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Move towards base-n expansions (#112)

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Patrick Stevens
2020-04-11 19:46:26 +01:00
committed by GitHub
parent e9aa1bcc05
commit 380548134d
22 changed files with 312 additions and 102 deletions
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6
Fields/CauchyCompletion/Setoid.agda
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@@ -18,7 +18,7 @@ open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Order
open import Semirings.Definition
module Fields.CauchyCompletion.Setoid {m n o : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {_<_ : Rel {m} {o} A} {pOrder : SetoidPartialOrder S _<_} {R : Ring S _+_ _*_} {pRing : PartiallyOrderedRing R pOrder} (order : TotallyOrderedRing pRing) (F : Field R) (charNot2 : Setoid._∼_ S ((Ring.1R R) + (Ring.1R R)) (Ring.0R R) → False) where
module Fields.CauchyCompletion.Setoid {m n o : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {_<_ : Rel {m} {o} A} {pOrder : SetoidPartialOrder S _<_} {R : Ring S _+_ _*_} {pRing : PartiallyOrderedRing R pOrder} (order : TotallyOrderedRing pRing) (F : Field R) where
open Setoid S
open SetoidTotalOrder (TotallyOrderedRing.total order)
@@ -31,9 +31,11 @@ open Field F
open import Fields.Lemmas F
open import Fields.CauchyCompletion.Definition order F
open import Fields.CauchyCompletion.Addition order F charNot2
open import Fields.CauchyCompletion.Addition order F
open import Rings.Orders.Partial.Lemmas pRing
open import Rings.Orders.Total.Lemmas order
open import Rings.InitialRing R
open import Fields.Orders.Total.Lemmas {F = F} (record { oRing = order })
isZero : CauchyCompletion → Set (m ⊔ o)
isZero record { elts = elts ; converges = converges } = ∀ ε → 0R < ε → Sg ℕ (λ N → ∀ {m : ℕ} → (N <N m) → (abs (index elts m)) < ε)