Languages and tilings
This page gathers ideas for refactorization of sage.combinat.words and implementation of tilings.
You can subscribe to the associated mailing-list to discuss about this.
Structure
The main structure should go in the patch #12224. Up to now the code is a bit dissaminated everywhere in Sage:
- sage.categories.languages
- sage.categories.factorial_languages
- sage.categories.shifts
- sage.categories.examples.languages
- sage.monoids.free_monoid
- sage.combinat.languages.*
- sage.combinat.words.*
- sage.dynamics.symbolic.full_shift
What is bad/nice with categories:
- inheritance of generic code
- a bit confusing for the user who want to find the implementation of a method
- confusing for the person who writes the code and ask "where should I put this ?"
What do we keep? What categories do we create?
Behavior of algorithms with infinite input data
What to do for equality of infinite words ?
What should do
sage: w1 == w2
Two possibilities:
- test the first XXX letters for finding a difference. If find one then returns False otherwise raise an error, "seems to be equal use .is_equal(force=True) to launch the infinite test".
- test all letters and never return True
Subprojects
Finite languages and factor set
Most of it was implemented by Franco (suffix tree and suffix trie). We would like to enhance it and make a specific data structure (called Rauzy castle) for FiniteFactorialLanguages. See #12225.
Substitutive and adic languages
There are many algorithms for languages described by a sequence of substitutions (called a directive word). The particular case of morphic and purely morphic languages correspond respectively to periodic and purely_periodic directive words.
Enumeration of factors, desubstitution (#12227)
Factor complexity for purely morphic languages (#12231)
- Equality for purely morphic languages (following J. Honkala, CANT, chapter 10)
Eventually periodic languages / words
They will be useful to define eventually periodic directive words for adic languages. See #12228.
TODO list
which should go in the main trac ticket
- words path (currently in sage.combinat.words.paths) which have to be modified to fit with the new implementation
other todos
- 1-dim subshift of finite type / sofic
- n-dim finite words and n-dimensional shifts
- n-dim subshifts of finite type
- n-dim substitutive subshift
- cellular automata
- ...