[boost] Re: [ublas-dev] Re: Boost Mathematicians

From: Jeremy Graham Siek (jsiek_at_[hidden])
Date: 2004-07-05 21:08:49

Hi Paul,

I agree with you. The use of operator* does not imply commutativity.

Cheers,
Jeremy

On Jul 5, 2004, at 6:04 PM, Paul C. Leopardi wrote:

> Hi all,
>  Reply to a sub-issue below.
>  Best regards
>
>  On Tuesday 06 July 2004 02:58, Peter Schmitteckert wrote:
>  >  This imples, that the elements of a matrix need not be commutative,
>  >  having again consequences for general routines using operator*(),
>  >  since this oftemn implies the commutativity of elements.
>
>  Can anyone explain to me why operator* implies the commutativity of 
> elements?
>  The GluCat library ( http://glucat.sf.net ) uses operator* and its 
> elements
>  do not necessarily commute under multiplication.
>
>  How would you use expression templates to implement a non-commutative 
> group
>  concept, or more to the point, a ring or an algebra? My first thought 
> for
>  this was to use operator* as it seems most natural, and in the case of
>  Clifford algebras, gives subalgebras isomorphic to the quaternions, 
> complex
>  numbers and real numbers.
>
>  Of course, this discussion comes from a mathematical viewpoint rather 
> than a
>  computer science viewpoint, but I don't see why these viewpoints need 
> be
>  incompatible.
>
>
>
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_______________________________________________
Jeremy Siek <jsiek_at_[hidden]>
http://www.osl.iu.edu/~jsiek
Ph.D. Candidate, Indiana University Bloomington
C++ Booster (http://www.boost.org)
_______________________________________________