[with patch, positive review] Improvements to weyl_group.py

[bump]

WeylGroup? gets a proper call method that produces a WeylGroup? element. Previously if G is a Weyl group then G(m) produced a MatrixRing? element. This part is a bugfix.

Root systems get a method to produce the highest root, relevant to the affine root system. This could be implemented as a case-by-case method and that would be faster, but searching through the roots for the highest weight is of acceptable speed.

Weyl Groups get a method to produce the long element of the Weyl group. Not implemented yet for E7 and E8.

Weyl group also gets a method to produce the identity element as a WeylGroup? element. Strictly speaking this is not necessary since W(1) will also produce the unit.

[bump]

These are patches against 3.0alpha6.

[bump]

There will be a further patch because I forgot to finish the doctests.

[mhansen]

Okay, excellent. I'll review them when you put them up.

[bump]

I added a third patch with doctest for long element and now I think it is OK.

Thanks, Dan

[mhansen]

Looks good to me. Apply all four patches.

[mabshoff]

Merged all four patches in Sage 3.0.rc0