  Intersection numbers of twisted cocycles arise in mathematics in the field of
algebraic geometry. Quite recently, they appeared in physics: Intersection
numbers of twisted cocycles define a scalar product on the vector space of
Feynman integrals. With this application, the practical and efficient
computation of intersection numbers of twisted cocycles becomes a topic of
interest. An existing algorithm for the computation of intersection numbers of
twisted cocycles requires in intermediate steps the introduction of algebraic
extensions (for example square roots), although the final result may be
expressed without algebraic extensions. In this article I present an
improvement of this algorithm, which avoids algebraic extensions.
