2025/11/18

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2025-11-18 02:24:50 +0100AlexZenon(~alzenon@178.34.162.20)
2025-11-18 02:24:07 +0100 <haskellbridge> <Zemyla> True.
2025-11-18 02:23:43 +0100merijn(~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 240 seconds)
2025-11-18 02:21:50 +0100 <monochrom> Combination may be N->2. Each of n elements may be chosen or not-chosen.
2025-11-18 02:18:55 +0100AlexNoo(~AlexNoo@178.34.151.158) (Ping timeout: 246 seconds)
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2025-11-18 02:17:08 +0100 <monochrom> So yeah it's both programming and category theory. I was coding up LU factorization with pivoting, and I recorded the permutation of rows by performing the same permutation on [0 .. n-1] and returning it.
2025-11-18 02:16:58 +0100AlexZenon(~alzenon@178.34.151.158) (Ping timeout: 256 seconds)
2025-11-18 02:16:42 +0100humasect(~humasect@dyn-192-249-132-90.nexicom.net) humasect
2025-11-18 02:15:27 +0100AlexNoo_(~AlexNoo@178.34.162.20)
2025-11-18 02:15:25 +0100 <monochrom> Moreover, it also hints that σ id is "backwards": It maps new indexes to old indexes. How to see it: Use N for old indexes, N' for new indexes. Then (N->a) -> (N'->a) is isomorphic to N' -> N.
2025-11-18 02:14:38 +0100trickard_trickard
2025-11-18 02:13:27 +0100peterbecich(~Thunderbi@172.222.148.214) peterbecich
2025-11-18 02:12:55 +0100 <EvanR> sounds like the theory of group action
2025-11-18 02:12:14 +0100 <monochrom> I don't know! Not interested for now.
2025-11-18 02:12:01 +0100 <monochrom> And the backward mapping maps e to \v -> v ∘ e
2025-11-18 02:11:51 +0100 <haskellbridge> <Zemyla> So is there a type that represents a combination?
2025-11-18 02:10:41 +0100 <monochrom> Model "array of length n with elements of type a" as N->a, N = {0 .. n-1}. Then permutations are a special cases of (N->a) -> (N->a). Then Yoneda embedding says that it's isomorphic to N->N, the forward mapping maps σ to σ id, id = [0 .. n-1].