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CAS that handles error terms?

  1. May 26, 2009 #1


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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 (Text):
    > x^2 Log[x] + x Log[x]^2 + x / Log[x] + O[x]

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

    1 + O(1/x)
    and harder functions like inverses and integrals
    Code (Text):
    > 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?
  2. jcsd
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