Computer algebra system that handles error terms?

CRGreathouse · 2009-05-26, 18:50

I was wondering if there was a CAS that could handle manipulations with big O error terms.

Mathematica has an O function, but it doesn't work properly:

Code:

> x^2 Log[x] + x Log[x]^2 + x / Log[x] + O[x]

O[x^1]

(it should be "x^2 Log[x] + x Log[x]^2 + O[x]")

But I'm interested in more than just cutting off small terms. I'd like to be able to do division

Code:

> (x^2 + 3)/(x^2 + O(x))

1 + O(1/x)

and harder functions like inverses and integrals

Code:

> inverse(x^2 + O(x), x)

±sqrt(x) + O(1)

(Note: the Os in my examples are about +infinity; a system handling other limits would be nice.)

Is there any system that can do this? If not, is there a reason? Is it harder than it seems?

2009-05-26, 18:50	#1
CRGreathouse Aug 2006 175B₁₆ Posts	Computer algebra system that handles error terms? I was wondering if there was a CAS that could handle manipulations with big O error terms. Mathematica has an O function, but it doesn't work properly: Code: > x^2 Log[x] + x Log[x]^2 + x / Log[x] + O[x] O[x^1] (it should be "x^2 Log[x] + x Log[x]^2 + O[x]") But I'm interested in more than just cutting off small terms. I'd like to be able to do division Code: > (x^2 + 3)/(x^2 + O(x)) 1 + O(1/x) and harder functions like inverses and integrals Code: > inverse(x^2 + O(x), x) ±sqrt(x) + O(1) (Note: the Os in my examples are about +infinity; a system handling other limits would be nice.) Is there any system that can do this? If not, is there a reason? Is it harder than it seems?

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