herta/src/math/symbolic.js

Advanced mathematics framework for scientific, engineering, and financial applications

/**
 * Symbolic mathematics module for herta.js
 * Provides methods for symbolic integration, differentiation, and equation solving
 */

const utils = require('../utils/utils');

// Symbolic mathematics module
const symbolic = {};

/**
 * Represents a symbolic expression
 * @param {string} expr - The expression string
 * @returns {Object} - Symbolic expression object
 */
symbolic.expression = function (expr) {
  if (typeof expr !== 'string') {
    throw new Error('Expression must be a string');
  }

  return {
    expr,

    /**
     * Convert the expression to a string
     * @returns {string} - String representation
     */
    toString() {
      return this.expr;
    },

    /**
     * Substitute a variable with a value or another expression
     * @param {string} variable - The variable to substitute
     * @param {string|number} value - The value or expression to substitute with
     * @returns {Object} - New symbolic expression
     */
    substitute(variable, value) {
      // Simple substitution implementation
      // In a real implementation, this would use a proper parser
      const valueStr = typeof value === 'number' ? value.toString() : value;
      const pattern = new RegExp(`\\b${variable}\\b`, 'g');
      const newExpr = this.expr.replace(pattern, `(${valueStr})`);

      return symbolic.expression(newExpr);
    },

    /**
     * Add another expression to this one
     * @param {Object|string|number} other - The expression to add
     * @returns {Object} - New symbolic expression
     */
    add(other) {
      const otherExpr = typeof other === 'object' ? other.expr : other.toString();
      return symbolic.expression(`(${this.expr}) + (${otherExpr})`);
    },

    /**
     * Subtract another expression from this one
     * @param {Object|string|number} other - The expression to subtract
     * @returns {Object} - New symbolic expression
     */
    subtract(other) {
      const otherExpr = typeof other === 'object' ? other.expr : other.toString();
      return symbolic.expression(`(${this.expr}) - (${otherExpr})`);
    },

    /**
     * Multiply this expression by another
     * @param {Object|string|number} other - The expression to multiply by
     * @returns {Object} - New symbolic expression
     */
    multiply(other) {
      const otherExpr = typeof other === 'object' ? other.expr : other.toString();
      return symbolic.expression(`(${this.expr}) * (${otherExpr})`);
    },

    /**
     * Divide this expression by another
     * @param {Object|string|number} other - The expression to divide by
     * @returns {Object} - New symbolic expression
     */
    divide(other) {
      const otherExpr = typeof other === 'object' ? other.expr : other.toString();
      return symbolic.expression(`(${this.expr}) / (${otherExpr})`);
    },

    /**
     * Raise this expression to a power
     * @param {Object|string|number} power - The power to raise to
     * @returns {Object} - New symbolic expression
     */
    pow(power) {
      const powerExpr = typeof power === 'object' ? power.expr : power.toString();
      return symbolic.expression(`(${this.expr}) ^ (${powerExpr})`);
    },

    /**
     * Differentiate the expression with respect to a variable
     * @param {string} variable - The variable to differentiate with respect to
     * @returns {Object} - New symbolic expression representing the derivative
     */
    differentiate(variable) {
      return symbolic.differentiate(this.expr, variable);
    },

    /**
     * Integrate the expression with respect to a variable
     * @param {string} variable - The variable to integrate with respect to
     * @returns {Object} - New symbolic expression representing the integral
     */
    integrate(variable) {
      return symbolic.integrate(this.expr, variable);
    },

    /**
     * Evaluate the expression by substituting all variables with values
     * @param {Object} scope - Object mapping variable names to values
     * @returns {number} - The evaluated result
     */
    evaluate(scope = {}) {
      // This would use a proper expression evaluator
      // For now, we'll use a simple approach with Function constructor
      // Note: This is not safe for untrusted input
      try {
        const variables = Object.keys(scope);
        const values = variables.map((v) => scope[v]);
        const func = new Function(...variables, `return ${this.expr};`);
        return func(...values);
      } catch (error) {
        throw new Error(`Error evaluating expression: ${error.message}`);
      }
    }
  };
};

/**
 * Differentiate an expression symbolically
 * @param {string|Object} expr - The expression to differentiate
 * @param {string} variable - The variable to differentiate with respect to
 * @returns {Object} - Symbolic expression representing the derivative
 */
symbolic.differentiate = function (expr, variable) {
  const exprStr = typeof expr === 'object' ? expr.expr : expr.toString();

  // This would implement symbolic differentiation rules
  // For now, we'll return a placeholder
  return symbolic.expression(`d/d${variable}(${exprStr})`);
};

/**
 * Integrate an expression symbolically
 * @param {string|Object} expr - The expression to integrate
 * @param {string} variable - The variable to integrate with respect to
 * @returns {Object} - Symbolic expression representing the integral
 */
symbolic.integrate = function (expr, variable) {
  const exprStr = typeof expr === 'object' ? expr.expr : expr.toString();

  // Parse the expression to identify its structure
  // This is a simplified implementation that handles basic cases

  // Check for simple power functions: x^n
  const powerMatch = exprStr.match(new RegExp(`\\b${variable}\\^(\\d+)\\b`));
  if (powerMatch) {
    const power = parseInt(powerMatch[1]);
    const newPower = power + 1;
    const coefficient = 1 / newPower;
    return symbolic.expression(`${coefficient} * ${variable}^${newPower} + C`);
  }

  // Check for simple polynomial terms: a*x
  const linearMatch = exprStr.match(new RegExp(`(\\d*\.?\\d*)\\s*\\*?\\s*\\b${variable}\\b`));
  if (linearMatch) {
    const coefficient = linearMatch[1] ? parseFloat(linearMatch[1]) : 1;
    return symbolic.expression(`${coefficient / 2} * ${variable}^2 + C`);
  }

  // Check for constants
  const constantMatch = exprStr.match(/^\s*(\d+\.?\d*)\s*$/);
  if (constantMatch) {
    const constant = parseFloat(constantMatch[1]);
    return symbolic.expression(`${constant} * ${variable} + C`);
  }

  // For more complex expressions, return a placeholder
  return symbolic.expression(`∫(${exprStr})d${variable}`);
};

/**
 * Solve an equation symbolically
 * @param {string|Object} lhs - Left-hand side of the equation
 * @param {string|Object} rhs - Right-hand side of the equation
 * @param {string} variable - The variable to solve for
 * @returns {Array<Object>} - Array of symbolic expressions representing solutions
 */
symbolic.solve = function (lhs, rhs, variable) {
  const lhsExpr = typeof lhs === 'object' ? lhs.expr : lhs.toString();
  const rhsExpr = typeof rhs === 'object' ? rhs.expr : rhs.toString();

  // This would implement symbolic equation solving
  // For now, we'll return a placeholder
  return [symbolic.expression(`${variable} = solution(${lhsExpr} = ${rhsExpr})`)];
};

/**
 * Expand an expression (distribute multiplication over addition)
 * @param {string|Object} expr - The expression to expand
 * @returns {Object} - Expanded symbolic expression
 */
symbolic.expand = function (expr) {
  const exprStr = typeof expr === 'object' ? expr.expr : expr.toString();

  // This would implement algebraic expansion
  // For now, we'll return a placeholder
  return symbolic.expression(`expand(${exprStr})`);
};

/**
 * Factor an expression
 * @param {string|Object} expr - The expression to factor
 * @returns {Object} - Factored symbolic expression
 */
symbolic.factor = function (expr) {
  const exprStr = typeof expr === 'object' ? expr.expr : expr.toString();

  // This would implement algebraic factorization
  // For now, we'll return a placeholder
  return symbolic.expression(`factor(${exprStr})`);
};

/**
 * Simplify an expression
 * @param {string|Object} expr - The expression to simplify
 * @returns {Object} - Simplified symbolic expression
 */
symbolic.simplify = function (expr) {
  const exprStr = typeof expr === 'object' ? expr.expr : expr.toString();

  // This would implement algebraic simplification rules
  // For now, we'll return a placeholder
  return symbolic.expression(`simplify(${exprStr})`);
};

/**
 * Compute the limit of an expression as a variable approaches a value
 * @param {string|Object} expr - The expression
 * @param {string} variable - The variable
 * @param {number|string} value - The value the variable approaches
 * @returns {Object} - Symbolic expression representing the limit
 */
symbolic.limit = function (expr, variable, value) {
  const exprStr = typeof expr === 'object' ? expr.expr : expr.toString();
  const valueStr = value.toString();

  // This would implement limit calculation
  // For now, we'll return a placeholder
  return symbolic.expression(`limit(${exprStr}, ${variable} -> ${valueStr})`);
};

module.exports = symbolic;