Getting started¶

Install gfa and use one Ma–Minda class to answer a concrete coefficient question.

Install¶

On macOS or Linux:

curl --proto '=https' --tlsv1.2 -LsSf https://raw.githubusercontent.com/Prasanna28Devadiga/geometric-function-atlas/main/scripts/install.sh | sh

On Windows, open PowerShell and run:

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

Both installers use the immutable published v0.6.0 wheel. They supply the gfa command and a uv-managed Python; no preinstalled Python is needed.

Understand the example¶

The exponential Ma–Minda class is determined by the generator

\[ \phi(z)=e^z. \]

It consists of normalized functions

\[ f(z)=z+a_2z^2+a_3z^3+\cdots \]

whose logarithmic derivative satisfies \(zf'(z)/f(z)\prec e^z\). The numbers \(a_2,a_3,\ldots\) are coefficients of functions in the class; they are not the coefficients of the generator \(\phi\).

We will ask for the sharp upper bound on \(|a_3-\mu a_2^2|\).

Compute one bound¶

Start with \(\mu=0\):

gfa fekete-szego exponential --mu 0

The command returns the exact value \(3/4\). Thus every function in this class satisfies \(|a_3|\leq 3/4\) under the assumptions reported by the command.

Change one input¶

Now set \(\mu=1/2\):

gfa fekete-szego exponential --mu 1/2

The exact value changes to \(1/2\), so

\[ \left|a_3-\frac12a_2^2\right|\leq\frac12. \]

The class has not changed. Only the coefficient functional has changed.

Continue¶

Choose one of the five research workflows when you have a specific class, coefficient problem, radius question, conjecture, or published claim to investigate.

For an optional command-line overview of several package features, run:

gfa walkthrough