ArfLab — Mathematical Environment Library in Python

ArfLab is a Python library that provides an abstract mathematical environment designed to represent and manipulate sets, intervals, and number systems in a symbolic and intuitive way.

The project is continuously growing, with new mathematical structures and operations being added every day.

Developed and maintained by a Mathematics undergraduate student at Marmara University, ArfLab aims to combine mathematical theory with computational representation, creating a bridge between abstract reasoning and code implementation.

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Features

• Abstract representation of Sets, Intervals, and Number Systems

• Support for Vector operations and linear algebra concepts

• Symbolic and numerical computation environment

• Integration with matplotlib for visualization

• Intuitive class structures and error handling for mathematical rigor

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Vector

• Magnitude

• Specific vector information

• Inner product

• Angle between two vectors

• Visualization with matplotlib

• Find unit vector

• Cosine value between two vectors

• Projection around two vectors

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Matrix

• Precisely defined mathematically

• Transpose

• Special matrix definitions

• Determinant

• Hadamard and classical product

• Symbolic Matris

• (3,3) Sarrus Method

• Permanent Algorithm

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Combinatorics

• Permutation

• Combination

• Posibilty

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Calculus

• Find Supremum İnfrimum value

• Σ and Π operations

• Transformation

• Monotonicity of the series

• Symbolid sequance

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Physics

• Wave equation analysis and visualization

$$ \psi(x,y) = \frac{2}{\sqrt{L_x L_y}} \sin\left(\frac{n_x \pi x}{L_x}\right) \sin\left(\frac{n_y \pi y}{L_y}\right) $$

• Energy levels of a particle in a two-dimensional cubic box

$$ E = \frac{\pi^2 \hbar^2}{2m} (n_x^2 + n_y^2 + n_z^2) $$

Wave_Equation(Lx=2.0, Ly=1.5, nx=4, ny=1, N=100)

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Visualization

ArfLab includes built-in vector visualization features using matplotlib, allowing users to plot and analyze vector relationships directly in Python. This helps bridge the gap between symbolic manipulation and geometric intuition.

Installation / Download

PyPI (Recommended)

pip install ArfLab

Git

git clone https://github.com/Jolankaa/ArfLab
cd ArfLab
pip install .

Few Examples

import ArfLab
# Example: Creating a vector
v = ArfLab.Vector([1,2,3])
print("Magnitude:", v.magnitude())
# For visualizationv.Visualization()
# Example: Creating a matrix
m = ArfLab.Matrix([[1,2],[3,4]])
print("Determinant:", m.determinant())