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Add Everything (#34)

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Patrick Stevens
2019-08-18 10:35:15 +01:00
committed by GitHub
parent a31ae0d1ea
commit e7c54fa48a
45 changed files with 415 additions and 378 deletions
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15
IntegersModNRing.agda
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@@ -2,11 +2,11 @@
open import LogicalFormulae
open import Orders
open import Groups
open import Naturals
open import Groups.Groups
open import Numbers.Naturals
open import PrimeNumbers
open import Rings
open import Setoids
open import Rings.Definition
open import Setoids.Setoids
open import IntegersModN
module IntegersModNRing where
@@ -54,12 +54,11 @@ module IntegersModNRing where
ℤnMultIdent {succ (succ n)} {pr} record { x = a ; xLess = aLess } | inl (inr ssn<a) = exFalso (PartialOrder.irreflexive (TotalOrder.order ℕTotalOrder) (PartialOrder.transitive (TotalOrder.order ℕTotalOrder) aLess ssn<a))
ℤnMultIdent {succ (succ n)} {pr} record { x = .(succ (succ n)) ; xLess = aLess } | inr refl = exFalso (PartialOrder.irreflexive (TotalOrder.order ℕTotalOrder) aLess)
ℤnRing : (n : ℕ) → (pr : 0 <N n) → Ring {_} (ℤn n pr)
Ring.additiveGroup (ℤnRing n 0<n) = AbelianGroup.grp (ℤnGroup n 0<n)
Ring._*_ (ℤnRing n 0<n) a b = a *n b
ℤnRing : (n : ℕ) → (pr : 0 <N n) → Ring (reflSetoid (ℤn n pr)) (_+n_) (_*n_)
Ring.additiveGroup (ℤnRing n 0<n) = (ℤnGroup n 0<n)
Ring.multWellDefined (ℤnRing n 0<n) = reflGroupWellDefined
Ring.1R (ℤnRing n pr) = ℤnIdent n pr
Ring.groupIsAbelian (ℤnRing n 0<n) = AbelianGroup.commutative (ℤnGroup n 0<n)
Ring.groupIsAbelian (ℤnRing n 0<n) = AbelianGroup.commutative (ℤnAbGroup n 0<n)
Ring.multAssoc (ℤnRing n 0<n) = {!!}
Ring.multCommutative (ℤnRing n 0<n) {a} {b} = ℤnMultCommutative a b
Ring.multDistributes (ℤnRing n 0<n) = {!!}