This problem naturally arise in automatic parallelization of programs (in particular vectorization of loops). It is also needed in computer aided design, where some mechanical parts are modeled by polyhedron and we need to know their volumes for cost/weight computation.
We describe an algorithm (improvement/completion of the previous algorithms). It essentially carries out recursion on the variables, where each recursion consists of projection (variables elimination) and lifting (symbolic integration in suitable measure). In order to control the huge intermediate result swell, inconsistent and redundant computational branches are detected and eliminated.
