2 ms·
A perhaps nicer way to look at things[0] is to hold onto your base points explicitly and say Df:: a -> (b, a -o b) = (f(p),A(p)) where f(p+v)≈f(p)+A(p)v. Then y
by ndriscoll 1y ago
A perhaps nicer way to look at things[0] is to hold onto your base points explicitly and say Df:: a -> (b, a -o b) = (f(p),A(p)) where f(p+v)≈f(p)+A(p)v. Then you retain the information you need to define composition Dg∘Df=D(g∘f)=(Dg._1∘Df._1, Dg(Df._1)_.2∘Df._2). i.e the chain rule.
[0] which I learned from this talk https://youtube.com/watch?v=17gfCTnw6uE https://youtube.com/watch?v=17gfCTnw6uE
- ziofill 1y agoYes! I love Conal Eliot’s work. The one you wrote is the compositional derivative which augments the regular derivative by also returning the function itself (otherwise composition won’t work well). For anyone interested look up “the simple essence of automatic differentiation”.
- dbacar 1y agoI respect the time you spent to write such a post with all those limited input alternatives (bowes).
- ndriscoll 1y agoYou can do ≈ by long holding = on Android/Gboard. The only way I know to get ∘ is to copy/paste it from a Unicode reference. Likewise with ⊸, which I was too lazy to look up and didn't know the name of, but now I know is MULTIMAP (U+22B8).
- tomsmeding 1y agoIt's also \multimap in TeX. The name never made sense to me because while I've seen it used for a variety of linear functions in math, I've never seen it used for a multimap, and indeed the math name in common use for it seems to be "lollipop".
- esafak 1y agoIt's deplorable that we can't write in Latex or something similar here in 2025, and have to resort to the gobbledygook above.