Robert Miller wrote:
> Hello all,
> 
> For those of you not in Seattle today / not at Chris's talk at the
> Sage seminar, here is a copy of his slides.
> 


Thanks! (and thanks, Chris, if you are listening too).

Some comments/questions:


1. What did Chris use to draw the graphs on page 48?  The drop-shadow 
looks very nice, for example.

2. determinants (p. 56): For the general case, we use LU decomposition 
now, instead of expansion by minors, so I don't think it is exponential 
time these days.  Integer and rational determinants are computed using a 
different algorithm, I believe.

sage: a=random_matrix(SR, 25)
sage: type(a)
<type 'sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense'>
sage: len(a.nonzero_positions())
509
sage: %time a.determinant()
CPU times: user 0.22 s, sys: 0.00 s, total: 0.22 s
Wall time: 0.23 s
-4932640057384336

For integer matrices:

sage: b=a.change_ring(ZZ)
sage: len(b.nonzero_positions())
509
sage: %time b.determinant()
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
-4932640057384336
sage: %timeit b.determinant()
1000000 loops, best of 3: 472 ns per loop


Thanks again for posting these slides.  It looks like it was a great talk!

Jason

--
Jason Grout


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