ga-codegen

Generate Clifford Algebra implementations for any language from ganja.js

Version: 1.0.0
Trit: +1 (PLUS - generative)

Overview

ganja.js includes a template-based code generator that produces optimized Geometric Algebra implementations for:

• C++ (header-only)
• C# (.NET)
• Rust (no-std compatible)
• Python (numpy-based)

Supported Algebras

Pre-generated algebras in

ganja.js/codegen/

R2.{cpp,cs,rs,py}

R3.{cpp,cs,rs,py}

R4.{cpp,cs,rs,py}

PGA2D.{cpp,cs,rs,py}

PGA3D.{cpp,cs,rs,py}

CGA2D.{cpp,cs,rs,py}

CGA3D.{cpp,cs,rs,py}

H.{cpp,cs,rs,py}

DQ.{cpp,cs,rs,py}

Code Structure

Each generated file contains:

// C++ Example: PGA3D.cpp
namespace PGA3D {
  
  // Multivector with flat storage
  struct Multivector {
    float data[16];  // 2^4 components
    
    // Constructors
    static Multivector scalar(float s);
    static Multivector vector(float e1, float e2, float e3, float e0);
    static Multivector bivector(...);
    
    // Products
    Multivector operator*(const Multivector& b) const;  // Geometric
    Multivector operator^(const Multivector& b) const;  // Wedge
    Multivector operator|(const Multivector& b) const;  // Dot
    Multivector operator&(const Multivector& b) const;  // Vee
    
    // Involutions
    Multivector reverse() const;
    Multivector conjugate() const;
    Multivector dual() const;
    
    // Transformations
    Multivector sandwich(const Multivector& v) const;
    Multivector exp() const;
    Multivector log() const;
  };
  
  // Helper constructors
  Multivector point(float x, float y, float z);
  Multivector line(float px, float py, float pz, float dx, float dy, float dz);
  Multivector plane(float a, float b, float c, float d);
  Multivector rotor(float angle, Multivector axis);
  Multivector translator(float dist, Multivector dir);
}

Rust Implementation

// PGA3D.rs
#![no_std]

#[derive(Clone, Copy, Debug)]
pub struct Multivector([f32; 16]);

impl Multivector {
    pub const fn zero() -> Self { Self([0.0; 16]) }
    pub const fn scalar(s: f32) -> Self { 
        let mut m = [0.0; 16]; m[0] = s; Self(m) 
    }
    
    // Geometric product - generated multiplication table
    pub fn mul(&self, b: &Self) -> Self {
        let mut res = [0.0; 16];
        // Generated from Cayley table
        res[0] = self.0[0]*b.0[0] + self.0[1]*b.0[1] + ...;
        // ... 16 lines of optimized multiplications
        Self(res)
    }
    
    pub fn wedge(&self, b: &Self) -> Self { ... }
    pub fn dot(&self, b: &Self) -> Self { ... }
    pub fn dual(&self) -> Self { ... }
    pub fn reverse(&self) -> Self { ... }
    
    pub fn exp(&self) -> Self {
        // Closed-form for bivectors
        let theta = self.norm();
        if theta < 1e-6 {
            return Self::scalar(1.0).add(&self);
        }
        Self::scalar(theta.cos())
            .add(&self.scale(theta.sin() / theta))
    }
}

// Operator overloading
impl core::ops::Mul for Multivector {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self { self.mul(&rhs) }
}

Python Implementation

# PGA3D.py
import numpy as np

class Multivector:
    def __init__(self, data=None):
        self.data = np.zeros(16) if data is None else np.array(data)
    
    @classmethod
    def scalar(cls, s): 
        m = cls(); m.data[0] = s; return m
    
    def __mul__(self, other):
        """Geometric product"""
        res = Multivector()
        # Generated multiplication
        res.data[0] = self.data[0]*other.data[0] + ...
        return res
    
    def __xor__(self, other):
        """Wedge product (^)"""
        return self.wedge(other)
    
    def __and__(self, other):
        """Vee product (&)"""
        return self.dual().wedge(other.dual()).dual()
    
    def exp(self):
        """Exponential map"""
        theta = np.sqrt(abs(self.dot(self).data[0]))
        if theta < 1e-6:
            return Multivector.scalar(1) + self
        return Multivector.scalar(np.cos(theta)) + self * (np.sin(theta)/theta)

def point(x, y, z):
    m = Multivector()
    m.data[14] = 1  # e123
    m.data[11] = -x  # e023
    m.data[12] = y   # e013  
    m.data[13] = -z  # e012
    return m

Template System

The generator uses Node.js templates:

// codegen/generate.js
const Algebra = require('../ganja.js');

function generateCPP(p, q, r, name) {
  const A = Algebra({p, q, r});
  const {basis, mulTable} = A.describe(true);
  
  // Generate multiplication code
  const mulCode = mulTable.map((row, i) => 
    `res[${i}] = ` + row.map((term, j) => 
      term !== '0' ? `a[${j}]*b[${getBasisIndex(term)}]` : null
    ).filter(Boolean).join(' + ') + ';'
  ).join('\n');
  
  return `
namespace ${name} {
  struct Multivector {
    float data[${basis.length}];
    
    Multivector operator*(const Multivector& b) const {
      Multivector res;
      ${mulCode}
      return res;
    }
  };
}`;
}

Custom Algebra Generation

// Generate algebra for your signature
const Algebra = require('ganja.js');

// Generate Cl(1,3) for spacetime
const spacetime = Algebra({p:1, q:3});

// Get multiplication table
const info = spacetime.describe(true);
console.log('Basis:', info.basis);
console.log('Cayley table:', info.mulTable);

// Use template to generate code
const code = generateRust(1, 3, 0, 'Spacetime');

GF(3) Integration

Assign trits to generated algebras:

const algebraTrits = {
  'R2':    0,   // Real 2D - ergodic
  'PGA2D': +1,  // Projective 2D - generative
  'CGA2D': -1,  // Conformal 2D - contractive
};

function getAlgebraTrit(name) {
  return algebraTrits[name] || 0;
}

Build Integration

CMake (C++)

add_library(pga3d INTERFACE)
target_include_directories(pga3d INTERFACE 
  ${CMAKE_CURRENT_SOURCE_DIR}/ganja.js/codegen/cpp)

Cargo (Rust)

[dependencies]
pga3d = { path = "ganja.js/codegen/rust/pga3d" }

pip (Python)

pip install ganja-algebras  # Hypothetical package

GF(3) Triads

ga-codegen (+1) ⊗ clifford-acset-bridge (0) ⊗ sheaf-cohomology (-1) = 0 ✓
ga-codegen (+1) ⊗ pga-motor-interpolation (0) ⊗ conformal-ga (-1) = 0 ✓

Commands

# Generate all algebras
cd ganja.js/codegen && node generate.js

# Generate specific algebra
node -e "require('./generate').cpp(3,0,1,'PGA3D')" > PGA3D.hpp

# List available pre-generated
ls ganja.js/codegen/{cpp,rust,python,csharp}/

Files

• Generator:

  ganja.js/codegen/generate.js

• C++ output:

  codegen/cpp/*.hpp

• Rust output:

  codegen/rust/*/src/lib.rs

• Python output:

  codegen/python/*.py

References

• ganja.js codegen
• klein C++ library (alternative)
• Grassmann.jl (Julia native)

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