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Re: "At long last, Sir, have you no shame?"
*To*: mathgroup at smc.vnet.net
*Subject*: [mg18524] Re: "At long last, Sir, have you no shame?"
*From*: colin at tri.org.au (Colin Rose)
*Date*: Thu, 8 Jul 1999 22:32:57 -0400
*Organization*: Theoretical Research Institute
*References*: <7luk6s$l95@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
David Withoff <withoff at wolfram.com> wrote:
> independent experts often disagree about what is or is not a bug.
Two cases instantly come to mind:
1. Sum in v4
_________
Consider say:
In[1]:= g = Exp[-i];
In[2]:= Sum[g, {i, 1, n}]
Out[2]= n/E^i
which is nonsense. This happens for almost ANY expression g=g(i).
To get the correct answer, you have to wrap Evaluate around g:
In[3]:= Sum[Evaluate[g], {i, 1, n}]
Out[3]= (-1 + E^n)/(E^n*(-1 + E))
Wolfram support says Out[2] is not a bug, since Sum has attribute HoldAll.
I say it is clearly (and obviously) an extremely serious bug,
in the sense that it gives the wrong answer to almost any Summation
where g is pre-defined. I reported it under v4 alpha, it was fixed
in the betas, and it is now back in the v4 final release. But then
it isn't a bug, apparently !?
2. Non-convergent integrals
________________________
Or how about the mean of a Cauchy random variable:
In[1]:= f = 1/(Pi(1 + x^2));
In[2]:= Integrate[x*f, {x, -Infinity, Infinity},
GenerateConditions -> False]
Out[2]= I
The correct answer is that the integral does not converge.
WRI claims it is not a bug, and won't fix it, even though:
(i) GenerateConditions -> True yields the
correct answer (convergence error), and
(ii) there are no conditions stated here anyway, so it is
not apparent why GenerateConditions -> False should yield a
different solution to -> True.
This is actually a general problem, with similar behaviour
in the Levy family,
f = (1/Sqrt[2*Pi]*Exp[-(1/(2*y))])/y^(3/2);
where the moments do not exist either.
___________
Cheers
Colin
--
Colin Rose
tr(I) - Theoretical Research Institute
__________________________________________
colin at tri.org.au http://www.tri.org.au/
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