These are chat archives for gxyd/sum_convergence

19th
Sep 2015
Gaurav Dhingra
@gxyd
Sep 19 2015 08:07

Perhaps something like real_order would be better.

@jksuom can you please tell, what you think this, real_order be doing then ?

here is the comment, in which you talked about it.
Kalevi Suominen
@jksuom
Sep 19 2015 09:08
I think it should return an element of the group of orders. And those could be the objects of class Order. At least I think those would be the best candidates.
The orders I have in mind should have the form O(x**a), O(x**a*log(x)**b), etc. (not to forget exponentials). It is important that they are defined by functions that do not change sign in a neighbouhood of the limit point. (Here I am thinking of oo.)
Kalevi Suominen
@jksuom
Sep 19 2015 09:18
Then there is the question what to do with expressions like O(sin(x)) (at oo). They have to be excluded somehow.
One possibility might be making O and Order non-equivalent. One could be applied to any function, the other one only to such that define a genuine order.
Kalevi Suominen
@jksuom
Sep 19 2015 09:24
So real_order (in want of a better name) applied to any function would return a genuine order suitable for the function. For example, real_order(sin(x)) == O(1).
Aaron Meurer
@asmeurer
Sep 19 2015 22:10
I’m still unclear why real_order is not just O at oo