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Re: Bug in symbolic inversion of matrices

• Subject: [mg2619] Re: Bug in symbolic inversion of matrices
• From: danl (Daniel Lichtblau)
• Date: Thu, 30 Nov 1995 20:58:38 -0500
• Approved: usenet@wri.com
• Distribution: local
• Newsgroups: wri.mathgroup
• Organization: Wolfram Research, Inc.

In article <49dp5g$8a6 at dragonfly.wri.com> chapman at bonnie.drea.dnd.ca  
(David M.F. Chapman) writes:
> I have not been following this newsgroup, so I apologize if the  
following is
> old hat:
> 
> We have found a probable bug involving the symbolic inversion of  
matrices. 
> Up to size 6x6 works fine, but starting with 7x7, all the memory is  
gobbled
> up and the abort calculation command does not work.  Funny thing, it  
only
> acts up when the result is printed, so it may have more to do with that
> aspect than the inversion itself.  I will send the annotated notebook
> documenting this bug to anyone interested. (I have already sent a copy  
to
> Wolfram Research.)
>  
************************************************************************** 
*****
> Dave Chapman                         DREA            phone: (902)  
426-3100 x228
> dave.chapman at drea.dnd.ca                               FAX: (902)  
426-9654      
> 

  Symbolic matrix inversion, and symbolic linear algebra in general, tends  
to suffer from pronounced expression swell. This is a problem we are  
addressing incrementally; as we improve our simplification capabilities we  
hope to improve the methods available to symbolic linear algebra as well.
  Having said all this, the misbehavior you noted was a bug specific to  
version 2.1 of Mathematica. The linear algebra inversion method switched  
at 7x7, and for many matrices this was a bad thing. Version 2.2 improved  
this in two ways, by keeping the default method consistent and by allowing  
other methods at the user's option. The bug you note in printing is that  
the formatting code is not easily interruptible. This is a separate  
problem, and to my knowledge it has not been fixed, at least not in  
version 2.2. The reason it is not seen in your 6x6 examples is that the  
method used for those does not (in your matrices) generate such tremendous  
output, and hence the formatter does not hang on them.

  Daniel Lichtblau
  Wolfram Research, Inc.