Re: Re: How to View Mathematica and Hardcopy Books

*To*: mathgroup at smc.vnet.net*Subject*: [mg62451] Re: Re: How to View Mathematica and Hardcopy Books*From*: "Steven T. Hatton" <hattons at globalsymmetry.com>*Date*: Thu, 24 Nov 2005 06:33:51 -0500 (EST)*References*: <dls5ig$qn1$1@smc.vnet.net> <200511220942.EAA23713@smc.vnet.net> <dm1abe$hr1$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski wrote: > On 22 Nov 2005, at 18:42, Steven T. Hatton wrote: > >> For purposes of number crunching Mathematica is quite often the >> wrong tool >> for the job. If you are doing things which involve very intensive >> mumeric >> calculation which are likely to be repeated in form, you are >> probably much >> better off translating your work to something like C++, or >> FORTRAN. My >> understanding is that MathCode C++ can produce executables which >> run orders >> of magnitude faster than the Mathematica implementation of the same >> algorithm > > > This is of course true in some cases. For example, if you are working > on simulations in molecular biology then Mathematica would normally > not be the right tool for the job. I suspect Mathematica can play a significant role in designing programs that perform specialized highperformance calculations. I've often turned to Mathematica as a means of exploring the mathematics behind 3D (OpenGL) graphics. > But the situation is quite > different when what might be called "mathematical number crunching" > is involved. First of all, the speed advantage of C++ usually > disappears in cases when Mathematica has a built-in function that by > itself does the job (and often the advantage lies with Mathematica > since such functions tend to use the best known algorithms and are > already highly optimised). There are some very good numerics libraries written in C++ (according to what others have told me.) I'm trust there are many cases in which both C++ and Mathematica provide comerable solutions. The question then becomes which is more convenient. If a person is already working with Mathematica, there is probably little reason to bother with the comparable C++ solution. > But more importantly, in problems in > numerical mathematics accuracy and the ability to keep track of > errors is much more important than speed. There is no great advantage > in getting a wrong answer several orders of magnitude faster. > Mathematica offers pretty sophisticated tools that help with this > task, which as far as I know no calculator does, nor is there, to my > knowledge, anything comparable available in C++. I can't claim expertise in either C++, nor Mathematica highperformance numerical calculations. I will say this - and the folks at WRI may want to take notice - the C++ Technical Report 1 (TR1) adds many specialized math functions to the C++ Standard Library. One gap I would like to bridge is between 3D graphics and Mathematica. I am aware that Mathematica produces graphics using 3-dimensional mathematical space, but it does not use specialized 3D libraries such as OpenGL. I suspect there is much improvement possible in how Mathematica handles graphics. I also suspect such improvements will be non-trivial to implement. -- The Mathematica Wiki: http://www.mathematica-users.org/ Math for Comp Sci http://www.ifi.unizh.ch/math/bmwcs/master.html Math for the WWW: http://www.w3.org/Math/

**References**:**Re: How to View Mathematica and Hardcopy Books***From:*"Steven T. Hatton" <hattons@globalsymmetry.com>

**Re: Timing of looping operators**

**Re: Boolean Integral**

**Re: Re: How to View Mathematica and Hardcopy Books**

**Re: Re: How to View Mathematica and Hardcopy Books**