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MathGroup Archive 1998

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Re: Re: Integrate Bug?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13335] Re: [mg13283] Re: Integrate Bug?
  • From: David Withoff <withoff>
  • Date: Mon, 20 Jul 1998 02:49:55 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

> Thanks to all those who have replied, and for the simplification of the
> problem statement. I can insert the assumptions concerning W into the
> arguments of Integrate but it does not change the result.
>
> In[9]:= Integrate[D[awm,W],W, Assumptions -> {0 < W, W < 1}]
>
> Out[9]= Log[-1 + W]

There are both mathematical and practical issues here.  The mathematical
issue is that the answer is correct, including consideration of the
assumptions, so Integrate did what it was asked to do.  The practical
issue is that Integrate is not currently programmed to do anything with
assumptions in indefinite integrals, and that assumptions are currently
intended primarily for controlling the mathematical correctness of the
result, not the form of the result.

> I did the numerical substitutions to further illustrate the point, but
> I'm more concerned with the difference in signs of the symbolic 
> results. It still seems to me Mathematica should come back with the
> original  expression.
> 
> Ed

It isn't possible to come back with the original expression (except by
accident, or by simply remembering what it was).  The information about
what the original expression was is lost when the expression is
differentiated.  Here is a simpler example.  This doesn't return the
original expression either.

In[1]:= awm=1+W

Out[1]= 1 + W

In[2]:= Integrate[D[awm,W],W]

Out[2]= W

Dave Withoff
Wolfram Research


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