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Documentation

This directory contains comprehensive documentation for the Composite Calculus library.

Documentation Structure

Tutorial - Getting Started

Explainer: Core Composite Class — Annotated Reference

Reference: Revised Notation System — Formal Rules - Current!

Reference: Composite Notation — Formal Rules - Deprecated - Reference

Implementation Guide

Roadmap (DRAFT)

Exploration & research (Turing completeness playground)

Theory & Papars)

Quick Links

For New Users

Start with the Tutorial to learn the basics in 10 minutes.

For Developers

Read the Implementation Guide to understand how the system works internally.

For Reference

Check the API Reference for complete function documentation.

For Learning by Example

Browse the Examples directory for practical code snippets.

Theory & Papers

📄 Preprint (coming soon): "Provenance-Preserving Arithmetic: A Unified Framework for Automatic Calculus"

Milovan, T. (2026). Provenance-Preserving Arithmetic. Zenodo.

Core insight: Reinterpret Laurent polynomials where z⁻¹ represents "zero with provenance" — an infinitesimal that remembers its origin. This single reinterpretation makes calculus algebraic.

Key results:

Theorem 1: Information preservation under ×0
Theorem 2: Zero-infinity duality (∞ × 0 = 1)
Theorem 3: Reversible zero operations
Theorem 4: Derivatives emerge from convolution (no separate rules needed)

Formal proofs available in papers/ directory.

© Toni Milovan. Documentation licensed under CC BY-SA 4.0. Code licensed under AGPL-3.0.