Separate style/shortcuts into class and package

Makefile

@@ -5,5 +5,6 @@ LATEX-DIR := $$HOME/texmf/tex/latex/local
 .PHONY: install
 install: homework.cls
  mkdir -p $(LATEX-DIR)
+ cp hw-shortcuts.sty $(LATEX-DIR)
  cp homework.cls $(LATEX-DIR)
  @echo Homework template installed in $(LATEX-DIR)/homework.cls

example.tex

@@ -1,21 +1,24 @@
-\documentclass[name=Jacob\ Strieb, andrewid=jstrieb, course=69-420, num=8]{homework}
+\documentclass[name=Jacob\ Strieb, andrewid=jstrieb, course=69-420, num=4]{homework}
+
+\usepackage{hw-shortcuts}
 
 \begin{document}
 
-\problem{1}
+\problem{1a}
 
 \begin{claim}
  The set of rational numbers ($\Q$) is countable.
 \end{claim}
 \begin{proof}
- Let $x \in \Q$. Then, by definition, we can write $x = \frac{a}{b}$ for some $a, b \in \Z$. This fraction can be uniquely mapped to a tuple $(a, b) \in \Z \times \Z$. This means that there exists an injective mapping $\Q \to \Z \times \Z$ that maps each fraction to a tuple. Thus, we have:
+ Let $x \in \Q$. Then, by definition, we can write $x = \frac{a}{b}$ for some $a, b \in \Z, b \neq 0$. This fraction can be uniquely mapped to a tuple $(a, b) \in \Z \times \Z$. This means that there exists an injective mapping $\Q \to \Z \times \Z$ that maps each fraction to a tuple. Thus, we have:
  $$ |\Q| \leq |\Z \times \Z| \leq |\N| $$
 
- By the countability of $|\N|$, we have shown that $\Q$ is countable.
+ By the countability of $\N$, we have shown that $\Q$ is countable.
 \end{proof}
-\newpage
 
-\problem2
+\separator
+
+\problem{1b}
 Let $E$ be an event, and let $1_E : \Omega \to \{ 0, 1 \}$ be an indicator random variable such that:
 $$ 1_E(\omega) = \begin{cases}
 1 & \omega \in E \\
@@ -36,7 +39,7 @@
 \end{proof}
 \newpage
 
-\problem3
+\problem2
 
 \begin{claim}
  $e^{iy} = \cos y + i \sin y$ for $y \in \R$
@@ -55,6 +58,18 @@
 \end{proof}
 \newpage
 
+\problem{3}
+\begin{claim}
+ $\P \neq \NP$
+\end{claim}
+
+\begin{proof}
+ We have already shown that $\P \subseteq \NP$, so to prove that $\NP \neq \P$ it suffices to show that $\NP \not \subseteq \P$. We begin by fixing a language $L \in \NP$. 
+
+ \todo % TODO: Complete this problem later
+\end{proof}
+\newpage
+
 \problem4
 
 \begin{claim}
@@ -64,9 +79,9 @@
 \begin{proof}
  First, we pick and order $k$ cards to be matched. The probability of the selected card orders matching is $\frac{1}{k!}$.
 
- Now, we consider the probability that the remaining $n - k$ cards \textit{do not} match. Similar to the examples from class and the textbook, this is an instance of an indexed union of sets $A_i \in \mathcal{F}$ such that $A_i$ is the set of permutations in which $f(i) = i$. But since we are looking for the probability of this not happening, we consider the probability of the complement, computed as 1 minus the probability of this union of events.
+ Now, we consider the probability that the remaining $n - k$ cards \textit{do not} match. Similar to the examples from class and the textbook, this is an instance of an indexed union of sets $A_i \in \mathcal{F}$ such that $A_i$ is the set of permutations in which $f(i) = i$. But since we are looking for the probability of this not happening, we consider the probability of the complement, computed as $1$ minus the probability of this union of events.
 
- By the Inclusion-Exclusion principle, based on the notes from class, we have that
+ By the Inclusion-Exclusion principle, based on the notes from class, we have that:
  $$ \prob{ \bigcup_{i = 1}^{n - k} A_i } = \sum_{i = 1}^{n - k} \frac{(-1)^i}{i!} $$
 
  Putting everything together, we get the following, and we're done.

homework.cls

@@ -6,9 +6,9 @@
 \LoadClass{article}
 
 
-%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Package options and document metadata
-%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \RequirePackage{xkeyval}
 
@@ -46,9 +46,9 @@
 \author{\name}
 
 
-%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Imports and formatting
-%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 % Set the page on letter paper with microtype improvements and better list formatting
 \RequirePackage[letterpaper]{geometry}
@@ -79,9 +79,9 @@
 \titlespacing{\section}{0em}{0em}{1em}
 
 
-%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Custom commands -- words, environments, and formatting
-%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 % Headers for numbered problems
 \newcommand{\problem}[1]{\section{Problem #1}}
@@ -96,9 +96,9 @@
 \newenvironment{claim}{\textit{Claim.}}{\vspace{-1em}}
 
 
-%%%%
-% Custom commands -- redefined
-%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Custom commands -- redefined commands that should look or behave differently
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 % Redefine the ampersand to use the italic version by default - as-per Elements of Typographic Style
 % See: https://tex.stackexchange.com/a/47353/150811
@@ -121,38 +121,3 @@
 % Redefine the bar and vec commands to use larger overlines and bold-faced vectors
 \renewcommand{\bar}{\overline}
 \renewcommand{\vec}{\mathbf}
-
-
-%%%%
-% Custom commands -- math symbols and math shortcuts
-%%%%
-
-% Shortcuts for left/right parentheses, square brackets, and curly braces
-\newcommand{\lrp}[1]{\left( #1 \right)}
-\newcommand{\lrs}[1]{\left[ #1 \right]}
-\newcommand{\lrc}[1]{\left{ #1 \right}}
-
-% Commonly-used sets
-\newcommand{\N}{\ensuremath{\mathbb{N}}}
-\newcommand{\Z}{\ensuremath{\mathbb{Z}}}
-\newcommand{\R}{\ensuremath{\mathbb{R}}}
-\newcommand{\Q}{\ensuremath{\mathbb{Q}}}
-\newcommand{\C}{\ensuremath{\mathbb{C}}}
-
-% Powerset and shortcut for derivative
-\newcommand{\powerset}{\ensuremath{\mathcal{P}}}
-\newcommand{\ddx}{\ensuremath{\frac{d}{dx}}}
-
-% Probability measure, expectation, and variance formatting
-\newcommand{\expect}[1]{\mathbb{E}\left[ #1 \right]}
-\newcommand{\prob}[1]{\mathbb{P}\left[ #1 \right]}
-\newcommand{\var}[1]{\mathrm{var}\left( #1 \right)}
-
-% Commonly-used computer science languages
-\renewcommand{\P}{\ensuremath{\mathsf{P}}}
-\newcommand{\NP}{\ensuremath{\mathsf{NP}}}
-\newcommand{\coNP}{\ensuremath{\mathsf{coNP}}}
-
-% Commonly-used reductions add semantic clarity
-\newcommand{\CookReducesTo}{\ensuremath{\leq^P_T}}
-\newcommand{\KarpReducesTo}{\ensuremath{\leq^P_m}}

hw-shortcuts.sty

@@ -0,0 +1,37 @@
+% Required for TeX packages
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{hw-shortcuts}[2020/03/27 Custom homework shortcuts as a package]
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Custom commands -- math symbols and math shortcuts
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Shortcuts for left/right parentheses, square brackets, and curly braces
+\newcommand{\lrp}[1]{\left( #1 \right)}
+\newcommand{\lrs}[1]{\left[ #1 \right]}
+\newcommand{\lrc}[1]{\left{ #1 \right}}
+
+% Commonly-used sets
+\newcommand{\N}{\ensuremath{\mathbb{N}}}
+\newcommand{\Z}{\ensuremath{\mathbb{Z}}}
+\newcommand{\R}{\ensuremath{\mathbb{R}}}
+\newcommand{\Q}{\ensuremath{\mathbb{Q}}}
+\newcommand{\C}{\ensuremath{\mathbb{C}}}
+
+% Powerset and shortcut for derivative
+\newcommand{\powerset}{\ensuremath{\mathcal{P}}}
+\newcommand{\ddx}{\ensuremath{\frac{d}{dx}}}
+
+% Probability measure, expectation, and variance formatting
+\newcommand{\expect}[1]{\mathbb{E}\left[ #1 \right]}
+\newcommand{\prob}[1]{\mathbb{P}\left[ #1 \right]}
+\newcommand{\var}[1]{\mathrm{var}\left( #1 \right)}
+
+% Commonly-used computer science languages
+\renewcommand{\P}{\ensuremath{\mathsf{P}}}
+\newcommand{\NP}{\ensuremath{\mathsf{NP}}}
+\newcommand{\coNP}{\ensuremath{\mathsf{coNP}}}
+
+% Commonly-used reductions add semantic clarity
+\newcommand{\CookReducesTo}{\ensuremath{\leq^P_T}}
+\newcommand{\KarpReducesTo}{\ensuremath{\leq^P_m}}