coxeter sorting words

[sagetrac-vpilaud]

Coxeter sorting is used to define sortable elements of a Coxeter group.

New methods are:

• rank of the Coxeter group
• support of an element (the simple reflections that appear in the reduced expressions of the element)
• has_full_support tells if the support contains all simple reflections
• coxeter_sorting_word returns the c-sorting word of an element
• is_coxeter_sortable tells if an element is c-sortable

CC: @stumpc5 @VivianePons

Component: combinatorics

Keywords: Sage Days 64.5

Author: Vincent Pilaud

Branch/Commit: 6b47229

Reviewer: Viviane Pons, Christian Stump

Issue created by migration from https://trac.sagemath.org/ticket/18590

[sagetrac-vpilaud]

Branch: u/vpilaud/coxeter_sorting_words

[sagetrac-vpilaud]

Commit: deea7d9

[sagetrac-vpilaud]

Changed keywords from none to Sage Days 64.5

[sagetrac-vpilaud]

New commits:

deea7d9

add support for sorting words

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

40cf52b

add rank function and documentation on coxeter sorting words in coxeter_groups

[sagetrac-git]

Changed commit from deea7d9 to 40cf52b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

d1d24a6

fix bug documentation

[sagetrac-git]

Changed commit from 40cf52b to d1d24a6

[VivianePons]

Changed branch from u/vpilaud/coxeter_sorting_words to u/VivianePons/coxeter_sorting_words

[VivianePons]

Reviewer: Viviane Pons

[VivianePons]

Author: Vincent Pilaud

[VivianePons]

Changed commit from d1d24a6 to d1db90c

[VivianePons]

comment:6

I did some small formating fixes, and I found this error:

sage: W = CoxeterGroup(["A",3])
sage: c = W.from_reduced_word([1,2,3])
sage: l = [w for w in W if w.is_coxeter_sortable(c)]
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-3-ab902ac679a2> in <module>()
----> 1 l = [w for w in W if w.is_coxeter_sortable(c)]

/home/viviane/sage/local/lib/python2.7/site-packages/sage/categories/coxeter_groups.pyc in is_coxeter_sortable(self, c, sorting_word)
   2064                         return False
   2065                 else:
-> 2066                     containment_list[s] = False
   2067                 i += 1
   2068                 if i == n:

IndexError: list assignment index out of range

Also, please update the ticket description to give more details

---

New commits:

d1d24a6	fix bug documentation
d1db90c	Some small doc formating fix

[sagetrac-vpilaud]

Changed branch from u/VivianePons/coxeter_sorting_words to u/vpilaud/coxeter_sorting_words

[sagetrac-vpilaud]

New commits:

70315c8

fix bug is_sortable_element

[sagetrac-vpilaud]

Changed commit from d1db90c to 70315c8

[VivianePons]

Changed commit from 70315c8 to 6b47229

[VivianePons]

comment:9

I've made a few small format fix. I'm happy with the ticket. Christian, if you're happy too you can put it to positive review.

---

New commits:

6b47229

Small formating fixes (adding outputs, fixing doc indent)

[VivianePons]

Changed branch from u/vpilaud/coxeter_sorting_words to u/VivianePons/coxeter_sorting_words

[stumpc5]

comment:10

looks good!

[stumpc5]

Changed reviewer from Viviane Pons to Viviane Pons, Christian Stump

[vbraun]

Changed branch from u/VivianePons/coxeter_sorting_words to 6b47229