michel paul wrote:
On Sat, Jan 9, 2010 at 7:37 AM, <[email protected]
<mailto:[email protected]>> wrote:
Then in Analysis class we hit matrices this week, and Sage was
perfect for this. I was able to show the kids how a matrix is
just a list of lists, and I showed how simple it is to create a
'dumb' matrix in Python and then how to make it a 'smart' matrix
in Sage.
<<
Could you give an example of this?
Sure - here's a 'dumb' matrix in pure Python:
M = [[2, 7, 6], [9, 5, 1], [4, 3, 8]]
It is quite literally just a list of lists. Structurally it's a
matrix, but it doesn't yet know how to act like a matrix. However,
with just this much you can illustrate indexing: M[0] returns [2, 7,
6]. M[1][1] returns 5, etc.
Now we can make it a 'smart' matrix:
M = matrix(M)
Magic! M can now do all kinds of useful matrixy things. Indexing
works just as before.
This is a great way to approach this subject. Thanks for sharing it!
A small technical note about indexing. While M[1][1] works (i.e., it
gives you the entry), M[1,1] is much, much more powerful. For example,
M[1, (1,2)] gives you a submatrix, M[1,:] gives you row 1; M[:, 1] gives
you column 1, etc. It's even more powerful than that, because you can
easily do operations involving submatrices. For example,
M[:, (0,1)] = M[:, (1,0)]
swaps columns 0 and 1. Do you see what is happening here? The right
hand side is giving you a matrix consisting of columns 1 and 0 (in that
order). You are assigning those to whatever is on the left side of the
equals, which is a placeholder for columns 0 and 1 (in that order). So
you've swapped the columns! You can't do this sort of thing with the
M[][]-type indexing.
Also, M[:, -1] gives you the last column.
For documentation, see M.__getitem__? and M.__setitem__?
We should make the indexing stuff examples in the reference manual (I
don't believe it's there now since it's for a "__" function). I've made
http://trac.sagemath.org/sage_trac/ticket/7877 to address this problem.
Thanks,
Jason
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