From 5347a9aabd363fb158482d16f6a70c73ba0bcaf2 Mon Sep 17 00:00:00 2001
From: orca <orcinus_orca@disroot.org>
Date: Sun, 4 Feb 2024 08:25:38 +0100
Subject: [PATCH] Added a manual file.

Resolves #3.
---
 README.md          |  4 +-
 makefile           |  6 +--
 source/example.typ | 91 ----------------------------------------------
 source/manual.typ  | 57 +++++++++++++++++++++++++++++
 4 files changed, 62 insertions(+), 96 deletions(-)
 delete mode 100644 source/example.typ
 create mode 100644 source/manual.typ

diff --git a/README.md b/README.md
index 1e1c458..62f2ec7 100644
--- a/README.md
+++ b/README.md
@@ -17,6 +17,6 @@ When there will be updates, run `git pull`.
 
 ## How to get started
 
-See the `source/example.typ` file for an example of it's usage.
+See the `source/manual.typ` file for an example of it's usage.
 
-Run `make example` to compile it.
+Run `make manual` to compile it.
diff --git a/makefile b/makefile
index 701133e..fed5cdc 100644
--- a/makefile
+++ b/makefile
@@ -1,6 +1,6 @@
 TARGET := ./main.pdf
 SOURCE := ./source/user/main.typ
-EXAMPLE := ./source/example.typ
+MANUAL := ./source/manual.typ
 PDF_VIEWER := zathura
 TYPST_FLAGS := --root ./source
 
@@ -16,7 +16,7 @@ clean:
 watch:
 	@typst w $(TYPST_FLAGS) $(SOURCE) $(TARGET) &> /dev/null &
 
-example: $(EXAMPLE)
+manual: $(MANUAL)
 	@typst c $(TYPST_FLAGS) $< $(TARGET)
 
-.PHONY: build view clean watch example
+.PHONY: build view clean watch manual
diff --git a/source/example.typ b/source/example.typ
deleted file mode 100644
index c8c5cbd..0000000
--- a/source/example.typ
+++ /dev/null
@@ -1,91 +0,0 @@
-#import "template/template.typ": *
-
-#show: paper => configuration(
-  title: lorem(5),
-  authors: (
-    (
-      name: "Lorem ipsum.",
-      affiliation: "Lorem institute",
-      email: "lorem.ipsum@example.org",
-    ),
-  ),
-  abstract: lorem(35),
-  paper
-)
-
-= #lorem(6)
-
-#lorem(70)
-
-= #lorem(5)
-#lorem(30)
-
-#definition(name: lorem(2))[
-  #lorem(5)
-
-  #lorem(18)
-]
-
-== #lorem(4)
-
-#lorem(50)
-
-#theorem(name: lorem(1))[
-  #lorem(4)
-
-  #lorem(20)
-
-  #numbered-equation[
-    $ integral.double_S arrow(A) dot arrow(dif S) $
-  ]
-
-  #lorem(7)
-]
-
-== #lorem(4)
-
-#lorem(40)
-
-#proposition[
-  #lorem(10)
-
-  $ integral_(a)^(+ oo) f(x) dif x $
-
-  #lorem(6)
-
-  $ sum f(n) $
-
-  #lorem(12)
-]
-
-#lorem(30)
-
-= #lorem(4)
-
-#lorem(20)
-
-== #lorem(7)
-
-#lorem(20)
-
-#remark(name: lorem(2))[
-  #lorem(30)
-]
-
-#lorem(10)
-
-#lemma[
-  #lorem(13)
-]
-
-#proof[
-  #lorem(25)
-]
-
-#example[
-  #lorem(30)
-]
-
-#exercise()[
-  #lorem(10)
-]
diff --git a/source/manual.typ b/source/manual.typ
new file mode 100644
index 0000000..eac9158
--- /dev/null
+++ b/source/manual.typ
@@ -0,0 +1,57 @@
+#import "template/template.typ": *
+
+#show: paper => configuration(
+  title: "Short guide to math-typst.",
+  authors: (
+    (
+      name: "Orca",
+      affiliation: "git.disroot.org/orca/math-typst",
+      email: "orcinus_orca@disroot.org",
+    ),
+  ),
+  abstract: "This PDF explains how to use math-typst.",
+  paper
+)
+
+= Introduction
+
+This packages aims to provide a good enough interface for writing a mathematical course in it.
+
+As of now, it consists of the most used mathematical environments in courses #footnote[The environments provided are: `proposition`, `lemma`, `theorem`, `corollary`,
+`definition`, `remark`, `example`, `exercise`, `proof`, and `numbered-equation`.].
+
+= How to use
+
+With the exception of `proof`, environments behave like `theorem`. Simply type the environment name followed by it's body
+in square brackets. You may name the particular environment by appending `(name: "The name")` after the environment name.
+
+== Example
+
+#theorem(name: "Orca")[
+  Let $P in ZZ[X]$ and $N in NN^*$ be such that for all $n in NN$, if $n >= N$, then $P(n)$ is prime.
+  We have that $P$ is constant.
+] <orca>
+
+#proof[
+  Let's consider
+
+  $ P: x |-> sum_(i = 0)^(deg P) a_i x^i, " with " a_i in ZZ " for " i in [|0, deg P|]. $
+
+  Suppose there exists $N in NN^*$ such that for all $n >= N$, $P(n)$ is prime.
+
+  We have, for $alpha, beta in NN^*$,
+
+  #numbered-equation(name: "E")[
+    $ P(alpha + beta) = P(alpha) + k beta, " with " k in ZZ $
+  ] <eq>
+
+  The equation @eq follows from the definition of $P$ and the binomial theorem.
+
+  In particular, if $alpha >= N$ and $beta = n abs(P(alpha))$ with $n in NN^*$, then $P(alpha)$ divides $P(alpha + beta)$.
+
+  Since they're both primes, we have $epsilon P(alpha) = P(alpha + beta)$, with $epsilon in {-1, 1}$ and $n$ a variable.
+
+  We then find that $P - epsilon P(alpha)$ cancels an infinite amount of times, showing that $P$ is constant.
+]
+
+Unfortunately, it seems like the theorem @orca is not useful at all.