🌟 PrimaLib: Math Made Magical ✨

"Because math should feel like poetry, not paperwork."

PrimaLib is your friendly algebraic playground for math operations, geometry, and infinite sequences using lazy sets. Think of it as a magical transformer that makes scalars, arrays, and infinite streams all dance to the same tune.

At its heart is primaSet ⭐ - the shining star that treats everything as a set: numbers, objects, trees, DOM elements, or infinite streams of primes.

🚀 Quick Start

Install

npm install primalib

Or install individual submodules:

npm install @primalib/core
npm install @primalib/num
npm install @primalib/geo
# etc.

For web development (optional, mainly for dev/tests):

npm install @primalib/web

Hello World

import { N, sq, sum } from 'primalib'

// Sum of squares of first 10 naturals: 1² + 2² + ... + 10² = 385
console.log(sum(sq(N(10))))  // → 385 ✨

// Works with arrays too!
console.log(sum(sq([1,2,3,4,5])))  // → 55

That's it! You're doing math like a wizard now. 🎩✨

⭐ Core Magic: primaSet

primaSet is PrimaLib's superpower - it treats everything as a set, seamlessly handling both finite and infinite sequences.

import { primaSet, primes, N } from 'primalib'

// Everything is a set!
primaSet(42)                    // → {42}
primaSet([1,2,3])               // → {1,2,3}
primaSet(N())                   // → {1,2,3,...} (infinite!)
primaSet(primes)                // → {2,3,5,7,11,...} (infinite primes!)
primaSet(null)                  // → {} // empty

primes.get(0)                    // → 2 (first prime)
primes.take(10)                 // → [2,3,5,7,11,13,17,19,23,29]
// Infinite sequences work like arrays
N(10).sq().sum()                // → 385 (sum of squares)

The magic: primaSet handles infinite sequences as naturally as finite arrays - no memory explosions, no precomputation, just pure lazy evaluation.

📚 Documentation

Quick Access

• QUICKREF.md - Quick reference & cheat sheet ⚡
• PATTERNS.md - Common patterns & recipes 🎯
• FAQ.md - Frequently asked questions ❓
• INTEGRATION.md - Framework integration guide 🔗
• IMPORT_GUIDE.md - Package structure & import guide 📦
• PACKAGE_STRUCTURE.md - Package structure details 📦
• PRIMALIB.md - Complete documentation with all modules
• PRIMAPROMPT.md - AI reference guide (for LLMs/Copilot) 🤖

Module Documentation

• PRIMASET.md - Core lazy set factory (the shining star ⭐)
• PRIMAOPS.md - Extended operations & methods
• PRIMANUM.md - Number theory & geometric primes
• PRIMAGEO.md - Geometry & hyperdimensional structures
• PRIMASTAT.md - Statistical analysis tools
• PRIMATOPO.md - Topology & topological invariants
• PRIMALIN.md - Linear algebra (vectors, matrices, polynomials)
• PRIMATREE.md - Tree handling & Virtual DOM foundation
• PRIMAWEB.md - Universal web pipeline (the cherry on top 🍒)

🎯 What's Included

PrimaLib provides:

• Infinite Sequences: Primes, naturals, integers - all as lazy sets
• Number Theory: Prime constellations, geometric sieves, CRT addresses
• Geometry: Points, hypercubes, hyperplanes in n-dimensional space
• Linear Algebra: Vectors, matrices, polynomials
• Statistics: Descriptive stats, correlation, time series
• Topology: Simplicial complexes, homology groups, Euler characteristics
• Trees: Tree structures with Virtual DOM foundation
• Web Pipeline: Universal web tools for demos and examples

🎨 Examples

Infinite Primes

import { primes } from 'primalib'

primes.get(0)      // → 2
primes.get(4)     // → 11
primes.take(10)   // → [2,3,5,7,11,13,17,19,23,29]

Geometry

import { point, space } from 'primalib'

point(1,2).add(point(3,4))  // → point(4,6)
space([0,0,0], [1,1,1]).vertices()  // → 8 corner points

Linear Algebra

import { vector, matrix } from 'primalib'

vector(1,2,3).dot(vector(4,5,6))  // → 32
matrix([[1,2],[3,4]]).det()       // → -2

Statistics

import { mean, stddev, correlation } from 'primalib'

mean([1,2,3,4,5])  // → 3
correlation([1,2,3], [2,4,6])  // → 1.0

🔌 Plugin System

Add your own operations:

import { primaSet } from 'primalib'

primaSet.plugin({
  cube: x => x * x * x
})


primaSet([1,2,3]).cube()  // → [1, 8, 27]

🧪 Testing

npm test

163+ tests covering all modules and operations.

📖 Learn More

• Quick Reference: See QUICKREF.md for quick lookup ⚡
• Getting Started: See PRIMALIB.md for complete overview
• Core Concepts: Read PRIMASET.md to understand the foundation
• Module Details: Check individual module documentation for specific features
• Examples: See examples/README.md for example guide
• Contributing: See CONTRIBUTING.md to contribute

🎓 Philosophy

PrimaLib believes math should be playful. It bridges:

• Imperative & Functional: Chain methods or compose functions
• Finite & Infinite: Work with arrays or never-ending streams
• Simple & Complex: Start with scalars, scale to hypercubes

One abstraction. Infinite possibilities. 🌌

PrimaLib — Math as poetry. Sets as magic. Infinity as playground. ✨

Ready to explore? Start with PRIMALIB.md for the complete guide, or dive into PRIMASET.md to understand the core magic.