  The main result is an elementary proof of holonomicity for A-hypergeometric
systems, with no requirements on the behavior of their singularities,
originally due to Adolphson [Ado94] after the regular singular case by Gelfand
and Gelfand [GG86]. Our method yields a direct de novo proof that
A-hypergeometric systems form holonomic families over their parameter spaces,
as shown by Matusevich, Miller, and Walther [MMW05].
