Professor James Davenport <[EMAIL PROTECTED]>
writes:
> On Wed, 10 Sep 2008, Peter Horn wrote:
>> (1) There is no reasonable representation for matrices.
>> (We developed a 'matrix1' CD, if you are interested, we'd love to
>> moot it.)
> David Carlisle commented on this, but I'd like to see your matrix1 to see
> what sort of functionality you thought was wanted.
Hi James,
for one, NONE of the provided matrix CDs actually define matrices (from an
algebraic point of view), a matrix is just an element of a matrix algebra
or, more generally, a specific representation of a linear mapping, so it's
an element of Hom(R,S), R,S being rings, Hom being the space of mappings
that preserve homomorphy.
>From a computational POV, it is quite essential to know the parent
structure (the space where the element lives) upfront, because usually you
equip your parent structures with certain methods (comparison, addition,
etc.) and not the elements themselves.
Well, and then we were thinking it's better to start over with a
fully-fledged CD instead of, um, `improving' the existing ones.
Sebastian
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