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.

Installation

To install GraffitiAI, use pip:

# Install GraffitiAI with pip
pip install graffitiai

Quick Start

Here's a simple example to get you started:

TxGraffitiAI

from graffitiai import GraffitiAI

# Point towards the URL hosted on Jillian's GitHub
url = 'https://raw.githubusercontent.com/jeddyhub/Polytope_Database/refs/heads/main/Simple_Polytope_Data/simple_polytope_properties.csv'

# Create an instance of the GraffitiAI class
ai = GraffitiAI()

# Read the data from the URL
ai.read_csv(url)

# Vectorize the p-vector column
ai.vectorize(['p_vector'])

# Define small face counts
ai.knowledge_table["p_3"] = ai.knowledge_table["p_vector"].apply(lambda x: x[0] if len(x) > 2 else 0)
ai.knowledge_table["p_4"] = ai.knowledge_table["p_vector"].apply(lambda x: x[1] if len(x) > 2 else 0)
ai.knowledge_table["p_5"] = ai.knowledge_table["p_vector"].apply(lambda x: x[2] if len(x) > 2 else 0)
ai.knowledge_table["p_6"] = ai.knowledge_table["p_vector"].apply(lambda x: x[3] if len(x) > 3 else 0)
ai.knowledge_table["p_7"] = ai.knowledge_table["p_vector"].apply(lambda x: x[4] if len(x) > 4 else 0)
ai.knowledge_table['sum(p_vector)'] = ai.knowledge_table['p_vector'].apply(sum)
ai.knowledge_table['sum(p_vector not p_6)'] = ai.knowledge_table['p_vector'].apply(lambda x: sum([i for i in x if i != 6]))
ai.knowledge_table['sum(p_vector) with p >= 7'] = ai.knowledge_table['p_vector'].apply(lambda x: sum([i for i in x if i >= 7]))

ai.update_invariant_knowledge()

# Optionally add statistics on the vector valued column
ai.add_statistics(['p_vector'])

# Drop the columns that are not needed
ai.drop_columns([
    'edgelist',
    'adjacency_matrix',
    'p_vector',
])

# Optionally increase the complexity of the types of conjectures applied
ai.set_complexity( max_complexity=1)

# Generate conjectures on a list of target properties (invariants)
ai.conjecture(
    target_invariants=[
        'sum(p_vector)',
        'p_6',
    ],
    hypothesis=[
      'simple_polytope_graph',
      'simple_polytope_graph_with_p6_greater_than_zero',
   ],
   other_invariants=[
        'p_3',
        'p_4',
        'p_5',
        'p_7',
        'order',
        'size',
        'sum(p_vector)',
        'size',
        'sum(p_vector)',
        'p_6',
        'median_absolute_deviation(p_vector)',
        'max(p_vector)',
        'independence_number',

   ],
    complexity_range=(1, 3),
    lower_b_max=2,
    lower_b_min=-2,
    upper_b_max=3,
    upper_b_min=-3,
    W_lower_bound=None,
    W_upper_bound=None,
    min_touch=1,
)

ai.write_on_the_wall(search=True)

Christine

from graffitiai import Christine

# Initialize Christine
ai =Christine()

# Read in data
ai.read_csv("https://raw.githubusercontent.com/RandyRDavila/GraffitiAI/refs/heads/main/graffitiai/data/data_437.csv")

# Drop unwanted columns
ai.drop_columns([
    "adjacency_matrix",
    "edge_list",
    "number_of_spanning_trees",
    'maximum_degree',
    'minimum_degree',
    'average_degree',
    'number_of_triangles',
    'vertex_connectivity',
    'edge_connectivity',
    'is_simple',
    'clique_number',
])
ai.drop_columns([
    f'number_of_{p}_gons' for p in range(12, 126)
])

# Conjecture on a target invariant with a time limit set to 5 minutes
ai.conjecture('number_of_6_gons', bound_type='lower', time_limit_minutes=5)

# Write conjectures to the wall.
ai.write_on_the_wall()

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.

License

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

Acknowledgments

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

Author

Randy R. Davila, PhD