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| = Language and tilings = | = Languages and tilings = |
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| You can subscribe to the associated [[https://lma.metelu.net/mailman/listinfo/sage-words|mailing-list]] to discuss about this. |
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| The main structure should go in the patch [[http://trac.sagemath.org/sage_trac/ticket/12224|#12224]]. Up to now the code is a bit dissaminated everywhere in Sage: | The refactorization of the current code should go in the patch [[http://trac.sagemath.org/sage_trac/ticket/12224|#12224]] which is almost done. Up to now the code is a bit dissaminated everywhere in Sage: |
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| * sage.categories.languages * sage.categories.factorial_languages * sage.categories.examples.languages * sage.monoids.free_monoid * sage.combinat.languages.* * sage.combinat.words.* * sage.dynamics.symbolic.full_shift |
* sage.categories * .languages: A language is a subset of A^N where A is a set called alphabet. It is naturally graded by N and the grading is called the length. * .factorial_languages: category of factorial languages * .shifts: the category of shift * sage.combinat.words * data structure for finite and infinite words * sage.monoids * .free_monoid: the free monoid (replaces sage.combinat.words.words.Words) * .free_monoid_morphism (replaces sage.combinat.words.morphism.WordMorphism) * sage.dynamics.symbolic * .full_shift: an implementation of the full shift (replaces sage.combinat.words.words.Words) * sage.combinat.languages * implementation of different languages * specific data structure (suffix tree/trie, rauzy graph, return tree, ...) |
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| === Tiling space === | 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 ?" * ... |
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| The highest level class should be something like TilingSpace. It contains an enumerated set, an alphabet (and optionally a way of plotting). Do we always assume that the enumerated set is either a group (like ZZ) or a sub-semigroup of a group (like NN) ? | What do we keep? What categories do we create? |
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| === Behavior of algorithms with infinite input data === | == Behavior of algorithms with infinite input data == |
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| What to do for equality comparison of infinite words ? | What to do for equality of infinite words ? What should do {{{ sage: w1 == w2 }}} Two possibilities: 1. 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". 2. test all letters and never return True Other suggestions ? == Subprojects == |
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| Most of it was implemented by Franco. We would like to enhance it and use Rauzy castle. See [[http://trac.sagemath.org/sage_trac/ticket/12225|#12225]]. | 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 [[http://trac.sagemath.org/sage_trac/ticket/12225|#12225]]. |
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| There are many algorithms for language described by a sequence of substitutions. The particular case of morphic and purely morphic languages corresponds respectively to periodic and purely_periodic directive word. | 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. |
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| * Factor complexity for purely morphic languages ([[http://trac.sagemath.org/sage_trac/ticket/12231/#12231]]) * Equality for purely morphic language (following J. Honkala, CANT, chapter 10) |
* Factor complexity for purely morphic languages ([[http://trac.sagemath.org/sage_trac/ticket/12231/|#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 [[http://trac.sagemath.org/sage_trac/ticket/12228|#12228]]. |
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| * specific data structure rauzy graphs and return tree (Thierry) | |
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| * ... ''add your whishes'' |
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 refactorization of the current code should go in the patch #12224 which is almost done. Up to now the code is a bit dissaminated everywhere in Sage:
- sage.categories
- .languages: A language is a subset of A^N where A is a set called alphabet. It is naturally graded by N and the grading is called the length.
- .factorial_languages: category of factorial languages
- .shifts: the category of shift
- sage.combinat.words
- data structure for finite and infinite words
- sage.monoids
- .free_monoid: the free monoid (replaces sage.combinat.words.words.Words)
.free_monoid_morphism (replaces sage.combinat.words.morphism.WordMorphism)
- sage.dynamics.symbolic
- .full_shift: an implementation of the full shift (replaces sage.combinat.words.words.Words)
- sage.combinat.languages
- implementation of different languages
- specific data structure (suffix tree/trie, rauzy graph, return tree, ...)
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
Other suggestions ?
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
- specific data structure rauzy graphs and return tree (Thierry)
- 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
... add your whishes