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https://github.com/Smaug123/agdaproofs
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33 lines
886 B
Agda
33 lines
886 B
Agda
{-# OPTIONS --safe --warning=error #-}
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open import LogicalFormulae
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open import Numbers.Naturals
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open import Numbers.Integers
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open import Groups.Groups
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open import Rings.RingDefinition
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open import Fields.Fields
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open import PrimeNumbers
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open import Setoids.Setoids
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open import Functions
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open import Fields.FieldOfFractions
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module Numbers.Rationals where
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ℚ : Set
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ℚ = fieldOfFractionsSet ℤIntDom
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_+Q_ : ℚ → ℚ → ℚ
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a +Q b = fieldOfFractionsPlus ℤIntDom a b
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_*Q_ : ℚ → ℚ → ℚ
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a *Q b = fieldOfFractionsTimes ℤIntDom a b
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ℚRing : Ring (fieldOfFractionsSetoid ℤIntDom) _+Q_ _*Q_
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ℚRing = fieldOfFractionsRing ℤIntDom
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ℚField : Field ℚRing
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ℚField = fieldOfFractions ℤIntDom
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ℚField : OrderedRing ℚRing (fieldOfFractionsTotalOrder ℤIntDom ℤOrderedRing)
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ℚField = fieldOfFractionsOrderedRing ℤIntDom ℤOrderedRing
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