Refactor and extend root systems plots

[nthiery]

The attached patch refactors in depth the root sytem plotting facilities of Sage.
In particular it contains all the features provided in MuPAD-Combinat and many more.

Some of those features came up during discussions with Reda Chaibi, Arthur Lubovski and Christopher Hanusa. Thanks to them!

See: http://wiki.sagemath.org/combinat/CoolPictures?action=AttachFile&do=get&target=root-system-plots.pdf for a (slightly outdated) version of the enclosed tutorial with all the pictures shown.

Depends on #14175
Depends on #14176
Depends on #14177
Depends on #2023

CC: @sagetrac-sage-combinat @sagetrac-alubovsky

Component: combinatorics

Author: Nicolas Borie, Nicolas M. Thiéry

Reviewer: Nicolas M. Thiéry, Nicolas Borie, Travis Scrimshaw

Merged: sage-5.10.beta4

Issue created by migration from https://trac.sagemath.org/ticket/4327

[sagetrac-nborie]

comment:2

I find this ticket is completely integrated inside #4326

I remember that i did this job. So feel free to merge/destroy/erase this ticket. I don't know the current way to dealt with such ticket...

[nthiery]

comment:3

Actually, there is still room for improvement to the current plots. So let's keep this open. I'll just update the description.

[nthiery]

Description changed:

--- 
+++ 
@@ -1,6 +1 @@
-Port from MuPAD-Combinat the plotting facilities for (affine) root systems.
-
-This will require in particular the port of:
-- row/column annihilator
-- a,acheck,c coeffs
-- translation factors
+Finish to port from MuPAD-Combinat the plotting facilities for (affine) root systems (see #4326 for a first implementation)

[sagetrac-nborie]

comment:4

Hello,

Here is a patch which realize the porting of what was done in MuPAD... I tried to do my best but this patch really need a strong English language review. For anybody interssinting in reviewing, commenting, or anything... here are some pointers :

MuPAD example :
http://wstein.org/home/wstein/www/home/nthiery/2008-03-01-RootSystemPlots.html

Sage-support discussion :
https://groups.google.com/forum/?hl=fr&fromgroups=#!topic/sage-support/fRTEE_IECzU

[nathanncohen]

comment:5

Hellooooooooooo !!

Nicolas M. Thiéry : that's the ticket that should have been set to needs_review ages ago and never was. It would be nice to have this into Sage, if only to be able to print beautifu Sage-combinat posters with fancy pictures inside.

Nathann

[nthiery]

Author: Nicolas Borie, Nicolas M. Thiéry

[nthiery]

comment:6

I'll upload a (quite heavily) refactored patch shortly.

[nthiery]

Dependencies: #14175, #14176, #14177