How to Perform Operations on Big O Terms?

[Avichal]

Is there a standard algorithm or procedure that defines addition, multiplication of big O terms.

I want definitions for problems like:-
1) (x-1) * O(x)
2) O((x-a)²) where a is some positive number
etc.

Since I want to implement this on a computer I would prefer some algorithm or paper that defines and tells you how to deal with operations on big O terms.
Thank you!

 

[voko]

The very first hit for "big O notation" was http://en.wikipedia.org/wiki/Big_O_notation =. Now I believe you would not have posted questions, answers to which are so easily found, so I assume there is a problem with that page. What is it?

 

[Avichal]

Yes, I had a look at the Wikipedia page. It's great but I wanted something more algorithmic.
I am looking for something like a research paper which would algorithmic-ally explain how to compute order of an expression.
For e.g.:- O(x) + O(y) .. multivariate order arithmetic is tough to handle
O(x-a) .. order around some arbitrary point

Basically I want it from the perspective of implementing a computer algebra system (CAS)

 

[voko]

I am not aware of such papers and I am not convinced this is something one should be bothered with. The big O notation is used almost exclusively with very particular arguments, such as powers of a variable or logarithms. The notation itself is never the most difficult, or even just difficult, thing in any research. Finding an estimate is the difficult part, wrapping it in the big O notation is trivial.

I suggest that you tackle something more useful.