Improvements to weyl_group.py

[dwbump]

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.

CC: @sagetrac-sage-combinat

Component: combinatorics

Issue created by migration from https://trac.sagemath.org/ticket/2964

[dwbump]

Attachment: 9564.patch.gz

[dwbump]

comment:1

Attachment: 9565.patch.gz

These are patches against 3.0alpha6.

[dwbump]

comment:3

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

[mwhansen]

comment:4

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

[dwbump]

Attachment: 9566.patch.gz

[dwbump]

comment:5

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

Thanks, Dan

[mwhansen]

Attachment: 2964-review.patch.gz

[mwhansen]

comment:6

Looks good to me. Apply all four patches.

[sagetrac-mabshoff]

comment:7

Merged all four patches in Sage 3.0.rc0