Comment #6 on issue 3638 by [email protected]: Automatic series expansion
while applying a function?
http://code.google.com/p/sympy/issues/detail?id=3638
I don't really deal with series expansions, so I can't comment on the
mathematical desirability of representing functions of series expansions,
but I think that the fact that this can be expensive in general should
automatically discounted.
Basically, stuff that happens automatically can be very annoying if you
ever don't want it done. One instance of that is if you just want to
represent log(x + O(x**2)) unevaluated, but another instance is if it's
expensive, and you don't necessarily want to evaluate it when you create
the log.
Applying a function is a bad example. A much simpler thing to think of is
just adding an Order term to an expression (this is applying the Add
function). Under your scheme, any_expression_at_all + O(x**2) would
automatically call series() on any_expression_at_all, even if it's very
expensive. We could make it more efficient by calling series(1), because we
already know that we don't care about terms above x**2. But conversely, if
we did some_expression + O(x**100), to be consistant, we would need to
compute some_expression.series(99).
I want to point out that in the simple cases, this *does* work. More
specifically, any polynomial plus an order term or times an order term
automatically combines with it. In this case, "calling series" is not
expensive, because you basically don't have to call series at all
(actually, I just found a counterexample to that, see issue 3654).
BTW, that's not a bug?!
Yeah, I guess it is. But note that my actual example doesn't really make
sense, because it is trying to expand log(x) at x = 0. But if you use
cos(x) instead of sin(x) it still doesn't work.
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