Welcome to Keçeci Numbers’s Documentation!

Keçeci Numbers is a Python library for generating, analyzing, and visualizing dynamic sequences inspired by the Collatz Conjecture across diverse number systems.

This library provides a unified algorithm that operates on 16 different number types, from standard integers to complex algebraic structures like quaternions and neutrosophic numbers. It is designed as a tool for academic research and exploration in number theory.

Getting Started

• Installation
  • Prerequisites
  • Option 1: Install with pip (Recommended)
  • Option 2: Install with Conda
  • Option 3: Install from Source
  • Verifying the Installation
• Quick Start
  • Step 1: Import the Necessary Libraries
  • Step 2: Generate the Keçeci Sequence
  • Step 3: Visualize the Sequence
  • Full Code Example
  • Expected Output
  • Next Steps

User Guide

• The Keçeci Conjecture
  • Statement of the Conjecture
  • Significance
  • The Conjecture in Multiple Languages

API Reference

• API Reference
  • High-Level Functions
  • Core Generation & Analysis
  • Custom Number Classes
  • Visualization & Reporting
  • Module Constants

What are Keçeci Numbers?

Keçeci Numbers are sequences generated from a specific starting value using a recursive rule. The process for each step is as follows:

1. Add: An increment value is added to the current value. This “added value” is recorded in the sequence.

2. Divide: An attempt is made to divide this “added value” by 3 or 2 (whichever was not used in the previous step).

3. ASK (Augment/Shrink then Check) Rule: If the number is indivisible and prime, a type-specific unit value is added or subtracted. This “modified value” is recorded, and the division is re-attempted.

4. Carry Over: If division fails, the number itself (either the “added value” or “modified value”) becomes the next element in the sequence.

Key Features

• 20 Different Number Types: Supports integers, rationals, complex numbers, quaternions, neutrosophic numbers, and more.

• Unified Generator: Uses a single, consistent unified_generator algorithm for all number types.

• Advanced Visualization: Provides a multi-dimensional plot_numbers function tailored to the nature of each number system.

• Keçeci Prime Number (KPN) Analysis: Identifies the most recurring prime representation in sequences to analyze their convergence behavior.

• Interactive and Programmatic Usage: Allows for both interactive parameter input (get_interactive) and direct use in scripts (get_with_params).

Indices and tables

• Index

• Module Index

• Search Page