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 Gradshteyn & Ryzhik (3.462 4). Mathematica 2.0 for SPARC Copyright 1988-91 Wolfram Research, Inc. -- 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 answer with $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 upgraded. 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