Analytic Continuation Server

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

Features

• Coordinate Transforms: Convert between screen and logical (complex plane) coordinates
• Meromorphic Function Building: Construct expressions from zeros and poles
• Domain Coloring: Generate visualization images (requires py-domaincolor)
• Laurent Series Fitting: Fit conformal maps to Jordan curves
• Analytic Continuation: Compute Schwarz reflection compositions
• Session Management: Track progress and recover interrupted computations
• WebGL Support: Export data optimized for GPU rendering

Installation

pip install analytic-continuation-server

With domain coloring support:

pip install analytic-continuation-server[domaincolor]

Quick Start

As a CLI

Start the server:

serve-analytic-continuation --port 8000

With custom CORS origins:

serve-analytic-continuation --cors-origin https://myapp.com --cors-origin https://api.myapp.com

Disable optional features:

serve-analytic-continuation --disable-domaincolor --disable-laurent

Using a config file:

serve-analytic-continuation --config server-config.json

Or with uvicorn directly:

uvicorn analytic_continuation_server:app --reload

As a Library

Use the package as an importable library in your own FastAPI application:

from analytic_continuation_server import create_app, ServerConfig

# Create with custom configuration
config = ServerConfig(
    cors_origins=["https://myapp.com"],
    enable_domaincolor=True,
    enable_laurent=True,
    log_level="debug",
)
app = create_app(config)

# Or use a dict for quick configuration
app = create_app({
    "cors_origins": ["https://myapp.com"],
    "debug": True,
})

# Or use environment variables (prefix: ACS_)
# ACS_CORS_ORIGINS=https://myapp.com,https://api.myapp.com
# ACS_ENABLE_DOMAINCOLOR=true
# ACS_LOG_LEVEL=debug
app = create_app()  # Reads from environment

Mount Specific Routes

If you only need specific functionality, mount individual routers:

from fastapi import FastAPI
from analytic_continuation_server.routes import laurent_router, health_router, transform_router

my_app = FastAPI(title="My Math API")

# Mount only the routes you need
my_app.include_router(health_router)
my_app.include_router(transform_router)
my_app.include_router(laurent_router, prefix="/api/laurent")

Available routers:

• health_router - /api/health endpoints
• transform_router - /api/transform/* coordinate transformation endpoints
• meromorphic_router - /api/meromorphic/* function building endpoints
• domaincolor_router - /api/domaincolor image generation (requires py-domaincolor)
• laurent_router - /api/laurent/* Laurent fitting pipeline
• session_router - /api/session/* session management

Configuration

ServerConfig Options

Option	Type	Default	Description
cors_origins	list[str]	["*"]	Allowed CORS origins
enable_domaincolor	bool	True	Enable domain coloring endpoints
enable_laurent	bool	True	Enable Laurent fitting endpoints
log_level	str	"info"	Logging level
title	str	"Analytic Continuation Server"	API title
description	str	...	API description
version	str	"0.1.0"	API version
debug	bool	False	Enable debug mode

Environment Variables

All configuration options can be set via environment variables with the ACS_ prefix:

Variable	Example
ACS_CORS_ORIGINS	"https://myapp.com,https://api.myapp.com"
ACS_ENABLE_DOMAINCOLOR	"true" or "false"
ACS_ENABLE_LAURENT	"true" or "false"
ACS_LOG_LEVEL	"debug", "info", "warning", "error"
ACS_DEBUG	"true" or "false"

Config File Format

{
    "cors_origins": ["https://myapp.com"],
    "enable_domaincolor": true,
    "enable_laurent": true,
    "log_level": "info",
    "debug": false
}

CLI Options

usage: serve-analytic-continuation [-h] [--host HOST] [--port PORT] [--reload]
                                   [--workers WORKERS]
                                   [--log-level {debug,info,warning,error,critical}]
                                   [--cors-origin CORS_ORIGINS] [--config FILE]
                                   [--disable-domaincolor] [--disable-laurent]
                                   [--debug] [--title TITLE]
                                   [--version-tag VERSION]

Options:
  --host HOST           Host to bind to (default: 0.0.0.0)
  --port PORT           Port to bind to (default: 8000)
  --reload              Enable auto-reload for development
  --workers WORKERS     Number of worker processes (default: 1)
  --log-level LEVEL     Log level (default: info)
  --cors-origin ORIGIN  Allowed CORS origin (can be specified multiple times)
  --config FILE         Path to JSON configuration file
  --disable-domaincolor Disable domain coloring endpoints
  --disable-laurent     Disable Laurent series fitting endpoints
  --debug               Enable debug mode
  --title TITLE         API title for OpenAPI docs
  --version-tag VERSION API version tag

API Overview

Endpoint Group	Description
/api/health	Health check
/api/transform/*	Coordinate transformations
/api/meromorphic/*	Function building
/api/domaincolor	Image generation
/api/laurent/*	Laurent fitting pipeline
/api/session/*	Session management

Example Usage

import httpx

client = httpx.Client(base_url="http://localhost:8000")

# Health check
response = client.get("/api/health")
print(response.json())
# {'status': 'ok', 'version': '0.1.0'}

# Build a meromorphic function
response = client.post("/api/meromorphic/build", json={
    "zeros": [{"x": 1, "y": 0}, {"x": -1, "y": 0}],
    "poles": [{"x": 0, "y": 1}, {"x": 0, "y": -1}],
    "coords": "logical"
})
print(response.json())
# {"expression": "(z-1)*(z+1)/((z-i)*(z+i))", ...}

# Transform a point
response = client.post("/api/transform/point", json={
    "point": {"x": 500, "y": 200},
    "params": {"offset_x": 400, "offset_y": 300, "scale_x": 100},
    "direction": "to_logical"
})
print(response.json())
# {'x': 1.0, 'y': 1.0, 'index': None}

Documentation

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

License

MIT License