Comment #5 on issue 3826 by [email protected]: trigsimp can't reverse tan
double angle formula
http://code.google.com/p/sympy/issues/detail?id=3826
How slow? The groebner algorithm is probably too slow to have on by
default, but unless fu is just as bad, I think it should be enabled by
default, especially if it is robust. Algorithms that aren't enabled by
default might as well not even exist for the vast majority of users,
because they will never bother to enable them. And furthermore, library
code in SymPy itself that calls trigsimp will not benefit (including
simplify()!), and it will be impossible for users to fix it.
Take heurisch as an example. It's ridiculously slow. In fact, if the
expression is just a little too big, it might take literally days to finish
(for all intents and purposes, it hangs). But it is also very powerful, and
before meijerg or full risch, it was all we had. In fact, it is able to
solve an integral that no other system can solve, and SymPy was for some
time listed on the Wikipedia article for the Risch algorithm because of
it. And even now there are a lot of integrals that SymPy can only do
because of it, even some very simple ones. If it were disabled by default,
SymPy would not be known for being able to do any integration, the code
would have gotten stale (no one would ever have found bugs in it and tried
to improve it), and there's even a decent chance that we would have never
made the jump to the more complete integration algorithms we have today.
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