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@osl.iu.edu> http://www.osl.iu.edu/~jsiek Ph.D. Candidate, Indiana University Bloomington C++ Booster (http://www.boost.org) _______________________________________________