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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

- symbolic computation program/software
- What is the best way to factor arbitrary polynomials?
- Find symbolic integral for expression containing multivariate polynomials
- Resultant of Two Univariate Polynomials
- Algorithms for Symbolic Manipulation
- Simplifying polynomials

```
<<"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.

- Is there a symbolic math package for octave?
- Find symbolic integral for expression containing multivariate polynomials
- What is the best way to factor arbitrary polynomials?
- Computing with ideals: over $K$ or over $\mathbb{Q}\subseteq K$? does it matter?
- symbolic computation program/software
- Resultant of Two Univariate Polynomials
- Algorithms for Symbolic Manipulation
- Algorithms for symbolic definite integration?
- Simplifying polynomials
- How much does symbolic integration mean to mathematics?

*Mathematica* can actually prove that `gauge-cft`

is exactly zero.

To carry out the proof observe that expression for `gauge`

is much smaller than the `cft`

. Hence we first canonicalize `gauge`

using `Together`

, and then multiply `cft`

by it denominator:

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
```

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