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# Farey (Sub)sequences: A Clojure namespace and a Haskell module #
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A Clojure namespace `fareysequences.clj` and a Haskell module `FareySequencesModule.hs` exporting a dozen of functions coded after several selected formulas presented
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in the monograph [A.O. Matveev, Farey Sequences: Duality and Maps Between Subsequences](https://doi.org/10.1515/9783110547665), Berlin, Boston: De Gruyter, 2017.
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# Farey (Sub)sequences: A Clojure namespace, and Haskell and Python modules #
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A Clojure namespace `fareysequences.clj`, and a Haskell module `FareySequencesModule.hs`, and a Python module `fareysequences.py` exporting a dozen of functions coded after several selected formulas presented in the monograph [A.O. Matveev, Farey Sequences: Duality and Maps Between Subsequences](https://doi.org/10.1515/9783110547665), Berlin, Boston: De Gruyter, 2017.
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## Our Dramatis Personae ##
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(See Table 1.1 of the monograph):
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If you have two neighboring fractions, then you proceed in the recurrent manner by means of a relatively fast function
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of the form `predecessor-of-pair-of-neighbors-in-personage` or `successor-of-pair-of-neighbors-in-personage`, in Clojure
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(`predecessorOfPairOfNeighborsInPersonage` or `successorOfPairOfNeighborsInPersonage`, in Haskell), depending on which direction (descending
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or ascending) you take.
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(`predecessorOfPairOfNeighborsInPersonage` or `successorOfPairOfNeighborsInPersonage`, in Haskell; `predecessor_of_pair_of_neighbors_in_personage`
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or `successor_of_pair_of_neighbors_in_personage`, in Python), depending on which direction (descending or ascending) you take.
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If you have one fraction then, in order to obtain your starting pair of neighboring fractions, you make one-time use of a relatively slow
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function of the form `predecessor-in-personage` or `successor-in-personage`, in Clojure (`predecessorInPersonage` or `successorInPersonage`, in Haskell),
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and then you proceed by calling, in the recurrent manner, the corresponding relatively fast function of the form
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`predecessor-of-pair-of-neighbors-in-personage` or `successor-of-pair-of-neighbors-in-personage`
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(`predecessorOfPairOfNeighborsInPersonage` or `successorOfPairOfNeighborsInPersonage`).
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function of the form `predecessor-in-personage` or `successor-in-personage`, in Clojure (`predecessorInPersonage` or `successorInPersonage`, in Haskell;
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`predecessor_in_personage` or `successor_in_personage`, in Python), and then you proceed by calling, in the recurrent manner, the corresponding relatively fast
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function of the form `predecessor-of-pair-of-neighbors-in-personage` or `successor-of-pair-of-neighbors-in-personage`
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(`predecessorOfPairOfNeighborsInPersonage` or `successorOfPairOfNeighborsInPersonage`; `predecessor_of_pair_of_neighbors_in_personage`
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or `successor_of_pair_of_neighbors_in_personage`).
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