Choose a research question

The Atlas focuses on five recurring parts of a geometric-function-theory investigation. Choose the question that matches the decision you need to make.

Understand a new Ma–Minda class

Connect a generator \(\phi\) to its canonical member \(f_\phi\), exact coefficients, and the different domains that can be plotted.

Investigate a coefficient problem

Derive a sharp Fekete–Szegő bound, locate parameter transitions, and identify equality cases.

Find and verify an inclusion radius

Fix the source-to-target direction, find the first boundary contact, and prove that the resulting radius is sharp.

Test a conjecture

Separate an exact counterexample from an inconclusive test and repair a false statement.

Reproduce and adapt a published result

Recompute a claim from its defining equation, check an extremal member, and determine what survives.

These are not examples of every command in the package. They are complete mathematical investigations that show when a computation is useful and what must still be proved.

Before you run an example

The workflow scripts live in the source repository. Set up a checkout once:

git clone https://github.com/Prasanna28Devadiga/geometric-function-atlas.git
cd geometric-function-atlas
uv sync --extra test

Run the command on the selected workflow page from that directory. Each example writes its results to a directory under /tmp, so it will not modify the source tree.

JSON files contain the values used to make the figures. SVG files open directly in a browser. When a page uses a numerical picture, it also tells you which part of the argument is exact.