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WIP: Document noteworthy unusual Julia features. #11998

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WIP: Document noteworthy unusual Julia features.
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33 changes: 33 additions & 0 deletions doc/manual/noteworthy-differences.rst
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Noteworthy Differences from other Languages
*******************************************

Noteworthy and unusual Julia features
---------------------------------

* Julia allows identifiers with complex Unicode, for example you could represent the value of a chi-squared test with ``χ²``,
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This sentence is way too long. Also, I don't think using Unicode in identifiers in general is what would cause problems, I think its more just this one particular case.

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It is a whole set of characters that at least as I understand the Unicode standard UAX 31, shouldn't be considered part of identifiers. (I have no problem at all with Unicode in identifiers, I just brought up a point where it seemed inconsistent with other uses of Unicode characters in Julia)

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Great. Instead of replying to me, write that in documentation form, which is not what is here right now.

similarly ``χ⁽³⁾`` is used in electromagnetism for the third-order nonlinear susceptibility, another example is ``∇²``
which is the name of the Laplacian operator. All of these Unicode symbols are valid Julia identifiers.

It can also be useful for caching powers of ``x`` to ensure that intermediate products are reused optimally in time-critical code.
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I get why this example was put here, but this is a microoptimization that is going to freak people out if its the first thing they see in a section of the manual. I'm not sure an example is needed.

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One would hope also that the compiler would be smart enough to lift things out of loops, if you have x*x or x^2 inside a loop. (If Jeff can't make the compiler do that, or more likely, has done it already, I'd eat my hat)

A classic example is in computing the [Lennard-Jones 12-6 potential energy](https://en.wikipedia.org/wiki/Lennard-Jones_potential) in computational chemistry and physics, in order to compute:

.. math::

A/x^12 - B/x^6

one can write:

.. doctest::

"Lennard-Jones potential"
function lj(x, A, B)
x⁻² = x^-2
x⁻⁶ = (x⁻²)^3
x⁻¹² = (x⁻⁶)^2
A*x⁻¹² - B*x⁻⁶
end

.. note::

Be wary about referencing a global variable while thinking it was an operator applied to a local variable and updating a
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I have no idea what this sentence is trying to say. Could you word it differently? Is this related to unicode?

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@ScottPJones would you mind showing a short example of this pitfall?

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This "pitfall" is a contrived strawman crafted to make a specific point.

variable without remembering to update the cached value.

* The ``/`` operator gives floating-point results for integer arguments, use ``div`` for truncating to an integer.
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Should probably just be in the C differences section, people coming from Python, MATLAB, R, etc. wouldn't find this a noteworthy or unusual Julia feature.

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I think it is a lot more languages than just C/C++, also Java, Lua, Python, etc.
Can you give an example of that actually working in MATLAB or R, or any other language?
AFAICT, it doesn't follow the Unicode standard for identifiers http://www.unicode.org/reports/tr31

>>> x³ = 5
  File "<stdin>", line 1
    x³ = 5
     ^
SyntaxError: invalid character in identifier
>

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@ScottPJones, its talking about division, not unicode, what are you talking about?

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Never mind, I thought you were talking about the part above.

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Ok I'll change it to the C part.


Noteworthy differences from MATLAB
----------------------------------

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