Egison Math Notebook

Number Theory
Elementary Number Theory	Tribonacci Number Euler's Totient Function
Quadratic Field	Gaussian Primes Eisenstein Primes

Algebra
Algebraic Equation	Quadratic Equation Cubic Equation Quartic Equation
Root of Unity	5th Root of Unity 7th Root of Unity 9th Root of Unity 17th Root of Unity

Mathematical Analysis
Derivative	Order of Partial Differentiation Laplacian, Hessian, and Jacobian Laplacian in Polar Coordinates Laplacian in Spherical Coordinates
Series	Euler's Formula
Fourier Analysis	Fourier Series Leibniz Formula

Geometry
Circular functions	Trigonometric Identities
Riemannian Geometry	Gaussian Curvature Riemann Curvature Tensor of `S^2` Riemann Curvature Tensor of `S^3` Riemann Curvature Tensor of `S^4` Riemann Curvature Tensor of `S^5` Riemann Curvature Tensor of `S^7` Riemann Curvature Tensor of `T^2` Riemann Curvature Tensor of `S^2 xx S^3` Schwarzschild Metric Friedmann–Lemaître–Robertson–Walker Metric
Differential Forms	Wedge Product Exterior Derivative Hodge Operator of `E^3` Hodge Operator of Minkowski Space Hodge Laplacian of Polar Coordinates Hodge Laplacian of Spherical Coordinates Curvature Form
Application to Physics	Vector Analysis Yang-Mills Equation of `U(1)` Gauge Theory
Characteristic Classes	Euler Form of `S^2` Euler Form of `T^2` Chern Form of a Complex Line Bundle of `CP_1` Highest-Power Coefficient in the EMR Curvature Formula Wodzicki–Chern–Simons Invariant on the Thurston Example

Run the notebooks on your computer

Every page above is rendered from an executed notebook in the math/ directory of egison-jupyter. Install Egison 5 and follow the kernel installation guide, then start Jupyter in the repository.

git clone https://github.com/egison/egison-jupyter.git
cd egison-jupyter
python3 -m venv .venv
source .venv/bin/activate
pip install . jupyter
python -m egison_kernel.install
jupyter notebook math/

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Egison Mathematics Notebook

Run the notebooks on your computer