herta/src/advanced/symbolic.js

Advanced mathematics framework for scientific, engineering, and financial applications

/**
 * Advanced symbolic computation module for herta.js
 * Provides symbolic mathematics capabilities for scientific users
 */

// Symbolic computation module
const symbolic = {};

/**
 * Symbolic expression representation and manipulation
 */
symbolic.expression = {
  /**
   * Parse a string into a symbolic expression tree
   * @param {string} expr - The expression string to parse
   * @returns {Object} - The expression tree
   */
  parse(expr) {
    // This would be implemented with a proper expression parser
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: expr,
      toString() {
        return expr;
      }
    };
  },

  /**
   * Convert an expression tree to a string representation
   * @param {Object} tree - The expression tree
   * @returns {string} - String representation
   */
  toString(tree) {
    if (typeof tree === 'string') {
      return tree;
    }

    if (tree.toString) {
      return tree.toString();
    }

    return String(tree);
  },

  /**
   * Substitute variables in an expression with values or other expressions
   * @param {Object|string} expr - The expression
   * @param {Object} substitutions - Map of variable names to values/expressions
   * @returns {Object} - The expression with substitutions applied
   */
  substitute(expr, substitutions) {
    const exprTree = typeof expr === 'string' ? symbolic.expression.parse(expr) : expr;

    // This would perform actual substitution in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: `substitute(${exprTree.toString()}, ${JSON.stringify(substitutions)})`,
      toString() {
        return this.value;
      }
    };
  }
};

/**
 * Symbolic algebra operations
 */
symbolic.algebra = {
  /**
   * Expand an algebraic expression
   * @param {Object|string} expr - The expression to expand
   * @returns {Object} - The expanded expression
   */
  expand(expr) {
    const exprTree = typeof expr === 'string' ? symbolic.expression.parse(expr) : expr;

    // This would perform actual expansion in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: `expand(${exprTree.toString()})`,
      toString() {
        return this.value;
      }
    };
  },

  /**
   * Factor an algebraic expression
   * @param {Object|string} expr - The expression to factor
   * @returns {Object} - The factored expression
   */
  factor(expr) {
    const exprTree = typeof expr === 'string' ? symbolic.expression.parse(expr) : expr;

    // This would perform actual factorization in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: `factor(${exprTree.toString()})`,
      toString() {
        return this.value;
      }
    };
  },

  /**
   * Simplify an algebraic expression
   * @param {Object|string} expr - The expression to simplify
   * @returns {Object} - The simplified expression
   */
  simplify(expr) {
    const exprTree = typeof expr === 'string' ? symbolic.expression.parse(expr) : expr;

    // This would perform actual simplification in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: `simplify(${exprTree.toString()})`,
      toString() {
        return this.value;
      }
    };
  },

  /**
   * Collect terms in an expression with respect to a variable
   * @param {Object|string} expr - The expression
   * @param {string} variable - The variable to collect terms for
   * @returns {Object} - The expression with collected terms
   */
  collect(expr, variable) {
    const exprTree = typeof expr === 'string' ? symbolic.expression.parse(expr) : expr;

    // This would perform actual term collection in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: `collect(${exprTree.toString()}, ${variable})`,
      toString() {
        return this.value;
      }
    };
  }
};

/**
 * Symbolic calculus operations
 */
symbolic.calculus = {
  /**
   * Compute the symbolic derivative of an expression
   * @param {Object|string} expr - The expression to differentiate
   * @param {string} variable - The variable to differentiate with respect to
   * @returns {Object} - The derivative expression
   */
  diff(expr, variable) {
    const exprTree = typeof expr === 'string' ? symbolic.expression.parse(expr) : expr;

    // This would perform actual symbolic differentiation in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: `diff(${exprTree.toString()}, ${variable})`,
      toString() {
        return this.value;
      }
    };
  },

  /**
   * Compute the symbolic integral of an expression
   * @param {Object|string} expr - The expression to integrate
   * @param {string} variable - The variable to integrate with respect to
   * @returns {Object} - The integral expression
   */
  integrate(expr, variable) {
    const exprTree = typeof expr === 'string' ? symbolic.expression.parse(expr) : expr;

    // This would perform actual symbolic integration in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: `integrate(${exprTree.toString()}, ${variable})`,
      toString() {
        return this.value;
      }
    };
  },

  /**
   * Compute the symbolic limit of an expression
   * @param {Object|string} expr - The expression
   * @param {string} variable - The variable
   * @param {number|string} value - The limit point
   * @returns {Object} - The limit expression
   */
  limit(expr, variable, value) {
    const exprTree = typeof expr === 'string' ? symbolic.expression.parse(expr) : expr;

    // This would perform actual limit calculation in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: `limit(${exprTree.toString()}, ${variable}, ${value})`,
      toString() {
        return this.value;
      }
    };
  },

  /**
   * Compute the Taylor series expansion of an expression
   * @param {Object|string} expr - The expression
   * @param {string} variable - The variable
   * @param {number|string} point - The expansion point
   * @param {number} order - The order of the expansion
   * @returns {Object} - The Taylor series expression
   */
  taylor(expr, variable, point, order) {
    const exprTree = typeof expr === 'string' ? symbolic.expression.parse(expr) : expr;

    // This would perform actual Taylor series expansion in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: `taylor(${exprTree.toString()}, ${variable}, ${point}, ${order})`,
      toString() {
        return this.value;
      }
    };
  }
};

/**
 * Symbolic equation solving
 */
symbolic.solve = {
  /**
   * Solve an equation or system of equations symbolically
   * @param {Object|string|Array} equations - The equation(s) to solve
   * @param {string|Array} variables - The variable(s) to solve for
   * @returns {Object} - The solution(s)
   */
  equations(equations, variables) {
    // Handle single equation case
    if (!Array.isArray(equations)) {
      equations = [equations];
    }

    // Handle single variable case
    if (!Array.isArray(variables)) {
      variables = [variables];
    }

    // Convert string equations to expression trees
    const eqTrees = equations.map((eq) => (typeof eq === 'string' ? symbolic.expression.parse(eq) : eq));

    // This would perform actual equation solving in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'solution',
      value: `solve([${eqTrees.map((eq) => eq.toString()).join(', ')}], [${variables.join(', ')}])`,
      toString() {
        return this.value;
      }
    };
  },

  /**
   * Solve a differential equation symbolically
   * @param {Object|string} equation - The differential equation
   * @param {string} dependent - The dependent variable
   * @param {string} independent - The independent variable
   * @returns {Object} - The solution
   */
  differentialEquation(equation, dependent, independent) {
    const eqTree = typeof equation === 'string' ? symbolic.expression.parse(equation) : equation;

    // This would perform actual differential equation solving in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'solution',
      value: `dsolve(${eqTree.toString()}, ${dependent}, ${independent})`,
      toString() {
        return this.value;
      }
    };
  }
};

/**
 * Symbolic matrix operations
 */
symbolic.matrix = {
  /**
   * Create a symbolic matrix
   * @param {Array} elements - Matrix elements (can contain symbolic expressions)
   * @returns {Object} - Symbolic matrix
   */
  create(elements) {
    // Convert string expressions to expression trees
    const processedElements = elements.map((row) => row.map((el) => (typeof el === 'string' ? symbolic.expression.parse(el) : el)));

    return {
      type: 'matrix',
      elements: processedElements,
      rows: elements.length,
      cols: elements[0].length,
      toString() {
        return `Matrix(${this.rows}x${this.cols})`;
      }
    };
  },

  /**
   * Compute the determinant of a symbolic matrix
   * @param {Object} matrix - The symbolic matrix
   * @returns {Object} - The determinant expression
   */
  determinant(matrix) {
    // This would perform actual symbolic determinant calculation in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'expression',
      value: `det(${matrix.toString()})`,
      toString() {
        return this.value;
      }
    };
  },

  /**
   * Compute the inverse of a symbolic matrix
   * @param {Object} matrix - The symbolic matrix
   * @returns {Object} - The inverse matrix
   */
  inverse(matrix) {
    // This would perform actual symbolic matrix inversion in a full implementation
    // For now, return a placeholder implementation
    return {
      type: 'matrix',
      value: `inverse(${matrix.toString()})`,
      rows: matrix.rows,
      cols: matrix.cols,
      toString() {
        return this.value;
      }
    };
  },

  /**
   * Compute the eigenvalues of a symbolic matrix
   * @param {Object} matrix - The symbolic matrix
   * @returns {Array} - The eigenvalue expressions
   */
  eigenvalues(matrix) {
    // This would perform actual symbolic eigenvalue calculation in a full implementation
    // For now, return a placeholder implementation
    return [
      {
        type: 'expression',
        value: `eigenvalues(${matrix.toString()})[0]`,
        toString() {
          return this.value;
        }
      }
    ];
  }
};

module.exports = symbolic;