[Om3] OpenMath Symbols for Symbolic Computation

[Paul Libbrecht]

Le 11-sept.-08 à 18:39, Sebastian Freundt a écrit :

>> 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.

Honestly, this is a linear mapping, not a matrix, at least to what I  
was educated in.
A matrix has a notion of being an array so associating the matrix to  
an element of Hom(R,S) actually requires a basis.

See what Wikipedia says of it:
   http://en.wikipedia.org/wiki/Matrix_(mathematics)
from there both the German and French versions tend to coincide: it is  
a table of ring-elements.

I would agree with an element Hom(R^k, S^k) maybe, then it is the same  
notion.

>> 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.

But when you define a function only the very eager people define their  
domain and range well!
(I agree it's best practice!).

> Well, and then we were thinking it's better to start over with a
> fully-fledged CD instead of, um, `improving' the existing ones.

Maybe you have a biassed interpretation?

Please be aware that "just inventing a CD" is an easy game (as per the  
freedom of OpenMath!) but maintaining it and getting it used by  
interoperating systems or converging authors tends to be a rather more  
difficult task!

paul
-------------- next part --------------
A non-text attachment was scrubbed...
Name: smime.p7s
Type: application/pkcs7-signature
Size: 2203 bytes
Desc: not available
Url : http://openmath.org/pipermail/om3/attachments/20080912/5ad6e614/attachment.bin