoretic framework for topological quantum
computation to explain how these representations describe the sets of logical
gates available to an anyonic quantum computer for information processing. In
doing so, we avoid venturing deep into topological or conformal quantum field
theory. Instead, we present anyons abstractly as sets of labels together with a
collection of data satisfying a number of axioms, including the pentagon and
hexagon equations, and explain how these data characterize ribbon fusion
categories (RFCs). In the language of RFCs, our solver can produce $F$-matrices
for anyon systems corresponding to multiplicity-free fusion rings arising in
connection with the representation theory of quantum groups associated to
simple Lie algebras with deformation parameter a root of unity.
