Add more usable interface to Sqrt module

Bodigrim / arithmoi

Number theory: primes, arithmetic functions, modular computations, special sequences

http://hackage.haskell.org/package/arithmoi

MIT License

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Add more usable interface to Sqrt module #108

Closed viviag closed 6 years ago

viviag commented 6 years ago

Covers #87 (Not closes since there is still strange internal design) Possible workaround here:

[x] Use PrimeNat.
[x] Check if residue is quadratic also outside and reflect it to types - ideally make type like data Residue a = Quadratic a | NonQuadratic a. It looks like reflecting terminology to type system is a good approach.

viviag commented 6 years ago

Seems that approach with toType functions is applicable for every restriction e.g. existing wrapper Prime. See message of https://github.com/cartazio/arithmoi/pull/108/commits/b0d0c1bd94f67321b08d59c233ca3ae9306e1572

viviag commented 6 years ago

Here we expect p is prime and it's checked earlier. We do not push errors here back and can expect nontermination later if p is actually not a prime let (Just c) = Moduli.sqrtModMaybe (-1) (FieldCharacteristic (PrimeNat . integerToNatural $ p) 1)

[ ] So I will make this function partial - it's better than to make partial sqrtModMaybe I'll leave direct calls to constructor in tests.
[ ] And it would be good idea not to export constructors at all and name fields in new types. Maybe.

Bodigrim commented 6 years ago

Merged! Huge thanks for your contribution.