Re: Bug in Simplify?

*To*: mathgroup at smc.vnet.net*Subject*: [mg33167] Re: Bug in Simplify?*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Wed, 6 Mar 2002 01:55:52 -0500 (EST)*References*: <a61v7q$gpt$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

adam.smith at hillsdale.edu (Adam Smith) wrote: > I was recently working with some trig functions. More specifically > for quantum mechanics where one often has terms like Sin[n Pi]. I > noticed what seemed a bug in Mathematica's Simplify[,Assumptions]. > > In[1]:= > Simplify[Sin[n*Pi]/n, Element[n,Integers]] > > Out[1]= > 0 This is certainly not a bug. Note that 0/x simplifies to 0, period. Of course, you might well argue that, when simplifying 0/x to 0, some indication should be provided that that result is not valid if x = 0. Are there computer algebra systems which standardly provide such qualifications? Is it possible to specifically request Mathematica to provide such qualifications? I don't know the answers to these two questions. But stating fully the qualifications required for all simplifications in a messy computation could easily overwhelm the ordinary user. You might take a look at "Crimes and Misdemeanors in the Computer Algebra Trade", David R. Stoutemyer, _Notices of the American Mathematical Society_ 38:7 (1991) 778-785. Does anyone have references to similar discussions by other authors? If so, I'd be quite interested in reading them. > Which is fine as long as n is not zero. > > In[2]:= > Limit[Sin[n*Pi]/n, n -> 0] > > Out[2]= > Pi > > It appears to me that Simplify is correctly determining that Sin[n > Pi]=0 for n an integer, but it ignores the fact that there is an > indeterminate 0/0. I realize that this is a special case, but it > seems to occur often enough that it should be handled properly I'm not entirely sure what you think "handled properly" would be. For me, in a system in which 0/0 is undefined, Simplify[Sin[n*Pi]/n, Element[n,Integers]] should yield 0 if n is nonzero, undefined if n is 0. > or at least provide a warning message that one should double check > the results. > > Am I being picky or do others feel the same? You're not being picky, at least IMO. But perhaps what you would like is not practical. Regards, David Cantrell -- -------------------- http://NewsReader.Com/ -------------------- Usenet Newsgroup Service

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**Bug in Simplify?**

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