Simplifications of 3*sqrt(2)/sqrt(3)/sqrt(6)

On Fri, Jul 3, 2009 at 1:48 PM, Robert Dodier <robert.dodier at gmail.com>wrote:

> > And I think always calling factor for these cases may not be such a good
> > idea.  What if the number is the product of two fairly large primes or
> > even a prime?  Maxima will spend a lot of time trying to find the
> factors.
>
> I don't have a very strong opinion about it, but I am leaning towards
> omitting the call to factor from simplification, and moving it into
> radcan or something like that, on the general theory that we should
> try to avoid potentially expensive operations in simplification
>

I agree that general simplification limit the amount of time it takes on
integer factorization, and that an explicit command (e.g. radcan) should be
called for larger cases.

Here's how I'd limit it...  suppose we think of a 'largish Maxima
calculation' as involving 1000 factorizations (that's a lot), and we don't
want more than say 10 seconds of CPU to be spent on factorization for this
simplification. Then we have a budget of about 10mS per factorization, which
on my machine would allow integers up to about 10^13.  This is a worst-case
analysis, but 10^13 should in any case be adequate for most work.

             -s