analytic-continuation Documentation

A Python package for coordinate transforms, Laurent series fitting, and analytic continuation pipeline utilities for complex analysis visualizations.

Overview

This package provides tools for working with complex analysis, including:

  • Coordinate Transforms: Transform between screen space and logical (complex plane) coordinates with the SpaceAdapter class

  • Laurent Series Fitting: Fit Laurent maps to Jordan curves, mapping the unit circle to approximate curve boundaries

  • Meromorphic Function Construction: Build meromorphic functions from zeros and poles

  • Analytic Continuation Pipeline: Utilities for holomorphic checking, inversion, and composition operations

  • Intrinsic Curve Analysis: Analyze curves using Cesaro and Whewell representations

  • Progress Tracking: Pipeline stage tracking and logging infrastructure

Installation

pip install analytic-continuation

For development with all optional dependencies:

pip install analytic-continuation[dev]

Quick Start

SpaceAdapter for Coordinate Transforms

from analytic_continuation import SpaceAdapter, TransformParams

# Create an adapter for a 800x600 screen viewing [-2, 2] x [-1.5, 1.5]
params = TransformParams.from_view_bounds(
    screen_width=800,
    screen_height=600,
    logical_x_range=(-2, 2),
    logical_y_range=(-1.5, 1.5),
)
adapter = SpaceAdapter(params)

# Convert screen coordinates to complex numbers
z = adapter.screen_to_complex(400, 300)  # Returns 0+0j (center)

Laurent Series Fitting

from analytic_continuation import LaurentFitConfig, fit_laurent_map, SplineExport

# Load curve data and fit a Laurent map
export = SplineExport.from_json(curve_json)
config = LaurentFitConfig(N_min=6, N_max=32)
result = fit_laurent_map(export, config)

if result.ok:
    # Evaluate on unit circle
    curve_points = result.laurent_map.eval_array(np.exp(1j * thetas))

Meromorphic Function Builder

from analytic_continuation import MeromorphicBuilder

builder = MeromorphicBuilder()
builder.add_zero(1, 0).add_zero(-1, 0)
builder.add_pole(0, 1).add_pole(0, -1)

expr = builder.build_expression()
# Returns: "(z-1)*(z+1)/((z-i)*(z+i))"

Contents

User Guide

Indices and tables