Universe

Ergo is a Typst suite of environments for taking notes and doing problem sets, especially for Mathematics, Computer Science, and Physics.

Typst is required to use this package (refer to Typst’s installation page here). For the best Typst experience, we recommend the integrated language service Tinymist.

Usage

To get started, add the following to your .typ file:

#import "@preview/ergo:0.1.1": *

#show: ergo-init

Example

#defn[Group][
  A *group* is an ordered pair $(G, star)$, where $G$ is a set and $star$ is a binary operation on $G$ satisfying
  1. _Associativity:_ $(a star b) star c = a star (b star c) forall a, b, c in G$
  2. _Identity:_ $exists e in G "such that" e star a = a star e = a forall a in G$
  3. _Invertibility:_ $forall a in G exists a^(-1) in G "such that" a star a^(-1) = a^(-1) star a = e$
]

#thm[Orbit-Stabilizer Theorem][
  Let $G$ be a group acting on a set $X$, with $x in X$.
  Then the map
  $
    G \/ G_x &-->              G dot x \
    a G_x    &arrow.r.bar.long a dot x
  $
  is well-defined and bijective, and therefore $|G dot x| = [G : G_x]$.
][
  Let $a, b in G$.
  Then
  $
    a G_x = b G_x
    &<==> b^(-1) a in  G_x \
    &<==> b^(-1) a dot x = x \
    &<==> a dot x  = b dot x.
  $
  Observe the map is well-defined by $(==>)$ and injective by $(<==)$.

  For surjectivity, note for any $a in G$, $a dot x$ is the image of $a G_x$.
]

Real Analysis Notes using the bootstrap color scheme with sidebar header style

Cryptography Problem Set using the bw color scheme with tab header style

Classical Mechanics Notes using the gruvbox-dark color scheme with sidebar header style (with Physica)

Abstract Algebra Notes using the bw color scheme with classic header style (with Fletcher)

Data Structures and Algorithms Notes using the gruvbox-dark color scheme with classic header style (with CeTZ and Lovelace)

Refer to gallery/ for more examples.

Environments

Ergo has three different types of environments: proofs, statements, and problems.

Type Arguments Environments
Proof
  1. name
  2. statement
  3. proof
  • theorem (thm)
  • lemma (lem)
  • corollary (cor)
  • proposition (prop)
Statement
  1. name
  2. statement
  • definition (defn)
  • remark (rem, rmk)
  • notation (notn)
  • example (ex)
  • concept (conc)
  • computational-problem (comp-prob)
  • algorithm (algo)
  • runtime
  • note
Problem
  1. name
  2. statement
  3. solution
  • problem (prob)
  • exercise (excs)

The arguments are all positional, but name is optional, meaning either of these work:

// no `name` given
#theorem[ statement ][ proof ]

// `name` given
#theorem[ name ][ statement ][ proof ]

If you wish to state a result without giving a proof, you can leave proof as an empty content block [].

All of these environments (regardless of type) share a set of (optional) keyword arguments:

  • breakable (default: false) — whether the current environment is breakable across multiple pages
  • width (default: 100%) — width of the current environment in its scope
  • height (default: auto) — height of the current environment in its scope

Also, the problem environment includes an automatic counter if no title is passed in, which can be helpful when working on problem sets.

Themes and Colors

To modify themes and colors, use the ergo-init function:

#import "@preview/ergo:0.1.1": *

#show: ergo-init.with(
    colors: "gruvbox-dark",
    headers: "sidebar",
    all-breakable: true,
    inline-qed: true,
    prob-nums: false,
)

The modifiable parameters are:

  • colors (default: "bootstrap") — colors of theme (refer to Color Palettes table for valid arguments)
  • headers (default: "tab") — header style of theme (refer to Header Styles table for valid arguments)
  • all-breakable (default: false) — the default value for breakable environment parameter
  • inline-qed (default: false) — whether the Q.E.D square is inline or right aligned in proof environments
  • prob-nums (default: true) — should excercise/problems environments have a numbering system
Color Palettes (values for colors)
bootstrap Color scheme adapted from the CSS framework Bootstrap
bw Black and white color scheme
gruvbox-dark Adapted from the dark version of the neovim color scheme gruvbox
ayu-light Adapated from ayu
Header Styles (values for headers)
tab Default header style, rounded
classic Original header style, rounded
sidebar Less padding, not rounded

This function should be called before any content is rendered to enforce consistency of the document content.

Extras

There are a few extra functions and macros that may be of interest:

  • correction(body) — Content with red text, useful for correcting a previous assignment
  • bookmark(title, info) — Add additional information with small box. Particularly useful for recording dates and times
  • equation-box(equation) (eqbox(equation)) — Box an equation
  • ergo-title-selector — A selector controlling the style of the headers in the blocks

Local Installation (MacOS / Linux)

  1. Clone this repository locally on your machine.
  2. Run setup.sh from the root of the project directory. This script symlinks the project directory to the Typst local packages directory. Refer to the Typst Packages repository for more information.
$ git clone https://github.com/EsotericSquishyy/ergo
$ cd ergo
$ chmod +x setup.sh
$ ./setup.sh

Testing

Test whether the installation worked by running the following commands in an empty directory:

$ cat <<EOF > test.typ
#import "@preview/ergo:0.1.1": *
#show: ergo-init
#defn[#lorem(5)][#lorem(50)]
EOF

$ typst compile test.typ

The installation is successful if the file compiled without errors and test.pdf looks like this: