[with patch; positive review] Add support for constructing irreducible matrix representations of the symmetric group

[saliola]

It would be great to be able to construct the matrices for the irreducible representations of the symmetric group.

[saliola]

The patch adds functionality to construct Young's seminormal and orthogonal representations as well as the Specht representation. This is done via Yang-Baxter graphs, so the patch implements that as well.

[saliola]

Warning: The patch depends on #5877.

But it doesn't have to though: #5877 fixes an issue that is required for the to_character method, and this method is not necessary for the rest of the code.

[mvngu]

Using sage-4.0.alpha0 with patch from #6048, doctesting with options -t -long gave me BOOM!:

[mvngu@sage sage-4.0.alpha0]$ ./sage -t -long devel/sage-5878/sage/combinat/symmetric_group_representations.py
<LOTS_OF_BOOM!>

 Here's the full (but very long) error log from the doctests.

[saliola]

Replying to mvngu:

Using sage-4.0.alpha0 with patch from #6048, doctesting with options -t -long gave me BOOM!:

I can't reproduce this. When I run the tests, with or without #6048, I get no failures:

karkwa: sage-4.0 -version
| Sage Version 4.0.alpha0, Release Date: 2009-05-15                  |

karkwa: hg qapplied 
non-ascii.patch
trac_5878.patch

karkwa: sage-4.0 -b && sage-4.0 -t -long symmetric_group_representations.py yang_baxter_graph.py 
...
real    0m1.263s
user    0m1.004s
sys     0m0.244s
sage -t -long "devel/sage-main/sage/combinat/symmetric_group_representations.py"
         [5.8 s]
sage -t -long "devel/sage-main/sage/combinat/yang_baxter_graph.py"
         [3.4 s]
 
----------------------------------------------------------------------
All tests passed!
Total time for all tests: 9.2 seconds

Can you re-check this?

Thanks, Franco

[mhansen]

Things look good to me after I've applied my reviewer patch which takes care of the issues with the upgrade to 4.0.

Franco, can you just check over these?

[saliola]

Replying to mhansen:

Things look good to me after I've applied my reviewer patch which takes care of the issues with the upgrade to 4.0.

Franco, can you just check over these?

Checked. They are correct.

Positive review for the reviewer patch.

[mvngu]

So all patches have proper review? If so, then the summary should be changed.

[ncalexan]

Patch looks good, tests pass on sage.math and my OS X 10.5 laptop. I'm not expert enough to say the code is correct. Is this positive review?

[boothby]

This is ridiculous. Mhansen gave it a positive review pending saliola's opinion. Saliola confirmed mhansen's review and +1'd mhansen's patch. I'm merging this one.