herta/examples/basic/getting-started.js

Advanced mathematics framework for scientific, engineering, and financial applications

/**
 * Getting Started with Herta.js
 * Basic examples demonstrating core functionality
 */

// Import the Herta.js library
const herta = require('../../src/index.js');

console.log('Herta.js Basic Examples');
console.log('=======================\n');

// Matrix operations
console.log('Matrix Operations:');
const A = herta.matrix.create([[1, 2], [3, 4]]);
const B = herta.matrix.create([[5, 6], [7, 8]]);
console.log('Matrix A:', A);
console.log('Matrix B:', B);
console.log('A + B:', herta.matrix.add(A, B));
console.log('A * B:', herta.matrix.multiply(A, B));
console.log('Determinant of A:', herta.matrix.determinant(A));
console.log('Inverse of A:', herta.matrix.inverse(A));
console.log();

// Basic calculus
console.log('Calculus Examples:');
const f = x => x * x + 2 * x + 1;
const df = herta.calculus.derivative(f);
console.log('f(x) = x² + 2x + 1');
console.log('f\'(2) =', df(2)); // Should be 6
console.log('∫f(x)dx from 0 to 2 =', herta.calculus.integrate(f, 0, 2));
console.log();

// Statistical functions
console.log('Statistical Functions:');
const data = [12, 15, 18, 22, 25, 30, 35, 40, 45, 50];
console.log('Data:', data);
console.log('Mean:', herta.statistics.mean(data));
console.log('Median:', herta.statistics.median(data));
console.log('Standard Deviation:', herta.statistics.standardDeviation(data));
console.log('Correlation:', herta.statistics.correlation([1, 2, 3, 4, 5], [2, 3, 4, 5, 6]));
console.log();

// Complex numbers
console.log('Complex Numbers:');
const c1 = herta.complex.create(3, 4);
const c2 = herta.complex.create(1, 2);
console.log('c1 = 3 + 4i');
console.log('c2 = 1 + 2i');
console.log('c1 + c2 =', herta.complex.add(c1, c2));
console.log('c1 * c2 =', herta.complex.multiply(c1, c2));
console.log('|c1| =', herta.complex.abs(c1));
console.log();

// Symbolic computation
console.log('Symbolic Computation:');
const expr = herta.symbolic.parse('x^2 + 2*x + 1');
console.log('Expression:', expr.toString());
console.log('Simplified:', herta.symbolic.simplify(expr).toString());
console.log('Derivative:', herta.symbolic.differentiate(expr, 'x').toString());
console.log('Evaluated at x=3:', herta.symbolic.evaluate(expr, { x: 3 }));
console.log();

// Creating a custom instance with configuration
console.log('Custom Configuration:');
const scientificHerta = herta.create({
  precision: 128,
  scientificMode: true
});
console.log('High precision calculation:');
console.log('π to 50 decimal places:', scientificHerta.constants.pi.toFixed(50));
console.log();

console.log('Examples completed successfully!');