Re: Mathematica can win against Tiger Woods

*To*: mathgroup at smc.vnet.net*Subject*: [mg19705] Re: [mg19677] Mathematica can win against Tiger Woods*From*: "Richard Finley" <rfinley at medicine.umsmed.edu>*Date*: Sat, 11 Sep 1999 16:36:08 -0400*Sender*: owner-wri-mathgroup at wolfram.com

William, There are certainly strong and weak points for all the packages. I think it depends to a large extent on your experience with the software you are working with and the sophistication of the problems you are working on. A package like Mathematica is very sophisticated and handles a lot of problems in more generality than people sometimes want (just note all the messages asking for help about why Sqrt[x^2] doesn't simplify to x etc...) ...so you lose some ease of use for a more powerful (general) system. But how you set up the problem also has a lot to do with it.....for example, the problem you describe is much more easily done in Mathematica if you solve it for four first order equations rather than two second order. This is probably better pedagogically also as that is probably how you would solve it "by hand". I solved the first two equations (for the velocities) and then substituted these solutions into the two equations for x[t] and y[t]. The first solution took 0.27 sec on a Pentium 450 Win98 and the second 1.43 sec and the answer was essentially the same I got from "another" comparable software package with no need to simplify in either case (real expressions with no complex exponentials etc...). To be honest, for particular problems like this I sometimes use one or another of the other packages, but I always come back to Mathematica in the end. For teaching you can always write notebooks for students to handle all the messy details. regards, RF >>> "William M. MacDonald" <wm2 at umail.umd.edu> 09/09/99 12:19AM >>> I want to use the study of golf drives in teaching theoretical methods. An approximate pair of equations to get insight assumes that the drag force is linearly proportional to velocity, instead of the actual quadratic dependence. The equations for a ball with backspin to provide lift are x''[t]== - (a x'[t]+b y'[t]), y''[t]== - g - (a y'[t]- b x'[t]) Mathematica returns a very complicated and apparently complex expression in about 9 seconds on my 250 MHz G3 Powerbook. Simplify takes 1min and 20 seconds and still returns an apparently complex expression. If I apply FullSimplify on the solution for say x[t], I get no answer in 6 minutes. I have a PC version of another system that I can run on my Powerbook using Virtual PC. It requires 6 seconds to deliver a lengthy but obviously real, no Exp[(a+ I b)t] terms or (a + I b)(a - I b) terms. I have never been able to learn why Mathematica is so slow in solving coupled equations and returns (as USUAL unless you use Simplify) such inelegant results. Is there any computer algebra NERD out there who knows the answer. (Don't tell me to use AlgebraicManipulation; I am trying to sell Mathematica to users who don't want to spend time learning fancy tricks.) -- William M. MacDonald Professor of Physics University of Maryland Internet: wm2 at umail.umd.edu

**Re: Mathematica can't win against Tiger Woods**

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