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{\bf Matthias K\"oppe and Sven Verdoolaege}
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{\bf Computing Parametric Rational Generating Functions with a Primal Barvinok Algorithm}
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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.



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