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MathGroup Archive 2005

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Re: global assumptions?? How far can I go?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53344] Re: global assumptions?? How far can I go?
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 6 Jan 2005 22:00:46 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200501060752.CAA28716@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

When I'm using Mathematica in complex analysis, I applaud such "anal" 
behavior.

When I'm doing plain calculus, yes, that gets rather frustrating.  For 
example:

    Assuming[t â?¥ 0, Integrate[1/(x^2), {x, 1, t}]]
If[t > 1, (-1 + t)/t, Integrate[x^(-2), {x, 1, t},
    Assumptions -> t <= 1]]

That, despite:

    Integrate[1/x^2, {x, 1, 1}]
0

    Integrate[1/x^2, {x, 1, 1/2}]
-1


Ron Griffin wrote:
> I'm an economist whose accustomed to emphasizing the first orthant in a 
> noncomplex world (positive, real prices; positive, real, quantities) so 
> I really get flustered when Mathematica "pollutes" my output with "using inverse 
> function" warnings and imaginary solutions.
> 
> Now I've "upgraded" to 5.1 from 4.2 and I find, as I expected from my 
> experience during previous upgrades, that Mathematica is even more anal than it 
> was before.  Hence, programs which ran well under 4.2 now are less 
> functional because Mathematica is increasingly careful. 
> 
> So, how global can I go in telling Mathematica to assume that all the variables 
> I create are real??  Must I list an assumption for each variable or each 
> command??  Jees, now it won't even integrate 1/x^2 from 1 to t without 
> dumping a bunch of worries on me.
> 
> ron
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305



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