fixed point and periodic point of word morphism

[videlec]

This ticket is motivated by #12454. The aim is to implement new functionalities for word morphism (in sage.combinat.words.morphism) for computing individual as well as list of fixed point and periodic points.

CC: @sagetrac-tjolivet

Component: combinatorics

Keywords: word morphism

Author: Vincent Delecroix

Reviewer: Timo Jolivet

Merged: sage-5.0.beta10

Issue created by migration from https://trac.sagemath.org/ticket/12512

[loefflerd]

comment:2

There is a typo "dictionnary" at line 99, and a rogue non-ASCII character at line 130. At line 131, f.domain should be in double backticks and "try" --> "tries".

[sagetrac-tjolivet]

comment:4

Hi,

The patch applies well, the doc builds fine, the tests pass and the previous comments have been taken into account.

This is a very nice and useful patch, thank you.

You could add an example of a morphism without fixed points but with periodic points, for example:

sage: f = WordMorphism('a->b,b->c,c->ab') 
sage: f.fixed_points()                    
[]
sage: f.periodic_points()                 
[[word: abbcbccabbccabcababbcbccabcababbccababbc..., word: bccabcababbccababbcabbcbccabcababbcabbcb..., word: cababbcabbcbccababbcbccabbccabcababbcabb...]]

[sagetrac-tjolivet]

Reviewer: tjolivet

[videlec]

comment:6

Hi Timo!

Actually there is yet such an example in the documentation of periodic_points a->bab, b->aa.

Vincent

[sagetrac-tjolivet]

comment:7

Oups, my bad, sorry!

[jdemeyer]

Changed author from vdelecroix to Vincent Delecroix

[jdemeyer]

Changed reviewer from tjolivet to Timo Jolivet

[jdemeyer]

comment:9

Attachment: trac_12512-periodic_point.patch.gz

Fixed commit message (removed the "trac 12512" line)

[jdemeyer]

Merged: sage-5.0.beta10