On Saturday, June 2, 2012 11:20:15 PM UTC-7, jason wrote:
>
> Hi everyone, 
>
> Rob (Beezer), Robert (Bradshaw), William, and I have been working on an 
> introduction for linear algebra for the next edition of CRC's Handbook 
> of Linear Algebra.  The publisher has agreed that a version of the final 
> article will be licensed CC-by so that we can include it in our official 
> documentation.  We're planning on including it in the thematic tutorial 
> section. 
>
> We are just about finished with this.  I've temporarily put up a version 
> in the *.sagenb.org servers except sagenb.org (for example, 
> http://demo.sagenb.org/doc/static/thematic_tutorials/linear_algebra.html, 
> or 
> if you're logged in, 
> http://demo.sagenb.org/doc/live/thematic_tutorials/linear_algebra.html 
> for the live version).   We are submitting this on Monday.  If you have 
> any comments or corrections, we'd love to hear them. 
>

As far as I understand it, there are two approaches to linear algebra in 
Sage: the one you describe, and then "CombinatorialFreeModule". The latter 
is good for working with the vector space spanned by symbols 'u', 'v', and 
'w', for example, or the vector space spanned by all partitions of 35, or 
all permutations of [1,2,3,4], or all simplices in some simplicial complex, 
and as such it is good for constructing algebras and modules.

I wish that these two approaches were more unified, or at least there were 
good ways to convert between the two. I also wish that you had discussed 
both approaches, not just one.

-- 
John

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