TITLE: Computer algebra system to simplify huge rational functions (of order 100 Mbytes)
QUESTION [12 upvotes]: I have a huge rational function of three variables (which is of order ~100Mbytes if dumped to a text file) which I believe to be identically zero.  Unfortunately, neither Mathematica nor Maple succeeded in simplifying the expression to zero. 
I substituted a random set of three integers to the rational function and indeed it evaluated to zero; but just for curiosity, I would like to  use a computer algebra system to simplify it. Which computer algebra system should I use? I've heard of Magma, Macaulay2, singular, GAP, sage to list a few. Which is best suited to simplify a huge rational expression?

In case you want to try simplifying the expressions yourself, I dumped available in two notations, Mathematica notation and Maple notation. Unzip the file and do 
<<"big.mathematica"

or 
read("big.maple")

from the interactive shell. This loads expressions called gauge and cft, both rational functions of a1, a2 and b. Each of which is non-zero, but I believe gauge=cft. So you should be able to simplify gauge-cft to zero. The relation comes from a string duality, see e.g. this paper by M. Taki.

REPLY [9 votes]: For highly recursive rational expressions it is better to factor.  Here is a Maple program that does it in 3 minutes on a Core i7 2600, suggested by Mike Monagan:
rec := proc(a) option remember;
  if type(a,{`*`,`+`}) then
    factor(map(rec, a));
  elif type(a,`^`) then
    rec(op(1,a))^op(2,a);
  else a;
  end if;
end proc:

read "big.maple":
CodeTools:-Usage(rec(gauge - cft));  # returns zero
memory used=24.06GiB, alloc change=276.79MiB, cpu time=3.53m, real time=3.00m