geometric-function-atlas

geometric-function-atlas is a standalone Python package for independently reproducing and reviewing computations published by the Geometric Function Atlas.

Source repository: https://github.com/Prasanna28Devadiga/geometric-function-atlas

This repository is intentionally separate from the registry website and its research workspace. It provides local commands and Python functions for reproducing the website's mathematical computations. It does not contain the Flask application, deployment configuration, private review state, or mutable registry database.

Phase 1

The first release provides:

• a typed catalog of the Ma–Minda generators used by the paper’s exact-radius portfolio;
• exact Taylor coefficients of a generator using SymPy;
• exact Ma–Minda Fekete–Szegő constants and their derivation metadata;
• certified re-evaluation of supplied counterexample witnesses;
• versioned structured result and fail-closed verification reports;
• JSON-capable command-line output suitable for independent checks.

Later phases will expose the remaining plots, certificates, registry queries, and application labs already available on the website.

Install — Python is not required

The supported user installation uses uv as an isolated tool manager. It downloads Python 3.12 and every runtime dependency automatically.

macOS and Linux:

curl -LsSf https://raw.githubusercontent.com/Prasanna28Devadiga/geometric-function-atlas/main/scripts/install.sh | sh

Windows PowerShell:

irm https://raw.githubusercontent.com/Prasanna28Devadiga/geometric-function-atlas/main/scripts/install.ps1 | iex

After restarting the terminal, run gfa --version. Existing uv users can install the GitHub release wheel directly:

uv tool install --managed-python --python 3.12 https://github.com/Prasanna28Devadiga/geometric-function-atlas/releases/download/v0.1.1/geometric_function_atlas-0.1.1-py3-none-any.whl

See docs/INSTALL.md for removal and maintainer installation from a local wheel.

Python API

from geometric_function_atlas import Generator, fekete_szego, generator_series, z

# phi(z) = 1 + sin(z) = 1 + z - z^3/6 + ...
series = generator_series("sine", order=4)
assert tuple(map(str, series.coefficients)) == (
    "1", "0", "-1/6", "0"
)
print(series.to_dict())

# Exact sharp constant under the declared Ma–Minda assumptions.
result = fekete_szego("exponential", mu=0)
assert str(result.value) == "3/4"
print(result.to_dict())

Custom normalized generators use preconstructed SymPy expressions; formula strings are deliberately rejected rather than passed to an eval-based parser:

custom = Generator(
    key="custom",
    name="Example",
    expression=1 + 2*z + 3*z**2,
    citation="User supplied",
)

Computations are not restricted to the built-in catalog. Analytic admissibility of custom input remains an explicit caller assumption, and undeclared free symbols are rejected.

Command line

gfa generators
gfa coefficients sine --order 5
gfa fekete-szego exponential --mu 1/2

# Re-check the witness z=-3/4 for f(z)=z+z².
gfa verify-counterexample --coefficients "1" --point=-0.75,0

The longer command name, geometric-function-atlas, is also supported. Add --json to any command when machine-readable output is useful.

--mu accepts an exact signed integer or integer/integer fraction. Decimal and scientific notation are rejected so untrusted short inputs cannot trigger unbounded symbolic integer construction.

See docs/WEB_PARITY.md for the website-to-package checklist, docs/PROVENANCE.md for claim semantics, and docs/ROADMAP.md for the incremental implementation path. The versioned result envelope, verification checks, failure states, and CLI exit codes are specified in docs/RESULT_CONTRACT.md.

Development

uv sync --extra test
uv run pytest

Scientific status

Every result reports its method and evidence status. Numerical screens are never presented as proofs, computational certification is distinct from literature novelty, and bibliographic review remains a separate human process.

License

MIT