diff --git a/.github/workflows/release.yml b/.github/workflows/release.yml
new file mode 100644
index 0000000..5700a10
--- /dev/null
+++ b/.github/workflows/release.yml
@@ -0,0 +1,58 @@
+name: Release
+
+on:
+  release:
+    types: [ published ]
+
+env:
+  RUST_BACKTRACE: 1
+  CARGO_TERM_COLOR: always
+
+jobs:
+  upload-binary:
+    permissions: write-all
+    name: ${{ matrix.target }}
+    strategy:
+      matrix:
+        include:
+          - target: aarch64-apple-darwin
+            os: macos-latest
+          - target: x86_64-unknown-linux-gnu
+          - target: x86_64-apple-darwin
+            os: macos-latest
+          - target: x86_64-pc-windows-msvc
+            os: windows-latest
+    runs-on: ${{ matrix.os || 'ubuntu-latest' }}
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+        with:
+          persist-credentials: false
+
+      - name: Install rust
+        uses: actions-rs/toolchain@v1
+        with:
+          toolchain: stable
+          profile: minimal
+          override: true
+
+      - if: ${{ !matrix.os }}
+        name: Install system dependencies
+        uses: awalsh128/cache-apt-pkgs-action@latest
+        with:
+          packages: xorg-dev libxcb-shape0-dev libxcb-xfixes0-dev fontconfig libfontconfig-dev libfreetype6-dev libfontconfig1-dev pkgconf
+          version: 1.0
+
+      - name: Upload binary
+        uses: taiki-e/upload-rust-binary-action@v1
+        with:
+          bin: jp2gmd
+          target: ${{ matrix.target }}
+          ref: refs/tags/${{ github.ref_name }}
+          tar: all
+          zip: windows
+          include: assets
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+          CARGO_PROFILE_RELEASE_CODEGEN_UNITS: 1
+          CARGO_PROFILE_RELEASE_LTO: true
diff --git a/.github/workflows/rust-checks.yml b/.github/workflows/rust-checks.yml
new file mode 100644
index 0000000..e0983f2
--- /dev/null
+++ b/.github/workflows/rust-checks.yml
@@ -0,0 +1,44 @@
+name: Rust Code Quality and Tests
+
+on:
+  pull_request:
+    branches: [ "main" ]
+
+env:
+  CARGO_TERM_COLOR: always
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: awalsh128/cache-apt-pkgs-action@latest
+        with:
+          packages: xorg-dev libxcb-shape0-dev libxcb-xfixes0-dev
+          version: 1.0
+      - uses: actions/checkout@v3
+      - name: Rust cache
+        uses: Swatinem/rust-cache@v2
+        with:
+          shared-key: 'kolezanka'
+      - name: Build
+        run: cargo build --verbose
+
+  checks:
+    needs: build
+    runs-on: ubuntu-latest
+    steps:
+      - uses: awalsh128/cache-apt-pkgs-action@latest
+        with:
+          packages: xorg-dev libxcb-shape0-dev libxcb-xfixes0-dev
+          version: 1.0
+      - uses: actions/checkout@v3
+      - name: Rust cache
+        uses: Swatinem/rust-cache@v2
+        with:
+          shared-key: 'kolezanka'
+      - name: Tests
+        run: cargo test --verbose
+      - name: Code Format
+        run: cargo fmt --check
+      - name: Code Lint
+        run: cargo clippy -- -D warnings
diff --git a/.github/workflows/rust-format.yml b/.github/workflows/rust-format.yml
new file mode 100644
index 0000000..82e0faf
--- /dev/null
+++ b/.github/workflows/rust-format.yml
@@ -0,0 +1,30 @@
+name: Format Rust Code
+
+on:
+  workflow_dispatch:
+  push:
+      branches: [ "main" ]
+
+jobs:
+  format:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: awalsh128/cache-apt-pkgs-action@latest
+        with:
+          packages: xorg-dev libxcb-shape0-dev libxcb-xfixes0-dev
+          version: 1.0
+      - uses: actions/checkout@v3
+      - name: Format code
+        run: cargo fmt
+      - name: Setup committer
+        run: |
+          git config --local user.name "Matrix Busters Automatic Agent"
+          git config --local user.email "matrix-busters@jnp3.mimuw.edu.pl"
+      - name: Commit changes
+        run: |
+          if [[ `git status --porcelain` ]]; then
+            git diff
+            git commit -am "Rust code reformatted automatically"
+          fi
+      - name: Create Pull Request
+        uses: peter-evans/create-pull-request@v4
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..f2f264b
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,5 @@
+/target
+/.idea
+/.fleet
+/out
+project-matrix-busters.iml
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
new file mode 100644
index 0000000..fff569f
--- /dev/null
+++ b/.pre-commit-config.yaml
@@ -0,0 +1,9 @@
+# See https://pre-commit.com for more information
+# See https://pre-commit.com/hooks.html for more hooks
+repos:
+-   repo: https://github.com/doublify/pre-commit-rust
+    rev: v1.0
+    hooks:
+        -   id: fmt
+        -   id: clippy
+        -   id: cargo-check
diff --git a/Cargo.lock b/Cargo.lock
new file mode 100644
index 0000000..fa97cd4
--- /dev/null
+++ b/Cargo.lock
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+checksum = "37c24dc0bed72f5f90d1f8bb5b07228cbf63b3c6e9f82d82559d4bae666e7ed9"
+dependencies = [
+ "proc-macro-crate",
+ "proc-macro2",
+ "quote",
+ "syn 1.0.109",
+ "zvariant_utils",
+]
+
+[[package]]
+name = "zvariant_utils"
+version = "1.0.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7234f0d811589db492d16893e3f21e8e2fd282e6d01b0cddee310322062cc200"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn 1.0.109",
+]
diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000..1393215
--- /dev/null
+++ b/Cargo.toml
@@ -0,0 +1,41 @@
+[workspace]
+members = [
+    "assets",
+]
+
+[package]
+name = "jp2gmd"
+version = "0.1.0"
+edition = "2021"
+authors = ["Mieszko Grodzicki", "Aleksander Tudruj"]
+
+[[bin]]
+name = "jp2gmd"
+path = "src/main.rs"
+
+[lib]
+name = "jp2gmd_lib"
+path = "src/lib.rs"
+doctest = true
+
+[features]
+fft = []
+clock = []
+easter-eggs = ["clock", "fft"]
+
+[dependencies]
+egui = "0.21"
+eframe = "0.21"
+num-rational = "0.4"
+num-traits = "0.2"
+anyhow = "1.0"
+image = "0.24"
+lazy_static = "1.4"
+arboard = "3.2"
+clap = { version = "4.1", features = ["derive"] }
+chrono = "0.4"
+time = "0.3"
+serde = { version = "1.0", features = ["derive"] }
+serde_json = "1.0"
+itertools = "0.10"
+egui-toast = "0.7"
diff --git a/GUIDE.md b/GUIDE.md
new file mode 100644
index 0000000..1cba899
--- /dev/null
+++ b/GUIDE.md
@@ -0,0 +1,225 @@
+# Usage
+
+## Types
+
+### Scalar
+
+Scalars are 2x64-bit rational numbers - let's call this field $\hat{Q}$. They can be signed. Examples
+
+```matlab
+10
+-45
+2/13
+-75/3
+```
+
+Rational numbers are always normalized e.g. if number is in form $\frac{p}{q}$ it will be
+displayed as $\frac{p/g}{q/g}$, where $g=\text{gcd}(p, q)$. Also if $q/g = 1$ the number is displayed as an integer.
+
+Scalars can be both added in *shell* or via *GUI editor*.
+
+### Matrix
+
+Matrices are 2D arrays of Scalars. More precisely matrix $A \in \hat{Q}^{N\times M}$
+is a matrix over field $\hat{Q}$ with width $N$ and height $M$.
+
+Currently, the only way to create a matrix is to use *GUI editor*.
+
+## Warning
+
+A matrix $M\in \hat{Q}^{1,1}$ is **not** a scalar. It is a matrix with one element.
+
+## Variables
+
+Variables are supported, and they are calculated during their initialization. Let's say
+there is a variable called `x` and it stores the value $\frac{1}{3}$. Creating variable
+`y = x` will result in copying the value of `x` into `y`, so later changes to `x`
+will not apply to `y`.
+
+## Operations
+
+* **Addition** - both `Scalars` and `Matrices` support addition operation.
+    * For `Scalars` it is defined as $\hat{Q} \times \hat{Q} \to \hat{Q}$, and works as expected for rational numbers.
+    * For `Matrices` it is defined as $\hat{Q}^{N\times M} \times \hat{Q}^{N\times M} \to \hat{Q}^{N\times M}$ and works
+      element-wise.
+* **Subtraction** - both `Scalars` and `Matrices` support subtraction operation.
+    * For both `Scalars` and `Matrices` it is defined as $\hat{Q} \times \hat{Q} \to \hat{Q}$ and works like addition.
+* **Multiplication** - both `Scalars` and `Matrices` support multiplication operation.
+    * For `Scalars` it is defined as $\hat{Q} \times \hat{Q} \to \hat{Q}$, and works as expected for rational numbers.
+    * For `Matrices` it is defined as $\hat{Q}^{N\times M} \times \hat{Q}^{M\times K} \to \hat{Q}^{N\times K}$ and works as expected for matrices.
+    * For `Matrices` and `Scalars` it is defined as $\hat{Q}^{N\times M} \times \hat{Q} \to \hat{Q}^{N\times M}$ and works as expected for matrices and scalars.
+* **Division** - only `Scalars` support division operation.
+    * For `Scalars` it is defined as $\hat{Q} \times \hat{Q} \to \hat{Q}$, and works as expected for rational numbers.
+* **Inverse** - only `Matrices` support inverse operation.
+    * For `Matrices` it is defined as $\hat{Q}^{N\times N} \to \hat{Q}^{N\times N}$. Inverse $A^{-1}$ of matrix $A$ is
+      defined as $A^{-1}A = AA^{-1} = I$, where $I$ is identity matrix.
+* **Echelon** - only `Matrices` support echelon operation.
+    * For `Matrices` it is defined as $\hat{Q}^{N\times M} \to \hat{Q}^{N\times M}$. Echelon form is
+      defined [here](https://en.wikipedia.org/wiki/Row_echelon_form).
+* **Power** - both `Scalars` and `Matrices` support power operation.
+    * For `Scalars` it is defined as $\hat{Q} \times \mathbb{N} \to \hat{Q}$, and works as expected for rational numbers.
+    * For `Matrices` it is defined as $\hat{Q}^{N\times N} \times \mathbb{N} \to \hat{Q}^{N\times N}$. Power $A^k$ of
+      matrix $A$ is defined as $A^k = A \cdot A \cdot \dots \cdot A$ where $k$ is a positive integer.
+
+## Examples
+
+```matlab
+x = 1/3
+y = 2/3
+M = [1 2; 5 3]  % This syntax is not supported yet.
+N = [6 7; 3 1]  % Use GUI editor instead.
+% Addition
+z = x + y   % z = 1
+P = M + N   % P = [7 9; 8 4]
+% Subtraction
+z = x - y   % z = -1/3
+P = M - N   % P = [-5 -5; 2 2]
+% Multiplication
+z = x * y   % z = 2/9
+P = M * N   % P = [18 10; 36 22]
+% Division
+z = x / y   % z = 1/2
+% Inverse (only in GUI)
+P = inv(M)    % P = 1/7 * [-3 2; 5 -1]
+% Echelon (only in GUI)
+P = echelon(M)    % P = [1 0; 0 1]
+% Power
+z = x^2   % z = 1/9
+P = M^2   % P = [11 8; 20 19]
+```
+
+## Shell
+
+Shell is a command line interface for the calculator. It is used to input commands.
+Supported commands are:
+
+* `x = <expression>` - creates a variable `x` and assigns it the value of `<expression>`.
+* `<expression>` - evaluates `<expression>` and stores it in special variable `$`.
+  Error messages are displayed as a popup notification toast.
+
+These are the rules expressed in BNF:
+```bnf
+<digit>      ::= "0" | "1" | ... | "9"
+<integer>    ::= <digit>+
+<letter>     ::= "a" | "ą" | "b" | ... | "ż"
+<identifier> ::= (<letter> | "_") (<letter> | <digit> | "_")* | "$"
+<unary_op>   ::= "+" | "-"
+<binary_op>  ::= "+" | "-" | "*" | "/"
+<expr>       ::= <integer> | <identifier> | <expr> <binary_op> <expr> | "(" <expr> ")" | <unary_op> <expr>
+```
+
+### Examples
+```matlab
+v = 1/3 + 4/15 - 4/19 * 2/3 - 4^5 * (3/4 - 2/3)
+w = ((((4/3 + 5/2) * 14) - 44) / 2) ^ 2
+N = M^14 - Z * 4 * (M - Z)    % where M, Z are square matrices
+a = -v
+very_simple_NAME_123 = 1/3
+```
+
+## GUI
+
+GUI is a graphical user interface for the calculator. All objects created in current environment are displayed
+on `Objects` list. Clicking on an object will open a new window with object's properties. In such window,
+the value can be edited. If the value is edited, the object will be updated.
+There are certain operations that can be performed on objects:
+
+* `Scalar`
+    * `Inverse` - calculates inverse of the scalar, copies its LaTeX representation to clipboard and stores the
+      numerical value in `$`.
+    * `LaTeX` - copies the scalar's LaTeX representation to clipboard.
+* `Matrix`
+    * `Inverse` - calculates inverse of the matrix, copies its LaTeX representation to clipboard and stores the
+      numerical value in `$`.
+    * `LaTeX` - copies the matrix's LaTeX representation to clipboard.
+      If an error occurs during the operation, the error message will be displayed as a popup toast.
+    * `Echelon` - calculates echelon form of the matrix, stores the numerical value in `$` and copies *all* transitions
+      in LaTeX to clipboard.
+
+### Echelon LaTeX example
+
+Let's say we have a matrix
+
+```math
+A = \begin{bmatrix} 1 & 2 & 3 \\ 11 & 67 & 2 \\ 8 & 1 & 34 \end{bmatrix}.
+```
+
+`Echelon` operation will result in LaTeX code representing this:
+
+```math
+\left[\begin{array}{ccc}
+1 & 2 & 3\\11 & 67 & 2\\8 & 1 & 34
+\end{array}\right]
+\xrightarrow{\substack{w_{2} - 11w_{1}\\w_{3} - 8w_{1}}} \left[\begin{array}{ccc}
+1 & 2 & 3\\0 & 45 & -31\\0 & -15 & 10
+\end{array}\right]
+\xrightarrow{w_{2} : 45} \left[\begin{array}{ccc}
+1 & 2 & 3\\0 & 1 & -\frac{31}{45}\\0 & -15 & 10
+\end{array}\right]
+\xrightarrow{\substack{w_{1} - 2w_{2}\\w_{3} + 15w_{2}}} \left[\begin{array}{ccc}
+1 & 0 & \frac{197}{45}\\0 & 1 & -\frac{31}{45}\\0 & 0 & -\frac{1}{3}
+\end{array}\right]
+\xrightarrow{w_{3} : \left(-\frac{1}{3}\right)} \left[\begin{array}{ccc}
+1 & 0 & \frac{197}{45}\\0 & 1 & -\frac{31}{45}\\0 & 0 & 1
+\end{array}\right]
+\xrightarrow{\substack{w_{1} - \frac{197}{45}w_{3}\\w_{2} + \frac{31}{45}w_{3}}} \left[\begin{array}{ccc}
+1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1
+\end{array}\right]
+```
+
+This may not look useful, as it produced an identity matrix, but when we take a different matrix
+
+```math
+B = \left[\begin{array}{cccc}1 & 4 & 0 & 15\\6 & 11 & 8 & 4\\-1 & 3 & 6 & -6\end{array}\right]
+```
+
+which represents a system of linear equations, we get a much more useful result:
+
+```math
+\left[\begin{array}{cccc}1 & 4 & 0 & 15\\6 & 11 & 8 & 4\\-1 & 3 & 6 & -6\end{array}\right]
+\xrightarrow{\substack{w_{2} - 6w_{1}\\w_{3} + w_{1}}} \left[\begin{array}{cccc}1 & 4 & 0 & 15\\0 & -13 & 8 & -86\\0 & 7 & 6 & 9\end{array}\right]
+\xrightarrow{w_{2} : \left(-13\right)} \left[\begin{array}{cccc}1 & 4 & 0 & 15\\0 & 1 & -\frac{8}{13} & \frac{86}{13}\\0 & 7 & 6 & 9\end{array}\right]
+\xrightarrow{\substack{w_{1} - 4w_{2}\\w_{3} - 7w_{2}}} \left[\begin{array}{cccc}1 & 0 & \frac{32}{13} & -\frac{149}{13}\\0 & 1 & -\frac{8}{13} & \frac{86}{13}\\0 & 0 & \frac{134}{13} & -\frac{485}{13}\end{array}\right]
+\xrightarrow{w_{3} : \frac{134}{13}} \left[\begin{array}{cccc}1 & 0 & \frac{32}{13} & -\frac{149}{13}\\0 & 1 & -\frac{8}{13} & \frac{86}{13}\\0 & 0 & 1 & -\frac{485}{134}\end{array}\right]
+\xrightarrow{\substack{w_{1} - \frac{32}{13}w_{3}\\w_{2} + \frac{8}{13}w_{3}}} \left[\begin{array}{cccc}1 & 0 & 0 & -\frac{171}{67}\\0 & 1 & 0 & \frac{294}{67}\\0 & 0 & 1 & -\frac{485}{134}\end{array}\right]
+```
+
+Producing a row echelon form is a very tedious task, but with this calculator, it is as easy as clicking a button.
+It may be very useful for students, as it can be used to create LaTeX for their homework.
+
+Another useful application is to calculate the inverse of a matrix. Let's say we have a matrix
+```math
+Z = \left[\begin{array}{cc}1 & 2\\6 & 1\end{array}\right]
+```
+If we produce a matrix
+```math
+Z' = \left[\begin{array}{cc|cc}1 & 2 & 1 & 0\\6 & 1 & 0 & 1\end{array}\right]
+```
+and perform `Echelon` operation on it, we get
+```math
+\left[\begin{array}{cccc}1 & 2 & 1 & 0\\6 & 1 & 0 & 1\end{array}\right]
+\xrightarrow{\substack{w_{2} - 6w_{1}}} \left[\begin{array}{cccc}1 & 2 & 1 & 0\\0 & -11 & -6 & 1\end{array}\right]
+\xrightarrow{w_{2} : \left(-11\right)} \left[\begin{array}{cccc}1 & 2 & 1 & 0\\0 & 1 & \frac{6}{11} & -\frac{1}{11}\end{array}\right]
+\xrightarrow{\substack{w_{1} - 2w_{2}}} \left[\begin{array}{cccc}1 & 0 & -\frac{1}{11} & \frac{2}{11}\\0 & 1 & \frac{6}{11} & -\frac{1}{11}\end{array}\right]
+```
+and as surprising as it may seem, the inverse of `Z` is
+```math
+\left[\begin{array}{cc}-\frac{1}{11} & \frac{2}{11}\\\frac{6}{11} & -\frac{1}{11}\end{array}\right]
+```
+We just inverted the matrix `Z` by performing elementary row operations on the augmented matrix and got all transformations in LaTeX. 
+Finally, the `Inverse` operation will also produce LaTeX code representing all the transformations.
+
+
+## GUI editor
+
+GUI editor is a graphical interface for creating matrices and scalars. To open it click on `Add matrix` or `Add scalar`
+button.
+A new variable has to have a name and a value, that can be evaluated using existing environment variables.
+If provided value is invalid, an error message will be displayed and new variable will not be created.
+
+## Features
+If you get bored with plain background and want to spice things up, you can turn `fft` feature on.
+It will draw an image of a Fourier transformed image provided in `assets/`. The other way to change
+the background is to turn `clock` feature on. It will draw a fractal clock in the background. If both 
+`fft` and `clock` are turned on, `fft` will prioritize `clock` - only if image file is missing
+the clock will be drawn.
diff --git a/README.md b/README.md
index 58e9e49..133e634 100644
--- a/README.md
+++ b/README.md
@@ -1,24 +1,66 @@
-# Frobnicator (this is a template)
+# Just Pure 2D Graphics Matrix Display
 
 ## Authors
-- Andrzej Głuszak (@agluszak on GitHub)
-- Linus Torvalds (@torvalds on GitHub)
+- Mieszko Grodzicki [@mgr0dzicki][#MieszkoGH]
+- Alek Tudruj [@tudny][#AlekGH]
+
+---
 
 ## Description
-Frobnicator is going to be a platformer game similar to Super Mario Bros made using Bevy game engine.
+**Just Pure 2D Graphics Matrix Display** (*JP2GMD*) is a powerful matrix calculator. 
+
+It allows you to perform basic operations on matrices, such as addition, subtraction, multiplication, and division.
+It also allows you to perform more advanced operations, such as finding the determinant, the inverse, and the transpose of a matrix.
+
+One of its most powerful features is the ability to generate `LaTeX` code for the matrix you are working with and all the operations you perform on it.
+
+---
+
+## Installation
+Install dependencies if applicable:
+
+Ubuntu
+```bash
+sudo apt-get install libfontconfig libfontconfig1-dev cmake xorg-dev libxcb-shape0-dev libxcb-xfixes0-dev
+```
 
-## Features
-- map generator
-- shooting
-- enemy AI
-- game state saving and loading
-- scores
+Run the program:
+```bash
+$ cargo run
+```
 
+Check program help using
+```bash
+$ cargo run -- --help
+```
+
+# Usage
+Check out [the guide](GUIDE.md).
+
+# Development
 ## Plan
-In the first part we're going to implement the basics: movement, physics and shooting. The enemies will simply bounce from one edge of the platform to the other. There will be only a single map.
+- [X] 1.1. Implement rational numbers representation.
+- [X] 1.2. Implement matrix module for given any number representation.
+- [X] 1.3. Implement basic operations on matrices.
+- [X] 1.4. Implement `LaTeX` code generation.
+- [X] 2.1. Implement GUI.
+- [ ] ~~2.2. Extend the number representation module to allow for more sophisticated numbers.~~
+- [ ] ~~2.3. Implement complex operations on matrices.~~
+
+and all other things added as GH Issues.
+Issue marked [NITD] (Not Intended To be Developed) 
+are ideas taken into consideration when 
+developing more critical features. They are not 
+intended to be developed during the JNP3 project - 
+maybe in the future if time allows.
 
-In the second part we're going to add random map generator, saving/loading, scores and a more sophisticated AI.
+## GUI Preview
+![gui.png](gui.png)
 
 ## Libraries
-- Bevy
-- Serde (for serialization)
+- [egui](https://crates.io/crates/egui) - (https://github.com/emilk/egui)
+- [num](https://docs.rs/num/latest/num/)
+
+
+[#MieszkoGH]: https://github.com/mgr0dzicki
+[#AlekGH]: https://github.com/tudny
diff --git a/assets/Cargo.toml b/assets/Cargo.toml
new file mode 100644
index 0000000..63bab16
--- /dev/null
+++ b/assets/Cargo.toml
@@ -0,0 +1,13 @@
+[package]
+name = "assets"
+version = "0.1.0"
+edition = "2021"
+authors = ["Aleksander Tudruj"]
+
+[[bin]]
+name = "dft"
+path = "dft.rs"
+
+[dependencies]
+serde_json = "1.0"
+serde = { version = "1.0", features = ["derive"] }
diff --git a/assets/dft.rs b/assets/dft.rs
new file mode 100644
index 0000000..42d0fba
--- /dev/null
+++ b/assets/dft.rs
@@ -0,0 +1,115 @@
+use serde::{Deserialize, Serialize};
+
+#[derive(Serialize, Deserialize)]
+struct DftMetadata {
+    height: u32,
+    width: u32,
+}
+
+#[derive(Serialize, Deserialize)]
+struct DftPoint {
+    re: f32,
+    im: f32,
+}
+
+#[derive(Serialize, Deserialize)]
+struct DftSource {
+    metadata: DftMetadata,
+    points: Vec<DftPoint>,
+}
+
+#[derive(Serialize, Deserialize)]
+struct DftEpicycle {
+    re: f32,
+    im: f32,
+    freq: f32,
+    amp: f32,
+    phase: f32,
+}
+
+#[derive(Serialize, Deserialize)]
+struct DftResult {
+    metadata: DftMetadata,
+    epicycles: Vec<DftEpicycle>,
+}
+
+const MISSING_FILE: &str = "Missing file: ";
+const INVALID_FILE: &str = "Invalid file: ";
+
+fn read_source(filename: &str) -> Result<DftSource, String> {
+    let file = std::fs::File::open(filename).map_err(|_| MISSING_FILE.to_string() + filename)?;
+    let reader = std::io::BufReader::new(file);
+    let source: DftSource =
+        serde_json::from_reader(reader).map_err(|_| INVALID_FILE.to_string() + filename)?;
+    Ok(source)
+}
+
+fn dft_algorithm(source: DftSource) -> Result<DftResult, String> {
+    let DftSource { metadata, points } = source;
+    let n = points.len();
+    let mut epicycles = Vec::with_capacity(n);
+    for k in 0..n {
+        let mut re = 0.;
+        let mut im = 0.;
+        for (i, point) in points.iter().enumerate() {
+            let angle = 2. * std::f32::consts::PI * k as f32 * i as f32 / n as f32;
+            re += point.re * angle.cos() + point.im * angle.sin();
+            im += point.im * angle.cos() - point.re * angle.sin();
+        }
+        re /= n as f32;
+        im /= n as f32;
+        let freq = k as f32;
+        let amp = (re * re + im * im).sqrt();
+        let phase = im.atan2(re);
+        epicycles.push(DftEpicycle {
+            re,
+            im,
+            freq,
+            amp,
+            phase,
+        });
+    }
+    Ok(DftResult {
+        metadata,
+        epicycles,
+    })
+}
+
+fn calculate_n(expected_points: usize, actual_points: usize) -> usize {
+    if actual_points < expected_points {
+        return actual_points;
+    }
+    return actual_points / expected_points;
+}
+
+fn take_every_nth<T>(source: Vec<T>, n: usize) -> Vec<T> {
+    source.into_iter().step_by(n).collect()
+}
+
+fn save_result(result: DftResult, filename: &str) -> Result<(), String> {
+    let file = std::fs::File::create(filename).map_err(|_| MISSING_FILE.to_string() + filename)?;
+    let writer = std::io::BufWriter::new(file);
+    serde_json::to_writer_pretty(writer, &result)
+        .map_err(|_| INVALID_FILE.to_string() + filename)?;
+    Ok(())
+}
+
+fn main() -> Result<(), String> {
+    println!("Generating DFT data...");
+
+    const EXPECTED_POINTS: usize = 1000;
+    const SOURCE_FILE: &str = "assets/dft_source.json";
+    const RESULT_FILE: &str = "assets/dft_result.json";
+
+    let source = read_source(SOURCE_FILE)?;
+    let number_of_points = source.points.len();
+    let source = DftSource {
+        points: take_every_nth(
+            source.points,
+            calculate_n(EXPECTED_POINTS, number_of_points),
+        ),
+        ..source
+    };
+    let result = dft_algorithm(source)?;
+    save_result(result, RESULT_FILE)
+}
diff --git a/assets/dft_result.json b/assets/dft_result.json
new file mode 100644
index 0000000..dce8202
--- /dev/null
+++ b/assets/dft_result.json
@@ -0,0 +1,7113 @@
+{
+  "metadata": {
+    "height": 800,
+    "width": 800
+  },
+  "epicycles": [
+    {
+      "re": -1.879803,
+      "im": 79.24335,
+      "freq": 0.0,
+      "amp": 79.26564,
+      "phase": 1.5945138
+    },
+    {
+      "re": 23.700554,
+      "im": -87.805786,
+      "freq": 1.0,
+      "amp": 90.94818,
+      "phase": -1.307159
+    },
+    {
+      "re": -102.57039,
+      "im": 23.985806,
+      "freq": 2.0,
+      "amp": 105.33757,
+      "phase": 2.9118733
+    },
+    {
+      "re": 19.417248,
+      "im": 81.002785,
+      "freq": 3.0,
+      "amp": 83.29754,
+      "phase": 1.3355248
+    },
+    {
+      "re": 6.641316,
+      "im": 56.868675,
+      "freq": 4.0,
+      "amp": 57.25516,
+      "phase": 1.4545395
+    },
+    {
+      "re": 49.109325,
+      "im": -22.933617,
+      "freq": 5.0,
+      "amp": 54.200336,
+      "phase": -0.43689352
+    },
+    {
+      "re": 26.222347,
+      "im": 13.165003,
+      "freq": 6.0,
+      "amp": 29.341589,
+      "phase": 0.4652885
+    },
+    {
+      "re": -16.761253,
+      "im": -1.0173748,
+      "freq": 7.0,
+      "amp": 16.7921,
+      "phase": -3.080969
+    },
+    {
+      "re": 0.20778044,
+      "im": 2.3615942,
+      "freq": 8.0,
+      "amp": 2.370717,
+      "phase": 1.4830391
+    },
+    {
+      "re": -4.305301,
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+    },
+    {
+      "re": -48,
+      "im": 13
+    },
+    {
+      "re": -46,
+      "im": 13
+    },
+    {
+      "re": -45,
+      "im": 14
+    },
+    {
+      "re": -44,
+      "im": 14
+    },
+    {
+      "re": -43,
+      "im": 14
+    },
+    {
+      "re": -42,
+      "im": 14
+    },
+    {
+      "re": -42,
+      "im": 14
+    },
+    {
+      "re": -41,
+      "im": 14
+    },
+    {
+      "re": -40,
+      "im": 14
+    },
+    {
+      "re": -38,
+      "im": 14
+    },
+    {
+      "re": -38,
+      "im": 14
+    },
+    {
+      "re": -38,
+      "im": 14
+    },
+    {
+      "re": -38,
+      "im": 14
+    },
+    {
+      "re": -37,
+      "im": 14
+    },
+    {
+      "re": -36,
+      "im": 14
+    },
+    {
+      "re": -36,
+      "im": 14
+    },
+    {
+      "re": -34,
+      "im": 13
+    },
+    {
+      "re": -34,
+      "im": 13
+    },
+    {
+      "re": -33,
+      "im": 13
+    },
+    {
+      "re": -32,
+      "im": 13
+    },
+    {
+      "re": -31,
+      "im": 13
+    },
+    {
+      "re": -30,
+      "im": 13
+    },
+    {
+      "re": -28,
+      "im": 13
+    },
+    {
+      "re": -28,
+      "im": 13
+    },
+    {
+      "re": -28,
+      "im": 12
+    },
+    {
+      "re": -28,
+      "im": 12
+    },
+    {
+      "re": -27,
+      "im": 12
+    },
+    {
+      "re": -26,
+      "im": 12
+    },
+    {
+      "re": -24,
+      "im": 12
+    },
+    {
+      "re": -23,
+      "im": 11
+    },
+    {
+      "re": -22,
+      "im": 11
+    },
+    {
+      "re": -22,
+      "im": 11
+    },
+    {
+      "re": -22,
+      "im": 11
+    },
+    {
+      "re": -22,
+      "im": 10
+    },
+    {
+      "re": -22,
+      "im": 10
+    },
+    {
+      "re": -22,
+      "im": 10
+    },
+    {
+      "re": -21,
+      "im": 10
+    },
+    {
+      "re": -21,
+      "im": 10
+    },
+    {
+      "re": -20,
+      "im": 9
+    },
+    {
+      "re": -20,
+      "im": 8
+    },
+    {
+      "re": -20,
+      "im": 7
+    },
+    {
+      "re": -20,
+      "im": 6
+    },
+    {
+      "re": -20,
+      "im": 5
+    },
+    {
+      "re": -20,
+      "im": 4
+    },
+    {
+      "re": -20,
+      "im": 4
+    },
+    {
+      "re": -20,
+      "im": 3
+    },
+    {
+      "re": -20,
+      "im": 2
+    },
+    {
+      "re": -21,
+      "im": 0
+    },
+    {
+      "re": -21,
+      "im": 0
+    },
+    {
+      "re": -22,
+      "im": 0
+    },
+    {
+      "re": -22,
+      "im": 0
+    },
+    {
+      "re": -22,
+      "im": 0
+    },
+    {
+      "re": -22,
+      "im": 0
+    },
+    {
+      "re": -22,
+      "im": -1
+    },
+    {
+      "re": -23,
+      "im": -2
+    },
+    {
+      "re": -24,
+      "im": -3
+    },
+    {
+      "re": -24,
+      "im": -3
+    },
+    {
+      "re": -25,
+      "im": -4
+    },
+    {
+      "re": -26,
+      "im": -4
+    },
+    {
+      "re": -26,
+      "im": -4
+    },
+    {
+      "re": -26,
+      "im": -4
+    },
+    {
+      "re": -27,
+      "im": -4
+    },
+    {
+      "re": -27,
+      "im": -4
+    },
+    {
+      "re": -28,
+      "im": -5
+    },
+    {
+      "re": -29,
+      "im": -5
+    },
+    {
+      "re": -29,
+      "im": -5
+    },
+    {
+      "re": -29,
+      "im": -5
+    },
+    {
+      "re": -29,
+      "im": -5
+    },
+    {
+      "re": -29,
+      "im": -5
+    },
+    {
+      "re": -30,
+      "im": -5
+    },
+    {
+      "re": -31,
+      "im": -5
+    },
+    {
+      "re": -31,
+      "im": -5
+    },
+    {
+      "re": -31,
+      "im": -3
+    },
+    {
+      "re": -31,
+      "im": -2
+    },
+    {
+      "re": -31,
+      "im": -1
+    },
+    {
+      "re": -30,
+      "im": -1
+    },
+    {
+      "re": -30,
+      "im": -1
+    },
+    {
+      "re": -30,
+      "im": -1
+    },
+    {
+      "re": -30,
+      "im": -1
+    },
+    {
+      "re": -30,
+      "im": 0
+    },
+    {
+      "re": -30,
+      "im": 1
+    },
+    {
+      "re": -30,
+      "im": 2
+    },
+    {
+      "re": -30,
+      "im": 2
+    },
+    {
+      "re": -30,
+      "im": 3
+    },
+    {
+      "re": -29,
+      "im": 3
+    },
+    {
+      "re": -29,
+      "im": 3
+    },
+    {
+      "re": -29,
+      "im": 3
+    },
+    {
+      "re": -29,
+      "im": 3
+    },
+    {
+      "re": -29,
+      "im": 4
+    },
+    {
+      "re": -29,
+      "im": 4
+    },
+    {
+      "re": -29,
+      "im": 5
+    },
+    {
+      "re": -29,
+      "im": 5
+    },
+    {
+      "re": -29,
+      "im": 5
+    },
+    {
+      "re": -28,
+      "im": 6
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    },
+    {
+      "re": -28,
+      "im": 7
+    }
+  ]
+}
diff --git a/assets/icon.png b/assets/icon.png
new file mode 100644
index 0000000..0f8a880
Binary files /dev/null and b/assets/icon.png differ
diff --git a/gui.png b/gui.png
new file mode 100644
index 0000000..b30374b
Binary files /dev/null and b/gui.png differ
diff --git a/src/constants.rs b/src/constants.rs
new file mode 100644
index 0000000..7f0bca6
--- /dev/null
+++ b/src/constants.rs
@@ -0,0 +1,21 @@
+pub const APP_NAME: &str = "JP2GMD - Matrix Calculator";
+pub const DEFAULT_WIDTH: f32 = 800.0;
+pub const DEFAULT_HEIGHT: f32 = 600.0;
+pub const DEFAULT_LEFT_PANEL_WIDTH: f32 = DEFAULT_WIDTH * 0.20;
+
+pub const TEXT_COLOR: egui::Color32 = egui::Color32::LIGHT_GRAY;
+pub const FONT_ID: egui::FontId = egui::FontId::proportional(18.);
+
+pub const MATRIX_HPADDING: f32 = 15.;
+pub const MATRIX_VPADDING: f32 = 8.;
+pub const FRACTION_FONT_SIZE_RATIO: f32 = 0.8;
+pub const FRACTION_HMARGIN: f32 = 2.;
+pub const FRACTION_VMARGIN: f32 = 1.;
+pub const FRACTION_LINE_WIDTH: f32 = 1.;
+pub const VALUE_PADDING: f32 = 15.;
+
+pub const FLOAT_STRING_PRECISION: usize = 3;
+
+pub const ICON_PATH: &str = "assets/icon.png";
+#[cfg(feature = "fft")]
+pub const DFT_PATH: &str = "assets/dft_result.json";
diff --git a/src/editor_gui.rs b/src/editor_gui.rs
new file mode 100644
index 0000000..396b196
--- /dev/null
+++ b/src/editor_gui.rs
@@ -0,0 +1,232 @@
+use crate::env_gui::insert_to_env;
+use crate::environment::{Environment, Identifier, Type};
+use crate::locale::Locale;
+use crate::matrices::Matrix;
+use crate::parser::parse_expression;
+use crate::traits::MatrixNumber;
+use crate::{State, WindowState};
+use anyhow::bail;
+use egui::{Sense, Ui};
+use std::collections::HashMap;
+
+pub enum EditorType {
+    Matrix(usize, usize, Vec<String>),
+    Scalar(String),
+}
+
+pub struct EditorContent {
+    identifier_name: String,
+    editor_type: EditorType,
+}
+
+#[derive(Default)]
+pub struct EditorState {
+    editor_content: Option<EditorContent>,
+}
+
+pub fn display_editor<K: MatrixNumber>(ctx: &egui::Context, state: &mut State<K>, locale: &Locale) {
+    if let Some(editor_content) = &mut state.editor.editor_content {
+        let result = display_editor_is_some::<K>(
+            ctx,
+            editor_content,
+            &mut state.env,
+            &mut state.windows,
+            locale,
+        );
+        match result {
+            Ok(true) => {
+                state.editor.editor_content = None;
+            }
+            Ok(false) => {}
+            Err(_) => {
+                panic!("It shouldn't return Err")
+            }
+        }
+    }
+}
+
+pub fn set_editor_to_matrix(state: &mut EditorState, def: &str) {
+    const DEFAULT_ROWS: usize = 2;
+    const DEFAULT_COLS: usize = 3;
+    state.editor_content = Some(EditorContent {
+        identifier_name: "".to_string(),
+        editor_type: EditorType::Matrix(
+            DEFAULT_ROWS,
+            DEFAULT_COLS,
+            vec![String::from(def); DEFAULT_ROWS * DEFAULT_COLS],
+        ),
+    });
+}
+
+pub fn set_editor_to_existing_matrix<K: MatrixNumber>(
+    state: &mut EditorState,
+    matrix: &Matrix<K>,
+    name: String,
+) {
+    let (w, h) = matrix.get_shape();
+    let data: Vec<K> = matrix.clone().into();
+    let data = data.iter().map(|el| el.to_string()).collect();
+    state.editor_content = Some(EditorContent {
+        identifier_name: name,
+        editor_type: EditorType::Matrix(w, h, data),
+    });
+}
+
+pub fn set_editor_to_scalar(state: &mut EditorState, def: &str) {
+    state.editor_content = Some(EditorContent {
+        identifier_name: "".to_string(),
+        editor_type: EditorType::Scalar(String::from(def)),
+    });
+}
+
+pub fn set_editor_to_existing_scalar<K: MatrixNumber>(
+    state: &mut EditorState,
+    value: &K,
+    name: String,
+) {
+    state.editor_content = Some(EditorContent {
+        identifier_name: name,
+        editor_type: EditorType::Scalar(value.to_string()),
+    })
+}
+
+fn display_editor_is_some<K: MatrixNumber>(
+    ctx: &egui::Context,
+    content: &mut EditorContent,
+    env: &mut Environment<K>,
+    windows: &mut HashMap<Identifier, WindowState>,
+    locale: &Locale,
+) -> anyhow::Result<bool> {
+    let mut handled: anyhow::Result<bool> = Ok(false);
+    let mut editor_opened = true;
+
+    egui::Window::new(locale.get_translated("Editor"))
+        .open(&mut editor_opened)
+        .show(ctx, |ui| {
+            let EditorContent {
+                identifier_name,
+                editor_type,
+            } = content;
+            ui.label(locale.get_translated("Identifier:"));
+            ui.text_edit_singleline(identifier_name);
+            let result = match editor_type {
+                EditorType::Matrix(h, w, data) => {
+                    display_matrix_editor((h, w), data, ui, locale);
+                    parse_matrix_data::<K>((h, w), data, env)
+                }
+                EditorType::Scalar(data) => {
+                    display_scalar_editor(data, ui, locale);
+                    parse_scalar_data::<K>(data, env)
+                }
+            };
+            let mut err_msg = if Identifier::is_valid(identifier_name) {
+                None
+            } else {
+                Some(locale.get_translated("Identifier is invalid!"))
+            };
+            if let Err(err) = &result {
+                err_msg = Some(
+                    locale.get_translated("Matrix is invalid!") + "\n" + err.to_string().as_str(),
+                );
+            };
+            ui.horizontal(|ui| {
+                let sense = if err_msg.is_some() {
+                    Sense::hover()
+                } else {
+                    Sense::click()
+                };
+                let add_button =
+                    ui.add(egui::Button::new(locale.get_translated("Add")).sense(sense));
+                if let Some(some) = &err_msg {
+                    ui.label(locale.get_translated("Error ") + some);
+                } else if add_button.clicked() {
+                    insert_to_env(
+                        env,
+                        Identifier::new(identifier_name.to_string()).expect("Should work"),
+                        result.expect("There should be a value."),
+                        windows,
+                    );
+                    handled = Ok(true);
+                };
+            })
+        });
+
+    // Editor was closed
+    if !editor_opened {
+        handled = Ok(true);
+    }
+
+    handled
+}
+
+fn parse_matrix_data<K: MatrixNumber>(
+    (h, w): (&mut usize, &mut usize),
+    data: &mut [String],
+    env: &Environment<K>,
+) -> anyhow::Result<Type<K>> {
+    let mut result: Vec<K> = vec![];
+    for element in data.iter() {
+        result.push(parse_scalar_with_env(element, env)?)
+    }
+    Ok(Type::Matrix(Matrix::from_vec(result, (*h, *w))?))
+}
+
+fn parse_scalar_data<K: MatrixNumber>(
+    data: &mut str,
+    env: &Environment<K>,
+) -> anyhow::Result<Type<K>> {
+    Ok(Type::Scalar(parse_scalar_with_env(data, env)?))
+}
+
+fn parse_scalar_with_env<K: MatrixNumber>(data: &str, env: &Environment<K>) -> anyhow::Result<K> {
+    match parse_expression(data, env)? {
+        Type::Scalar(scalar) => Ok(scalar),
+        Type::Matrix(_) => bail!("Invalid expression! Result is not a scalar."),
+    }
+}
+
+fn display_matrix_editor(
+    (h, w): (&mut usize, &mut usize),
+    data: &mut Vec<String>,
+    ui: &mut Ui,
+    locale: &Locale,
+) {
+    ui.label(locale.get_translated("Enter the matrix:"));
+    egui::Grid::new("dimensions").show(ui, |ui| {
+        ui.label(locale.get_translated("Height"));
+        ui.add(egui::DragValue::new(h));
+        ui.end_row();
+        ui.label(locale.get_translated("Width"));
+        ui.add(egui::DragValue::new(w));
+        ui.end_row();
+    });
+    ui.separator();
+    if data.len() != *h * *w {
+        data.resize(*h * *w, String::from("0"));
+    }
+
+    egui::Grid::new("matrix_editor").show(ui, |ui| {
+        ui.label("");
+        for j in 0..*w {
+            ui.label(format!("{}", j + 1).as_str());
+        }
+        ui.end_row();
+        for i in 0..*h {
+            ui.label(format!("{}", i + 1).as_str());
+            for j in 0..*w {
+                display_k_editor((i, j), data, ui, *w);
+            }
+            ui.end_row();
+        }
+    });
+}
+
+fn display_k_editor((i, j): (usize, usize), data: &mut [String], ui: &mut Ui, width: usize) {
+    let id = i * width + j;
+    ui.add(egui::TextEdit::singleline(&mut data[id]));
+}
+
+fn display_scalar_editor(data: &mut String, ui: &mut Ui, locale: &Locale) {
+    ui.label(locale.get_translated("Enter the scalar:"));
+    ui.add(egui::TextEdit::singleline(data));
+}
diff --git a/src/env_gui.rs b/src/env_gui.rs
new file mode 100644
index 0000000..fffa508
--- /dev/null
+++ b/src/env_gui.rs
@@ -0,0 +1,14 @@
+use crate::environment::{Environment, Identifier, Type};
+use crate::traits::MatrixNumber;
+use crate::WindowState;
+use std::collections::HashMap;
+
+pub fn insert_to_env<T: MatrixNumber>(
+    env: &mut Environment<T>,
+    identifier: Identifier,
+    value: Type<T>,
+    windows: &mut HashMap<Identifier, WindowState>,
+) {
+    env.insert(identifier.clone(), value);
+    windows.insert(identifier, WindowState { is_open: true });
+}
diff --git a/src/environment.rs b/src/environment.rs
new file mode 100644
index 0000000..4b84af5
--- /dev/null
+++ b/src/environment.rs
@@ -0,0 +1,224 @@
+use std::collections::btree_map::IterMut;
+use std::collections::BTreeMap;
+
+use anyhow::{bail, Context};
+
+use crate::locale::Locale;
+use crate::traits::{GuiDisplayable, LaTeXable};
+use crate::{matrices::Matrix, traits::MatrixNumber};
+
+#[derive(Debug, Clone, PartialEq, Eq, Hash, Ord, PartialOrd)]
+pub struct Identifier {
+    id: String,
+}
+
+impl Identifier {
+    pub const RESULT: &'static str = "$";
+
+    pub fn new(id: String) -> anyhow::Result<Self> {
+        if Self::is_valid(&id) {
+            Ok(Self { id })
+        } else {
+            bail!("Invalid identifier.")
+        }
+    }
+
+    fn new_unsafe(id: String) -> Self {
+        Self { id }
+    }
+
+    pub fn result() -> Self {
+        Self {
+            id: Self::RESULT.to_string(),
+        }
+    }
+
+    pub fn is_result(&self) -> bool {
+        self.id == Self::RESULT
+    }
+
+    pub fn is_valid(id: &str) -> bool {
+        id.chars().all(|c| c.is_alphanumeric() || c == '_')
+            && id.starts_with(|c: char| c.is_alphabetic() || c == '_')
+    }
+}
+
+impl ToString for Identifier {
+    fn to_string(&self) -> String {
+        self.id.clone()
+    }
+}
+
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub enum Type<T: MatrixNumber> {
+    Scalar(T),
+    Matrix(Matrix<T>),
+}
+
+impl<T: MatrixNumber> Type<T> {
+    pub fn from_scalar_option(opt: Option<T>) -> anyhow::Result<Self> {
+        match opt {
+            Some(val) => Ok(Self::Scalar(val)),
+            None => Err(anyhow::anyhow!(
+                "Arithmetic operation resulted in overflow!"
+            )),
+        }
+    }
+
+    pub fn from_matrix_result(opt: anyhow::Result<Matrix<T>>) -> anyhow::Result<Self> {
+        Ok(Self::Matrix(opt?))
+    }
+
+    pub fn into_scalar(self) -> anyhow::Result<T> {
+        match self {
+            Type::Scalar(s) => Ok(s),
+            Type::Matrix(_) => bail!("Expected scalar, got matrix."),
+        }
+    }
+
+    pub fn into_matrix(self) -> anyhow::Result<Matrix<T>> {
+        match self {
+            Type::Matrix(m) => Ok(m),
+            Type::Scalar(_) => bail!("Expected matrix, got scalar."),
+        }
+    }
+}
+
+impl<T: MatrixNumber> ToString for Type<T> {
+    fn to_string(&self) -> String {
+        match self {
+            Type::Scalar(s) => s.to_string(),
+            Type::Matrix(m) => m.to_string(),
+        }
+    }
+}
+
+impl<T: MatrixNumber> GuiDisplayable for Type<T> {
+    fn display_string(&self, locale: &Locale) -> String {
+        match self {
+            Type::Scalar(s) => s.display_string(locale),
+            Type::Matrix(m) => m.display_string(locale),
+        }
+    }
+
+    fn to_shape(
+        &self,
+        ctx: &egui::Context,
+        font_id: egui::FontId,
+        color: egui::Color32,
+    ) -> egui::Shape {
+        match self {
+            Type::Scalar(s) => s.to_shape(ctx, font_id, color),
+            Type::Matrix(m) => m.to_shape(ctx, font_id, color),
+        }
+    }
+}
+
+impl<T: MatrixNumber> LaTeXable for Type<T> {
+    fn to_latex(&self) -> String {
+        match self {
+            Type::Scalar(s) => s as &dyn LaTeXable,
+            Type::Matrix(m) => m,
+        }
+        .to_latex()
+    }
+}
+
+pub type Callable<T> = dyn Fn(Type<T>) -> anyhow::Result<Type<T>>;
+
+fn builtin_functions<T: MatrixNumber>() -> BTreeMap<Identifier, Box<Callable<T>>> {
+    BTreeMap::from([
+        (
+            Identifier::new_unsafe("transpose".to_string()),
+            Box::new(|t: Type<T>| Ok(Type::Matrix(t.into_matrix()?.transpose())))
+                as Box<Callable<T>>,
+        ),
+        (
+            Identifier::new_unsafe("identity".to_string()),
+            Box::new(|t: Type<T>| {
+                Ok(Type::Matrix(Matrix::identity(
+                    t.into_scalar()?
+                        .to_usize()
+                        .context("Invalid identity argument")?,
+                )))
+            }) as Box<Callable<T>>,
+        ),
+        (
+            Identifier::new_unsafe("inverse".to_string()),
+            Box::new(|t: Type<T>| Ok(Type::Matrix(t.into_matrix()?.inverse()?.result)))
+                as Box<Callable<T>>,
+        ),
+    ])
+}
+
+pub struct Environment<T: MatrixNumber> {
+    env: BTreeMap<Identifier, Type<T>>,
+    fun: BTreeMap<Identifier, Box<Callable<T>>>,
+}
+
+impl<T: MatrixNumber> Environment<T> {
+    pub fn new() -> Self {
+        Self {
+            env: BTreeMap::new(),
+            fun: builtin_functions(),
+        }
+    }
+
+    pub fn insert(&mut self, id: Identifier, value: Type<T>) {
+        self.env.insert(id, value);
+    }
+
+    pub fn get_value(&self, id: &Identifier) -> Option<&Type<T>> {
+        self.env.get(id)
+    }
+
+    pub fn get_function(&self, id: &Identifier) -> Option<&Callable<T>> {
+        self.fun.get(id).map(|f| f.as_ref())
+    }
+
+    pub fn iter_mut(&mut self) -> IterMut<'_, Identifier, Type<T>> {
+        self.env.iter_mut()
+    }
+}
+
+impl<T: MatrixNumber> Default for Environment<T> {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_identifier_validation() {
+        assert!(Identifier::is_valid("f32_sdsa3_"));
+        assert!(Identifier::is_valid("_fsd3_"));
+        assert!(!Identifier::is_valid("4fd"));
+        assert!(!Identifier::is_valid(""));
+        assert!(!Identifier::is_valid("gdfg+gdf"));
+    }
+
+    #[test]
+    fn test_identifier_new() {
+        assert!(matches!(Identifier::new("pociąg".to_string()), Ok(_)));
+        assert!(matches!(Identifier::new("32".to_string()), Err(_)));
+        assert!(matches!(Identifier::new("".to_string()), Err(_)));
+    }
+
+    #[test]
+    fn test_env_contains_std_fun() {
+        let env = Environment::<i64>::new();
+
+        assert!(env
+            .get_function(&Identifier::new_unsafe("transpose".to_string()))
+            .is_some());
+        assert!(env
+            .get_function(&Identifier::new_unsafe("identity".to_string()))
+            .is_some());
+        assert!(env
+            .get_function(&Identifier::new_unsafe("inverse".to_string()))
+            .is_some());
+    }
+}
diff --git a/src/float.rs b/src/float.rs
new file mode 100644
index 0000000..e7ce891
--- /dev/null
+++ b/src/float.rs
@@ -0,0 +1,310 @@
+use crate::constants::FLOAT_STRING_PRECISION;
+use crate::locale::Locale;
+use crate::traits::{GuiDisplayable, LaTeXable};
+use eframe::epaint::{Color32, FontId, Shape, TextShape};
+use egui::{pos2, Context};
+use num_traits::{
+    CheckedAdd, CheckedDiv, CheckedMul, CheckedSub, FromPrimitive, Num, One, Signed, ToPrimitive,
+    Zero,
+};
+use std::ops::{Add, Div, Mul, Neg, Rem, Sub};
+use std::str::FromStr;
+
+#[derive(Debug, Clone, Copy)]
+pub struct Float64 {
+    value: f64,
+}
+
+impl Num for Float64 {
+    type FromStrRadixErr = <f64 as Num>::FromStrRadixErr;
+
+    fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
+        <f64 as Num>::from_str_radix(str, radix).map(|v| v.into())
+    }
+}
+
+impl PartialEq for Float64 {
+    fn eq(&self, other: &Self) -> bool {
+        <f64 as PartialEq>::eq(&self.value, &other.value)
+    }
+}
+
+impl From<Float64> for f64 {
+    fn from(value: Float64) -> Self {
+        value.value
+    }
+}
+
+impl From<f64> for Float64 {
+    fn from(value: f64) -> Self {
+        Float64 { value }
+    }
+}
+
+impl Zero for Float64 {
+    fn zero() -> Self {
+        <f64 as Zero>::zero().into()
+    }
+
+    fn is_zero(&self) -> bool {
+        <f64 as Zero>::is_zero(&self.value)
+    }
+}
+
+impl Add<Self> for Float64 {
+    type Output = Self;
+
+    fn add(self, rhs: Self) -> Self::Output {
+        self.value.add(rhs.value).into()
+    }
+}
+
+impl One for Float64 {
+    fn one() -> Self {
+        <f64 as One>::one().into()
+    }
+}
+
+impl Mul<Self> for Float64 {
+    type Output = Self;
+
+    fn mul(self, rhs: Self) -> Self::Output {
+        self.value.mul(rhs.value).into()
+    }
+}
+
+impl Sub<Self> for Float64 {
+    type Output = Self;
+
+    fn sub(self, rhs: Self) -> Self::Output {
+        self.value.sub(rhs.value).into()
+    }
+}
+
+impl Div<Self> for Float64 {
+    type Output = Self;
+
+    fn div(self, rhs: Self) -> Self::Output {
+        self.value.div(rhs.value).into()
+    }
+}
+
+impl Rem<Self> for Float64 {
+    type Output = Self;
+
+    fn rem(self, rhs: Self) -> Self::Output {
+        self.value.rem(rhs.value).into()
+    }
+}
+
+impl CheckedAdd for Float64 {
+    fn checked_add(&self, v: &Self) -> Option<Self> {
+        Some(self.value.add(v.value).into())
+    }
+}
+
+impl CheckedSub for Float64 {
+    fn checked_sub(&self, v: &Self) -> Option<Self> {
+        Some(self.value.sub(v.value).into())
+    }
+}
+
+impl CheckedMul for Float64 {
+    fn checked_mul(&self, v: &Self) -> Option<Self> {
+        Some(self.value.mul(v.value).into())
+    }
+}
+
+impl CheckedDiv for Float64 {
+    fn checked_div(&self, v: &Self) -> Option<Self> {
+        if v.is_zero() {
+            return None;
+        }
+        Some(self.value.div(v.value).into())
+    }
+}
+
+impl FromPrimitive for Float64 {
+    fn from_i64(n: i64) -> Option<Self> {
+        Some((n as f64).into())
+    }
+
+    fn from_u64(n: u64) -> Option<Self> {
+        Some((n as f64).into())
+    }
+}
+
+impl ToPrimitive for Float64 {
+    fn to_i64(&self) -> Option<i64> {
+        Some(self.value as i64)
+    }
+
+    fn to_u64(&self) -> Option<u64> {
+        Some(self.value as u64)
+    }
+}
+
+impl Signed for Float64 {
+    fn abs(&self) -> Self {
+        self.value.abs().into()
+    }
+
+    fn abs_sub(&self, other: &Self) -> Self {
+        (self.value - other.value).abs().into()
+    }
+
+    fn signum(&self) -> Self {
+        self.value.signum().into()
+    }
+
+    fn is_positive(&self) -> bool {
+        self.value.is_sign_positive()
+    }
+
+    fn is_negative(&self) -> bool {
+        self.value.is_sign_negative()
+    }
+}
+
+impl Neg for Float64 {
+    type Output = Self;
+
+    fn neg(self) -> Self::Output {
+        self.value.neg().into()
+    }
+}
+
+impl FromStr for Float64 {
+    type Err = ();
+
+    fn from_str(s: &str) -> Result<Self, Self::Err> {
+        s.parse::<f64>().map(|v| v.into()).map_err(|_| ())
+    }
+}
+
+impl ToString for Float64 {
+    fn to_string(&self) -> String {
+        self.value.to_string()
+    }
+}
+
+impl LaTeXable for Float64 {
+    fn to_latex(&self) -> String {
+        self.value.to_latex()
+    }
+}
+
+impl GuiDisplayable for Float64 {
+    fn display_string(&self, locale: &Locale) -> String {
+        self.value.display_string(locale)
+    }
+
+    fn to_shape(&self, ctx: &Context, font_id: FontId, color: Color32) -> Shape {
+        self.value.to_shape(ctx, font_id, color)
+    }
+}
+
+impl LaTeXable for f64 {
+    fn to_latex(&self) -> String {
+        trim_trailing_zeros_float_str(&format!("{:.*}", FLOAT_STRING_PRECISION, self))
+    }
+}
+
+/// Trims trailing zeros from a float string.
+/// # Arguments
+/// * `s` - String to trim zeros from
+/// # Returns
+/// A string representing the same floating point number, but without trailing zeros
+/// # Examples
+/// ```rust
+/// # use crate::jp2gmd_lib::trim_trailing_zeros_float_str;
+/// assert_eq!(trim_trailing_zeros_float_str("10.0"), "10");
+/// assert_eq!(trim_trailing_zeros_float_str("123.450"), "123.45");
+/// assert_eq!(trim_trailing_zeros_float_str("1.0"), "1");
+/// ```
+pub fn trim_trailing_zeros_float_str(s: &str) -> String {
+    let mut s = s.to_string();
+    if s.contains('.') {
+        s = s.trim_end_matches('0').to_string();
+        if s.ends_with('.') {
+            s.pop();
+        }
+    }
+    s
+}
+
+impl GuiDisplayable for f64 {
+    fn display_string(&self, _locale: &Locale) -> String {
+        self.to_latex()
+    }
+
+    fn to_shape(&self, ctx: &Context, font_id: FontId, color: Color32) -> Shape {
+        let text_shape = TextShape::new(
+            pos2(0., 0.),
+            ctx.fonts(|f| f.layout_no_wrap(self.to_latex(), font_id, color)),
+        );
+        Shape::Text(text_shape)
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+    use crate::locale::Language;
+
+    #[test]
+    fn test_zeros() {
+        assert_eq!(Float64::from_str("0").unwrap(), 0.0.into());
+        assert_eq!(Float64::from_str("0.0").unwrap(), 0.0.into());
+        assert_eq!(Float64::from_str("0.00").unwrap(), 0.0.into());
+        assert_eq!(Float64::from_str("0.000").unwrap(), 0.0.into());
+    }
+
+    #[test]
+    fn test_zeros_to_string() {
+        assert_eq!(Float64::from_str("0").unwrap().to_string(), "0");
+        assert_eq!(Float64::from_str("0.0").unwrap().to_string(), "0");
+        assert_eq!(Float64::from_str("0.00").unwrap().to_string(), "0");
+        assert_eq!(Float64::from_str("0.000").unwrap().to_string(), "0");
+    }
+
+    #[test]
+    fn test_trim_trailing_zeros_float_str() {
+        assert_eq!(trim_trailing_zeros_float_str("10.0"), "10");
+        assert_eq!(trim_trailing_zeros_float_str("123.450"), "123.45");
+        assert_eq!(trim_trailing_zeros_float_str("1.0"), "1");
+    }
+
+    #[test]
+    fn test_float64_from_str() {
+        assert_eq!(Float64::from_str("10.0").unwrap(), 10.0.into());
+        assert_eq!(Float64::from_str("123.450").unwrap(), 123.45.into());
+        assert_eq!(Float64::from_str("1.0").unwrap(), 1.0.into());
+    }
+
+    #[test]
+    fn test_float64_to_latex() {
+        assert_eq!(Float64::from_str("10.0").unwrap().to_latex(), "10");
+        assert_eq!(Float64::from_str("123.450").unwrap().to_latex(), "123.45");
+        assert_eq!(Float64::from_str("1.0").unwrap().to_latex(), "1");
+    }
+
+    #[test]
+    fn test_float64_display_string() {
+        let locale = Locale::new(Language::English);
+        assert_eq!(
+            Float64::from_str("10.0").unwrap().display_string(&locale),
+            "10"
+        );
+        assert_eq!(
+            Float64::from_str("123.450")
+                .unwrap()
+                .display_string(&locale),
+            "123.45"
+        );
+        assert_eq!(
+            Float64::from_str("1.0").unwrap().display_string(&locale),
+            "1"
+        );
+    }
+}
diff --git a/src/fourier.rs b/src/fourier.rs
new file mode 100644
index 0000000..ccfbd66
--- /dev/null
+++ b/src/fourier.rs
@@ -0,0 +1,138 @@
+use eframe::epaint::{Color32, Shape};
+use egui::{Painter, Pos2, Stroke, Ui};
+use itertools::Itertools;
+use serde::{Deserialize, Serialize};
+use std::f32::consts::PI;
+use std::fs::File;
+use std::io::BufReader;
+
+pub struct Fourier {
+    data: FourierData,
+    time: f32,
+    path: Vec<(f32, f32)>,
+}
+
+#[derive(Serialize, Deserialize)]
+struct FourierData {
+    epicycles: Vec<FourierEpicycle>,
+    metadata: FourierMetadata,
+}
+
+#[derive(Serialize, Deserialize)]
+struct FourierMetadata {
+    height: f32,
+    width: f32,
+}
+
+#[derive(Serialize, Deserialize)]
+struct FourierEpicycle {
+    re: f32,
+    im: f32,
+    freq: f32,
+    amp: f32,
+    phase: f32,
+}
+
+impl Fourier {
+    pub fn from_json_file(file: String) -> anyhow::Result<Fourier> {
+        let file = File::open(file)?;
+        let reader = BufReader::new(file);
+        let mut fourier: FourierData = serde_json::from_reader(reader)?;
+        fourier.epicycles.sort_by(|a, b| b.amp.total_cmp(&a.amp));
+
+        Ok(Fourier {
+            data: fourier,
+            time: 0.0,
+            path: vec![],
+        })
+    }
+
+    pub fn ui(&mut self, ui: &mut Ui, left_offset: f32, top_offset: f32) {
+        let left_offset = left_offset + ui.available_rect_before_wrap().width() / 2.;
+        let top_offset = top_offset + ui.available_rect_before_wrap().height() / 2.;
+
+        let img_scalar = Self::img_scalars(
+            (&self.data.metadata.width, &self.data.metadata.height),
+            (
+                &ui.available_rect_before_wrap().width(),
+                &ui.available_rect_before_wrap().height(),
+            ),
+        );
+
+        ui.ctx().request_repaint();
+        let painter = Painter::new(
+            ui.ctx().clone(),
+            ui.layer_id(),
+            ui.available_rect_before_wrap(),
+        );
+        let ((x, y), epicycles) =
+            self.epi_cycles(left_offset, top_offset, 0.0, img_scalar, self.time);
+        self.time += PI * 2. / self.data.epicycles.len() as f32;
+        self.path.push((
+            (x - left_offset) / img_scalar,
+            (y - top_offset) / img_scalar,
+        ));
+
+        let mut path_shapes = vec![];
+        for ((x, y), (a, b)) in self
+            .path
+            .iter()
+            .map(|(x, y)| (x * img_scalar + left_offset, y * img_scalar + top_offset))
+            .tuple_windows()
+        {
+            path_shapes.push(Shape::line_segment(
+                [Pos2::new(x, y), Pos2::new(a, b)],
+                Stroke::new(1.0, Color32::WHITE),
+            ));
+        }
+        painter.extend(path_shapes);
+        painter.extend(epicycles);
+
+        ui.expand_to_include_rect(painter.clip_rect());
+
+        if self.time > PI * 2. {
+            self.time = 0.0;
+            self.path.clear();
+        }
+    }
+
+    fn epi_cycles(
+        &mut self,
+        mut x: f32,
+        mut y: f32,
+        rotation: f32,
+        scale: f32,
+        time: f32,
+    ) -> ((f32, f32), Vec<Shape>) {
+        let mut shapes = vec![];
+        let mut prevx = x;
+        let mut prevy = y;
+        for epicycle in &self.data.epicycles {
+            let freq = epicycle.freq;
+            let radius = epicycle.amp * scale;
+            let phase = epicycle.phase;
+            x += radius * (rotation + freq * time + phase).cos();
+            y += radius * (rotation + freq * time + phase).sin();
+            shapes.push(Shape::line_segment(
+                [Pos2::new(prevx, prevy), Pos2::new(x, y)],
+                Stroke::new(0.01, Color32::WHITE),
+            ));
+            shapes.push(Shape::circle_stroke(
+                Pos2::new(prevx, prevy),
+                radius,
+                Stroke::new(0.01, Color32::WHITE),
+            ));
+            prevx = x;
+            prevy = y;
+        }
+        ((x, y), shapes)
+    }
+
+    fn img_scalars((ori_x, ori_y): (&f32, &f32), (width, height): (&f32, &f32)) -> f32 {
+        if width * ori_y > height * ori_x {
+            height / ori_y
+        } else {
+            width / ori_x
+        }
+    }
+}
diff --git a/src/fractal_clock.rs b/src/fractal_clock.rs
new file mode 100644
index 0000000..d4ffff2
--- /dev/null
+++ b/src/fractal_clock.rs
@@ -0,0 +1,167 @@
+// This file was yonked from https://github.com/emilk/egui
+// We are not the authors of this file.
+
+use egui::*;
+use std::f32::consts::TAU;
+
+#[derive(PartialEq)]
+pub struct FractalClock {
+    paused: bool,
+    time: f64,
+    zoom: f32,
+    start_line_width: f32,
+    depth: usize,
+    length_factor: f32,
+    luminance_factor: f32,
+    width_factor: f32,
+    line_count: usize,
+}
+
+impl Default for FractalClock {
+    fn default() -> Self {
+        Self {
+            paused: false,
+            time: 0.0,
+            zoom: 0.25,
+            start_line_width: 2.5,
+            depth: 9,
+            length_factor: 0.8,
+            luminance_factor: 0.8,
+            width_factor: 0.9,
+            line_count: 0,
+        }
+    }
+}
+
+impl FractalClock {
+    pub fn ui(&mut self, ui: &mut Ui, seconds_since_midnight: Option<f64>) {
+        if !self.paused {
+            self.time = seconds_since_midnight.unwrap_or_else(|| ui.input(|i| i.time));
+            ui.ctx().request_repaint();
+        }
+
+        let painter = Painter::new(
+            ui.ctx().clone(),
+            ui.layer_id(),
+            ui.available_rect_before_wrap(),
+        );
+        self.paint(&painter);
+        // Make sure we allocate what we used (everything)
+        ui.expand_to_include_rect(painter.clip_rect());
+    }
+
+    fn paint(&mut self, painter: &Painter) {
+        struct Hand {
+            length: f32,
+            angle: f32,
+            vec: Vec2,
+        }
+
+        impl Hand {
+            fn from_length_angle(length: f32, angle: f32) -> Self {
+                Self {
+                    length,
+                    angle,
+                    vec: length * Vec2::angled(angle),
+                }
+            }
+        }
+
+        let angle_from_period =
+            |period| TAU * (self.time.rem_euclid(period) / period) as f32 - TAU / 4.0;
+
+        let hands = [
+            // Second hand:
+            Hand::from_length_angle(self.length_factor, angle_from_period(60.0)),
+            // Minute hand:
+            Hand::from_length_angle(self.length_factor, angle_from_period(60.0 * 60.0)),
+            // Hour hand:
+            Hand::from_length_angle(0.5, angle_from_period(12.0 * 60.0 * 60.0)),
+        ];
+
+        let mut shapes: Vec<Shape> = Vec::new();
+
+        let rect = painter.clip_rect();
+        let to_screen = emath::RectTransform::from_to(
+            Rect::from_center_size(Pos2::ZERO, rect.square_proportions() / self.zoom),
+            rect,
+        );
+
+        let mut paint_line = |points: [Pos2; 2], color: Color32, width: f32| {
+            let line = [to_screen * points[0], to_screen * points[1]];
+
+            // culling
+            if rect.intersects(Rect::from_two_pos(line[0], line[1])) {
+                shapes.push(Shape::line_segment(line, (width, color)));
+            }
+        };
+
+        let hand_rotations = [
+            hands[0].angle - hands[2].angle + TAU / 2.0,
+            hands[1].angle - hands[2].angle + TAU / 2.0,
+        ];
+
+        let hand_rotors = [
+            hands[0].length * emath::Rot2::from_angle(hand_rotations[0]),
+            hands[1].length * emath::Rot2::from_angle(hand_rotations[1]),
+        ];
+
+        #[derive(Clone, Copy)]
+        struct Node {
+            pos: Pos2,
+            dir: Vec2,
+        }
+
+        let mut nodes = Vec::new();
+
+        let mut width = self.start_line_width;
+
+        for (i, hand) in hands.iter().enumerate() {
+            let center = pos2(0.0, 0.0);
+            let end = center + hand.vec;
+            paint_line([center, end], Color32::from_additive_luminance(255), width);
+            if i < 2 {
+                nodes.push(Node {
+                    pos: end,
+                    dir: hand.vec,
+                });
+            }
+        }
+
+        let mut luminance = 0.7; // Start dimmer than main hands
+
+        let mut new_nodes = Vec::new();
+        for _ in 0..self.depth {
+            new_nodes.clear();
+            new_nodes.reserve(nodes.len() * 2);
+
+            luminance *= self.luminance_factor;
+            width *= self.width_factor;
+
+            let luminance_u8 = (255.0 * luminance).round() as u8;
+            if luminance_u8 == 0 {
+                break;
+            }
+
+            for &rotor in &hand_rotors {
+                for a in &nodes {
+                    let new_dir = rotor * a.dir;
+                    let b = Node {
+                        pos: a.pos + new_dir,
+                        dir: new_dir,
+                    };
+                    paint_line(
+                        [a.pos, b.pos],
+                        Color32::from_additive_luminance(luminance_u8),
+                        width,
+                    );
+                    new_nodes.push(b);
+                }
+            }
+
+            std::mem::swap(&mut nodes, &mut new_nodes);
+        }
+        self.line_count = shapes.len();
+        painter.extend(shapes);
+    }
+}
diff --git a/src/lib.rs b/src/lib.rs
new file mode 100644
index 0000000..8761141
--- /dev/null
+++ b/src/lib.rs
@@ -0,0 +1,560 @@
+mod constants;
+mod editor_gui;
+mod env_gui;
+mod environment;
+mod float;
+#[cfg(feature = "fft")]
+mod fourier;
+#[cfg(feature = "clock")]
+mod fractal_clock;
+mod locale;
+mod matrices;
+mod matrix_algorithms;
+mod parser;
+mod rationals;
+mod traits;
+
+#[cfg(feature = "fft")]
+use crate::constants::DFT_PATH;
+use crate::constants::{
+    APP_NAME, DEFAULT_HEIGHT, DEFAULT_LEFT_PANEL_WIDTH, DEFAULT_WIDTH, ICON_PATH,
+};
+use crate::editor_gui::{
+    display_editor, set_editor_to_existing_matrix, set_editor_to_existing_scalar,
+    set_editor_to_matrix, set_editor_to_scalar, EditorState,
+};
+use crate::environment::{Environment, Identifier, Type};
+use crate::locale::{Language, Locale};
+use crate::matrix_algorithms::Aftermath;
+use crate::parser::parse_instruction;
+use crate::traits::{GuiDisplayable, LaTeXable, MatrixNumber};
+use arboard::Clipboard;
+use constants::{FONT_ID, TEXT_COLOR, VALUE_PADDING};
+use eframe::{egui, IconData};
+
+use egui::{gui_zoom, vec2, Align2, Context, Response, Sense, Ui};
+use env_gui::insert_to_env;
+use std::collections::HashMap;
+use std::default::Default;
+use std::time::Duration;
+use traits::BoxedShape;
+
+#[cfg(feature = "fft")]
+use crate::fourier::Fourier;
+#[cfg(feature = "clock")]
+use crate::fractal_clock::FractalClock;
+use clap::builder::TypedValueParser;
+use clap::{arg, Parser};
+use egui_toast::{Toast, ToastKind, ToastOptions, Toasts};
+use num_rational::Rational64;
+
+pub use float::trim_trailing_zeros_float_str;
+pub use matrices::*;
+
+use crate::float::Float64;
+
+/// Field for matrices.
+type F = Rational64;
+
+/// Approximate field for matrices.
+type R = Float64;
+
+pub fn run_application() -> Result<(), eframe::Error> {
+    let options = eframe::NativeOptions {
+        initial_window_size: Some(vec2(DEFAULT_WIDTH, DEFAULT_HEIGHT)),
+        icon_data: load_icon(ICON_PATH),
+        ..Default::default()
+    };
+    let args = MatrixAppArgs::parse();
+    let locale = Locale::new(args.language);
+
+    match args.approx {
+        true => exec_app::<R>(locale, options),
+        false => exec_app::<F>(locale, options),
+    }
+}
+
+fn exec_app<T: MatrixNumber + 'static>(
+    locale: Locale,
+    options: eframe::NativeOptions,
+) -> Result<(), eframe::Error> {
+    eframe::run_native(
+        &locale.get_translated(APP_NAME),
+        options,
+        Box::new(|_cc| Box::<MatrixApp<T>>::new(MatrixApp::new(locale))),
+    )
+}
+
+fn load_icon(path: &str) -> Option<IconData> {
+    let image = image::open(path).ok()?.into_rgba8();
+    let (width, height) = image.dimensions();
+    Some(IconData {
+        rgba: image.into_raw(),
+        width,
+        height,
+    })
+}
+
+#[derive(Parser, Debug)]
+#[command(
+    author,
+    version,
+    about,
+    long_about = "**Just Pure 2D Graphics Matrix Display** is a powerful matrix calculator written in Rust using egui."
+)]
+struct MatrixAppArgs {
+    #[arg(
+    long,
+    default_value_t = Language::English,
+    value_parser = clap::builder::PossibleValuesParser::new(["English", "Polish", "Spanish"])
+    .map(| s | Language::of(Some(s))),
+    )]
+    language: Language,
+
+    #[arg(long, default_value = "false")]
+    approx: bool,
+}
+
+pub struct WindowState {
+    is_open: bool,
+}
+
+#[derive(Default)]
+struct ShellState {
+    text: String,
+}
+
+pub struct State<K: MatrixNumber> {
+    env: Environment<K>,
+    windows: HashMap<Identifier, WindowState>,
+    shell: ShellState,
+    editor: EditorState,
+    toasts: Toasts,
+    clipboard: Clipboard,
+    #[cfg(feature = "clock")]
+    clock: FractalClock,
+    #[cfg(feature = "fft")]
+    fourier: Option<Fourier>,
+}
+
+impl<K: MatrixNumber> Default for State<K> {
+    fn default() -> Self {
+        Self {
+            env: Default::default(),
+            windows: Default::default(),
+            shell: Default::default(),
+            editor: Default::default(),
+            toasts: Default::default(),
+            #[cfg(feature = "clock")]
+            clock: Default::default(),
+            clipboard: Clipboard::new().expect("Failed to create Clipboard context!"),
+            #[cfg(feature = "fft")]
+            fourier: Fourier::from_json_file(DFT_PATH.to_string()).ok(),
+        }
+    }
+}
+
+struct MatrixApp<K: MatrixNumber> {
+    state: State<K>,
+    locale: Locale,
+}
+
+impl<K: MatrixNumber> MatrixApp<K> {
+    fn new(locale: Locale) -> Self {
+        Self {
+            state: State::default(),
+            locale,
+        }
+    }
+
+    // Get Translated
+    fn gt(&self, str: &str) -> String {
+        self.locale.get_translated(str)
+    }
+}
+
+impl<K: MatrixNumber> eframe::App for MatrixApp<K> {
+    fn update(&mut self, ctx: &Context, frame: &mut eframe::Frame) {
+        if !frame.is_web() {
+            gui_zoom::zoom_with_keyboard_shortcuts(ctx, frame.info().native_pixels_per_point);
+        }
+
+        self.state.toasts = Toasts::default()
+            .anchor(Align2::RIGHT_BOTTOM, (-10.0, -40.0))
+            .direction(egui::Direction::BottomUp);
+
+        let (_top_menu, new_locale) = display_menu_bar(ctx, &mut self.state, &self.locale);
+        display_editor::<K>(ctx, &mut self.state, &self.locale);
+
+        let _left_panel = egui::SidePanel::left("objects")
+            .resizable(true)
+            .default_width(DEFAULT_LEFT_PANEL_WIDTH)
+            .show(ctx, |ui| {
+                egui::trace!(ui);
+                ui.vertical_centered(|ui| {
+                    ui.heading(self.gt("objects"));
+                });
+
+                ui.separator();
+
+                self.state.env.iter_mut().for_each(|element| {
+                    ui.horizontal(|ui| {
+                        display_env_element(&mut self.state.windows, ui, element, &self.locale);
+                    });
+                });
+            })
+            .response;
+
+        let mut windows_result = None;
+        for (id, window) in self.state.windows.iter_mut() {
+            if window.is_open {
+                let element = self.state.env.get_value(id).unwrap();
+                let local_result = display_env_element_window(
+                    ctx,
+                    (id, element),
+                    &self.locale,
+                    &mut self.state.clipboard,
+                    &mut self.state.editor,
+                    &mut self.state.toasts,
+                    &mut window.is_open,
+                );
+                windows_result = windows_result.or(local_result);
+            }
+        }
+
+        if let Some(value) = windows_result {
+            insert_to_env(
+                &mut self.state.env,
+                Identifier::result(),
+                value,
+                &mut self.state.windows,
+            );
+        }
+
+        display_shell::<K>(ctx, &mut self.state, &self.locale);
+
+        // Center panel has to be added last, otherwise the side panel will be on top of it.
+        egui::CentralPanel::default().show(ctx, |ui| {
+            ui.heading(self.gt(APP_NAME));
+            #[cfg(feature = "fft")]
+            match &mut self.state.fourier {
+                Some(fourier) => {
+                    fourier.ui(ui, _left_panel.rect.width(), _top_menu.rect.height());
+                }
+                None => {
+                    #[cfg(feature = "clock")]
+                    self.state.clock.ui(ui, Some(seconds_since_midnight()));
+                }
+            }
+            #[cfg(feature = "clock")]
+            #[cfg(not(feature = "fft"))]
+            self.state.clock.ui(ui, Some(seconds_since_midnight()));
+        });
+
+        self.state.toasts.show(ctx);
+
+        if let Some(new_locale) = new_locale {
+            self.locale = new_locale
+        }
+    }
+}
+
+#[cfg(feature = "clock")]
+fn seconds_since_midnight() -> f64 {
+    use chrono::Timelike;
+    let time = chrono::Local::now().time();
+    time.num_seconds_from_midnight() as f64 + 1e-9 * (time.nanosecond() as f64)
+}
+
+fn display_menu_bar<K: MatrixNumber>(
+    ctx: &Context,
+    state: &mut State<K>,
+    locale: &Locale,
+) -> (Response, Option<Locale>) {
+    let mut new_locale = None;
+    (
+        egui::TopBottomPanel::top("menu_bar")
+            .show(ctx, |ui| {
+                egui::menu::bar(ui, |ui| {
+                    display_add_matrix_button(ui, state, locale);
+                    display_add_scalar_button(ui, state, locale);
+                    ui.with_layout(egui::Layout::right_to_left(egui::Align::Center), |ui| {
+                        display_zoom_panel(ui, ctx);
+                        ui.separator();
+                        new_locale = Some(display_language_panel(ui, locale));
+                        ui.allocate_space(ui.available_size());
+                    });
+                })
+            })
+            .response,
+        new_locale,
+    )
+}
+
+fn display_zoom_panel(ui: &mut Ui, ctx: &Context) {
+    if ui.button("+").clicked() {
+        gui_zoom::zoom_in(ctx);
+    }
+    if ui
+        .button(format!("{} %", (ctx.pixels_per_point() * 100.).round()))
+        .clicked()
+    {
+        ctx.set_pixels_per_point(1.);
+    }
+    if ui.button("-").clicked() {
+        gui_zoom::zoom_out(ctx);
+    }
+}
+
+fn display_language_panel(ui: &mut Ui, locale: &Locale) -> Locale {
+    let mut selected = locale.get_language();
+    egui::ComboBox::from_label(locale.get_translated("Language"))
+        .selected_text(locale.get_translated_from(selected.to_string()))
+        .show_ui(ui, |ui| {
+            ui.selectable_value(
+                &mut selected,
+                Language::English,
+                locale.get_translated("English"),
+            );
+            ui.selectable_value(
+                &mut selected,
+                Language::Polish,
+                locale.get_translated("Polish"),
+            );
+            ui.selectable_value(
+                &mut selected,
+                Language::Spanish,
+                locale.get_translated("Spanish"),
+            );
+        });
+    Locale::new(selected)
+}
+
+fn display_add_matrix_button<K: MatrixNumber>(ui: &mut Ui, state: &mut State<K>, locale: &Locale) {
+    if ui.button(locale.get_translated("Add Matrix")).clicked() {
+        set_editor_to_matrix(&mut state.editor, &K::zero().to_string());
+    }
+}
+
+fn display_add_scalar_button<K: MatrixNumber>(ui: &mut Ui, state: &mut State<K>, locale: &Locale) {
+    if ui.button(locale.get_translated("Add Scalar")).clicked() {
+        set_editor_to_scalar(&mut state.editor, &K::zero().to_string());
+    }
+}
+
+fn display_env_element<K: MatrixNumber>(
+    windows: &mut HashMap<Identifier, WindowState>,
+    ui: &mut Ui,
+    (identifier, value): (&Identifier, &mut Type<K>),
+    locale: &Locale,
+) {
+    let mut is_open = windows.get(identifier).unwrap().is_open;
+    ui.horizontal(|ui| {
+        ui.checkbox(&mut is_open, identifier.to_string());
+        ui.label(value.display_string(locale));
+    });
+    windows.insert(identifier.clone(), WindowState { is_open });
+}
+
+fn display_env_element_window<K: MatrixNumber>(
+    ctx: &Context,
+    (identifier, value): (&Identifier, &Type<K>),
+    locale: &Locale,
+    clipboard: &mut Clipboard,
+    editor: &mut EditorState,
+    toasts: &mut Toasts,
+    is_open: &mut bool,
+) -> Option<Type<K>> {
+    let mut window_result = None;
+
+    egui::Window::new(identifier.to_string())
+        .open(is_open)
+        .resizable(false)
+        .show(ctx, |ui| {
+            ui.horizontal(|ui| {
+                if ui.button("LaTeX").clicked() {
+                    let latex = value.to_latex();
+                    set_clipboard(Ok(latex), clipboard, toasts, locale);
+                }
+                let mut update_by_result = |matrix_op_res| match matrix_op_res {
+                    Ok(Aftermath { result, steps }) => {
+                        window_result = Some(Type::Matrix(result));
+                        Ok(steps.join("\n"))
+                    }
+                    Err(err) => Err(err),
+                };
+                if let Type::Matrix(m) = value {
+                    if ui.button(locale.get_translated("Echelon")).clicked() {
+                        let echelon = update_by_result(m.echelon());
+                        set_clipboard(echelon, clipboard, toasts, locale);
+                    }
+                }
+                if ui.button(locale.get_translated("Inverse")).clicked() {
+                    let inverse = match value {
+                        Type::Scalar(s) => match K::one().checked_div(s) {
+                            Some(inv) => {
+                                window_result = Some(Type::Scalar(inv.clone()));
+                                Ok(inv.to_latex())
+                            }
+                            None => Err(anyhow::Error::msg(
+                                locale.get_translated("Failed to calculate inverse"),
+                            )),
+                        },
+                        Type::Matrix(m) => update_by_result(m.inverse()),
+                    };
+                    set_clipboard(inverse, clipboard, toasts, locale);
+                }
+                if let Type::Matrix(m) = value {
+                    if ui.button(locale.get_translated("Transpose")).clicked() {
+                        let transpose = m.transpose();
+                        window_result = Some(Type::Matrix(transpose));
+                    }
+                }
+            });
+            let mut value_shape = value.to_shape(ctx, FONT_ID, TEXT_COLOR);
+            let value_rect = value_shape.get_rect();
+
+            ui.set_min_width(value_rect.width() + 2. * VALUE_PADDING);
+            ui.set_max_width(ui.min_size().x);
+            ui.separator();
+
+            let bar_height = ui.min_size().y;
+
+            ui.add_space(value_rect.height() + VALUE_PADDING);
+
+            value_shape.translate(
+                ui.clip_rect().min.to_vec2()
+                    + vec2(
+                        (ui.min_size().x - value_rect.width()) / 2.,
+                        bar_height + VALUE_PADDING,
+                    ),
+            );
+            ui.painter().add(value_shape);
+
+            if !identifier.is_result() {
+                ui.separator();
+                if ui.button(locale.get_translated("Edit")).clicked() {
+                    match value {
+                        Type::Scalar(s) => {
+                            set_editor_to_existing_scalar(editor, s, identifier.to_string())
+                        }
+                        Type::Matrix(m) => {
+                            set_editor_to_existing_matrix(editor, m, identifier.to_string())
+                        }
+                    }
+                }
+            };
+        });
+
+    window_result
+}
+
+fn set_clipboard(
+    message: anyhow::Result<String>,
+    clipboard: &mut Clipboard,
+    toasts: &mut Toasts,
+    locale: &Locale,
+) {
+    const CLIPBOARD_TOAST_DURATION: Duration = Duration::from_secs(5);
+    match message {
+        Ok(latex) => match clipboard.set_text(latex) {
+            Ok(_) => {
+                toasts_info(
+                    toasts,
+                    locale.get_translated("LaTeX copied to clipboard"),
+                    CLIPBOARD_TOAST_DURATION,
+                );
+            }
+            Err(e) => {
+                toasts_error(
+                    toasts,
+                    locale.get_translated("Failed to copy LaTeX to clipboard")
+                        + "\n"
+                        + e.to_string().as_str(),
+                    CLIPBOARD_TOAST_DURATION,
+                );
+            }
+        },
+        Err(e) => {
+            toasts_error(
+                toasts,
+                locale.get_translated("Failed to generate LaTeX") + "\n" + e.to_string().as_str(),
+                CLIPBOARD_TOAST_DURATION,
+            );
+        }
+    }
+}
+
+fn display_shell<K: MatrixNumber>(
+    ctx: &Context,
+    State {
+        shell,
+        env,
+        windows,
+        toasts,
+        ..
+    }: &mut State<K>,
+    locale: &Locale,
+) {
+    let mut run_shell_command = |shell_text: &mut String| match parse_instruction(shell_text, env) {
+        Ok(identifier) => {
+            shell_text.clear();
+            windows.insert(identifier, WindowState { is_open: true });
+        }
+        Err(error) => {
+            println!("{error}");
+            toasts_error(toasts, error.to_string(), Duration::from_secs(5));
+        }
+    };
+
+    egui::TopBottomPanel::bottom("shell")
+        .resizable(false)
+        .default_height(128.0)
+        .show(ctx, |ui| {
+            let button_sense = if shell.text.is_empty() {
+                Sense::hover()
+            } else {
+                Sense::click()
+            };
+
+            ui.horizontal(|ui| {
+                ui.with_layout(egui::Layout::right_to_left(egui::Align::BOTTOM), |ui| {
+                    if ui
+                        .add(egui::Button::new(locale.get_translated("Run")).sense(button_sense))
+                        .clicked()
+                    {
+                        run_shell_command(&mut shell.text);
+                    }
+
+                    let response = ui.add(
+                        egui::TextEdit::singleline(&mut shell.text)
+                            .desired_rows(1)
+                            .desired_width(ui.available_width())
+                            .code_editor(),
+                    );
+                    if response.lost_focus() && ui.input(|i| i.key_pressed(egui::Key::Enter)) {
+                        run_shell_command(&mut shell.text);
+                        response.request_focus();
+                    }
+                });
+            });
+        });
+}
+
+fn toasts_add_kind(toasts: &mut Toasts, text: String, duration: Duration, kind: ToastKind) {
+    toasts.add(Toast {
+        text: text.into(),
+        kind,
+        options: ToastOptions::default()
+            .duration(duration)
+            .show_progress(true),
+    });
+}
+
+fn toasts_info(toasts: &mut Toasts, text: String, duration: Duration) {
+    toasts_add_kind(toasts, text, duration, ToastKind::Info);
+}
+
+fn toasts_error(toasts: &mut Toasts, text: String, duration: Duration) {
+    toasts_add_kind(toasts, text, duration, ToastKind::Error);
+}
diff --git a/src/locale.rs b/src/locale.rs
new file mode 100644
index 0000000..74b84c3
--- /dev/null
+++ b/src/locale.rs
@@ -0,0 +1,174 @@
+use lazy_static::lazy_static;
+use std::collections::HashMap;
+use std::fmt::Display;
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
+pub enum Language {
+    English,
+    Spanish,
+    Polish,
+}
+
+impl Display for Language {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        match self {
+            Language::English => write!(f, "English"),
+            Language::Spanish => write!(f, "Spanish"),
+            Language::Polish => write!(f, "Polish"),
+        }
+    }
+}
+
+impl Language {
+    pub fn of(str: Option<String>) -> Language {
+        str.map_or(Language::English, |str| match str.to_lowercase().as_str() {
+            "en" | "english" => Language::English,
+            "es" | "spanish" => Language::Spanish,
+            "pl" | "polish" => Language::Polish,
+            _ => Language::English,
+        })
+    }
+}
+
+pub struct Locale {
+    language: Language,
+    translation_map: &'static HashMap<String, String>,
+}
+
+impl Locale {
+    pub fn new(language: Language) -> Self {
+        Self {
+            language,
+            translation_map: match language {
+                Language::English => &TRANS_EN_MAP,
+                Language::Polish => &TRANS_PL_MAP,
+                Language::Spanish => &TRANS_ES_MAP,
+            },
+        }
+    }
+
+    fn unwrap_or_default(str: Option<&String>, default: &str) -> String {
+        match str {
+            Some(str) => str.to_string(),
+            None => default.to_string(),
+        }
+    }
+
+    pub fn get_language(&self) -> Language {
+        self.language
+    }
+
+    pub fn get_translated(&self, s: &str) -> String {
+        Self::unwrap_or_default(self.translation_map.get(s), s)
+    }
+
+    pub fn get_translated_from(&self, s: String) -> String {
+        self.get_translated(&s)
+    }
+}
+
+lazy_static! {
+    pub static ref TRANS_EN_RAW: Vec<(&'static str, &'static str)> = vec![
+        ("objects", "Objects"),
+        ("matrix", "Matrix"),
+        ("Add Matrix", "Add Matrix"),
+        ("Add Scalar", "Add Scalar"),
+        ("JP2GMD - Matrix Calculator", "JP2GMD - Matrix Calculator"),
+        ("Echelon", "Echelon"),
+        ("Inverse", "Inverse"),
+        ("Transpose", "Transpose"),
+        ("Run", "Run"),
+        ("Editor", "Editor"),
+        ("Identifier:", "Identifier:"),
+        ("Matrix is invalid!", "Matrix is invalid!"),
+        ("Add", "Add"),
+        ("Error", "Error"),
+        ("Enter the matrix:", "Enter the matrix:"),
+        ("Enter the scalar:", "Enter the scalar:"),
+        ("Height", "Height"),
+        ("Width", "Width"),
+        ("Edit", "Edit"),
+        ("Error ", "Error "),
+        ("Identifier is invalid!", "Identifier is invalid!"),
+        ("LaTeX copied to clipboard", "LaTeX copied to clipboard"),
+        ("Failed to generate LaTeX", "Failed to generate LaTeX"),
+        ("Language", "Language"),
+        ("English", "English"),
+        ("Polish", "Polish"),
+        ("Spanish", "Spanish"),
+    ];
+    pub static ref TRANS_PL_RAW: Vec<(&'static str, &'static str)> =
+        vec![
+        ("objects", "Obiekty"),
+        ("matrix", "Macierz"),
+        ("Add Matrix", "Dodaj Macierz"),
+        ("Add Scalar", "Dodaj Skalar"),
+        (
+            "JP2GMD - Matrix Calculator",
+            "Jaki Potężny 2-wymiarowy Generator Macierzy Diagonalizowalnych - Kalkulator Macierzy"
+        ),
+        ("Echelon", "Schodkuj"),
+        ("Inverse", "Odwrotność"),
+        ("Transpose", "Transponuj"),
+        ("Run", "Uruchom"),
+        ("Editor", "Edytor"),
+        ("Identifier:", "Identyfikator:"),
+        ("Matrix is invalid!", "Macierz jest niepoprawna!"),
+        ("Add", "Dodaj"),
+        ("Error", "Błąd"),
+        ("Enter the matrix:", "Wprowadź macierz:"),
+        ("Enter the scalar:", "Wprowadź skalar:"),
+        ("Height", "Wysokość"),
+        ("Width", "Szerokość"),
+        ("Edit", "Edytuj"),
+        ("Error ", "Błąd "),
+        ("Identifier is invalid!", "Identyfikator jest niepoprawny!"),
+        ("LaTeX copied to clipboard", "Skopiowano LaTeX'a do schowka"),
+        ("Failed to generate LaTeX", "Nie udało się wygenerować LaTeX'a"),
+        ("Language", "Język"),
+        ("English", "Angielski"),
+        ("Polish", "Polski"),
+        ("Spanish", "Hiszpański"),
+    ];
+    pub static ref TRANS_ES_RAW: Vec<(&'static str, &'static str)> = vec![
+        ("objects", "Objetos"),
+        ("matrix", "Matriz"),
+        ("Add Matrix", "Añadir Matriz"),
+        ("Add Scalar", "Añadir Escalar"),
+        (
+            "JP2GMD - Matrix Calculator",
+            "JP2GMD - Calculadora de Matrices"
+        ),
+        ("Echelon", "Echelon"),
+        ("Inverse", "Inversa"),
+        ("Transpose", "Transpuesta"),
+        ("Run", "Ejecutar"),
+        ("Editor", "Editor"),
+        ("Identifier:", "Identificador:"),
+        ("Matrix is invalid!", "¡La matriz es inválida!"),
+        ("Add", "Añadir"),
+        ("Error", "Error"),
+        ("Enter the matrix:", "Introduzca la matriz:"),
+        ("Enter the scalar:", "Introduzca el escalar:"),
+        ("Height", "Altura"),
+        ("Width", "Anchura"),
+        ("Editor", "Editar"),
+        ("Error ", "Error "),
+        ("Identifier is invalid!", "¡El identificador es inválido!"),
+        ("LaTeX copied to clipboard", "LaTeX copiado al portapapeles"),
+        ("Failed to generate LaTeX", "No se pudo generar LaTeX"),
+        ("Language", "Idioma"),
+        ("English", "Inglés"),
+        ("Polish", "Polaco"),
+        ("Spanish", "Español"),
+    ];
+    pub static ref TRANS_EN_MAP: HashMap<String, String> = gen_map(&TRANS_EN_RAW);
+    pub static ref TRANS_PL_MAP: HashMap<String, String> = gen_map(&TRANS_PL_RAW);
+    pub static ref TRANS_ES_MAP: HashMap<String, String> = gen_map(&TRANS_ES_RAW);
+}
+
+fn gen_map(vec: &[(&'static str, &'static str)]) -> HashMap<String, String> {
+    vec.iter()
+        .map(|(k, v)| (k.to_string(), v.to_string()))
+        .collect()
+}
diff --git a/src/main.rs b/src/main.rs
new file mode 100644
index 0000000..f3f341d
--- /dev/null
+++ b/src/main.rs
@@ -0,0 +1,3 @@
+fn main() -> Result<(), eframe::Error> {
+    jp2gmd_lib::run_application()
+}
diff --git a/src/matrices.rs b/src/matrices.rs
new file mode 100644
index 0000000..1b44332
--- /dev/null
+++ b/src/matrices.rs
@@ -0,0 +1,1119 @@
+use crate::constants::{MATRIX_HPADDING, MATRIX_VPADDING};
+use crate::locale::Locale;
+use crate::traits::{BoxedShape, LaTeXable};
+use crate::traits::{GuiDisplayable, MatrixNumber};
+use anyhow::{bail, Context};
+use egui::{pos2, Color32, FontId, Rect};
+use std::ops::{Add, Mul, Neg, Sub};
+
+/// A matrix of type `T`.
+/// Matrices are immutable.
+/// Empty matrices have shape (0, 0), so be careful.
+#[derive(Debug, Clone, Default)]
+pub struct Matrix<T: MatrixNumber> {
+    data: Vec<Vec<T>>,
+
+    /// Index of a column that is followed by a vertical separator (counting
+    /// from 0). This only affects exporting to LaTeX.
+    separator: Option<usize>,
+}
+
+impl<T: MatrixNumber> Matrix<T> {
+    /// Creates a new matrix from a 2D vector.
+    /// The matrix is not checked for validity.
+    /// If you want to check for validity, use `Matrix::new`.
+    /// Calling methods on an invalid matrix will result in undefined behavior.
+    /// # Arguments
+    /// * `data` - The data of the matrix.
+    /// # Returns
+    /// A new matrix.
+    /// # Examples
+    /// ```
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::new_unsafe(vec![vec![1, 2, 3], vec![4, 5, 6]]);
+    /// // m corresponds to the matrix
+    /// // | 1 2 3 |
+    /// // | 4 5 6 |
+    /// ```
+    pub fn new_unsafe(data: Vec<Vec<T>>) -> Self {
+        Self {
+            data,
+            separator: None,
+        }
+    }
+
+    /// Creates a new matrix from a 2D vector.
+    /// The matrix is checked for validity.
+    /// If you don't want to check for validity, use `Matrix::new_unsafe`.
+    /// # Arguments
+    /// * `data` - The data of the matrix.
+    /// # Returns
+    /// A new matrix.
+    /// # Examples
+    /// ```
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::new(vec![vec![1, 2, 3], vec![4, 5, 6]]);
+    /// // m corresponds to the matrix
+    /// // | 1 2 3 |
+    /// // | 4 5 6 |
+    /// ```
+    /// # Errors
+    /// If the data is not a valid matrix.
+    /// ```
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::new(vec![vec![1, 2, 3], vec![4, 5]]);
+    /// // m is an error
+    /// ```
+    pub fn new(data: Vec<Vec<T>>) -> anyhow::Result<Self> {
+        let matrix = Self {
+            data,
+            separator: None,
+        };
+        if !matrix.is_valid() {
+            bail!("Invalid matrix.")
+        } else if matrix.is_empty() {
+            Ok(Self::empty())
+        } else {
+            Ok(matrix)
+        }
+    }
+
+    /// Creates a new matrix from a 2D vector.
+    /// The matrix is checked for validity.
+    /// The initial data is passed as a vector of flattened rows.
+    /// The shape of the matrix is passed as a tuple.
+    /// # Arguments
+    /// * `data` - The data of the matrix.
+    /// * `(rows, cols)` - The shape of the matrix.
+    /// # Returns
+    /// A new matrix.
+    /// # Examples
+    /// ```
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::from_vec(vec![1, 2, 3, 4, 5, 6], (2, 3));
+    /// // m corresponds to the matrix
+    /// // | 1 2 3 |
+    /// // | 4 5 6 |
+    /// ```
+    /// # Errors
+    /// If the data is not a valid matrix.
+    pub fn from_vec(data: Vec<T>, (rows, cols): (usize, usize)) -> anyhow::Result<Self> {
+        if data.len() != rows * cols {
+            bail!("Invalid size.")
+        } else if rows == 0 || cols == 0 {
+            Ok(Self::empty())
+        } else {
+            Self::new(data.chunks(cols).map(|c| c.to_vec()).collect())
+        }
+    }
+
+    /// Gets the index of a column that is followed by a vertical separator (if any).
+    /// # Returns
+    /// The index of the separator (or None if there is no separator).
+    pub fn get_separator(&self) -> Option<usize> {
+        self.separator
+    }
+
+    /// Sets the index of a column that is followed by a vertical separator
+    /// (counting from 0).
+    /// # Arguments
+    /// * `separator` - The index of the separator (or None if there is no separator).
+    /// # Examples
+    /// ```
+    /// # use jp2gmd_lib::Matrix;
+    /// let mut m = Matrix::new(vec![vec![1, 2, 3], vec![4, 5, 6]]).unwrap();
+    /// // m corresponds to the matrix
+    /// // | 1 2 3 |
+    /// // | 4 5 6 |
+    /// m.set_separator(Some(1));
+    /// // m corresponds to the matrix
+    /// // | 1 2 | 3 |
+    /// // | 4 5 | 6 |
+    /// ```
+    pub fn set_separator(&mut self, separator: Option<usize>) {
+        self.separator = separator;
+    }
+
+    /// Creates a new matrix by setting the index of a column that is followed
+    /// by a vertical separator (counting from 0).
+    /// # Arguments
+    /// * `separator` - The index of the separator (or None if there is no separator).
+    /// # Returns
+    /// A new matrix.
+    pub fn with_separator(mut self, separator: Option<usize>) -> Self {
+        self.set_separator(separator);
+        self
+    }
+
+    /// Creates a new matrix by reshaping an existing matrix.
+    /// If new shape is not compatible with the old shape, an error is returned.
+    /// # Arguments
+    /// * `matrix` - The matrix to reshape.
+    /// * `(rows, cols)` - The new shape of the matrix.
+    /// # Returns
+    /// A new matrix.
+    /// # Examples
+    /// ```
+    /// # use anyhow::Context;
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::new(vec![vec![1, 2, 3], vec![4, 5, 6]]).expect("Invalid matrix.");
+    /// // m corresponds to the matrix
+    /// // | 1 2 3 |
+    /// // | 4 5 6 |
+    /// let m = Matrix::reshape(&m, (3, 2)).expect("Invalid size.");
+    /// // m corresponds to the matrix
+    /// // | 1 2 |
+    /// // | 3 4 |
+    /// // | 5 6 |
+    /// ```
+    pub fn reshape(&self, (rows, cols): (usize, usize)) -> anyhow::Result<Self> {
+        let (h, w) = self.get_shape();
+        if h * w != rows * cols {
+            bail!("Invalid size.")
+        } else {
+            Self::from_vec(self.data.iter().flatten().cloned().collect(), (rows, cols))
+        }
+    }
+
+    /// Creates a new matrix of shape (h, w) with given supplier.
+    /// # Arguments
+    /// * `(h, w)` - The shape of the matrix - height and width.
+    /// * `supplier` - The supplier of the matrix.
+    /// # Returns
+    /// A new matrix of shape (h, w) with given supplier.
+    /// # Examples
+    /// ```
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::filled((2, 3), |i, j| (i + j) as i64);
+    /// // m corresponds to the matrix
+    /// // | 0 1 2 |
+    /// // | 1 2 3 |
+    /// let m = Matrix::filled((2, 3), |i, j| (i * j) as i64);
+    /// // m corresponds to the matrix
+    /// // | 0 0 0 |
+    /// // | 0 1 2 |
+    /// ```
+    pub fn filled<F>((h, w): (usize, usize), supp: F) -> Self
+    where
+        F: Fn(usize, usize) -> T,
+    {
+        if h == 0 || w == 0 {
+            return Self::empty();
+        }
+        let mut data = vec![vec![T::zero(); w]; h];
+        for (i, row) in data.iter_mut().enumerate().take(h) {
+            for (j, elem) in row.iter_mut().enumerate().take(w) {
+                *elem = supp(i, j);
+            }
+        }
+        Self {
+            data,
+            separator: None,
+        }
+    }
+
+    /// Creates zero matrix of shape (h, w).
+    /// # Arguments
+    /// * `(h, w)` - The shape of the matrix - height and width.
+    /// # Returns
+    /// A zero matrix of shape (h, w).
+    /// # Examples
+    /// ```
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::<i64>::zeros((2, 3));
+    /// // m corresponds to the matrix
+    /// // | 0 0 0 |
+    /// // | 0 0 0 |
+    /// ```
+    pub fn zeros((h, w): (usize, usize)) -> Self {
+        Self::filled((h, w), |_, _| T::zero())
+    }
+
+    /// Creates ones matrix of shape (h, w).
+    /// # Arguments
+    /// * `(h, w)` - The shape of the matrix - height and width.
+    /// # Returns
+    /// A ones matrix of shape (h, w).
+    /// # Examples
+    /// ```
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::<i64>::ones((2, 3));
+    /// // m corresponds to the matrix
+    /// // | 1 1 1 |
+    /// // | 1 1 1 |
+    /// ```
+    pub fn ones((h, w): (usize, usize)) -> Self {
+        Self::filled((h, w), |_, _| T::one())
+    }
+
+    /// Creates identity (square) matrix of shape (n, n).
+    /// # Arguments
+    /// * `n` - The length of the side of the matrix.
+    /// # Returns
+    /// An identity matrix of shape (n, n).
+    /// # Examples
+    /// ```
+    /// # use num_rational::Rational64;
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::<Rational64>::identity(3);
+    /// // m corresponds to the matrix
+    /// // | 1 0 0 |
+    /// // | 0 1 0 |
+    /// // | 0 0 1 |
+    /// ```
+    pub fn identity(n: usize) -> Self {
+        Self::filled((n, n), |i, j| if i == j { T::one() } else { T::zero() })
+    }
+
+    /// Creates empty matrix of shape (0, 0).
+    /// # Returns
+    /// An empty matrix of shape (0, 0).
+    pub fn empty() -> Self {
+        Self::new_unsafe(vec![])
+    }
+
+    /// Returns the shape of the matrix.
+    /// If the matrix is not valid, the behavior is undefined.
+    /// If the matrix is empty, the shape is (0, 0).
+    /// # Returns
+    /// A tuple of the form `(height, width)`.
+    /// # Examples
+    /// ```
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::new(vec![vec![1, 2, 3], vec![4, 5, 6]]).unwrap();
+    /// assert_eq!(m.get_shape(), (2, 3));
+    /// ```
+    pub fn get_shape(&self) -> (usize, usize) {
+        if self.is_empty() {
+            (0, 0)
+        } else {
+            (self.data.len(), self.data[0].len())
+        }
+    }
+
+    /// Checks if matrix is empty.
+    /// Matrix is empty if it has no rows or no columns.
+    /// Matrix has to be valid. Otherwise, the behavior is undefined.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// assert!(!m.is_empty());
+    /// let m = Matrix::<i64>::new(vec![vec![], vec![], vec![]]).unwrap();
+    /// assert!(m.is_empty());
+    /// let m = Matrix::<i64>::new(vec![]).unwrap();
+    /// assert!(m.is_empty());
+    /// ```
+    pub fn is_empty(&self) -> bool {
+        self.data.is_empty() || self.data[0].is_empty()
+    }
+
+    /// Checks if matrix is valid.
+    /// Matrix is valid if all rows have the same length.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::new_unsafe(vec![vec![1, 2], vec![3, 4]]);
+    /// assert!(m.is_valid());
+    /// let m = Matrix::new_unsafe(vec![vec![1, 2], vec![3, 4, 5]]);
+    /// assert!(!m.is_valid());
+    /// ```
+    pub fn is_valid(&self) -> bool {
+        return if self.data.is_empty() {
+            true
+        } else {
+            !self
+                .data
+                .iter()
+                .skip(1)
+                .fold((false, self.data[0].len()), |(acc, row_len), next| {
+                    (acc || row_len != next.len(), row_len)
+                })
+                .0 // does any row have different length?
+        };
+    }
+
+    /// Returns the raw data of the matrix.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// assert_eq!(m.get_data(), &vec![vec![1, 2], vec![3, 4]]);
+    /// ```
+    pub fn get_data(&self) -> &Vec<Vec<T>> {
+        &self.data
+    }
+
+    /// Returns the raw data of the matrix and consumes the matrix.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// assert_eq!(m.consume(), vec![vec![1, 2], vec![3, 4]]);
+    /// ```
+    pub fn consume(self) -> Vec<Vec<T>> {
+        self.data
+    }
+
+    /// Checks if two matrices have the same shape.
+    /// Shape of a matrix is a tuple of the form `(height, width)`.
+    /// # Arguments
+    /// * `other` - The other matrix.
+    /// # Returns
+    /// `true` if the matrices have the same shape, `false` otherwise.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m1 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m2 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// assert!(m1.same_shapes(&m2));
+    /// let m1 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m2 = Matrix::new(vec![vec![1, 2, 3], vec![4, 5, 6]]).unwrap();
+    /// assert!(!m1.same_shapes(&m2));
+    /// ```
+    pub fn same_shapes(&self, other: &Self) -> bool {
+        let self_shape = self.get_shape();
+        let other_shape = other.get_shape();
+        self_shape == other_shape
+    }
+
+    /// Return the shape of a matrix after multiplication.
+    /// # Arguments
+    /// * `other` - The other matrix.
+    /// # Returns
+    /// A tuple of the form `(height, width)`.
+    /// # Errors
+    /// Returns `Err` if the matrices cannot be multiplied - e.g. if they have incompatible shapes.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m1 = Matrix::new(vec![vec![1, 2, 3], vec![4, 5, 6]]).unwrap();
+    /// let m2 = Matrix::new(vec![vec![1, 2], vec![3, 4], vec![5, 6]]).unwrap();
+    /// assert_eq!(m1.result_shape_for_mul(&m2).unwrap(), (2, 2));
+    /// let m1 = Matrix::new(vec![vec![1, 2, 3], vec![4, 5, 6]]).unwrap();
+    /// let m2 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// assert!(m1.result_shape_for_mul(&m2).is_err());
+    /// ```
+    pub fn result_shape_for_mul(&self, other: &Self) -> anyhow::Result<(usize, usize)> {
+        let (h, self_w) = self.get_shape();
+        let (other_h, w) = other.get_shape();
+        if self_w == other_h {
+            Ok((h, w))
+        } else {
+            Err(anyhow::anyhow!(
+                "Cannot multiply matrices of shapes ({h}, {self_w}) and ({other_h}, {w})"
+            ))
+        }
+    }
+
+    /// Performs element-wise operation on two matrices.
+    /// # Arguments
+    /// * `other` - The other matrix.
+    /// * `op` - The operation to perform.
+    /// # Returns
+    /// A new matrix with the result of the operation.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m1 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m2 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m3 = m1.checked_operation_on_two(&m2, |a, b| Some(a + b)).unwrap();
+    /// assert_eq!(m3, Matrix::new(vec![vec![2, 4], vec![6, 8]]).unwrap());
+    /// ```
+    pub fn checked_operation_on_two<F>(&self, other: &Self, operation: F) -> anyhow::Result<Self>
+    where
+        F: Fn(&T, &T) -> Option<T>,
+    {
+        self.same_shapes(other)
+            .then_some(())
+            .context("Matrices have different shapes!")?;
+        let data = self
+            .data
+            .iter()
+            .zip(other.data.iter())
+            .map(|(row_self, row_other)| {
+                row_self
+                    .iter()
+                    .zip(row_other.iter())
+                    .map(|(elem_self, elem_other)| operation(elem_self, elem_other))
+                    .collect::<Option<Vec<T>>>()
+            })
+            .collect::<Option<Vec<Vec<T>>>>()
+            .ok_or_else(|| anyhow::anyhow!("Operation failed!"))?;
+        Self::new(data)
+    }
+
+    /// Performs matrix operation element-wise.
+    /// # Arguments
+    /// * `op` - The operation to perform.
+    /// # Returns
+    /// A new matrix with the result of the operation.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m2 = m.checked_operation(|a| Some(a + 1)).unwrap();
+    /// assert_eq!(m2, Matrix::new(vec![vec![2, 3], vec![4, 5]]).unwrap());
+    /// ```
+    pub fn checked_operation<F>(&self, operation: F) -> anyhow::Result<Self>
+    where
+        F: Fn(&T) -> Option<T>,
+    {
+        // In order to avoid code duplication, we use `checked_operation_on_two`
+        //  with `self` as the second argument and ignore it later.
+        //  It is more memory efficient as we don't need to allocate a new matrix.
+        //  First approach was to use some mock matrix, but it was less efficient.
+        self.checked_operation_on_two(self, |a, _| operation(a))
+    }
+
+    /// Performs matrix addition.
+    /// # Arguments
+    /// * `other` - The other matrix.
+    /// # Returns
+    /// A new matrix with the result of the addition.
+    /// # Errors
+    /// Returns `Err` if the matrices have different shapes.
+    /// # Examples
+    /// ```
+    /// # use jp2gmd_lib::Matrix;
+    /// let m1 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m2 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m3 = m1.checked_add(&m2).unwrap();
+    /// assert_eq!(m3, Matrix::new(vec![vec![2, 4], vec![6, 8]]).unwrap());
+    /// ```
+    pub fn checked_add(&self, rhs: &Self) -> anyhow::Result<Self> {
+        self.checked_operation_on_two(rhs, |a, b| a.checked_add(b))
+    }
+
+    /// Performs matrix subtraction.
+    /// # Arguments
+    /// * `other` - The other matrix.
+    /// # Returns
+    /// A new matrix with the result of the subtraction.
+    /// # Errors
+    /// Returns `Err` if the matrices have different shapes.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m1 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m2 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m3 = m1.checked_sub(&m2).unwrap();
+    /// assert_eq!(m3, Matrix::new(vec![vec![0, 0], vec![0, 0]]).unwrap());
+    /// ```
+    pub fn checked_sub(&self, v: &Self) -> anyhow::Result<Self> {
+        self.checked_operation_on_two(v, |a, b| a.checked_sub(b))
+    }
+
+    /// Performs matrix negation.
+    /// # Returns
+    /// A new matrix with the result of the negation.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m1 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m2 = m1.checked_neg().unwrap();
+    /// assert_eq!(m2, Matrix::new(vec![vec![-1, -2], vec![-3, -4]]).unwrap());
+    /// ```
+    pub fn checked_neg(&self) -> anyhow::Result<Self> {
+        Self::zeros(self.get_shape()).checked_sub(self)
+    }
+
+    /// Performs matrix multiplication.
+    /// # Arguments
+    /// * `other` - The other matrix.
+    /// # Returns
+    /// A new matrix with the result of the multiplication.
+    /// # Errors
+    /// Returns `Err` if height of the first matrix is not equal to the width of the second matrix.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m1 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m2 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m3 = m1.checked_mul(&m2).unwrap();
+    /// assert_eq!(m3, Matrix::new(vec![vec![7, 10], vec![15, 22]]).unwrap());
+    /// ```
+    pub fn checked_mul(&self, v: &Self) -> anyhow::Result<Self> {
+        const OVERFLOW_MSG: &str = "Overflow during matrix multiplication!";
+        let (h, w) = self.result_shape_for_mul(v)?;
+
+        let mut res = Matrix::<T>::zeros((h, w)).data;
+        for (i, item) in self.data.iter().enumerate() {
+            for j in 0..w {
+                for (k, item_item) in item.iter().enumerate() {
+                    res[i][j] = (item_item.checked_mul(&v.data[k][j]).context(OVERFLOW_MSG)?)
+                        .checked_add(&res[i][j])
+                        .context(OVERFLOW_MSG)?;
+                }
+            }
+        }
+        Self::new(res)
+    }
+
+    /// Performs matrix multiplication by a scalar.
+    /// # Arguments
+    /// * `other` - The scalar.
+    /// # Returns
+    /// A new matrix with the result of the multiplication.
+    /// # Errors
+    /// Returns `Err` if the multiplication overflows.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m1 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m2 = m1.checked_mul_scl(&2).unwrap();
+    /// assert_eq!(m2, Matrix::new(vec![vec![2, 4], vec![6, 8]]).unwrap());
+    /// ```
+    pub fn checked_mul_scl(&self, other: &T) -> anyhow::Result<Self> {
+        self.checked_operation(|a| a.checked_mul(other))
+    }
+
+    /// Performs matrix to the power.
+    /// # Arguments
+    /// * `exponent` - The power to raise the matrix to.
+    /// # Returns
+    /// $M^{exponent}$ where $M$ is the matrix.
+    pub fn checked_pow(&self, mut exponent: usize) -> anyhow::Result<Self> {
+        let (h, w) = self.get_shape();
+        if h != w {
+            bail!("Only square matrices can be used in exponentiation!");
+        }
+
+        let mut pow2 = self.clone();
+        let mut result = Self::identity(h);
+        while exponent > 0 {
+            if exponent % 2 == 1 {
+                result = result
+                    .checked_mul(&pow2)
+                    .context("Multiplication failed!")?;
+            }
+            pow2 = pow2.checked_mul(&pow2).context("Multiplication failed!")?;
+            exponent /= 2;
+        }
+
+        Ok(result)
+    }
+
+    /// Concats two matrices horizontally. Assumes that both matrices have the
+    /// same number of rows.
+    /// # Arguments
+    /// * `other` - The other matrix.
+    /// # Returns
+    /// A new matrix with the result of the operation.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m1 = Matrix::new(vec![vec![1, 2], vec![3, 4]]).unwrap();
+    /// let m2 = Matrix::new(vec![vec![5, 6], vec![7, 8]]).unwrap();
+    /// let m3 = m1.concat(m2).unwrap();
+    /// assert_eq!(m3, Matrix::new(vec![vec![1, 2, 5, 6], vec![3, 4, 7, 8]]).unwrap());
+    /// ```
+    pub fn concat(mut self, other: Self) -> anyhow::Result<Self> {
+        let (rows, columns) = self.get_shape();
+        if rows != other.get_shape().0 {
+            bail!("Cannot concatenate matrices with different number of rows!");
+        }
+
+        std::iter::zip(self.data.iter_mut(), other.data).for_each(|(a, b)| a.extend(b));
+        Ok(self.with_separator(Some(columns)))
+    }
+
+    /// Splits the matrix horizontally at the given column. Drops the separator.
+    /// # Arguments
+    /// * `column` - The column to split at.
+    /// # Returns
+    /// A tuple of two matrices.
+    /// # Examples
+    /// ```rust
+    /// # use jp2gmd_lib::Matrix;
+    /// let m1 = Matrix::new(vec![vec![1, 2, 3, 4], vec![5, 6, 7, 8]]).unwrap();
+    /// let (m2, m3) = m1.split(2).unwrap();
+    /// assert_eq!(m2, Matrix::new(vec![vec![1, 2], vec![5, 6]]).unwrap());
+    /// assert_eq!(m3, Matrix::new(vec![vec![3, 4], vec![7, 8]]).unwrap());
+    /// ```
+    pub fn split(mut self, column: usize) -> anyhow::Result<(Self, Self)> {
+        let (_, columns) = self.get_shape();
+        if column > columns {
+            bail!("Cannot split matrix at column {}!", column);
+        }
+
+        let right = Self::new_unsafe(
+            self.data
+                .iter_mut()
+                .map(|row| row.split_off(column))
+                .collect(),
+        );
+        self.separator = None;
+        Ok((self, right))
+    }
+}
+
+impl<T: MatrixNumber> PartialEq for Matrix<T> {
+    fn eq(&self, other: &Self) -> bool {
+        if self.is_empty() && other.is_empty() {
+            return true;
+        }
+        if self.get_shape() != other.get_shape() {
+            return false;
+        }
+        self.data == other.data
+    }
+}
+
+impl<T: MatrixNumber> Eq for Matrix<T> {}
+
+impl<T: MatrixNumber> LaTeXable for Matrix<T> {
+    fn to_latex(&self) -> String {
+        let mut column_format = "c".repeat(self.data[0].len());
+        if let Some(s) = self.separator {
+            column_format.insert(s, '|')
+        }
+
+        format!(
+            r"\left[\begin{{array}}{{{}}}{}\end{{array}}\right]",
+            column_format,
+            &self
+                .data
+                .iter()
+                .map(|row| {
+                    row.iter()
+                        .map(|elem| elem.to_latex())
+                        .collect::<Vec<_>>()
+                        .join(" & ")
+                })
+                .collect::<Vec<_>>()
+                .join(r"\\")
+        )
+    }
+
+    fn to_latex_single(&self) -> String {
+        self.to_latex()
+    }
+}
+
+impl<T: MatrixNumber> GuiDisplayable for Matrix<T> {
+    fn display_string(&self, locale: &Locale) -> String {
+        let (h, w) = self.get_shape();
+        let name = locale.get_translated("matrix");
+        format!("{name}::<{h}, {w}>")
+    }
+
+    fn to_shape(&self, ctx: &egui::Context, font_id: FontId, color: Color32) -> egui::Shape {
+        let (rows, cols) = self.get_shape();
+        let mut shapes: Vec<Vec<egui::Shape>> = self
+            .get_data()
+            .iter()
+            .map(|row| {
+                row.iter()
+                    .map(|element| element.to_shape(ctx, font_id.clone(), color))
+                    .collect()
+            })
+            .collect();
+
+        let mut row_heights = vec![0_f32; rows];
+        let mut column_widths = vec![0_f32; cols];
+        for (i, row) in shapes.iter().enumerate() {
+            for (j, shape) in row.iter().enumerate() {
+                let rect = shape.get_rect();
+                row_heights[i] = row_heights[i].max(rect.height());
+                column_widths[j] = column_widths[j].max(rect.width());
+            }
+        }
+
+        let mut upper_left = pos2(0., 0.);
+        for (i, row) in shapes.iter_mut().enumerate() {
+            for (j, shape) in row.iter_mut().enumerate() {
+                let rect = shape.get_rect().size();
+                shape.translate(
+                    egui::Align2::CENTER_CENTER
+                        .align_size_within_rect(
+                            rect,
+                            Rect {
+                                min: upper_left,
+                                max: pos2(
+                                    upper_left.x + column_widths[j],
+                                    upper_left.y + row_heights[i],
+                                ),
+                            },
+                        )
+                        .min
+                        .to_vec2(),
+                );
+                upper_left.x += column_widths[j] + MATRIX_HPADDING;
+            }
+            upper_left.x = 0.;
+            upper_left.y += row_heights[i] + MATRIX_VPADDING;
+        }
+
+        egui::Shape::Vec(shapes.into_iter().flat_map(|row| row.into_iter()).collect())
+    }
+}
+
+impl<T: MatrixNumber> Add for Matrix<T> {
+    type Output = Self;
+
+    fn add(self, rhs: Self) -> Self::Output {
+        self.checked_add(&rhs).expect("Addition failed!")
+    }
+}
+
+impl<T: MatrixNumber> Sub for Matrix<T> {
+    type Output = Self;
+
+    fn sub(self, rhs: Self) -> Self::Output {
+        self.checked_sub(&rhs).expect("Matrix subtraction failed!")
+    }
+}
+
+impl<T: MatrixNumber + Neg> Neg for Matrix<T>
+where
+    T: Neg<Output = T>,
+{
+    type Output = Self;
+
+    fn neg(self) -> Self::Output {
+        self.checked_operation(|a| Some(-a.clone()))
+            .expect("Negation failed!")
+    }
+}
+
+impl<T: MatrixNumber> Mul<Self> for Matrix<T> {
+    type Output = Self;
+
+    fn mul(self, rhs: Self) -> Self::Output {
+        self.checked_mul(&rhs)
+            .expect("Matrix multiplication failed!")
+    }
+}
+
+impl<T: MatrixNumber> Mul<T> for Matrix<T> {
+    type Output = Self;
+
+    fn mul(self, rhs: T) -> Self::Output {
+        self.checked_mul_scl(&rhs)
+            .expect("Matrix multiplication failed!")
+    }
+}
+
+impl<T: MatrixNumber> ToString for Matrix<T> {
+    fn to_string(&self) -> String {
+        self.data
+            .iter()
+            .map(|row| {
+                row.iter()
+                    .map(|elem| elem.to_string())
+                    .collect::<Vec<_>>()
+                    .join(" ")
+            })
+            .collect::<Vec<_>>()
+            .join("\n")
+    }
+}
+
+impl<T: MatrixNumber> From<Matrix<T>> for Vec<T> {
+    fn from(value: Matrix<T>) -> Self {
+        value.data.into_iter().flatten().collect()
+    }
+}
+
+/// Create a matrix row (vector) of Rational64 numbers passed as integers.
+/// # uses ri! macro.
+/// # used as helper macro for rm! macro.
+/// rv stands for Rational Vector.
+/// Example:
+/// ```
+/// # use jp2gmd_lib::{rv, ri};
+/// # use num_rational::Rational64;
+/// rv!(1, 2, 3); // Creates a row vector [ri!(1), ri!(2), ri!(3)]
+/// ```
+#[macro_export]
+macro_rules! rv {
+    ($($x:expr),+ $(,)?) => (
+        vec![
+            $(ri!($x)),+
+        ]
+    );
+}
+
+/// Create a matrix of Rational64 numbers passed as integers.
+/// # uses ri! and rv! macros.
+/// rm stands for Rational Matrix.
+/// Example:
+/// ```
+/// # use jp2gmd_lib::*;
+/// # use num_rational::Rational64;
+/// // Creates a matrix
+/// // | 1 2 3 |
+/// // | 4 5 6 |
+/// // values of the matrix are Rational64 numbers
+/// rm!(1, 2, 3; 4, 5, 6);
+/// ```
+#[macro_export]
+macro_rules! rm {
+    ($($($x:expr),+ $(,)?);+ $(;)?) => (
+        Matrix::<Rational64>::new_unsafe(vec![
+            $(rv!($($x),+)),+
+        ])
+    );
+}
+
+/// Create a matrix row (vector) of i32 numbers passed as integers.
+/// im stands for Integer Matrix.
+/// Example:
+/// ```
+/// # use jp2gmd_lib::{im, Matrix};
+/// // Creates a matrix
+/// // | 1 2 3 |
+/// // | 4 5 6 |
+/// // values of the matrix are i32 numbers
+/// im!(1, 2, 3; 4, 5, 6);
+/// ```
+#[macro_export]
+macro_rules! im {
+    ($($($x:expr),+ $(,)?);+ $(;)?) => (
+        Matrix::new_unsafe(vec![
+            $(vec![
+                $($x),+
+            ]),+
+        ])
+    );
+}
+
+#[cfg(test)]
+mod tests {
+    use crate::ri;
+    use num_rational::Rational64;
+
+    use super::*;
+
+    #[test]
+    fn test_matrix() {
+        let matrix = im![1, 2, 3; 4, 5, 6];
+        assert_eq!(
+            matrix.to_latex(),
+            r"\left[\begin{array}{ccc}1 & 2 & 3\\4 & 5 & 6\end{array}\right]"
+        );
+    }
+
+    #[test]
+    fn test_new_unsafe() {
+        let matrix = Matrix::new_unsafe(vec![vec![1, 2, 3], vec![4, 5, 6]]);
+        let matrix2 = Matrix::new(vec![vec![1, 2, 3], vec![4, 5, 6]]).unwrap();
+        assert_eq!(matrix, matrix2);
+    }
+
+    #[test]
+    fn test_new() {
+        let matrix = Matrix::new(vec![vec![1, 2, 3], vec![4, 5, 6]]).unwrap();
+        assert_eq!(matrix, im![1, 2, 3; 4, 5, 6]);
+        let invalid = Matrix::new(vec![vec![1, 2, 3], vec![4, 5]]);
+        assert!(invalid.is_err());
+    }
+
+    #[test]
+    fn test_is_valid() {
+        let matrix = Matrix::new_unsafe(vec![vec![1, 2, 3], vec![4, 5, 6]]);
+        assert!(matrix.is_valid());
+        let matrix = Matrix::new_unsafe(vec![vec![1, 2, 3], vec![4, 5]]);
+        assert!(!matrix.is_valid());
+    }
+
+    #[test]
+    fn test_filled() {
+        let matrix = Matrix::filled((4, 5), |x, y| ri!((x * y) as i64));
+        assert_eq!(
+            matrix,
+            rm![
+                0, 0, 0, 0, 0;
+                0, 1, 2, 3, 4;
+                0, 2, 4, 6, 8;
+                0, 3, 6, 9, 12;
+            ]
+        );
+        let matrix = Matrix::filled((4, 5), |x, y| ri!((x + y) as i64));
+        assert_eq!(
+            matrix,
+            rm![
+                0, 1, 2, 3, 4;
+                1, 2, 3, 4, 5;
+                2, 3, 4, 5, 6;
+                3, 4, 5, 6, 7;
+            ]
+        );
+    }
+
+    #[test]
+    fn test_zeros() {
+        let matrix = Matrix::zeros((4, 5));
+        assert_eq!(
+            matrix,
+            rm![
+                0, 0, 0, 0, 0;
+                0, 0, 0, 0, 0;
+                0, 0, 0, 0, 0;
+                0, 0, 0, 0, 0;
+            ]
+        );
+    }
+
+    #[test]
+    fn test_ones() {
+        let matrix = Matrix::ones((4, 5));
+        assert_eq!(
+            matrix,
+            rm![
+                1, 1, 1, 1, 1;
+                1, 1, 1, 1, 1;
+                1, 1, 1, 1, 1;
+                1, 1, 1, 1, 1;
+            ]
+        );
+    }
+
+    #[test]
+    fn test_identity() {
+        let matrix = Matrix::identity(4);
+        assert_eq!(
+            matrix,
+            rm![
+                1, 0, 0, 0;
+                0, 1, 0, 0;
+                0, 0, 1, 0;
+                0, 0, 0, 1;
+            ]
+        );
+    }
+
+    #[test]
+    fn test_empty() {
+        let matrix = Matrix::<Rational64>::empty();
+
+        assert_eq!(matrix, Matrix::zeros((0, 0)));
+        assert_eq!(matrix, Matrix::zeros((0, 7)));
+        assert_eq!(matrix, Matrix::zeros((2, 0)));
+
+        assert_eq!(matrix, Matrix::new_unsafe(vec![]));
+        assert_eq!(matrix, Matrix::new_unsafe(vec![vec![]]));
+    }
+
+    #[test]
+    fn test_simple_addition() {
+        let m = im![1, 2, 3; 4, 5, 6];
+        let n = im![1, 2, 3; 4, 5, 6];
+
+        let result = m + n;
+        assert_eq!(
+            result.to_latex(),
+            r"\left[\begin{array}{ccc}2 & 4 & 6\\8 & 10 & 12\end{array}\right]"
+        );
+    }
+
+    #[test]
+    fn test_simple_subtraction() {
+        let m = im![1, 2, 3; 4, 5, 6];
+        let n = im![1, 2, 3; 4, 5, 6];
+
+        let result = m - n;
+        assert_eq!(
+            result.to_latex(),
+            r"\left[\begin{array}{ccc}0 & 0 & 0\\0 & 0 & 0\end{array}\right]"
+        );
+    }
+
+    #[test]
+    fn test_simple_negation() {
+        let m = im![1, 2, 3; 4, 5, 6];
+
+        let result = -m;
+        assert_eq!(
+            result.to_latex(),
+            r"\left[\begin{array}{ccc}-1 & -2 & -3\\-4 & -5 & -6\end{array}\right]"
+        );
+    }
+
+    #[test]
+    fn test_simple_multiplication() {
+        let m = im![1, 2, 3; 4, 5, 6];
+        let n = im![1, 2; 3, 4; 5, 6];
+
+        let result = m * n;
+        assert_eq!(
+            result.to_latex(),
+            r"\left[\begin{array}{cc}22 & 28\\49 & 64\end{array}\right]"
+        );
+    }
+
+    #[test]
+    fn test_simple_multiplication_with_scalar() {
+        let m = im![1, 2, 3; 4, 5, 6];
+
+        let result = m * 2;
+        assert_eq!(
+            result.to_latex(),
+            r"\left[\begin{array}{ccc}2 & 4 & 6\\8 & 10 & 12\end{array}\right]"
+        );
+    }
+
+    #[test]
+    fn test_simple_multiplication_with_rational() {
+        let m = rm![1, 2, 3; 4, 5, 6];
+
+        let result = m * ri!(2);
+        assert_eq!(
+            result.to_latex(),
+            r"\left[\begin{array}{ccc}2 & 4 & 6\\8 & 10 & 12\end{array}\right]"
+        );
+    }
+
+    #[test]
+    fn test_simple_exponentiation() {
+        let m = im![1, 1; 1, 0];
+        assert_eq!(m.checked_pow(0).unwrap(), im![1, 0; 0, 1]);
+        assert_eq!(m.checked_pow(1).unwrap(), im![1, 1; 1, 0]);
+        assert_eq!(m.checked_pow(2).unwrap(), im![2, 1; 1, 1]);
+        assert_eq!(m.checked_pow(9).unwrap(), im![55, 34; 34, 21]);
+        assert_eq!(m.checked_pow(10).unwrap(), im![89, 55; 55, 34]);
+
+        let m2 = Matrix::new(vec![
+            vec![Rational64::new(1, 1), Rational64::new(1, 2)],
+            vec![Rational64::new(1, 3), Rational64::new(1, 4)],
+        ])
+        .context("Failed to create matrix - something is wrong with the test")
+        .unwrap();
+        assert_eq!(m2.checked_pow(0).unwrap(), rm![1, 0; 0, 1]);
+        assert_eq!(m2.checked_pow(1).unwrap(), m2);
+        assert_eq!(m2.checked_pow(2).unwrap(), m2.clone() * m2.clone());
+        assert_eq!(m2.checked_pow(3).unwrap(), m2.clone() * m2.clone() * m2);
+    }
+
+    #[test]
+    fn test_from_vec() {
+        let m = Matrix::from_vec(rv![1, 2, 3, 4, 5, 6], (2, 3)).expect("Failed to create matrix");
+        assert_eq!(
+            m,
+            rm![
+                1, 2, 3;
+                4, 5, 6;
+            ]
+        );
+
+        let m = Matrix::from_vec(vec![1, 2, 3, 4, 5, 6], (2, 3)).expect("Failed to create matrix");
+        assert_eq!(
+            m,
+            im![
+                1, 2, 3;
+                4, 5, 6;
+            ]
+        );
+    }
+
+    #[test]
+    fn test_reshape() {
+        let m = im![1, 2, 3, 4, 5, 6];
+        let reshape = |m: &Matrix<i64>, shape| m.reshape(shape).expect("Failed to reshape matrix");
+        assert_eq!(reshape(&m, (2, 3)), im![1, 2, 3; 4, 5, 6]);
+        assert_eq!(reshape(&m, (3, 2)), im![1, 2; 3, 4; 5, 6]);
+        assert_eq!(reshape(&m, (6, 1)), im![1; 2; 3; 4; 5; 6]);
+        assert_eq!(reshape(&m, (1, 6)), im![1, 2, 3, 4, 5, 6]);
+    }
+}
diff --git a/src/matrix_algorithms.rs b/src/matrix_algorithms.rs
new file mode 100644
index 0000000..3bec91e
--- /dev/null
+++ b/src/matrix_algorithms.rs
@@ -0,0 +1,352 @@
+use crate::matrices::Matrix;
+use crate::traits::{LaTeXable, MatrixNumber};
+use anyhow::Context;
+
+#[derive(Debug, Clone)]
+pub struct Aftermath<T: MatrixNumber> {
+    pub result: Matrix<T>,
+    pub steps: Vec<String>,
+}
+
+impl<T: MatrixNumber> Matrix<T> {
+    /// Returns a copy of the matrix which is in the row echelon form along
+    /// with all steps represented in human-friendly LaTeX notation.
+    /// Uses Gaussian elimination combined with some heuristics aiming at
+    /// making the number of steps as small as possible.
+    pub fn echelon(&self) -> anyhow::Result<Aftermath<T>> {
+        const CONTEXT: &str = "Calculations error!";
+
+        if self.is_empty() {
+            return Ok(Aftermath {
+                result: self.clone(),
+                steps: vec![],
+            });
+        }
+
+        let (rows, cols) = self.get_shape();
+
+        let mut steps = vec![self.to_latex()];
+        let mut c = 0;
+        let mut i = 0;
+        let mut data = self.deep_matrix_data_clone();
+
+        while c < cols && i < rows {
+            let mut j = i;
+            for k in i + 1..rows {
+                if Self::nice(&data[k][c]).context(CONTEXT)?
+                    < Self::nice(&data[j][c]).context(CONTEXT)?
+                {
+                    j = k;
+                }
+            }
+
+            if !data[j][c].is_zero() {
+                if i != j {
+                    data.swap(i, j);
+                    data = Self::push_step(
+                        &mut steps,
+                        format!(r"w_{{{}}} \leftrightarrow w_{{{}}}", i + 1, j + 1).as_str(),
+                        data,
+                        self.get_separator(),
+                    );
+                }
+
+                if !data[i][c].is_one() {
+                    let d = data[i][c].clone();
+                    for j in c..cols {
+                        data[i][j] = data[i][j].checked_div(&d).context(CONTEXT)?;
+                    }
+
+                    data = Self::push_step(
+                        &mut steps,
+                        format!(r"w_{{{}}} : {}", i + 1, d.to_latex_single()).as_str(),
+                        data,
+                        self.get_separator(),
+                    );
+                }
+
+                let mut step_ops: Vec<String> = Vec::new();
+                for j in 0..rows {
+                    if j != i && !data[j][c].is_zero() {
+                        let p = data[j][c].checked_div(&data[i][c]).context(CONTEXT)?;
+                        for k in c..cols {
+                            data[j][k] = data[j][k]
+                                .checked_sub(&data[i][k].checked_mul(&p).context(CONTEXT)?)
+                                .context(CONTEXT)?;
+                        }
+
+                        step_ops.push(format!(
+                            "w_{{{}}} {}w_{{{}}}",
+                            j + 1,
+                            Self::sub_coefficient_to_latex(&p).context(CONTEXT)?,
+                            i + 1
+                        ));
+                    }
+                }
+
+                if !step_ops.is_empty() {
+                    data = Self::push_step(
+                        &mut steps,
+                        format!(r"\substack{{{}}}", &step_ops.join(r"\\")).as_str(),
+                        data,
+                        self.get_separator(),
+                    );
+                }
+
+                i += 1;
+            }
+
+            c += 1;
+        }
+
+        Ok(Aftermath {
+            result: Self::new_unsafe(data),
+            steps,
+        })
+    }
+
+    /// Returns the inverse of the matrix along with all steps represented in
+    /// human-friendly LaTeX notation.
+    pub fn inverse(&self) -> anyhow::Result<Aftermath<T>> {
+        if self.is_empty() {
+            anyhow::bail!("Cannot calculate inverse of an empty matrix!");
+        }
+
+        let (rows, cols) = self.get_shape();
+        if rows != cols {
+            anyhow::bail!("Matrix is not square!");
+        }
+
+        let extended_matrix = self.clone().concat(Matrix::identity(rows))?;
+        let echelon_aftermath = extended_matrix.with_separator(Some(rows)).echelon()?;
+        let (left, right) = echelon_aftermath.result.split(rows)?;
+        if left != Matrix::identity(rows) {
+            anyhow::bail!("Matrix is not invertible!");
+        }
+
+        Ok(Aftermath {
+            result: right,
+            steps: echelon_aftermath.steps,
+        })
+    }
+
+    /// Returns the transpose of the matrix.
+    /// The transpose of a matrix is an operator which flips a matrix over its
+    /// diagonal, that is it switches the row and column indices of the matrix
+    /// by producing another matrix denoted as A^T.
+    pub fn transpose(&self) -> Matrix<T> {
+        let (rows, cols) = self.get_shape();
+        let mut data = Matrix::zeros((cols, rows)).consume();
+        for i in 0..rows {
+            for (j, col) in data.iter_mut().enumerate() {
+                col[i] = self.get_data()[i][j].clone();
+            }
+        }
+        Self::new_unsafe(data)
+    }
+
+    /// Returns a deep copy of matrix data vector.
+    fn deep_matrix_data_clone(&self) -> Vec<Vec<T>> {
+        self.get_data().iter().map(|row| row.to_vec()).collect()
+    }
+
+    /// Inserts the LaTeX representation of a single echelonization step with
+    /// transitions `transitions` and matrix containing `data` with separator
+    /// `separator` into `steps`.
+    fn push_step(
+        steps: &mut Vec<String>,
+        transitions: &str,
+        data: Vec<Vec<T>>,
+        separator: Option<usize>,
+    ) -> Vec<Vec<T>> {
+        let temp_matrix = Self::new_unsafe(data).with_separator(separator);
+        steps.push(format!(
+            r"\xrightarrow{{{}}} {}",
+            transitions,
+            temp_matrix.to_latex(),
+        ));
+        temp_matrix.consume()
+    }
+
+    /// Returns an integer representing how nice a row starting with the given
+    /// coefficient is to be used in a step of Gaussian elimination. The smaller
+    /// value means the better choice.
+    fn nice(coefficient: &T) -> Option<i64> {
+        if coefficient.is_zero() {
+            // should not be chosen if there is any row with nonzero leading coefficient
+            Some(1000)
+        } else if coefficient.is_one() {
+            // the easiest one, does not need to be changed
+            Some(0)
+        } else if (T::zero().checked_sub(coefficient)?).is_one() {
+            // we only have to negate all elements
+            Some(1)
+        } else {
+            // if there is no better choice...
+            Some(2)
+        }
+    }
+
+    /// How the substraction of an identifier multiplied by the given coefficient
+    /// should be printed in LaTeX.
+    /// For example, `sub_coefficient_to_latex(1)` returns `- `, as it is not
+    /// necessary to write `- 1w`, but `- w` is sufficient and
+    /// `sub_coefficient_to_latex(-5)` returns `+ 5`, because `+ 5w` is easier
+    /// to read than `- (-5)w`.
+    /// Assumes that the coefficient is nonzero.
+    fn sub_coefficient_to_latex(coefficient: &T) -> Option<String> {
+        if coefficient.is_one() {
+            Some("- ".to_string())
+        } else if (T::zero().checked_sub(coefficient)?).is_one() {
+            Some("+ ".to_string())
+        } else if coefficient.is_positive() {
+            Some(format!("- {}", coefficient.to_latex()))
+        } else if coefficient.is_negative() {
+            Some(format!(
+                "+ {}",
+                (T::zero().checked_sub(coefficient)?.to_latex())
+            ))
+        } else {
+            unreachable!("Should not be used for zero coefficient!")
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use crate::traits::LaTeXable;
+    use crate::{matrices::Matrix, ri, rm, rv};
+    use num_rational::Rational64;
+    use num_traits::One;
+
+    #[test]
+    fn test_echelon_rational1() {
+        let m = rm![-2, 1; 1, 1];
+        let expected = rm![1, 0; 0, 1];
+
+        let aftermath = m.echelon().unwrap();
+
+        assert_eq!(aftermath.result.to_latex(), expected.to_latex());
+        assert_eq!(
+            aftermath.steps,
+            vec![
+                r"\left[\begin{array}{cc}-2 & 1\\1 & 1\end{array}\right]",
+                r"\xrightarrow{w_{1} \leftrightarrow w_{2}} \left[\begin{array}{cc}1 & 1\\-2 & 1\end{array}\right]",
+                r"\xrightarrow{\substack{w_{2} + 2w_{1}}} \left[\begin{array}{cc}1 & 1\\0 & 3\end{array}\right]",
+                r"\xrightarrow{w_{2} : 3} \left[\begin{array}{cc}1 & 1\\0 & 1\end{array}\right]",
+                r"\xrightarrow{\substack{w_{1} - w_{2}}} \left[\begin{array}{cc}1 & 0\\0 & 1\end{array}\right]",
+            ]
+        );
+    }
+
+    #[test]
+    fn test_echelon_rational2() {
+        let m = rm![4, 3; 2, 1];
+        let expected = rm![1, 0; 0, 1];
+
+        let aftermath = m.echelon().unwrap();
+
+        assert_eq!(aftermath.result.to_latex(), expected.to_latex());
+        assert_eq!(
+            aftermath.steps,
+            vec![
+                r"\left[\begin{array}{cc}4 & 3\\2 & 1\end{array}\right]",
+                r"\xrightarrow{w_{1} : 4} \left[\begin{array}{cc}1 & \frac{3}{4}\\2 & 1\end{array}\right]",
+                r"\xrightarrow{\substack{w_{2} - 2w_{1}}} \left[\begin{array}{cc}1 & \frac{3}{4}\\0 & -\frac{1}{2}\end{array}\right]",
+                r"\xrightarrow{w_{2} : \left(-\frac{1}{2}\right)} \left[\begin{array}{cc}1 & \frac{3}{4}\\0 & 1\end{array}\right]",
+                r"\xrightarrow{\substack{w_{1} - \frac{3}{4}w_{2}}} \left[\begin{array}{cc}1 & 0\\0 & 1\end{array}\right]",
+            ]
+        );
+    }
+
+    #[test]
+    fn test_echelon_rational3() {
+        let id = rm![1, 0; 0, 1];
+
+        let aftermath = id.echelon().unwrap();
+
+        assert_eq!(aftermath.result.to_latex(), id.to_latex());
+        assert_eq!(
+            aftermath.steps,
+            vec![r"\left[\begin{array}{cc}1 & 0\\0 & 1\end{array}\right]"]
+        );
+    }
+
+    #[test]
+    fn test_echelon_rational4() {
+        let m = rm![1, -1, 1; 1, 1, -1; -1, 1, -1];
+        let expected = rm![1, 0, 0; 0, 1, -1; 0, 0, 0];
+
+        let aftermath = m.echelon().unwrap();
+
+        assert_eq!(aftermath.result.to_latex(), expected.to_latex());
+        assert_eq!(
+            aftermath.steps,
+            vec![
+                r"\left[\begin{array}{ccc}1 & -1 & 1\\1 & 1 & -1\\-1 & 1 & -1\end{array}\right]",
+                r"\xrightarrow{\substack{w_{2} - w_{1}\\w_{3} + w_{1}}} \left[\begin{array}{ccc}1 & -1 & 1\\0 & 2 & -2\\0 & 0 & 0\end{array}\right]",
+                r"\xrightarrow{w_{2} : 2} \left[\begin{array}{ccc}1 & -1 & 1\\0 & 1 & -1\\0 & 0 & 0\end{array}\right]",
+                r"\xrightarrow{\substack{w_{1} + w_{2}}} \left[\begin{array}{ccc}1 & 0 & 0\\0 & 1 & -1\\0 & 0 & 0\end{array}\right]",
+            ]
+        );
+    }
+
+    #[test]
+    fn test_inverse_rational1() {
+        let m = rm![1, 2; 3, 4];
+        let expected = Matrix::new(vec![
+            vec![(-2).into(), 1.into()],
+            vec![Rational64::new(3, 2), Rational64::new(-1, 2)],
+        ])
+        .unwrap();
+
+        let aftermath = m.inverse().unwrap();
+
+        assert_eq!(aftermath.result.to_latex(), expected.to_latex());
+        assert_eq!(
+            aftermath.steps,
+            vec![
+                r"\left[\begin{array}{cc|cc}1 & 2 & 1 & 0\\3 & 4 & 0 & 1\end{array}\right]",
+                r"\xrightarrow{\substack{w_{2} - 3w_{1}}} \left[\begin{array}{cc|cc}1 & 2 & 1 & 0\\0 & -2 & -3 & 1\end{array}\right]",
+                r"\xrightarrow{w_{2} : \left(-2\right)} \left[\begin{array}{cc|cc}1 & 2 & 1 & 0\\0 & 1 & \frac{3}{2} & -\frac{1}{2}\end{array}\right]",
+                r"\xrightarrow{\substack{w_{1} - 2w_{2}}} \left[\begin{array}{cc|cc}1 & 0 & -2 & 1\\0 & 1 & \frac{3}{2} & -\frac{1}{2}\end{array}\right]",
+            ]
+        );
+    }
+
+    #[test]
+    fn test_transpose_rational1() {
+        let m = rm![1, 2; 3, 4];
+        let expected = rm![1, 3; 2, 4];
+
+        let transposition = m.transpose();
+
+        assert_eq!(transposition, expected);
+    }
+
+    #[test]
+    fn test_transpose_rational2() {
+        let m = rm![1, 2, 3; 4, 5, 6];
+        let expected = rm![1, 4; 2, 5; 3, 6];
+
+        let transposition = m.transpose();
+
+        assert_eq!(transposition, expected);
+    }
+
+    #[test]
+    fn test_transpose_rational_null_matrix() {
+        let expected = Matrix::empty();
+        let test_null_matrix = |cols, rows| {
+            let m = Matrix::<Rational64>::filled((cols, rows), |_, _| Rational64::one());
+
+            let transposition = m.transpose();
+
+            assert_eq!(transposition, expected);
+        };
+
+        test_null_matrix(0, 0);
+        test_null_matrix(0, 7);
+        test_null_matrix(7, 0);
+    }
+}
diff --git a/src/parser.rs b/src/parser.rs
new file mode 100644
index 0000000..ebfdf05
--- /dev/null
+++ b/src/parser.rs
@@ -0,0 +1,689 @@
+use std::collections::VecDeque;
+use std::fmt::{Display, Formatter};
+
+use anyhow::{bail, Context};
+use num_traits::checked_pow;
+
+use crate::environment::{Environment, Identifier, Type};
+use crate::traits::MatrixNumber;
+
+#[derive(Debug, Clone, PartialEq, Eq)]
+enum Token {
+    Integer(u64),
+    Identifier(Identifier),
+    Operator(char),
+    LeftBracket,
+    RightBracket,
+}
+
+impl Display for Token {
+    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
+        match self {
+            Token::Integer(i) => write!(f, "int {i}"),
+            Token::Identifier(id) => write!(f, "id {}", id.to_string()),
+            Token::Operator(op) => write!(f, "operator \"{op}\""),
+            Token::LeftBracket => write!(f, "( bracket"),
+            Token::RightBracket => write!(f, ") bracket"),
+        }
+    }
+}
+
+struct Tokenizer<'a> {
+    raw: &'a str,
+}
+
+impl<'a> Tokenizer<'a> {
+    fn new(raw: &'a str) -> Self {
+        Tokenizer { raw }
+    }
+
+    fn next_token(&mut self) -> anyhow::Result<Option<Token>> {
+        self.raw = self.raw.trim_start();
+        if self.raw.is_empty() {
+            Ok(None)
+        } else if self.raw.starts_with('(') {
+            self.raw = &self.raw[1..];
+            Ok(Some(Token::LeftBracket))
+        } else if self.raw.starts_with(')') {
+            self.raw = &self.raw[1..];
+            Ok(Some(Token::RightBracket))
+        } else if self.raw.starts_with(|c| "+-*/^=".contains(c)) {
+            let op = self.raw.chars().next().unwrap();
+            self.raw = &self.raw[1..];
+            Ok(Some(Token::Operator(op)))
+        } else if self.raw.starts_with(|c: char| c.is_ascii_digit()) {
+            let i = self
+                .raw
+                .find(|c: char| !c.is_ascii_digit())
+                .unwrap_or(self.raw.len());
+            let num = &self.raw[..i];
+            self.raw = &self.raw[i..];
+            Ok(Some(Token::Integer(num.parse::<u64>()?)))
+        } else if let Some(rest) = self.raw.strip_prefix(Identifier::RESULT) {
+            self.raw = rest;
+            Ok(Some(Token::Identifier(Identifier::result())))
+        } else {
+            let i = self
+                .raw
+                .find(|c: char| !c.is_alphanumeric() && c != '_')
+                .unwrap_or(self.raw.len());
+            let id = Identifier::new(self.raw[..i].to_string())?;
+            self.raw = &self.raw[i..];
+            Ok(Some(Token::Identifier(id)))
+        }
+    }
+}
+
+#[derive(Clone, PartialEq, Eq)]
+enum WorkingToken<T: MatrixNumber> {
+    Type(Type<T>),
+    Function(Identifier),
+    UnaryOp(char),
+    BinaryOp(char),
+    LeftBracket,
+    RightBracket,
+}
+
+impl<T: MatrixNumber> Display for WorkingToken<T> {
+    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
+        match self {
+            WorkingToken::Type(_) => write!(f, "value token"),
+            WorkingToken::Function(_) => write!(f, "function token"),
+            WorkingToken::UnaryOp(op) => write!(f, "unary operator \"{op}\""),
+            WorkingToken::BinaryOp(op) => write!(f, "binary operator \"{op}\""),
+            WorkingToken::LeftBracket => write!(f, "( bracket"),
+            WorkingToken::RightBracket => write!(f, ") bracket"),
+        }
+    }
+}
+
+fn binary_op<T: MatrixNumber>(left: Type<T>, right: Type<T>, op: char) -> anyhow::Result<Type<T>> {
+    match op {
+        '+' => match (left, right) {
+            (Type::Matrix(l), Type::Matrix(r)) => Type::from_matrix_result(l.checked_add(&r)),
+            (Type::Scalar(l), Type::Scalar(r)) => Type::from_scalar_option(l.checked_add(&r)),
+            _ => bail!("Adding scalar to matrix is not supported!"),
+        },
+        '-' => match (left, right) {
+            (Type::Matrix(l), Type::Matrix(r)) => Type::from_matrix_result(l.checked_sub(&r)),
+            (Type::Scalar(l), Type::Scalar(r)) => Type::from_scalar_option(l.checked_sub(&r)),
+            _ => bail!("Substraction of scalar and matrix is not supported!"),
+        },
+        '*' => match (left, right) {
+            (Type::Matrix(l), Type::Matrix(r)) => Type::from_matrix_result(l.checked_mul(&r)),
+            (Type::Scalar(l), Type::Scalar(r)) => Type::from_scalar_option(l.checked_mul(&r)),
+            (Type::Matrix(l), Type::Scalar(r)) => Type::from_matrix_result(l.checked_mul_scl(&r)),
+            (Type::Scalar(l), Type::Matrix(r)) => Type::from_matrix_result(r.checked_mul_scl(&l)),
+        },
+        '/' => match (left, right) {
+            (Type::Scalar(l), Type::Scalar(r)) => {
+                if !r.is_zero() {
+                    Type::from_scalar_option(l.checked_div(&r))
+                } else {
+                    bail!("Division by zero!")
+                }
+            }
+            (Type::Matrix(_), Type::Matrix(_)) => {
+                bail!("WTF dividing by matrix? You should use the `inverse` function instead!")
+            }
+            (Type::Matrix(_), Type::Scalar(_)) => {
+                bail!("Diving matrix by scalar is not supported yet...")
+            }
+            (Type::Scalar(_), Type::Matrix(_)) => {
+                bail!("Diving scalar by matrix does not make sense!")
+            }
+        },
+        '^' => {
+            if let Type::Scalar(exp) = right {
+                let exp = exp
+                    .to_usize()
+                    .context("Exponent should be a nonnegative integer.")?;
+                match left {
+                    Type::Scalar(base) => Type::from_scalar_option(checked_pow(base, exp)),
+                    Type::Matrix(base) => Type::from_matrix_result(base.checked_pow(exp)),
+                }
+            } else {
+                bail!("Exponent cannot be a matrix!");
+            }
+        }
+        _ => unimplemented!(),
+    }
+}
+
+fn unary_op<T: MatrixNumber>(arg: Type<T>, op: char) -> anyhow::Result<Type<T>> {
+    match op {
+        '+' => Ok(arg),
+        '-' => match arg {
+            Type::Matrix(m) => Type::from_matrix_result(m.checked_neg()),
+            Type::Scalar(s) => Type::from_scalar_option(T::zero().checked_sub(&s)),
+        },
+        _ => unimplemented!(),
+    }
+}
+
+/*
+<digit>      ::= "0" | "1" | ... | "9"
+<integer>    ::= <digit>+
+<letter>     ::= "a" | "ą" | "b" | ... | "ż"
+<identifier> ::= (<letter> | "_") (<letter> | <digit> | "_")* | "$"
+<unary_op>   ::= "+" | "-"
+<binary_op>  ::= "+" | "-" | "*" | "/"
+<expr>       ::= <integer> | <identifier> | <expr> <binary_op> <expr>
+               | "(" <expr> ")" | <unary_op> <expr> | <identifier> "(" <expr> ")"
+ */
+pub fn parse_expression<T: MatrixNumber>(
+    raw: &str,
+    env: &Environment<T>,
+) -> anyhow::Result<Type<T>> {
+    let mut tokenizer = Tokenizer::new(raw);
+    let mut operators: VecDeque<WorkingToken<T>> = VecDeque::new();
+    let mut outputs: VecDeque<WorkingToken<T>> = VecDeque::new();
+    let mut prev_token = None;
+
+    fn precedence(c: &char) -> u8 {
+        match c {
+            '+' | '-' => 0,
+            '*' | '/' => 1,
+            '^' => 2,
+            _ => unreachable!(),
+        }
+    }
+
+    fn validate_neighbours<T: MatrixNumber>(
+        previous: &Option<&WorkingToken<T>>,
+        current: &Token,
+    ) -> bool {
+        match current {
+            Token::Integer(_) | Token::Identifier(_) | Token::LeftBracket => matches!(
+                previous,
+                None | Some(WorkingToken::LeftBracket)
+                    | Some(WorkingToken::BinaryOp(_))
+                    | Some(WorkingToken::UnaryOp(_))
+                    | Some(WorkingToken::Function(_))
+            ),
+            Token::Operator(_) => matches!(
+                previous,
+                None | Some(WorkingToken::RightBracket)
+                    | Some(WorkingToken::Type(_))
+                    | Some(WorkingToken::BinaryOp(_))
+                    | Some(WorkingToken::LeftBracket)
+            ),
+            Token::RightBracket => matches!(
+                previous,
+                Some(WorkingToken::RightBracket) | Some(WorkingToken::Type(_))
+            ),
+        }
+    }
+
+    while let Some(token) = tokenizer.next_token()? {
+        if !validate_neighbours(&prev_token, &token) {
+            match prev_token {
+                Some(prev_token) => {
+                    bail!("Invalid expression! The {token} cannot follow {prev_token}")
+                }
+                None => bail!("Invalid expression! The {token} cannot be the first token!"),
+            }
+        }
+
+        prev_token = match &token {
+            Token::Integer(num) => {
+                outputs.push_back(WorkingToken::Type(Type::Scalar(
+                    T::from_u64(*num).context(format!(
+                        "Number conversion failed! {num:?} cannot be parsed into {:?}",
+                        std::any::type_name::<T>()
+                    ))?,
+                )));
+                outputs.back()
+            }
+            Token::Identifier(id) => {
+                if let Some(value) = env.get_value(id) {
+                    outputs.push_back(WorkingToken::Type(value.clone()));
+                    outputs.back()
+                } else if env.get_function(id).is_some() {
+                    operators.push_front(WorkingToken::Function(id.clone()));
+                    operators.front()
+                } else {
+                    bail!(
+                        "Undefined identifier! Object \"{}\" is unknown.",
+                        id.to_string()
+                    )
+                }
+            }
+            Token::LeftBracket => {
+                operators.push_front(WorkingToken::LeftBracket);
+                operators.front()
+            }
+            Token::RightBracket => {
+                let mut left_found = false;
+                while let Some(op) = operators.pop_front() {
+                    if matches!(op, WorkingToken::LeftBracket) {
+                        left_found = true;
+                        break;
+                    }
+                    outputs.push_back(op);
+                }
+                if !left_found {
+                    bail!("Mismatched brackets!");
+                }
+                if let Some(op) = operators.pop_front() {
+                    match op {
+                        WorkingToken::UnaryOp(_) | WorkingToken::Function(_) => {
+                            outputs.push_back(op)
+                        }
+                        _ => operators.push_front(op),
+                    }
+                }
+                Some(&WorkingToken::RightBracket)
+            }
+            Token::Operator(op)
+                if matches!(
+                    prev_token,
+                    None | Some(WorkingToken::LeftBracket) | Some(WorkingToken::BinaryOp(_))
+                ) =>
+            {
+                if "+-".contains(*op) {
+                    operators.push_front(WorkingToken::UnaryOp(*op));
+                    operators.front()
+                } else {
+                    bail!("Operator {op} cannot be used as a unary operator.")
+                }
+            }
+            Token::Operator(op) if "+-*/^".contains(*op) => {
+                while let Some(stack_token) = operators.pop_front() {
+                    if let WorkingToken::BinaryOp(stack_op) = stack_token {
+                        if precedence(&stack_op) >= precedence(op) {
+                            outputs.push_back(WorkingToken::BinaryOp(stack_op));
+                        } else {
+                            operators.push_front(WorkingToken::BinaryOp(stack_op));
+                            break;
+                        }
+                    } else if let WorkingToken::UnaryOp(stack_op) = stack_token {
+                        outputs.push_back(WorkingToken::UnaryOp(stack_op))
+                    } else {
+                        operators.push_front(stack_token);
+                        break;
+                    }
+                }
+                operators.push_front(WorkingToken::BinaryOp(*op));
+                operators.front()
+            }
+            Token::Operator(_) => bail!("Assignment is not allowed in expressions!"),
+        };
+    }
+
+    while let Some(token) = operators.pop_front() {
+        if matches!(token, WorkingToken::LeftBracket) {
+            bail!("Mismatched brackets!");
+        }
+        outputs.push_back(token);
+    }
+
+    let mut val_stack: VecDeque<Type<T>> = VecDeque::new();
+    while let Some(token) = outputs.pop_front() {
+        match token {
+            WorkingToken::Type(value) => val_stack.push_front(value),
+            WorkingToken::BinaryOp(op) => {
+                let right = val_stack.pop_front().context("Invalid expression!")?;
+                let left = val_stack.pop_front().context("Invalid expression!")?;
+                val_stack.push_front(binary_op(left, right, op)?)
+            }
+            WorkingToken::UnaryOp(op) => {
+                let arg = val_stack.pop_front().context("Invalid expression!")?;
+                val_stack.push_front(unary_op(arg, op)?);
+            }
+            WorkingToken::Function(id) => {
+                let arg = val_stack.pop_front().context("Invalid expression!")?;
+                val_stack.push_front(env.get_function(&id).unwrap()(arg)?);
+            }
+            _ => unreachable!(),
+        }
+    }
+
+    val_stack.pop_front().context("Invalid expression!")
+}
+
+/*
+<inst> ::= <identifier> = <expr> | <expr>
+ */
+pub fn parse_instruction<T: MatrixNumber>(
+    raw: &str,
+    env: &mut Environment<T>,
+) -> anyhow::Result<Identifier> {
+    let mut tokenizer = Tokenizer::new(raw);
+    if let Some(Token::Identifier(id)) = tokenizer.next_token()? {
+        if tokenizer.next_token()? == Some(Token::Operator('=')) {
+            let value = parse_expression(tokenizer.raw, env)?;
+            env.insert(id.clone(), value);
+            return Ok(id);
+        }
+    }
+
+    let value = parse_expression(raw, env)?;
+    env.insert(Identifier::result(), value);
+    Ok(Identifier::result())
+}
+
+#[cfg(test)]
+mod tests {
+    use crate::matrices::Matrix;
+    use num_rational::Rational64;
+
+    use crate::im;
+
+    use super::*;
+
+    #[test]
+    fn test_expression_simple() {
+        let mut env = Environment::new();
+        env.insert(Identifier::new("a".to_string()).unwrap(), Type::Scalar(2));
+        env.insert(Identifier::new("b".to_string()).unwrap(), Type::Scalar(3));
+        assert_eq!(parse_expression("a+b*b", &env).unwrap(), Type::Scalar(11));
+        assert_eq!(parse_expression("(a+b)*b", &env).unwrap(), Type::Scalar(15));
+    }
+
+    #[test]
+    fn test_expression_numbers() {
+        let env = Environment::new();
+
+        let test_expr = |raw, a, b| {
+            assert_eq!(
+                parse_expression(raw, &env).unwrap(),
+                Type::Scalar(Rational64::new(a, b))
+            )
+        };
+
+        test_expr("2+2", 4, 1);
+        test_expr("(2-6*9)/5", -52, 5);
+        test_expr("2-6*9/5", -44, 5);
+        test_expr("(2-6)*9/5", -36, 5);
+        test_expr("(2-6*9/5)", -44, 5);
+        test_expr("1/2^8", 1, 256);
+    }
+
+    #[test]
+    fn test_expression_unary() {
+        let mut env = Environment::new();
+        env.insert(Identifier::new("x".to_string()).unwrap(), Type::Scalar(-5));
+        let a = im![1, 2, 3; 4, 5, 6];
+        env.insert(
+            Identifier::new("A".to_string()).unwrap(),
+            Type::Matrix(a.clone()),
+        );
+
+        let test_expr = |raw, expected| assert_eq!(parse_expression(raw, &env).unwrap(), expected);
+
+        test_expr("-1", Type::Scalar(-1));
+        test_expr("-x", Type::Scalar(5));
+        test_expr("-1+3", Type::Scalar(2));
+        test_expr("-(1+3)", Type::Scalar(-4));
+        test_expr("2+(-2)", Type::Scalar(0));
+        test_expr("1 - -1", Type::Scalar(2));
+        test_expr("+1 + +1", Type::Scalar(2));
+        test_expr("2 * -3", Type::Scalar(-6));
+        test_expr("+2 * +3", Type::Scalar(6));
+
+        test_expr("-A", Type::Matrix(a.checked_neg().unwrap()));
+        test_expr("+A + -A - -A", Type::Matrix(a.clone()));
+        test_expr("+A - +A + +A", Type::Matrix(a));
+    }
+
+    #[test]
+    fn test_expression_identifiers() {
+        let mut env = Environment::new();
+        env.insert(
+            Identifier::new("_i_love_rust_69".to_string()).unwrap(),
+            Type::Scalar(69),
+        );
+        env.insert(
+            Identifier::new("_i_love_rust_42".to_string()).unwrap(),
+            Type::Scalar(42),
+        );
+        assert_eq!(
+            parse_expression("_i_love_rust_69-_i_love_rust_42", &env).unwrap(),
+            Type::Scalar(27)
+        );
+    }
+
+    #[test]
+    fn test_expression_whitespaces() {
+        let mut env = Environment::new();
+        env.insert(Identifier::new("a".to_string()).unwrap(), Type::Scalar(2));
+        assert_eq!(
+            parse_expression("a + 1+2\t*a", &env).unwrap(),
+            Type::Scalar(7)
+        );
+    }
+
+    #[test]
+    fn test_expression_matrices() {
+        let mut env = Environment::new();
+        let a = im![1, 2, 3; 4, 5, 6];
+        let b = im![1, 2; 3, 4; 5, 6];
+        let i2 = im![1, 0; 0, 1];
+
+        env.insert(
+            Identifier::new("A".to_string()).unwrap(),
+            Type::Matrix(a.clone()),
+        );
+        env.insert(
+            Identifier::new("B".to_string()).unwrap(),
+            Type::Matrix(b.clone()),
+        );
+        env.insert(
+            Identifier::new("Id_2".to_string()).unwrap(),
+            Type::Matrix(i2.clone()),
+        );
+
+        let test_expr = |raw, expected| {
+            assert_eq!(parse_expression(raw, &env).unwrap(), Type::Matrix(expected))
+        };
+
+        test_expr("A+A", a.clone() + a.clone());
+        test_expr("A*B", a.clone() * b.clone());
+        test_expr("A*B*Id_2", a * b * i2.clone());
+        test_expr("Id_2-Id_2", i2.clone() - i2);
+    }
+
+    #[test]
+    fn test_expression_matrices_scalar() {
+        let mut env = Environment::new();
+        let a = im![1, 2, 3; 4, 5, 6];
+        let b = im![1, 2; 3, 4; 5, 6];
+        let c = im![2, 3; 0, -1];
+        let i2 = im![1, 0; 0, 1];
+
+        env.insert(
+            Identifier::new("A".to_string()).unwrap(),
+            Type::Matrix(a.clone()),
+        );
+        env.insert(
+            Identifier::new("B".to_string()).unwrap(),
+            Type::Matrix(b.clone()),
+        );
+        env.insert(
+            Identifier::new("C".to_string()).unwrap(),
+            Type::Matrix(c.clone()),
+        );
+        env.insert(
+            Identifier::new("Id_2".to_string()).unwrap(),
+            Type::Matrix(i2.clone()),
+        );
+        env.insert(Identifier::new("a".to_string()).unwrap(), Type::Scalar(2));
+
+        let test_expr = |raw, expected| {
+            assert_eq!(parse_expression(raw, &env).unwrap(), Type::Matrix(expected))
+        };
+
+        test_expr("A+a*A", a.clone() + a.clone() * 2);
+        test_expr("A*2*B", a.clone() * b.clone() * 2);
+        test_expr("A*B*a*Id_2", a * b * i2.clone() * 2);
+        test_expr("2*Id_2-Id_2", i2.clone() * 2 - i2.clone());
+        test_expr("C^0", i2);
+        test_expr("C^1", c.clone());
+        test_expr("C^2", c.clone() * c);
+    }
+
+    #[test]
+    fn test_nested_multiplication() {
+        let mut env = Environment::new();
+        let fib = im![0, 1; 1, 1];
+
+        env.insert(Identifier::new("A".to_string()).unwrap(), Type::Matrix(fib));
+
+        let test_expr = |raw, expected| {
+            assert_eq!(parse_expression(raw, &env).unwrap(), Type::Matrix(expected))
+        };
+
+        test_expr("A^10", im![34, 55; 55, 89]);
+        test_expr("A*A*A*A*A*A*A*A*A*A", im![34, 55; 55, 89]);
+        test_expr("A*A*A*A*(A*A*A)*A*A*A", im![34, 55; 55, 89]);
+        test_expr("A*A*A*A*(A*(A*A))*A*A*A", im![34, 55; 55, 89]);
+        test_expr("A*A*(A*A)*(A*(A*A))*A*A*A", im![34, 55; 55, 89]);
+    }
+
+    #[test]
+    fn test_invalid_expressions() {
+        let env = Environment::<i64>::new();
+
+        let test_invalid_expr = |raw| assert!(matches!(parse_expression(raw, &env), Err(_)));
+
+        test_invalid_expr("2**3");
+        test_invalid_expr("2*(3*)5");
+        test_invalid_expr("3*()4");
+        test_invalid_expr("(2+(3-)3)");
+        test_invalid_expr("()");
+    }
+
+    #[test]
+    fn test_assignments_fibonacci() {
+        let mut env = Environment::<i64>::new();
+
+        let mut exec = |raw| parse_instruction(raw, &mut env).unwrap();
+
+        exec("a = 0");
+        exec("b = 1");
+        for _ in 0..10 {
+            exec("c = a + b");
+            exec("a = b");
+            exec("b = c");
+        }
+
+        assert_eq!(
+            *env.get_value(&Identifier::new("b".to_string()).unwrap())
+                .unwrap(),
+            Type::<i64>::Scalar(89)
+        );
+    }
+
+    #[test]
+    fn test_expression_as_instruction() {
+        let mut env = Environment::<i64>::new();
+
+        let mut exec = |raw| parse_instruction(raw, &mut env).unwrap();
+
+        exec("2 + 2");
+        exec("a = $ ^ $");
+
+        assert_eq!(
+            *env.get_value(&Identifier::new("a".to_string()).unwrap())
+                .unwrap(),
+            Type::<i64>::Scalar(256)
+        );
+    }
+
+    #[test]
+    fn test_expression_functions() {
+        let mut env = Environment::new();
+
+        let a = im![1, 2, 3; 4, 5, 6];
+        let at = im![1, 4; 2, 5; 3, 6];
+        let b = im![1, 2; 3, 4];
+
+        env.insert(Identifier::new("A".to_string()).unwrap(), Type::Matrix(a));
+        env.insert(
+            Identifier::new("B".to_string()).unwrap(),
+            Type::Matrix(b.clone()),
+        );
+
+        assert_eq!(
+            parse_expression("transpose(A)", &env).unwrap(),
+            Type::Matrix(at)
+        );
+        assert_eq!(
+            parse_expression("identity(4)", &env).unwrap(),
+            Type::Matrix(Matrix::identity(4))
+        );
+        assert_eq!(
+            parse_expression("inverse(B)", &env).unwrap(),
+            Type::Matrix(b.inverse().unwrap().result)
+        );
+    }
+
+    #[test]
+    fn test_nested_functions() {
+        let mut env = Environment::new();
+
+        let a = im![1, 2, 3; 4, 5, 6];
+        let att = im![1, 2, 3; 4, 5, 6];
+
+        env.insert(Identifier::new("A".to_string()).unwrap(), Type::Matrix(a));
+
+        assert_eq!(
+            parse_expression("transpose(transpose(A))", &env).unwrap(),
+            Type::Matrix(att)
+        )
+    }
+
+    #[test]
+    fn test_expr_with_function() {
+        let mut env = Environment::new();
+
+        let a = im![1, 2, 3; 4, 5, 6];
+        let b = im![1, 2; 3, 4];
+
+        env.insert(Identifier::new("A".to_string()).unwrap(), Type::Matrix(a));
+        env.insert(
+            Identifier::new("B".to_string()).unwrap(),
+            Type::Matrix(b.clone()),
+        );
+
+        assert_eq!(
+            parse_expression("transpose(A) * B", &env).unwrap(),
+            Type::Matrix(im![13, 18; 17, 24; 21, 30])
+        );
+    }
+
+    #[test]
+    fn test_expr_in_function() {
+        let mut env = Environment::new();
+
+        let a = im![1, 2, 3; 4, 5, 6];
+        let i = Matrix::identity(2);
+        let at = im![1, 4; 2, 5; 3, 6];
+
+        env.insert(Identifier::new("A".to_string()).unwrap(), Type::Matrix(a));
+        env.insert(Identifier::new("I".to_string()).unwrap(), Type::Matrix(i));
+
+        assert_eq!(
+            parse_expression("transpose(I * A)", &env).unwrap(),
+            Type::Matrix(at)
+        );
+    }
+
+    #[test]
+    fn test_complex_nested_function_with_expr() {
+        let mut env = Environment::new();
+
+        let a = im![1, 2, 3; 4, 5, 6];
+
+        env.insert(Identifier::new("A".to_string()).unwrap(), Type::Matrix(a));
+
+        assert_eq!(
+            parse_expression(
+                "transpose(transpose(identity(2137 - 2135 + 1 - 1 + (42 - 420) * 0) * A) + transpose(identity(2) * A))",
+                &env
+            ).unwrap(),
+            Type::Matrix(im![2, 4, 6; 8, 10, 12])
+        );
+    }
+}
diff --git a/src/rationals.rs b/src/rationals.rs
new file mode 100644
index 0000000..a0ec972
--- /dev/null
+++ b/src/rationals.rs
@@ -0,0 +1,152 @@
+use crate::{
+    constants::{
+        FRACTION_FONT_SIZE_RATIO, FRACTION_HMARGIN, FRACTION_LINE_WIDTH, FRACTION_VMARGIN,
+    },
+    traits::{BoxedShape, GuiDisplayable, LaTeXable},
+};
+use egui::{pos2, vec2, FontId, Rect, Rounding, Shape};
+use num_rational::Rational64;
+use num_traits::sign::Signed;
+
+impl LaTeXable for Rational64 {
+    fn to_latex(&self) -> String {
+        match self.is_integer() {
+            true => format!("{}", self.numer()),
+            false => format!(
+                "{}\\frac{{{}}}{{{}}}",
+                if self.is_positive() { "" } else { "-" },
+                self.numer().unsigned_abs(),
+                self.denom().unsigned_abs()
+            ),
+        }
+    }
+
+    fn to_latex_single(&self) -> String {
+        if self.is_positive() {
+            self.to_latex()
+        } else {
+            format!(r"\left({}\right)", self.to_latex())
+        }
+    }
+}
+
+impl GuiDisplayable for Rational64 {
+    fn display_string(&self, _locale: &crate::locale::Locale) -> String {
+        self.to_string()
+    }
+
+    fn to_shape(
+        &self,
+        ctx: &egui::Context,
+        font_id: egui::FontId,
+        color: egui::Color32,
+    ) -> egui::Shape {
+        if self.is_integer() {
+            self.numer().to_shape(ctx, font_id, color)
+        } else {
+            let mut num_shape = self.numer().to_shape(
+                ctx,
+                FontId {
+                    size: font_id.size * FRACTION_FONT_SIZE_RATIO,
+                    family: font_id.family.clone(),
+                },
+                color,
+            );
+            let mut denom_shape = self.denom().to_shape(
+                ctx,
+                FontId {
+                    size: font_id.size * FRACTION_FONT_SIZE_RATIO,
+                    family: font_id.family,
+                },
+                color,
+            );
+
+            let num_rect = num_shape.get_rect();
+            let denom_rect = denom_shape.get_rect();
+            let single_width = num_rect.width().max(denom_rect.width()) + 2. * FRACTION_HMARGIN;
+
+            num_shape.translate(vec2((single_width - num_rect.width()) / 2., 0.));
+            denom_shape.translate(vec2(
+                (single_width - denom_rect.width()) / 2.,
+                num_rect.height() + 2. * FRACTION_VMARGIN + FRACTION_LINE_WIDTH,
+            ));
+
+            let line_shape = Shape::rect_filled(
+                Rect {
+                    min: pos2(0., num_rect.height() + FRACTION_VMARGIN),
+                    max: pos2(
+                        single_width,
+                        num_rect.height() + FRACTION_VMARGIN + FRACTION_LINE_WIDTH,
+                    ),
+                },
+                Rounding::none(),
+                color,
+            );
+
+            Shape::Vec(vec![num_shape, denom_shape, line_shape])
+        }
+    }
+}
+
+// Macro to generate a Rational64 from a integer.
+// `ri!(1)` is equivalent to `Rational64::from_integer(1)`, but shorter.
+// ri stands for Rational from Integer.
+#[macro_export]
+macro_rules! ri {
+    ($($t:expr),*) => {
+        $(
+            Rational64::from_integer($t)
+        )*
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::traits::MatrixNumber;
+    use num_rational::Rational64;
+
+    #[test]
+    fn test_simple_fraction() {
+        let r = Rational64::new(7, 21);
+        assert_eq!(r.to_latex(), "\\frac{1}{3}");
+    }
+
+    #[test]
+    fn test_negative_fraction() {
+        let r = Rational64::new(-42, 2 * 42);
+        assert_eq!(r.to_latex(), "-\\frac{1}{2}");
+    }
+
+    #[test]
+    fn test_negative_denominator() {
+        let r = Rational64::new(151, -2 * 151);
+        assert_eq!(r.to_latex(), "-\\frac{1}{2}");
+    }
+
+    #[test]
+    fn test_negative_numerator_and_denominator() {
+        let r = Rational64::new(-10, -20);
+        assert_eq!(r.to_latex(), "\\frac{1}{2}");
+    }
+
+    #[test]
+    fn test_fraction_normalization() {
+        let r = Rational64::new(4, 1);
+        assert_eq!(r.to_latex(), "4");
+    }
+
+    #[test]
+    fn test_fraction_zero() {
+        let r = Rational64::new(0, 1);
+        assert_eq!(r.to_latex(), "0");
+    }
+
+    #[test]
+    fn test_matrix_num() {
+        fn test<T: MatrixNumber>(_: T) {}
+
+        let r = Rational64::new(4, 1);
+        test(r);
+    }
+}
diff --git a/src/traits.rs b/src/traits.rs
new file mode 100644
index 0000000..9a141ca
--- /dev/null
+++ b/src/traits.rs
@@ -0,0 +1,130 @@
+use eframe::epaint::TextShape;
+use egui::{pos2, Color32, FontId, Shape};
+use num_traits::{
+    CheckedAdd, CheckedDiv, CheckedMul, CheckedSub, FromPrimitive, Signed, ToPrimitive,
+};
+use std::str::FromStr;
+
+use crate::locale::Locale;
+use num_traits::Num;
+
+pub trait LaTeXable {
+    fn to_latex(&self) -> String;
+    fn to_latex_single(&self) -> String {
+        self.to_latex()
+    }
+}
+
+pub trait CheckedOps: CheckedAdd + CheckedSub + CheckedMul + CheckedDiv {}
+
+impl<T> CheckedOps for T where T: CheckedAdd + CheckedSub + CheckedMul + CheckedDiv {}
+
+pub trait GuiDisplayable {
+    fn display_string(&self, locale: &Locale) -> String;
+
+    fn to_shape(&self, ctx: &egui::Context, font_id: FontId, color: Color32) -> Shape;
+}
+
+pub trait BoxedShape {
+    fn get_rect(&self) -> egui::Rect;
+}
+
+impl BoxedShape for Shape {
+    fn get_rect(&self) -> egui::Rect {
+        match self {
+            Shape::Text(text_shape) => text_shape.galley.rect,
+            _ => self.visual_bounding_rect(),
+        }
+    }
+}
+
+pub trait MatrixNumber:
+    Num
+    + CheckedOps
+    + FromPrimitive
+    + ToPrimitive
+    + Signed
+    + LaTeXable
+    + GuiDisplayable
+    + Clone
+    + FromStr
+    + ToString
+{
+}
+
+impl<T> MatrixNumber for T where
+    T: Num
+        + CheckedOps
+        + FromPrimitive
+        + ToPrimitive
+        + Signed
+        + LaTeXable
+        + GuiDisplayable
+        + Clone
+        + FromStr
+        + ToString
+{
+}
+
+#[macro_export]
+macro_rules! to_string_to_latex {
+    ($($t:ty),*) => {
+        $(
+            impl LaTeXable for $t {
+                fn to_latex(&self) -> String {
+                    self.to_string()
+                }
+            }
+        )*
+    }
+}
+
+#[macro_export]
+macro_rules! gui_displayable_for_primitive {
+    ($($t:ty),*) => {
+        $(
+            impl GuiDisplayable for $t {
+                fn display_string(&self, _locale: &Locale) -> String {
+                    self.to_string()
+                }
+
+                fn to_shape(&self, ctx: &egui::Context, font_id: FontId, color: Color32) -> Shape {
+                    let text_shape = TextShape::new(
+                        pos2(0., 0.),
+                        ctx.fonts(|f| f.layout_no_wrap(self.to_string(), font_id, color)),
+                    );
+                    Shape::Text(text_shape)
+                }
+            }
+        )*
+    }
+}
+
+// We add LaTeX support for all the basic types
+to_string_to_latex!(i8, i16, i32, i64, i128, isize);
+
+// We add display support for all the basic types
+gui_displayable_for_primitive!(i8, i16, i32, i64, i128, isize);
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_matrix_number() {
+        fn test<T: MatrixNumber>() {
+            let t = T::one();
+            assert_eq!(t.to_latex(), t.to_string());
+        }
+
+        macro_rules! test_matrix_number {
+            ($($t:ty),*) => {
+                $(
+                    test::<$t>();
+                )*
+            }
+        }
+
+        test_matrix_number!(i8, i16, i32, i64, i128, isize);
+    }
+}