daviddoji/CalculusWithJuliaNotes.jl
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jverzani
2024-04-26 18:26:12 -04:00
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6
quarto/derivatives/symbolic_derivatives.qmd
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@@ -34,7 +34,7 @@ The `Symbolics` package provides native symbolic manipulation abilities for `Jul
An expression is an unevaluated portion of code that for our purposes below contains other expressions, symbols, and numeric literals. They are held in the `Expr` type. A symbol, such as `:x`, is distinct from a string (e.g. `"x"`) and is useful to the programmer to distinguish between the contents a variable points to from the name of the variable. Symbols are fundamental to metaprogramming in `Julia`. An expression is a specification of some set of statements to execute. A numeric literal is just a number.
The three main functions from `TermInterface` we leverage are `istree`, `operation`, and `arguments`. The `operation` function returns the "outside" function of an expression. For example:
The three main functions from `TermInterface` we leverage are `isexpr`, `operation`, and `arguments`. The `operation` function returns the "outside" function of an expression. For example:
```{julia}
@@ -65,7 +65,7 @@ function arity(ex)
end
```
Differentiation must distinguish between expressions, variables, and numbers. Mathematically expressions have an "outer" function, whereas variables and numbers can be directly differentiated. The `istree` function in `TermInterface` returns `true` when passed an expression, and `false` when passed a symbol or numeric literal. The latter two may be distinguished by `isa(..., Symbol)`.
Differentiation must distinguish between expressions, variables, and numbers. Mathematically expressions have an "outer" function, whereas variables and numbers can be directly differentiated. The `isexpr` function in `TermInterface` returns `true` when passed an expression, and `false` when passed a symbol or numeric literal. The latter two may be distinguished by `isa(..., Symbol)`.
Here we create a function, `D`, that when it encounters an expression it *dispatches* to a specific method of `D` based on the outer operation and arity, otherwise if it encounters a symbol or a numeric literal it does the differentiation:
@@ -73,7 +73,7 @@ Here we create a function, `D`, that when it encounters an expression it *dispat
```{julia}
function D(ex, var=:x)
if istree(ex)
if isexpr(ex)
op, args = operation(ex), arguments(ex)
D(Val(op), arity(ex), args, var)
elseif isa(ex, Symbol) && ex == :x