Total order examples (#130)

Everything/Guardedness.agda

@@ -8,6 +8,7 @@ open import Rings.Orders.Partial.Bounded
 open import Rings.Orders.Total.Bounded
 open import Rings.Orders.Total.BaseExpansion
 open import Fields.Orders.Limits.Lemmas
+open import Rings.Orders.Total.Examples
 --open import Fields.CauchyCompletion.Archimedean
 
 open import Sets.Cardinality.Infinite.Examples

Rings/Orders/Total/Examples.agda

@@ -0,0 +1,58 @@
+{-# OPTIONS --safe --warning=error --without-K --guardedness #-}
+
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+open import LogicalFormulae
+open import Groups.Lemmas
+open import Groups.Definition
+open import Setoids.Orders.Total.Definition
+open import Setoids.Setoids
+open import Functions.Definition
+open import Sets.EquivalenceRelations
+open import Rings.Definition
+open import Rings.Orders.Total.Definition
+open import Rings.Orders.Partial.Definition
+open import Numbers.Naturals.Semiring
+open import Numbers.Naturals.Order
+open import Numbers.Modulo.Definition
+open import Semirings.Definition
+open import Orders.Total.Definition
+open import Sequences
+open import Numbers.Integers.Definition
+open import Numbers.Integers.Addition
+open import Numbers.Integers.Multiplication
+open import Numbers.Integers.Order
+open import Numbers.Rationals.Definition
+open import Vectors
+open import Fields.Fields
+
+module Rings.Orders.Total.Examples where
+
+open import Rings.Orders.Total.BaseExpansion (ℚOrdered) {10} (le 8 refl)
+open Field ℚField
+
+t : Vec ℚ 5
+t = take 5 (partialSums (funcToSequence injectionNQ))
+
+u : Vec ℚ 5
+u = vecMap injectionNQ (0 ,- (1 ,- (3 ,- (6 ,- (10 ,- [])))))
+
+pr : Vec (ℚ && ℚ) 5
+pr = vecZip t u
+
+ans : vecAllTrue (λ x → _&&_.fst x =Q _&&_.snd x) pr
+ans = refl ,, (refl ,, (refl ,, (refl ,, (refl ,, record {}))))
+
+open import Rings.InitialRing ℚRing
+
+a : Sequence ℚ
+a with allInvertible (fromN 10) (λ ())
+... | 1/10 , pr1/10 = approximations 1/10 pr1/10 (baseNExpansion (underlying (allInvertible (injectionNQ 7) λ ())) (lessInherits (succIsPositive 0)) (lessInherits (le 5 refl)))
+
+expected : Vec ℚ _
+expected = record { num = nonneg 1 ; denom = nonneg 10 ; denomNonzero = f } ,- record { num = nonneg 14 ; denom = nonneg 100 ; denomNonzero = λ () } ,- record { num = nonneg 142 ; denom = nonneg 1000 ; denomNonzero = λ () } ,- []
+  where
+    f : nonneg 10 ≡ nonneg 0 → False
+    f ()
+
+ans' : vecAllTrue (λ x → _&&_.fst x =Q _&&_.snd x) (vecZip (take _ a) expected)
+ans' = refl ,, (refl ,, (refl ,, record {}))