Rational Expression Simplification in Maple.

Roman Pearce, CECM

Wednesday September 28th in K9509, Time TBA.


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.