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	Laplacian in Polar Coordinates Laplacian in Spherical Coordinates
Series	Euler's Formula
Fourier Analysis	Leibniz Formula

Geometry
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`

How to try Egison Math Notebook on your computer

We can execute all of the above calculations on our computers by executing the following commands.
All programs are under /sample/math director of the git repository of Egison.

% egison -t sample/math/geometry/exterior-derivative.egi
[| (f|1 x y z) (f|2 x y z) (f|3 x y z) |]
[| [| 0 0 0 |] [| 0 0 0 |] [| 0 0 0 |] |]

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Egison Mathematics Notebook

How to try Egison Math Notebook on your computer