> So now I've at least learned that in this instance, a symbolic
solution isn't really practical :-)
I think the correct conclusion is actually that an *exact* symbolic
solution is sometimes not practical. Symbolic methods could be very
helpful in characterizing the qualitative behavior of this system in
various ways.
As for:
> ?!?!?! Did I read that correctly? Days?
> Seriously, is that sort of run time something I should expect?
Most things are actually very fast:
factor(expand(product(sum((random(20)-10)*x^i,i,0,20),j,1,2))))
taylor(log(cos(x)),x,0,50)
But Radcan in particular can be very slow. As the documentation says:
"For some expressions RADCAN can be quite time consuming. This is the
cost of exploring certain relationships among the components of the
expression for simplifications based on factoring and partial-fraction
expansions of exponents." Though it probably wouldn't have done any
good in this particular case, isn't it satisfying to think that Maxima
is working hard on your behalf while you sleep :-) ?
> how can I tell if Maxima is actually working on something vs spinning
its wheels
There really is no way to tell, I'm afraid. Sometimes a huge mess
simplifies down to something compact after much grinding away, sometimes
it doesn't ... and sometimes Maxima is simply in an infinite loop. But
most things really do come back very quickly. I think you'll discover
that the real problem is not so much that things take too long to
return, but rather than the result is not useful because it is too big,
or in the wrong form, or whatever.
-s