From ec1f31b5a1492d5e0ab260397291d4449483bbd9 Mon Sep 17 00:00:00 2001
From: Eduardo Julian
Date: Mon, 23 Aug 2021 02:30:53 -0400
Subject: The Python compiler can now be compiled by the new JVM compiler.

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+# Appendix B: Math in Lux
+
+Math in Lux is a bit different from what you might be used to in other languages.
+
+For starters, Lux is a _lisp_, which means that it uses prefix syntax for everything.
+
+That means, familiar operations such as `3 + 5` or `8 = 8` get written as `(+ 3 5)` and `(= 8 8)`.
+
+There's also the issue of different operators for different types.
+
+Whereas other programming languages often overload the math operators `+`, `-`, `>`, etc. for all numeric (and some non-numeric) types, Lux actual offers different versions for different types (defined in the respective modules for those types).
+
+The differences may look trivial, but since the numeric types are treated differently in Lux, you must be aware of which function-set you're using when working with your data.
+
+However, this is not the biggest difference in Lux's math operators in comparison to other languages.
+The difference that takes the crown is the ordering of the arguments.
+
+What do I mean?
+
+In most languages you'd write `4 - 7`.
+In other lisps you'd write `(- 4 7)`.
+But in Lux, you'd write `(- 7 4)`.
+
+_What is going on!? This is so bizarre!_
+
+Calm down.
+Everything is going to be fine.
+
+What's going on is that in functional programming, there is this convention of putting the most significant argument to a function as the last one.
+In the case of math functions, this would be the argument on which you're operating. I call it the _"subject"_ of the function.
+
+In the case of the subtraction operation, it would be the 4, since you're subtracting 7 from it.
+
+In most lisps, the order of the arguments is such that the subject is the first argument; but not so in Lux.
+
+Now, you may be wondering: _what could possibly be the benefit of making this bizarre change?_
+
+Piping. Piping convinced me to make this change.
+
+You see; this might look very impractical to those accustomed to the old way, but when you're writing complex calculations with many levels of nesting, being able to pipe your operations helps a lot, and this style of doing math lends itself perfectly for it.
+
+Consider this:
+
+```
+(|> x (/ scale) (pow 3.0) (- shift))
+```
+
+If I was using the traditional way of doing math, I wouldn't be able to pipe it, and it would look like this:
+
+```
+(- (pow (/ x scale)
+        3.0)
+   shift)
+```
+
+	`pow` is the _power_ function, located in `library/lux/math`.
+
+You can complain all you want about me breaking with tradition, but that just looks ugly.
+
+So, I'm just going to say it: I broke with tradition because tradition wasn't helping, and I'm not one to just comply because I'm supposed to.
+
+However, I'm not without a heart; and I know that a lot of people would prefer to have a more... traditional way of doing math.
+
+So, for you guys, I've introduced a special macro in the `library/lux/math/infix` module.
+
+It's called `infix`, and it allows you to do infix math, with nested expressions.
+
+Here's an example:
+
+```
+(infix [[3.0 pow 2.0] + [5.0 * 8.0]])
+```
+
+So, that corresponds to `3^2 + 5*8`.
+
+Note that `infix` doesn't enforce any grouping rules, since you can actually use it with arbitrary functions that you import or define (even with partially applied functions).
+
+The rule is simple, the argument to the right of the operator will be taken first, and then the argument to the left.
+
+So `[3.0 pow 2.0]` becomes `(pow 2.0 3.0)`, and `[5.0 * 8.0]` becomes `(* 8.0 5.0)`.
+Thus, the infix syntax is transformed into Lux's prefix variation.
+
+---
+
+I know that Lux's way of doing math is a bit... foreign; but I made that change to ensure math fit the rest of the language perfectly.
+
+Hopefully you'll come to see that getting used to the new way is a piece of cake and has its advantages as soon as you write complex calculations.
+
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