Comment #7 on issue 3638 by [email protected]: Automatic series
expansion while applying a function?
http://code.google.com/p/sympy/issues/detail?id=3638
I think that the fact that this can be expensive in general should
automatically discounted
Yes. That's why I point to another CAS: it seems that this is doable
efficiently.
Basically, stuff that happens automatically can be very annoying if you
ever don't want it done.
Well, what's reason to declare some clear policy for automatically
evaluated stuff or to provide for user some fine-tuning controls like Hold,
HoldPattern, ReleaseHold, etc.
But conversely, if we did some_expression + O(x**100), to be consistant,
we would need to compute some_expression.series(99).
But we already do things like that for
factorial(factorial(1000000000000000000000000000))!
actually, I just found a counterexample to that, see issue 3654
I'm not so sure why. All we need is to know in Mul: we want O(x) terms for
first operand.
(1+x**2)**1000 * O(x) -> ((1+x**2)**1000).series(x,0,1) * O(x) ->
(1+O(x))*O(x)-> O(x)
But if you use cos(x) instead of sin(x) it still doesn't work.
This isn't implemented, as I sad (cos(x)+O(x**2) should be evaluated first,
before Application's eval()). log(1+O(x**2)) - works fine.
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