graffitiai 0.1.4

A Python package for automated mathematical conjecturing.

GraffitiAI

GraffitiAI is a Python package for automated mathematical conjecturing, inspired by the legacy of GRAFFITI. It provides tools for exploring relationships between mathematical invariants and properties, with a focus on graph theory and polytopes. This package supports generating conjectures, applying heuristics, and visualizing results.

Features

• Load and preprocess datasets with ease.
• Identify possible invariants and hypotheses for conjecturing.
• Generate upper and lower bounds for a target invariant.
• Apply customizable heuristics to refine conjectures.
• Export results to PDF for presentation and sharing.
• Includes a sample dataset of 3-regular polytopes for experimentation.

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Installation

To install GraffitiAI, use pip:

# Install GraffitiAI with pip
pip install graffitiai

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Quick Start

Here's a simple example to get you started:

Using the Built-in Dataset

from graffitiai import Optimist

# Initialize the Optimist instance
optimist = Optimist()

# Load the sample dataset
optimist.load_sample_3_regular_polytope_data()

# Describe available invariants and hypotheses
optimist.describe_invariants_and_hypotheses()

# Generate conjectures
optimist.conjecture(
    target_invariant='independence_number',
    other_invariants=['n', 'matching_number'],
    hypothesis=['cubic_polytope'],
    complexity=2,
    show=True
)

# Save conjectures to a PDF
optimist.save_conjectures_to_pdf("conjectures.pdf")

Using a Custom CSV File

from graffitiai import Optimist

# Initialize the Optimist instance
optimist = Optimist()

# Load a custom dataset
optimist.read_csv("path_to_your_data.csv")

# Describe available invariants and hypotheses
optimist.describe_invariants_and_hypotheses()

# Generate conjectures
optimist.conjecture(
    target_invariant='your_target_invariant',
    other_invariants=['invariant1', 'invariant2'],
    hypothesis=['your_hypothesis_column'],
    complexity=2,
    show=True
)

# Save conjectures to a PDF
optimist.save_conjectures_to_pdf("custom_conjectures.pdf")

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API Reference

class Optimist

Methods

1. load_sample_3_regular_polytope_data() Loads the included sample dataset of 3-regular polytopes into the knowledge table.

2. read_csv(path_to_csv) Loads a dataset from a CSV file, standardizing column names and ensuring compatibility for conjecturing.

3. get_possible_invariants() Returns a list of numerical columns suitable for conjecturing.

4. get_possible_hypotheses() Returns a list of boolean columns suitable for hypotheses.

5. describe_invariants_and_hypotheses() Prints the possible invariants and hypotheses from the knowledge table.

6. conjecture(target_invariant, other_invariants, hypothesis, complexity=2, show=False, min_touch=0, use_morgan=True, use_smokey=True) Generates conjectures for a given target invariant using the specified invariants and hypotheses.

7. write_on_the_wall(target_invariants=None) Displays generated conjectures for specified or all target invariants.

8. save_conjectures_to_pdf(file_name="conjectures.pdf", target_invariants=None) Exports generated conjectures to a PDF file, including the date and time of generation.

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Sample Dataset

GraffitiAI includes a sample dataset of 3-regular polytopes. It contains properties such as independence number, domination number, and average shortest path length, among others. This dataset is ideal for experimenting with the package's features.

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Contributing

Contributions are welcome! If you have suggestions, find bugs, or want to add features, feel free to create an issue or submit a pull request.

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License

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

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Acknowledgments

GraffitiAI is inspired by the pioneering work of GRAFFITI and built using the ideas of TxGraffiti.

Author

Randy R. Davila, PhD