42 lines
1.0 KiB
Agda
42 lines
1.0 KiB
Agda
-- ignore
|
||
module 1FundamentalGroup.Quest2Solutions where
|
||
open import 1FundamentalGroup.Preambles.P2
|
||
|
||
-- sucℤ : ℤ → ℤ
|
||
-- sucℤ (pos n) = pos (suc n)
|
||
-- sucℤ (negsuc zero) = pos zero
|
||
-- sucℤ (negsuc (suc n)) = negsuc n
|
||
|
||
-- predℤ : ℤ → ℤ
|
||
-- predℤ (pos zero) = negsuc zero
|
||
-- predℤ (pos (suc n)) = pos n
|
||
-- predℤ (negsuc n) = negsuc (suc n)
|
||
|
||
-- sucℤIso : ℤ ≅ ℤ
|
||
-- sucℤIso = iso sucℤ predℤ s r where
|
||
|
||
-- s : section sucℤ predℤ
|
||
-- s (pos zero) = refl
|
||
-- s (pos (suc n)) = refl
|
||
-- s (negsuc zero) = refl
|
||
-- s (negsuc (suc n)) = refl
|
||
|
||
-- r : retract sucℤ predℤ
|
||
-- r (pos zero) = refl
|
||
-- r (pos (suc n)) = refl
|
||
-- r (negsuc zero) = refl
|
||
-- r (negsuc (suc n)) = refl
|
||
|
||
-- sucℤPath : ℤ ≡ ℤ
|
||
-- sucℤPath = isoToPath sucℤIso
|
||
|
||
-- helix : S¹ → Type
|
||
-- helix base = ℤ
|
||
-- helix (loop i) = sucℤPath i
|
||
|
||
-- windingNumberBase : base ≡ base → ℤ
|
||
-- windingNumberBase p = endPt helix p (pos zero)
|
||
|
||
-- windingNumber : (x : S¹) → base ≡ x → helix x
|
||
-- windingNumber x p = endPt helix p (pos zero)
|