Rational Expression Simplification in Maple.
Roman Pearce, CECM
Wednesday September 28th in K9509, Time TBA.
Abstract We present some improvements to Maple's normal command which is used to simplify rational expressions. The current Maple places the expression over a common denominator which is not the LCM before it cancels a GCD. This is a problem on large multivariate examples. The new code factors sub-expressions and replaces the factors with variables. This factored form simplifies quickly. To undo the substitution we must expand a multivariate polynomial with products of powers of factors. We show how to do this efficiently. The algorithm was added to Maple and on the first Fermat benchmark it runs about 40x faster than Magma and 18x faster than Fermat.