Constructing morphisms and morphic relations for multiplication tables. input: two multiplication tables (source, target) output: hash-maps describing morphisms, index i -> image
These functions are relatively inefficient (compared to generator table methods). They are for reference purposes, not for the high-end computations.
This is a reference implementation for the paper: Finite Computational Structures and Implementations: Semigroups and Morphic Relations International Journal of Networking and Computing, Volume 7, Number 2, pages 318-335, July 2017 https://doi.org/10.15803/ijnc.7.2_318
Constructing morphisms and morphic relations for multiplication tables. input: two multiplication tables (source, target) output: hash-maps describing morphisms, index i -> image These functions are relatively inefficient (compared to generator table methods). They are for reference purposes, not for the high-end computations. This is a reference implementation for the paper: Finite Computational Structures and Implementations: Semigroups and Morphic Relations International Journal of Networking and Computing, Volume 7, Number 2, pages 318-335, July 2017 https://doi.org/10.15803/ijnc.7.2_318
(divisions S T)All divisions from S to T.
All divisions from S to T.
(generator-fn S morphims?-fn candidates)For extension mechanisms for fixed candidate sets. We extend the morphism by a new mapping using the size of the hash-map as the key for the new entry, using candidates for possible values.
For extension mechanisms for fixed candidate sets. We extend the morphism by a new mapping using the size of the hash-map as the key for the new entry, using candidates for possible values.
(homomorphisms S T)All homomorphisms from multiplication table S to T.
All homomorphisms from multiplication table `S` to `T`.
(isomorphisms S T)All isomorphisms from S to T.
All isomorphisms from S to T.
(multab-homomorphism? S T morph-m)Decides whether the partial mapping morph-m from S to T is homomorphic or not. It lazily checks all products.
Decides whether the partial mapping morph-m from S to T is homomorphic or not. It lazily checks all products.
(multab-relmorphism? S T morph-m)Decides whether the (partial) mapping morph-m from multab S to multab T is a relational morphism or not.
Decides whether the (partial) mapping morph-m from multab S to multab T is a relational morphism or not.
(relmorphisms S T)All relational morphisms from multiplication table S to T.
These are one-to-many set-valued morphic mappings.
All relational morphisms from multiplication table `S` to `T`. These are one-to-many set-valued morphic mappings.
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