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# bijective | ||
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When used with a function domain will restrict solutions to functions that are both [injective](https://github/conjure-cp/conjure/docs/bits/attribute/L_injective.md) and [surjective](https://github/conjure-cp/conjure/docs/bits/attribute/L_surjective.md). | ||
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This means that every element of the defined set has a unique mapping to a range element and every range element has a defined element that maps to it. | ||
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See it demonstrated [here](https://github/conjure-cp/conjure/docs/notebooks/functionDemonstration.ipynb). |
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# injective | ||
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When used with a function domain will restrict solutions to functions where elements of the defined map uniquely to elements of the range. | ||
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See it demonstrated [here](https://github/conjure-cp/conjure/docs/notebooks/functionDemonstration.ipynb). |
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# maxSize | ||
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Takes an integer parameter, n. | ||
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When used with a function domain will limit the solutions to functions that contains at most n mappings. | ||
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See it demonstrated [here](https://github/conjure-cp/conjure/docs/notebooks/functionDemonstration.ipynb). |
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# minSize | ||
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Takes an integer parameter, n. | ||
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When used with a function domain will limit the solutions to functions that contains at least n mappings. | ||
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See it demonstrated [here](https://github/conjure-cp/conjure/docs/notebooks/functionDemonstration.ipynb). |
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# size | ||
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Takes an integer parameter, n. | ||
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When used with a function domain will limit the solutions to functions that contain n mappings. | ||
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See it demonstrated [here](https://github/conjure-cp/conjure/docs/notebooks/functionDemonstration.ipynb). |
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# surjective | ||
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When used with a function domain will restrict solutions to functions where there is a mapping to every element in the range. | ||
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See it demonstrated [here](https://github/conjure-cp/conjure/docs/notebooks/functionDemonstration.ipynb). |
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# total | ||
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When used with a function domain will only return solutions that have mappings for every element in the defined set. | ||
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See it demonstrated [here](https://github/conjure-cp/conjure/docs/notebooks/functionDemonstration.ipynb). |
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# function | ||
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Takes 2 [domains](https://conjure.readthedocs.io/en/latest/essence.html#domains) as arguments: the ```defined``` set and the ```range``` set of the function. | ||
The ```defined``` set is the domain of the function - the set of inputs for the function | ||
the ```range``` set is the codomain of the function - the set of possible outputs for the function | ||
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```essence | ||
**function** < comma separated attributes(optional)> <defined> --> <range> | ||
``` | ||
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There are 3 groups of function attributes: | ||
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- related to cardinality = [size](https://github/conjure-cp/conjure/docs/bits/attribute/L_size.md), [minSize](https://github/conjure-cp/conjure/docs/bits/attribute/L_minSize.md), and [maxSize](https://github/conjure-cp/conjure/docs/bits/attribute/L_maxSize.md). They take arguments. | ||
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- related to function properties = [injective](https://github/conjure-cp/conjure/docs/bits/attribute/L_injective.md), [surjective](https://github/conjure-cp/conjure/docs/bits/attribute/L_surjective.md), [bijective](https://github/conjure-cp/conjure/docs/bits/attribute/L_size.md). | ||
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- related to partiality = [total](https://github/conjure-cp/conjure/docs/bits/attribute/L_total.md). | ||
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Functions are partial by default | ||
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You can also explicity define a function as seen [here](https://github/conjure-cp/conjure/docs/notebooks/functionDemonstration.ipynb). | ||
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See demonstrations of the function attributes [here](https://github/conjure-cp/conjure/docs/notebooks/functionDemonstration.ipynb). | ||
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Or see functions used to solve the Magic Hexagon Problem [here](https://github.com/conjure-cp/conjure/tree/main/docs/notebooks/magicHexagon.ipynb). | ||
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Much of the information about functions lifted from [the readthedocs](https://conjure.readthedocs.io/en/latest/essence.html). | ||
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