Upgrades that aren't (old and new bugs).

• To: mathgroup at yoda.physics.unc.edu
• Subject: Upgrades that aren't (old and new bugs).
• From: pmcguire at amethyst.bucknell.edu
• Date: Fri, 10 Apr 92 09:30:00 EDT

```To follow up on the Gaussian integration bug noticed by
lsf at holmes.astro.nwu.edu (Sam Finn) it seems to be the case that the more
recent versions of Mathematica 2.0 are the ones with that particular error.
Recall the problem  occurred with Mathematica on a Sparcstation:
Mathematica version 2.0.4.5

The following integral is incorrect. The sign of the result is a clear
tip-off; moreover, it is a tabulated integral and can be found in
Mathematica 2.0 for SPARC
-- OPEN LOOK graphics initialized --

In[1]:= Integrate[x Exp[-(x-1)^2] , {x, -Infinity, Infinity}]

3  3
-(2 E Sqrt[Pi] + HypergeometricU[-, -, 1])
2  2
Out[1]= ------------------------------------------
2 E

In[2]:= N[%]

Out[2]= -1.86153

I noticed the version I have ( \$Version  Macintosh 2.0 (September 3, 1991)
) returned the
correct answer.  It was pointed out to me by "Lawrence M. Seiford, IEOR,
UMass, 413/545-1658." <SEIFORD at ecs.umass.edu> that he gets the incorrect
\$Version Macintosh 2.0 (December 12, 1991).  It seems that in trying to
correct a problem
in HyperGeometricRule they created another.  This isn't the only such
example as it is also
the case that Mathematica's handling of roots has been degraded rather than
On newer versions of Mathematica the cube root of -1 is no longer -1 but
has become the complex cube root of -1 with the least positive argument.

N[(-1)^(1/3)]
0.5 + 0.866025 I

This messes up  the internal structure and built in routines of Mathematica
and is most apparent when one tries to plot a function involving odd roots
over a negative interval.
For example try

Plot[x^(1/3), {x,-1,1}]

Paul McGuire
pmcguire at bucknell.edu

```

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