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0 pointsmagicalhippo3y ago0 comments

I still don't get how sin ends up as cos, without any coordination.

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Presumably the Ad package has a list of known derivatives. The Sym package now "automatically" uses it, without ever having to have known of it.

The "coordination" is that they both use the "symbol" sin to refer to the idea of sine function.

shele3y ago

Interesting that is is this way in Haskell in this example: In Julia, there are community/consensus-based processes to what the "idea" of a symbol is (or rather, the idea of a function with its current methods and its future methods defined for new types) and package interoperability often works in a similar way.

leephillips3y ago

There is some confusion about what a symbol is in Julia due to bad tutorial information floating around the web. Here is Stefan Karpinski’s masterful explanation of what a Symbol really is:

https://stackoverflow.com/a/23482257

krastanov3y ago

As the sibling comment mentioned, this thread started using the word "symbol" in two different ways. There is the Julia/Lisp/Ruby use of the word symbol which is related to representing code in code and to homoiconicity. That is discussed in the sibling stack-overflow link.

Earlier in this thread though "symbol" was used in a less formal, handwavy way as "a named handle to some concept in the language". In that sense, indeed, the way that Julia adds multiple methods to a single named function and supports multiple dispatch permits amazing interoperability (and has little to do with Julia/Lisp/Ruby symbol datastructures).

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magicalhippoOP3y ago

Right, I was confused because for some reason I imagined "sin" coming from the symbolic library, but I'm assuming it's just built-in so AD knows about.

cryptonector3y ago

The `sin` function comes from this bit at the end of TFA:

    instance VectorSpace d => Floating (Dual d) where
      pi             = D pi zero
      exp   (D u u') = D (exp u)  (scale (exp u) u')
      log   (D u u') = D (log u)  (scale (log u) u')
  --->sin   (D u u') = D (sin u)  (scale (cos u) u')
      cos   (D u u') = D (cos u)  (scale (-sin u) u')
      sinh  (D u u') = D (sinh u) (scale (cosh u) u')
      cosh  (D u u') = D (cosh u) (scale (sinh u) u')

and the `sin` function on the right-hand side comes from `Float`, since `Float` is the type of the argument `u` in `sin u` in `D (sin u) (scale (cos u) u')`.

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krastanov3y ago

Presumably the Ad package has a list of known derivatives. The Sym package now "automatically" uses it, without ever having to have known of it.

The "coordination" is that they both use the "symbol" sin to refer to the idea of sine function.

shele3y ago

leephillips3y ago

There is some confusion about what a symbol is in Julia due to bad tutorial information floating around the web. Here is Stefan Karpinski’s masterful explanation of what a Symbol really is:

https://stackoverflow.com/a/23482257

krastanov3y ago

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magicalhippoOP3y ago

Right, I was confused because for some reason I imagined "sin" coming from the symbolic library, but I'm assuming it's just built-in so AD knows about.

cryptonector3y ago

The `sin` function comes from this bit at the end of TFA:

    instance VectorSpace d => Floating (Dual d) where
      pi             = D pi zero
      exp   (D u u') = D (exp u)  (scale (exp u) u')
      log   (D u u') = D (log u)  (scale (log u) u')
  --->sin   (D u u') = D (sin u)  (scale (cos u) u')
      cos   (D u u') = D (cos u)  (scale (-sin u) u')
      sinh  (D u u') = D (sinh u) (scale (cosh u) u')
      cosh  (D u u') = D (cosh u) (scale (sinh u) u')

and the `sin` function on the right-hand side comes from `Float`, since `Float` is the type of the argument `u` in `sin u` in `D (sin u) (scale (cos u) u')`.

1 more reply

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