Root poset should treat type A1 properly

[stumpc5]

The patch fixes the issue that the one element root poset in type A1 was not returned correctly.

sage: Phi = RootSystem(['A',1]).root_poset(); Phi
Finite poset containing 1 elements
sage: Phi.cover_relations()
[]

I also added the facade option for root posets.

Component: combinatorics

Keywords: root poset

Author: Christian Stump

Reviewer: Frédéric Chapoton

Merged: sage-5.1.beta0

Issue created by migration from https://trac.sagemath.org/ticket/12838

[fchapoton]

Reviewer: Frédéric Chapoton

[fchapoton]

comment:2

In sage/combinat/root_system/root_system.py,

it should be written

- ``restricted`` -- 

(i.e. there are missing backquotes)

Otherwise, it seems ok.

[stumpc5]

comment:3

Replying to @fchapoton:

In sage/combinat/root_system/root_system.py,

it should be written

- ``restricted`` -- 

(i.e. there are missing backquotes)

Otherwise, it seems ok.

done.

[jdemeyer]

comment:6

This patch needs a commit message and also needs to be rebased to sage-5.0.beta14 (or later).

[jdemeyer]

comment:7

ping

[stumpc5]

comment:8

Replying to @jdemeyer:

ping

Sorry for being slow...

I added a commit message -- the patch applies smoothly on 5.0.rc0.

[jdemeyer]

Attachment: trac_12838-root_poset_A1-cs.patch.gz

[jdemeyer]

comment:9

Not quite smoothly:

applying trac_12838-root_poset_A1-cs.patch
patching file sage/combinat/root_system/root_lattice_realizations.py
Hunk #1 succeeded at 507 with fuzz 2 (offset -34 lines).

Anyway, I rebased it.

[jdemeyer]

Merged: sage-5.1.beta0