Examples

Interactive Jupyter Notebook

For comprehensive, interactive examples with beautiful mathematical rendering, please see our Jupyter notebook:

📓 `View Examples Notebook on GitHub <https://github.com/wildducktheories/plumial/blob/main/examples.ipynb>`_

The notebook includes:

  • Quick Start - Basic usage of path objects and polynomial operations

  • Symbolic Mathematics - Working with d polynomials, k polynomials, and uv transformations

  • Functional Programming - Using the F namespace for elegant cycle operations

  • Forced vs Unforced Analysis - Critical for Collatz conjecture research

  • Data Analysis - Converting cycles to pandas DataFrames for statistical analysis

  • Advanced Mathematics - Polynomial arithmetic and relationship verification

  • Performance Examples - Caching analysis and batch processing

Why Jupyter?

The examples are provided as an interactive Jupyter notebook because:

  • Better Math Rendering: Polynomial equations display beautifully with LaTeX formatting

  • Interactive Exploration: Run, modify, and experiment with examples in real-time

  • Rich Output: DataFrames, plots, and mathematical expressions render properly

  • Comprehensive Coverage: All features demonstrated with working code

  • Easy Testing: Validate examples and experiment with different parameters

Quick Example

Here’s a taste of what you’ll find in the notebook:

from plumial import P
from plumial.core import B
from plumial.utils import S, F

# Create path object and explore
p = P(133)
display("Binary:", p.b())           # '10000101'
display("D polynomial:", p.d())     # h**5 - g**2
display("Evaluated:", p.encode(B.Collatz).d())  # 23

# Analyze forced vs unforced cycles
display(f"P(9) forced: {P(9).isforced()}")    # False (unforced)
display(f"P(291) forced: {P(291).isforced()}") # True (forced)

# Functional operations on cycles
collatz_p281 = P(281).encode(B.Collatz)
odd_k_values = list(collatz_p281.cycle(map=F.k(), filter=F.isodd))

→ `Open the full notebook <https://github.com/wildducktheories/plumial/blob/main/examples.ipynb>`_ for complete examples