Analytic Continuation Server

FastAPI server for domain coloring visualization, coordinate transforms, Laurent series fitting, and analytic continuation.

Contents:

• Installation
  • Requirements
  • Basic Installation
  • With Domain Coloring Support
  • Development Installation
  • From Source
  • Using uv
  • Verifying Installation
• Quick Start Guide
  • Starting the Server
  • Health Check
  • Example: Coordinate Transform
  • Example: Build Meromorphic Function
  • Example: Python Client
  • API Documentation
  • Configuration
• API Reference
  • Application Factory
  • Routes
  • Converters
  • Code Generation
  • CLI
• Pydantic Models
  • PointModel
  • ComplexModel
  • TransformParamsModel
  • ViewBoundsModel
  • SingularityModel
  • SplineParametersModel
  • SplineExportModel
  • TransformPointRequest
  • TransformPointsRequest
  • TransformSplineExportRequest
  • ZoomRequest
  • PanRequest
  • DomainColorRequest
  • ValidationRenderRequest
  • MeromorphicRequest
  • MeromorphicResponse
  • LaurentMapModel
  • LaurentFitRequest
  • LaurentFitResponse
  • PoleModel
  • InvertRequest
  • InvertResponse
  • HolomorphicCheckRequest
  • HolomorphicCheckResponse
  • CompositionRequest
  • CompositionResponse
  • ContourPreCheckRequest
  • ContourPreCheckResponse
  • IntrinsicCurveRequest
  • CurvatureMetricsModel
  • JacobianMetricsModel
  • ComplexityScoresModel
  • SuggestedConfigModel
  • IntrinsicCurveResponse
  • WebGLLaurentCoeffs
  • ContinuationDefinition
  • WebGLRenderDataRequest
  • WebGLRenderDataResponse
  • WebGLRenderWithProgressRequest
  • SessionStartRequest
  • SessionResponse
  • CheckResumableRequest
  • Base Models
  • Request Models
  • Response Models

Installation

Install from PyPI:

pip install analytic-continuation-server

Or install with optional domain coloring support:

pip install analytic-continuation-server[domaincolor]

Quick Start

Run the server with uvicorn:

uvicorn analytic_continuation_server:app --reload

Or use the CLI entry point:

serve-analytic-continuation --port 8000

Once running, visit:

• Swagger UI: http://localhost:8000/docs

• ReDoc: http://localhost:8000/redoc

• Health check: http://localhost:8000/api/health

API Overview

The server provides the following endpoint groups:

Health (/api/health)

Health check and API information

Transform (/api/transform/*)

Coordinate transformation between screen and logical space:

• POST /api/transform/point - Transform a single point

• POST /api/transform/points - Transform multiple points

• POST /api/transform/params-from-bounds - Create params from view bounds

• POST /api/transform/zoom - Apply zoom to parameters

• POST /api/transform/pan - Apply pan to parameters

Meromorphic (/api/meromorphic/*)

Build meromorphic functions from zeros and poles:

• POST /api/meromorphic/build - Build expression from zeros/poles

• POST /api/meromorphic/domaincolor - Build and visualize

Domain Coloring (/api/domaincolor)

Generate domain coloring images:

• POST /api/domaincolor - Generate PNG image

• GET /api/domaincolor/validate - Validate expression

• POST /api/domaincolor/validation-render - Render with overlays

Laurent (/api/laurent/*)

Laurent series fitting and analytic continuation:

• POST /api/laurent/precheck - Quick contour validation

• POST /api/laurent/fit - Fit Laurent map to curve

• POST /api/laurent/invert - Invert point through map

• POST /api/laurent/compose - Compute continuation

• POST /api/laurent/webgl-data - Get WebGL render data

Session (/api/session/*)

Session management and progress tracking:

• POST /api/session/start - Start new session

• GET /api/session/{id}/progress/stream - SSE progress stream

• GET /api/session/{id}/continuation - Get continuation definition

Indices and tables

• Index

• Module Index

• Search Page