\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Matthias K\"oppe and Sven Verdoolaege}
%
%
\medskip
\noindent
%
%
{\bf Computing Parametric Rational Generating Functions with a Primal Barvinok Algorithm}
%
%
\vskip 5mm
\noindent
%
%
%
%
Computations with Barvinok's short rational generating functions are
traditionally being performed in the dual space, to avoid the
combinatorial complexity of inclusion--exclusion formulas for the
intersecting proper faces of cones. We prove that, on the level of
indicator functions of polyhedra, there is no need for using
inclusion--exclusion formulas to account for boundary effects: All
linear identities in the space of indicator functions can be purely
expressed using partially open variants of the full-dimensional
polyhedra in the identity. This gives rise to a practically
efficient, parametric Barvinok algorithm in the primal space.
\bye