Is There a Computer Algebra System That Can Handle Big O Error Terms?

Thread starter CRGreathouse
Start date May 26, 2009
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Cas Error Terms

AI Thread Summary

The discussion centers around the need for a computer algebra system capable of manipulating big O error terms effectively, beyond basic term truncation. While Mathematica includes an O function, it fails to handle certain expressions correctly, such as simplifying terms involving big O notation in division and more complex operations like inverses and integrals. The user expresses a desire for a system that can manage these tasks, particularly with limits approaching positive infinity. The conversation raises questions about the feasibility of implementing such functionality in existing systems and whether the challenges are more complex than they appear.

May 26, 2009

CRGreathouse

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I was wondering if there was a computer algebra system (like Math'ca, Maple, or Maxima) 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?