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Jul. 2nd, 2007 12:59 pmi finally got around to reading the proof of the poincaré lemma. moosehead_beer, do you want a proof post? how familiar are you with differential forms (
)?
like does this make sense:
i think i can get away with no more than that.
poincaré lemma in three dimensions states that (all functions are C∞)
1. If grad f = 0, then f is constant. (obvious)
2. If curl (f, g, h) = 0 then (f, g, h) = grad F. (semi-obvious)
3. If div (f, g, h) = 0 then (f, g, h) = curl (F, G, H).
4. All f = div(F, G, H). (obvious)
it does some other stuff in higher dimensions.
like does this make sense:
i think i can get away with no more than that.
poincaré lemma in three dimensions states that (all functions are C∞)
1. If grad f = 0, then f is constant. (obvious)
2. If curl (f, g, h) = 0 then (f, g, h) = grad F. (semi-obvious)
3. If div (f, g, h) = 0 then (f, g, h) = curl (F, G, H).
4. All f = div(F, G, H). (obvious)
it does some other stuff in higher dimensions.
