Re: unwarranted assumption?
- To: mathgroup at yoda.physics.unc.edu
- Subject: Re: unwarranted assumption?
- From: rubin at msu.edu (Paul A. Rubin)
- Date: Tue, 28 Jun 94 12:00:04 EDT
>Dear Mathgroup > >The following expression > >Simplify[x*D[x^(1/3)/(k+x^(1/3)), x]/((x^(1/3)/(k+x^(1/3)))* >(1-(x^(1/3)/(k+x^(1/3)))))] > >gives the possibly surprising and rather elegant result > >Out [] = > > 1 > - > 3 > >[Turns out that this expression approximates dependence of cloud >reflectivity on number concentration of cloud drops] > >I was surprised however that mathematica didn't choke on this expression. >My question is how does mathematica know that k is not zero? It doesn't. >I would have >expected mathematica to consider all possible values of k and at least flag >the possibility. Actually, in doing algebraic manipulations, I think it tends to cancel factors without concern for zero/zero - which isn't all that bad, really (if you assuming that the final 1/3 is really 1/3 times a bunch of fractions of the form expr/expr, where numerator and denominator are the same expression, than if any denominators go to zero the numerators go at the same rate, and the limit is 1. (Or did I just commit some freshman error in that logic?) >Feel free to knock me over the head if this is a trivial question. I was >kinda surprised that mma gave me the answer I "expected" instead of a bunch >of red flags. > >Generally my experience with mathematica is the contrary; that I would have >had to have told it that k was not zero. Sometimes yes, sometimes no. For instance, Reduce[] typically gives a "logic tree" of solutions contingent on assumptions, while Solve[] just gives a "generic" solution. Some simplifications are not done unless manually forced, suggesting that Mma was reluctant to do it because there is a possible pitfall. Then again, on sci.math.symbolic there has been some flaming of Mma for giving Integrate results that didn't consider all possible parameter values. > >mathematically yours -steve > > >- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - >Stephen E. Schwartz Phone: (516) 282-3100 >Environmental Chemistry Division Fax: (516) 282-2887 >Brookhaven National Laboratory Secretary: (516) 282-3275 >Bldg. 426 (51 Bell Ave.) PO Box 5000 Internet: steves at BNLUX1.BNL.GOV >Upton NY 11973-5000 Bitnet: steves at BNLUX1 >- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - > ************************************************************************** * Paul A. Rubin Phone: (517) 336-3509 * * Department of Management Fax: (517) 336-1111 * * Eli Broad Graduate School of Management Net: RUBIN at MSU.EDU * * Michigan State University * * East Lansing, MI 48824-1122 (USA) * ************************************************************************** Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. J. W. v. GOETHE