GeoConstructAndVerify

A Python library for constructing and verifying geometric constructions in Euclidean geometry.

Description

GeoConstructAndVerify is an engine capable of verifying the correctness of geometric constructions introduced through a sequence of primitive or complex steps. The library implements algorithms to compare constructions with original solutions to verify their equivalence, allowing users to determine if a particular construction is correct.

The library uses symbolic computation to represent and manipulate geometric objects and their relationships, enabling precise verification of geometric constructions.

Installation

pip install GeoConstructAndVerify

Or install from source:

git clone https://github.com/Petko0321/GeoConstructAndVerify.git
cd GeoConstructAndVerify
pip install -e .

Dependencies

• Python >= 3.6
• sympy >= 1.13.3
• mpmath >= 1.3.0

Features

• Representation of basic geometric objects (points, lines, circles)
• Implementation of geometric operations (intersection, perpendicular, parallel)
• Verification of construction equivalence
• A collection of geometric utility functions
• Support for both primitive and complex geometric constructions
• Symbolic computation to ensure precise results

Usage

Here's a simple example of using the library to translate a vector:

from sympy import symbols
from basics import Point, Construction
from utils import Vector, translate

# Create symbolic points
a1, b1, a2, b2, a3, b3 = symbols('a1, b1, a2, b2, a3, b3')
p1 = Point(a1, b1)
p2 = Point(a2, b2)
p3 = Point(a3, b3)

# Initialize the construction
cons = Construction(p1, p2, p3)

# Create a line and vector
line1 = cons.create_line(p1, p2)
v1 = Vector(p1, p2)

# Translate the vector
v2 = translate(v1, p3, optimized=True)

# Print the system
print("Construction system:")
print(cons.system)

Geometric Constructions

The library supports various geometric constructions including:

• Perpendicular bisector
• Angle bisector
• Perpendicular and parallel lines
• Vector translation
• Circle constructions
• And more...

Examples

The samples directory contains numerous examples showcasing the library's capabilities:

• Basic constructions (examples 1-10)
• Verification of equivalence between different construction approaches
• Complex geometric problems and their solutions

License

This project is licensed under the MIT License - see the LICENSE file for details.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.