#4326: Root systems improvements
---------------------------+------------------------------------------------
Reporter: nthiery | Owner: nthiery
Type: enhancement | Status: new
Priority: major | Milestone: sage-combinat
Component: combinatorics | Keywords:
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Description changed by aschilling:
Old description:
> Doc:
> - Use $F_4$ instead of F4
>
> DynkinDiagram:
> - allow for slicing notation for column/row extraction: c[i,:]
>
> AmbientSpace:
> - fundamental coweights by appropriate scaling of the fundamental
> weights
> - embedding coweight lattice
>
> WeightLatticeRealization
> - scalar product with coweight lattice in finite dimension
>
> Generic:
> - (signed) reduced word for a chamber/alcove
>
> Classical case:
> - reverse map to coroot space and coroot lattice by scalar product with
> the fundamental weights
> - => associated coroot
> - s_\alpha on the (co)root and (co)weight lattice for any root \alpha
>
> Affine case:
> - analogues whenever well defined
> - reduced words for translations elements.
New description:
Doc:
- Use $F_4$ instead of F4
DynkinDiagram:
- allow for slicing notation for column/row extraction: c[i,:]
AmbientSpace:
- fundamental coweights by appropriate scaling of the fundamental weights
- embedding coweight lattice
WeightLatticeRealization
- scalar product with coweight lattice in finite dimension
Generic:
- (signed) reduced word for a chamber/alcove
- fix rank(): for the affine cases it currently returns the same
as n.
Classical case:
- reverse map to coroot space and coroot lattice by scalar product with
the fundamental weights
- => associated coroot
- s_\alpha on the (co)root and (co)weight lattice for any root \alpha
Affine case:
- analogues whenever well defined
- reduced words for translations elements.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4326#comment:2>
Sage <http://sagemath.org/>
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