An Efficient Representation for Large Arrays of Rational Expressions∗

The paper describes a method of representing an n-dimensional array of rational expressions as an (n + 1)-dimensional array of scalars and shows how this representation readily supports the implementation of various common array operations. A feature of the representation is that it can take advantage of memorysaving schemes for encoding large, sparse scalar arrays using multi-terminal binary decision diagrams (MTBDDs). The representation involves taking partial fraction expansions of the entries of the array; refining the factorizations of the denominator polynomials as required rather than presupposing the existence of a complete factorization at the outset.