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[Axiom-developer] Re: special functions

From: Yigal Weinstein
Subject: [Axiom-developer] Re: special functions
Date: Mon, 30 Jan 2006 17:20:56 -0800

First and foremost it is important to realize there is a computational history before Axiom.  What I think is important from this history is that several programs have been developed to find approximate results also known as non-exact or numerical results for problems.  I will call them approximating programs as a set.  These include Fortran, C, etc.. 

Now for where I think I differ with you Bill.  Axiom is a CAS.  As such it has built in capabilities and certain tools that are different than an approximating programs.  It has the ability to help us solve a problem exactly.  This makes Axiom as well as all other CAS's vastly different than approximating programs. 

Should Axiom be an all in one computer program for solving math problems?  I believe this is asking too much for any program.  Should an NR program be converted to SPAD? As such this is  in my opinion very low if non-existent on the agenda for improving Axiom. 

The one way gpl'd programs have an advantage on proprietary software is that they can use existing gpl'd programs without worrying about licenses etc..  For instance consider all the work done in Fortran like quadpack etc..  Axiom if asked for a numerical result could if linking was considered could use the existing libraries to compute practically any function.  

In fact this is just the strategy used by the proprietary Axiom.  To link it to NAG was what was done.  There are plenty of high quality libraries that can be used for numerical approximations in Fortran that are gpl: lapack is but one of them.

Is this better than Mathematica?  Well I guess the analogy may be something like is it better to sleep with many partners than with just one.  By this I mean, problems of using other programs to calculate numerical values may include trusting the approximating program that you are using and the library that it uses to find a numerical value.  That is if many sources are used then we have to trust each one is not faulty.  Mathematica or Maple probably rely on there own programs for approximate results.   However there are trusted libraries to approximately solve math problems that are gpl'd and that people are working right now on, like GSL.

If I am not seeing the full picture please enlighten me.  Otherwise I do not understand why any approximation for a function need be incorporated into SPAD.


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