doc: slight updates to noteworthy differences from Python (#38027)

* Correct a few typos
* Mention that Python comes with single-dispatch
* Correct method example for Python and Julia
* Apply suggestions from code review

Co-authored-by: Stefan Karpinski <[email protected]>

doc/src/manual/noteworthy-differences.md

@@ -203,7 +203,7 @@ For users coming to Julia from R, these are some noteworthy differences:
  is not significant as it is in Python. Unlike Python, Julia has no `pass` keyword.
  * Strings are denoted by double quotation marks (`"text"`) in Julia (with three double quotation marks for multi-line strings), whereas in Python they can be denoted either by single (`'text'`) or double quotation marks (`"text"`). Single quotation marks are used for characters in Julia (`'c'`).
  * String concatenation is done with `*` in Julia, not `+` like in Python. Analogously, string repetition is done with `^`, not `*`. Implicit string concatenation of string literals like in Python (e.g. `'ab' 'cd' == 'abcd'`) is not done in Julia.
- * Python Lists—flexible but slow—correspond to the Julia `Vector{Any}` type or more generally `Vector{T}` where `T` is some non-concrete element type. "Fast" arrays like Numpy arrays that store elements in-place (i.e., `dtype` is `np.float64`, `[('f1', np.uint64), ('f2', np.int32)]`, etc.) can be represented by `Array{T}` where `T` is a concrete, immutable element type. This includes built-in types like `Float64`, `Int32`, `Int64` but also more complex types like `Tuple{UInt64,Float64}` and many user-defined types as well.
+ * Python Lists—flexible but slow—correspond to the Julia `Vector{Any}` type or more generally `Vector{T}` where `T` is some non-concrete element type. "Fast" arrays like NumPy arrays that store elements in-place (i.e., `dtype` is `np.float64`, `[('f1', np.uint64), ('f2', np.int32)]`, etc.) can be represented by `Array{T}` where `T` is a concrete, immutable element type. This includes built-in types like `Float64`, `Int32`, `Int64` but also more complex types like `Tuple{UInt64,Float64}` and many user-defined types as well.
  * In Julia, indexing of arrays, strings, etc. is 1-based not 0-based.
  * Julia's slice indexing includes the last element, unlike in Python. `a[2:3]` in Julia is `a[1:3]`
  in Python.
@@ -215,7 +215,7 @@ For users coming to Julia from R, these are some noteworthy differences:
  * Julia has no line continuation syntax: if, at the end of a line, the input so far is a complete
  expression, it is considered done; otherwise the input continues. One way to force an expression
  to continue is to wrap it in parentheses.
- * Julia arrays are column major (Fortran ordered) whereas NumPy arrays are row major (C-ordered)
+ * Julia arrays are column-major (Fortran-ordered) whereas NumPy arrays are row-major (C-ordered)
  by default. To get optimal performance when looping over arrays, the order of the loops should
  be reversed in Julia relative to NumPy (see [relevant section of Performance Tips](@ref man-performance-column-major)).
  * Julia's updating operators (e.g. `+=`, `-=`, ...) are *not in-place* whereas NumPy's are. This
@@ -239,12 +239,12 @@ For users coming to Julia from R, these are some noteworthy differences:
  * Julia uses `nothing` of type `Nothing` to represent a null value, whereas Python uses `None` of type `NoneType`.
  * In Julia, the standard operators over a matrix type are matrix operations, whereas, in Python, the standard operators are element-wise operations. When both `A` and `B` are matrices, `A * B` in Julia performs matrix multiplication, not element-wise multiplication as in Python. `A * B` in Julia is equivalent with `A @ B` in Python, whereas `A * B` in Python is equivalent with `A .* B` in Julia.
  * The adjoint operator `'` in Julia returns an adjoint of a vector (a lazy representation of row vector), whereas the transpose operator `.T` over a vector in Python returns the original vector (non-op).
- * In Julia, a function may contain multiple concrete implementations (called *Methods*), selected via multiple dispatch, whereas functions in Python have a single implementation (no polymorphism).
+ * In Julia, a function may contain multiple concrete implementations (called *methods*), which are selected via multiple dispatch based on the types of all arguments to the call, as compared to functions in Python, which have a single implementation and no polymorphism (as opposed to Python method calls which use a different syntax and allows dispatch on the receiver of the method).
  * There are no classes in Julia. Instead they are structures (mutable or immutable), containing data but no methods.
- * Calling a method of a class in Python (`a = MyClass(x), x.func(y)`) corresponds to a function call in Julia, e.g. `a = MyStruct(x), func(x::MyStruct, y)`. In general, multiple dispatch is more flexible and powerful than the Python class system.
+ * Calling a method of a class instance in Python (`x = MyClass(*args); x.f(y)`) corresponds to a function call in Julia, e.g. `x = MyType(args...); f(x, y)`. In general, multiple dispatch is more flexible and powerful than the Python class system.
  * Julia structures may have exactly one abstract supertype, whereas Python classes can inherit from one or more (abstract or concrete) superclasses.
- * The logical Julia program structure (Packages and Modules) is independent of the file strucutre (`include` for additional files), whereas the Python code structure is defined by directories (Packages) and files (Modules).
- * The ternary operator `x > 0 ? 1 : -1` in Julia corresponds to conditional expression in Python `1 if x > 0 else -1`.
+ * The logical Julia program structure (Packages and Modules) is independent of the file structure (`include` for additional files), whereas the Python code structure is defined by directories (Packages) and files (Modules).
+ * The ternary operator `x > 0 ? 1 : -1` in Julia corresponds to a conditional expression in Python `1 if x > 0 else -1`.
  * In Julia the `@` symbol refers to a macro, whereas in Python it refers to a decorator.
  * Exception handling in Julia is done using `try` — `catch` — `finally`, instead of `try` — `except` — `finally`. In contrast to Python, it is not recommended to use exception handling as part of the normal workflow in Julia due to performance reasons.
  * In Julia loops are fast, there is no need to write "vectorized" code for performance reasons.