Development methodology for "Math::NIntegrate"

Introduction

This document outlines the development methodology for the Raku package "Math::NIntegrate".

Motivation

In order to better understand some of the methodological points is helpful to list a few motivational reasons for how the decision to develop "Math::NIntegrate" was made.

TBF...

Methodology

Done by human mind (or "manually")

• The Object-Oriented Design (OOP) of numerical integration framework

• The complete dynamics of the interaction between regions, rules, and variable transformers

• The method parsing grammar

  • The grammar for parsing the method option has several unique properties

  • A similar grammar in BNF was originally developed for WL's NIntegrate

  • Framework's grammar is written to be general and executable by Raku

  • It handles several different style of method specification: JSON-strings, WL-code-string, Raku data structures

  • Tests fo"Sentences" par

Done via LLM / AI-agent support

• Many/most of the integration rules are well known for decades and centuries

  • Hence, LLMs / AI-agents know them well, and can reliably generate computational code for them

• Reprogramming of Fortran codes from articles

  • Some numerical integration articles have corresponding Fortran code text files available on Web

• Grammar actions

  • For a well written grammar with tests simple interpreters are easy to generate via LLMs / AI-agents