Add fields about semirings HOT 13 CLOSED

this is released. thank you everyone

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I've actually had the same thought, and wanted this several times.

I'll take a PR for this. If there isn't a PR by the time I take up a sudden obsessive interest for 20 minutes, I'll do this

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A PR should consist of (in Data.Semiring or perhaps another module):

• Adding the Field typeclass
• Adding all instances for that typeclass
• documenting the laws of the typeclass
• useful functions acting on types which are instances of the typeclass

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This is secondary, and not necessary work to be done in semirings, but I'd also like fieldLaws to be added to quickcheck-classes and hedgehog-classes. (I will do this)

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Perhaps the name should not be called invert? I know it fits, but doesn't mesh well with the popular groups package? If there's no better name then I'll yield on that. Note that I'm not worried about name-clashing with the Prelude. Perhaps call it recip?

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Some useful functions that can be defined in terms of recip:

a / b = a * recip b
fromRational r = fromInteger (numerator r) / fromInteger (denonimator r)

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Also, not sure what other instances in base there are other than Float,Double,Ratio,Complex.

My strategy thus far has been to supply instances for all types in base that have relevant instances (here i think that would be Fractional). Though, this recently got me into trouble with windows users (see #34)

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Also, we should probably only allow instances we know to be "traditional". To that end, ratios of functions form a commutative ring (field), so i wonder if we should provide a type/instance for that?

An example of a non-traditional instance would be for a non-field where the density of units is high, e.g. certain residue classes. This high density of units allows the instance to still be useful.

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This corresponds to division/reciprocal numbers, and can be implemented for e.g. rational numbers and reals.

We already have Fractional for this. Are there any examples of Field (in base, containers, etc.), which are not Num? If there are none, I struggle to find a use case for a new type class.

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Except for adding fieldLaws to quickcheck-classes and hedgehog-classes (and possibly instances for ratios of functions and non-fields), this issue should be completed with the latest pull request #48.

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Will this be released on Hackage anytime soon?

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Yes, tomorrow

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Thanks!

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