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| * sage.categories.shifts * sage.categories.examples.languages |
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| * sage.categories.examples.languages | |
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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 |
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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 should we keep? What categories should 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 ? |
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| == Substitutive and adic languages == | What should do {{{ sage: w1 == w2 }}} Two possibilities: |
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| * Equality for purely morphic words is decidable (J. Honkala, CANT, chapter 10) | 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 == 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 [[http://trac.sagemath.org/sage_trac/ticket/12225|#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 ([[http://trac.sagemath.org/sage_trac/ticket/12227|#12227]]) * 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) |
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| which should go in the ticket * WordsPath and cutting sequences |
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 |
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| other request | other todos |
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| * rauzy castle and fine datastructure for small complexity languages (Stepan) * substitutive language (Stepan, Vincent) |
* n-dim subshifts of finite type * n-dim substitutive subshift * cellular automata * ... |
Language and tilings
This page gathers ideas for refactorization of sage.combinat.words and implementation of tilings.
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
What should we keep? What categories should 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)
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
- ...