noiioiu/nimbers - Change ASGE7I4JJ3HTHHSQKVNL74ZVZQ6WTYX6M54FYKOUE4PCPRPUNSUQC

Add Nat type for small natural numbers

Created by noiioiu on April 19, 2024

ASGE7I4JJ3HTHHSQKVNL74ZVZQ6WTYX6M54FYKOUE4PCPRPUNSUQC

Dependencies

In channels

main

Change contents

Insertion in src/Nimbers.hs at line 14 [3.880]
[3.1521]
[3.1521]
```
-- | Small natural numbers.
type Nat = Int
```
Insertion in src/Nimbers.hs at line 18 [3.880]
[3.1522]
[4.687]
```
-- | Arbitrarily large natural numbers.
```

Replacement in src/Nimbers.hs at line 23 [3.880]

B:BD[3.1853] → [3.1853:1914]

newtype Nimber = Nimber {getNimber :: S.Set (S.Set Natural)}

[3.1853]

[3.1914]

newtype Nimber = Nimber {getNimber :: S.Set (S.Set Nat)}

Replacement in src/Nimbers.hs at line 38 [3.880]
B:BD[3.2456] → [3.2456:2494]
```
twoPowers :: Natural -> S.Set Natural
```
[3.2456]
[3.2494]
```
twoPowers :: (Integral a, Integral b) => a -> S.Set b
```

Replacement in src/Nimbers.hs at line 56 [3.880]

B:BD[3.3017] → [3.3017:3082]

  Nimber a + Nimber b = Nimber $ (a S.\\ b) `S.union` (b S.\\ a)

[3.2841]

[3.3082]

  (+) = (Nimber .) . (. getNimber) . delta . getNimber

Replacement in src/Nimbers.hs at line 79 [3.880]

B:BD[2.51] → [2.51:466]

    let m     = foldl max 0 $ S.unions s          -- D = 2^2^m is the largest Fermat 2-power less than or equal to n
        aD    = Nimber $ S.filter (S.member m) s  -- n = aD+b
        b     = Nimber $ S.filter (S.notMember m) s
        a     = Nimber $ S.map (S.delete m) $ getNimber aD
        semiD = Nimber . S.singleton $ S.fromList [0..m-1] -- semimultiple of D
     in (aD+a+b) / (semiD * a^2 + a*b + b^2)

[2.51]

[3.3767]

    let m = foldl max 0 $ S.unions s -- D = 2^2^m is the largest Fermat 2-power less than or equal to n
        aD = Nimber $ S.filter (S.member m) s -- n = aD+b
        b = Nimber $ S.filter (S.notMember m) s
        a = Nimber $ S.map (S.delete m) $ getNimber aD
        semiD = Nimber . S.singleton $ S.fromList [0 .. m - 1] -- semimultiple of D
     in (aD + a + b) / (semiD * a ^ 2 + a * b + b ^ 2)