maths.ts/src/core/Node.ts

Math utilities library for TypeScript, JavaScript and Node.js

/**
 * @author Hector J. Vasquez <ipi.vasquez@gmail.com>
 *
 * @licence
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

/**
 * Introduction
 * Any math expression may be seen as a tree. An example of how maths.ts builds
 * an expression tree would be the next:
 * 'sqrt(a) * ln(b-c)' may be seen as a tree where '*' is the tree's root. e.g:
 *      *
 *     / \
 * sqrt   ln
 *   |     |
 *   a     -
 *        / \
 *       b   c
 *
 * Annotations: Node class is not ready yet. There are many improvements to
 * make. Node class is just functional for the functions implemented in
 * maths.ts.
 * Any improvement on this will be very welcome.
 */

import {gcd} from '../arithmetic';
import {InputError} from './Error';
import * as scope from './scope';

/**
 * Works as a helper on simplification of numbers. When a number is
 * converted to a string, this constant represents the maximum length that
 * string may have to be simplified.
 */
const VALID_FLOAT_LENGTH = 10;

/**
 * Inside the expressions, whenever numberPattern matches a string, it will be
 * considered as a number.
 */
export const numberRegex = /-?(((\d+)(\.\d+)?)|(\.\d+))/;
/**
 * Inside the expressions, whenever symbolPattern matches a string, it will be
 * considered as a symbol.
 */
export const symbolRegex = /[a-z]\w*/i;
/**
 * The types the Node class accepts for performing its operations from
 * creating the Node to adding, etc.
 */
export type ValidNumber = number | string | Node;

/**
 * Node represents the basic tree node class. Any implementation of a tree
 * expression must be extended through Node internally.
 */
export default class Node {
// The operators, constants and functions accepted by Node instances
  public static scope: any = scope;
// The children of this
  public children: Node[] = [];
// The exponent for this
  public exponent: Node | number = 1;
// Represents the type of the node
  public type: NodeType = NodeType.Constant;
// The value of this (1, 2, 'x', '+', 'sin', etc...)
  public value: number | string = NaN;

  /**
   * Builds the tree for expression.
   * @param exp The expression to be represented with this.
   * @param parent The parent for this Node.
   */
  constructor(exp?: ValidNumber, public parent?: Node) {
    if (isNumber(exp)) {
// Assign a value and a type to this
      this.value = Number(exp);
      this.type = NodeType.Constant;
      this.rationalize();
    } else if (exp instanceof Node) {
// Creates a copy of exp
      this.value = exp.value;
      this.parent = exp.parent;
      this.type = exp.type;
      this.exponent = typeof exp.exponent === 'number' ?
        exp.exponent : new Node(exp.exponent);
      this._positive = exp._positive;
// This will recursively build each child
      for (const child of exp.children) {
        this.children.push(new Node(child));
      }
    } else if (typeof exp === 'string') {
      exp = formatString(exp);
      let pieces: string[] = breakPieces(exp);
// Eliminates extra brackets
      while (pieces.length === 1) {
        exp = pieces[0];
        pieces = breakPieces(exp);
        if (pieces[0] === exp) {
          break;
        }
      }
// Build this tree from the pieces obtained
      buildTree(this, pieces);
      this.simplify();
    }
  }

  /**
   * Access the operators in Node's scope.
   * @return The operators in the scope.
   */
  static get operators(): any {
    return Node.scope.operators;
  }

  /**
   * Access the functions in Node's scope.
   * @return The functions in the scope.
   */
  static get functions(): any {
    return Node.scope.functions;
  }

  /**
   * Access the constants in Node's scope.
   * @return The constants in the scope.
   */
  static get constants(): any {
    return Node.scope.constants;
  }

// Represents the sign of this expression
  private _positive = true;

  /**
   * Returns whether this is positive or not.
   * @return true if this is positive, false otherwise.
   */
  get positive(): boolean {
    return this._positive;
  }

  /**
   * Sets the sign of this.
   */
  set positive(value: boolean) {
    if (this.type === NodeType.Constant && this.positive !== value) {
      this.value = -this.value;
    } else {
      this._positive = value;
    }
  }

  get isFraction(): boolean {
    return this.value === '/';
  }

  /**
   * Calculates the value of this Node as a number type. If this contains
   * an element that cannot be converted to a number it will return undefined.
   * @return The value of this as a number.
   */
  get numberValue(): number {
    return this.getNumberValue();
  }

  /**
   * Returns whether this is positive or not.
   * @return true if this is positive, false otherwise.
   */
  get negative(): boolean {
    return !this.positive;
  }

  /**
   * Sets the sign of this.
   */
  set negative(value: boolean) {
    this.positive = !value;
  }

  /**
   * Creates a new Node from the given expression.
   * @param exp The expression from where to create the node.
   * @return A new node representing the expression.
   */
  static newNode(exp?: ValidNumber): Node {
    return new Node(exp);
  }

  /**
   * Returns a new Node representing the addition of a plus b.
   * @param a A number to add.
   * @param b A number to add.
   * @return new Node(a + b).
   */
  static add(a: ValidNumber, b: ValidNumber): Node {
    if (a instanceof Node) {
      return a.add(b);
    }
    if (b instanceof Node) {
      return b.add(a);
    }
    return new Node(a).add(b);
  }

  /**
   * Returns a new Node representing the multiplication of a times b.
   * @param a A number to multiply.
   * @param b A number to multiply.
   * @return new Node(a * b).
   */
  static multiply(a: ValidNumber, b: ValidNumber): Node {
    if (a instanceof Node) {
      return a.multiply(b);
    }
    if (b instanceof Node) {
      return b.multiply(a);
    }
    return new Node(a).multiply(b);
  }

  /**
   * Adds a constant to the scope.
   * @param c The constant to be added.
   * @param v The value the constant will get.
   */
  static setConstant(c: string, v: number) {

  }

  /**
   * Gets the value as a number for this node. In the event that there is
   * a variable in this expression, that variable must be declared in the
   * global scope or sent through the scope param in order to interpret
   * the variable in the expression, if a variable has no number value in
   * scope then the value returned will be undefined.
   * @param lScope The scope in which some variables inside this will be
   * evaluated.
   * @return The value for this according to the scope provided. In the
   * event that a variable is missed in the scope it will return undefined.
   */
  public getNumberValue(lScope?: any): number {
    let value;

    if (this.type === NodeType.Constant && typeof this.value === 'number') {
      value = this.value;
    } else if (this.type === NodeType.Operator) {
      value = Node.operators[this.value]
        .fn(this.children[0], this.children[1], lScope);
    } else if (this.type === NodeType.Function) {
      value = Node.functions[this.value].fn(this.children[0], lScope);
    } else {
      try {
        value = lScope[this.value];
      } catch (Error) {
        value = Node.constants[this.value];
      }
    }

    if (this.exponent !== 1) {
      if (typeof this.exponent === 'number') {
        value = Math.pow(value, this.exponent);
      } else {
        value = Math.pow(value, this.exponent.getNumberValue(lScope));
      }
    }

    return this._positive ? value : -value;
  }

  /**
   * Adds to this another value in a new Node.
   * @param s The expression to operate with.
   * @return A new Node with the value of this plus s.
   */
  public add(s: ValidNumber): Node {
    const result: Node = new Node();
    const op: Node = new Node(s); // Operating
    result.type = NodeType.Operator;
    result.value = '+';

    if (this.isFraction) {
      if (op.isFraction) {
// Numerator
        result.children[0] = this.children[0].multiply(op.children[1])
          .add(this.children[1].multiply(op.children[0]));
// Denominator
        result.children[1] = this.children[1].multiply(op.children[1]);
      } else {
// Numerator
        result.children[0] = this.children[0]
          .add(this.children[1].multiply(op));
// Denominator
        result.children[1] = this.children[1].clone();
      }
      result.value = '/';
    } else if (op.isFraction) {
// Numerator
      result.children[0] = op.children[1].multiply(this)
        .add(op.children[0]);
// Denominator
      result.children[1] = op.children[1];
      result.value = '/';
    } else {
      result.children[0] = this.clone();
      result.children[1] = op;
    }

    result.simplify();
    return result;
  }

  /**
   * Subtracts to this another value in a new Node.
   * @param s The expression to operate with.
   * @return A new Node with the value of this minus s.
   */
  public subtract(s: ValidNumber): Node {
    const result: Node = new Node();
    const op: Node = new Node(s); // Operating
    result.type = NodeType.Operator;
    result.value = '-';

    if (this.isFraction) {
      if (op.isFraction) {
// Numerator
        result.children[0] = this.children[0].multiply(op.children[1])
          .subtract(this.children[1].multiply(op.children[0]));
// Denominator
        result.children[1] = this.children[1].multiply(op.children[1]);
      } else {
// Numerator
        result.children[0] = this.children[0]
          .subtract(this.children[1].multiply(op));
// Denominator
        result.children[1] = this.children[1].clone();
      }
      result.value = '/';
    } else if (op.isFraction) {
// Numerator
      result.children[0] = op.children[1].multiply(this)
        .subtract(op.children[0]);
// Denominator
      result.children[1] = op.children[1];
      result.value = '/';
    } else {
      result.children[0] = this.clone();
      result.children[1] = op;
    }

    result.simplify();
    return result;
  }

  /**
   * Multiplies to this another value in a new Node.
   * @param s The expression to operate with.
   * @return A new Node with the value of this times s.
   */
  public multiply(s: ValidNumber): Node {
    const result: Node = new Node();
    const op: Node = new Node(s); // Operating
    result.type = NodeType.Operator;
    result.value = '*';

    if (this.isFraction) {
      if (op.isFraction) {
// Numerator
        result.children[0] = this.children[0].multiply(op.children[0]);
// Denominator
        result.children[1] = this.children[1].multiply(op.children[1]);
      } else {
// Numerator
        result.children[0] = this.children[0].multiply(op);
// Denominator
        result.children[1] = this.children[1].clone();
      }
      result.value = '/';
    } else if (op.isFraction) {
// Numerator
      result.children[0] = op.children[0].multiply(this);
// Denominator
      result.children[1] = op.children[1];
      result.value = '/';
    } else {
      result.children[0] = this.clone();
      result.children[1] = op;
    }

    result.simplify();
    return result;
  }

  /**
   * Divides to this another value in a new Node.
   * @param s The expression to operate with.
   * @return A new Node with the value of this between s.
   */
  public divide(s: ValidNumber): Node {
    const result: Node = new Node();
    const op: Node = new Node(s); // Operating
    result.type = NodeType.Operator;
    result.value = '/';

    if (this.isFraction) {
      if (op.isFraction) {
// Numerator
        result.children[0] = this.children[0].multiply(op.children[1]);
// Denominator
        result.children[1] = this.children[1].multiply(op.children[0]);
      } else {
// Numerator
        result.children[0] = this.children[0].clone();
// Denominator
        result.children[1] = this.children[1].multiply(op);
      }
    } else if (op.isFraction) {
// Numerator
      result.children[0] = op.children[1].multiply(this);
// Denominator
      result.children[1] = op.children[0];
    } else {
      result.children[0] = this.clone();
      result.children[1] = op;
    }

    result.simplify();
    return result;
  }

  /**
   * Powers to this another value in a new Node.
   * @param s The expression to operate with.
   * @return A new Node with the value of this pow s.
   */
  public pow(s: ValidNumber): Node {
    const n = new Node(this);
    n.powHere(s);
    n.simplify();
    return n;
  }

  /**
   * Creates a new node equivalent to -this.
   * @return A negation of this.
   */
  public negate(): Node {
    const n = this.clone();
    n.negateHere();
    return n;
  }

  /**
   * Adds to this another value and keeps the result in this Node.
   * @param s The expression to operate with.
   */
  public addHere(s: ValidNumber): Node {
    this.update(this.add(s));
    return this;
  }

  /**
   * Subtracts to this another value and keeps the result in this Node.
   * @param s The expression to operate with.
   */
  public subtractHere(s: ValidNumber): Node {
    this.update(this.subtract(s));
    return this;
  }

  /**
   * Multiplies to this another value and keeps the result in this Node.
   * @param s The expression to operate with.
   */
  public multiplyHere(s: ValidNumber): Node {
    this.update(this.multiply(s));
    return this;
  }

  /**
   * Divides to this another value and keeps the result in this Node.
   * @param s The expression to operate with.
   */
  public divideHere(s: ValidNumber): Node {
    this.update(this.divide(s));
    return this;
  }

  /**
   * Powers to this another value in a new Node.
   * @param s The expression to operate with.
   * @return A new Node with the value of this pow s.
   */
  public powHere(s: ValidNumber): Node {
    if (typeof this.exponent === 'number') {
      this.exponent = new Node(this.exponent + '*(' + s + ')');
    } else {
      this.exponent.multiplyHere(s);
    }

    return this;
  }

  /**
   * Changes this node's sign.
   */
  public negateHere(): Node {
    this.positive = !this.positive;

    return this;
  }

  /**
   * Compare this and other number with the given operator.
   * @param n The number which to compare this.
   * @param operator The operator to compare this with n.
   * @return this {operator} n.
   */
  public compare(n: Node | number, operator: string = '=') {
    const t = this.numberValue;
    if (n instanceof Node) {
      n = n.numberValue;
    }
    switch (operator) {
      case '>':
        return t > n;
      case '<':
        return t < n;
      case '>=':
        return t >= n;
      case '<=':
        return t <= n;
      case '!=':
        return t !== n;
      default:
        return t === n;
    }
  }

  /**
   * Converts this to a string.
   * @return The string that represents this.
   */
  public toString(): string {
    let s: string;
    if (this.type === NodeType.Function) {
      s = this.value + '(' + this.children.join(', ') + ')';
    } else if (this.type === NodeType.Operator) {
      s = this.printChild(this.children[0]) + this.value +
        this.printChild(this.children[1]);
    } else {
      s = this.value + ''; // In case is a variable or a constant
    }

    if (this._positive) {
      return s;
    }
    if (this.type === NodeType.Operator) {
      return '-(' + s + ')';
    }

    return '-' + s;
  }

  /**
   * Creates a copy of this Node.
   * @return A copy of this Node.
   */
  public clone(): Node {
    return new Node(this);
  }

  /**
   * Checks if this is Not a Number.
   * @return true if this is NaN, false otherwise.
   */
  public isNaN(): boolean {
    return isNaN(this.numberValue);
  }

  /**
   * Simplifies each children of this, then simplifies this. At this
   * moment simplify uses a very simple simplification that is yet waiting
   * to be completed.
   */
  public simplify(): void {
// TODO: Exponents here?
    for (const child of this.children) {
      child.simplify();
    }
    const n = this.numberValue;
// The most simple simplification
    if (this.type !== NodeType.Constant && !isNaN(n) &&
      n === Math.floor(n)) {
      this.update(n);
      return;
    }

    if (this.type === NodeType.Operator) {
// TODO: There is still many work to do in simplification of nodes
      switch (this.value) {
        case '+':
          this.simplifyAddition();
          break;
        case '-':
          this.simplifySubtraction();
          break;
        case '*':
          this.simplifyProduct();
          break;
        case '/':
          this.simplifyDivision();
          break;
        case '^':
          break;
      }
    }
  }

  /**
   * Whenever this.value is a number, it may be seen as a rational number.
   * If it has a decimal point then it is better to represent that value
   * as a fraction in order to keep accuracy on later operations.
   * Rationalize transforms this node to a fraction if this.value is a non
   * integer number.
   */
  public rationalize(): void {
    const wasNegative = this.value < 0;
// Checks if there is no need to process a constant
    if (typeof this.value !== 'number'
      || Math.floor(this.value) === this.value) {
      return;
    }
// Stringify value
    const n = '' + (this.value < 0 ? -this.value : this.value);
// Check how many digits does this.value have
    const nDigits = n.length - 1;
// Checks how many of those digits are at the left of the decimal point
    const nIntDigits = (Math.round(this.value) + '').length;
// Based on nIntDigits it creates a denominator for this.value
    const numerator = Number(n.replace('.', ''));
    const denominator = Math.pow(10, nDigits - nIntDigits);
// Simplify before create fraction
    const common = gcd(Number(numerator), denominator);
// Build this as a fraction
    this.type = NodeType.Operator;
    this.value = '/';
    this.children = [
// new Node without decimal point
      new Node((wasNegative ? -numerator : numerator) / common),
// new Node being the denominator created
      new Node(denominator / common)
    ];
  }

  /**
   * Updates this to a new value or type of node.
   * @param n The new value.
   */
  public update(n: number | Node): void {
    if (typeof n === 'number') {
      this.type = NodeType.Constant;
      this.value = n;
      this.children = [];
      this._positive = true;
      this.exponent = 1;
      this.rationalize();
    } else {
      this.type = n.type;
      this.value = n.value;
      this.children = n.children;
      this._positive = n._positive;
      this.exponent = n.exponent;
    }
  }

  /**
   * Prints the child sent with or without parentheses according to this
   * operator's priority.
   * @param n The child to be printed.
   * @return The string as how n should be printed.
   */
  private printChild(n: Node): string {
    const nOp = Node.operators[n.value];
    if (nOp === undefined) {
      return n.toString();
    }

    const thisOp = Node.operators[this.value];
    if (nOp.priority >= thisOp.priority && n.value !== '/') {
      return n.toString();
    }

    return '(' + n.toString() + ')';
  }

  /**
   * Simplifies this when it is a division.
   */
  private simplifyDivision(): void {
    if (Math.abs(this.children[1].numberValue) === 1) {
      const aux = this.children[1].numberValue === -1;
      this.update(this.children[0]);
      if (aux) {
        this.negateHere();
      }
      return;
    }
    const num = this.children[0].numberValue;
    const den = this.children[1].numberValue;
    if (num !== undefined && den !== undefined &&
      Math.floor(num) === num && Math.floor(den) === den) {
      const common = gcd(num, den);
      this.children[0].value = num / common;
      this.children[1].value = den / common;
    }
  }

  /**
   * Simplifies this when it is a product.
   */
  private simplifyProduct(): void {
    let aux: any;

    if (Math.abs(this.children[0].numberValue) === 1) {
      aux = this.children[0].numberValue === -1;
      this.update(this.children[1]);
      if (aux) {
        this.negateHere();
      }
      return;
    }
    if (Math.abs(this.children[1].numberValue) === 1) {
      aux = this.children[1].numberValue === -1;
      this.update(this.children[0]);
      if (aux) {
        this.negateHere();
      }
      return;
    }
  }

  /**
   * Simplifies this when it is a division.
   */
  private simplifyAddition(): void {
    if (this.children[0].numberValue === 0) {
      this.update(this.children[1]);
    }
    if (this.children[1].numberValue === 0) {
      this.update(this.children[0]);
    }
  }

  /**
   * Simplifies this when it is a product.
   */
  private simplifySubtraction(): void {
    if (this.children[0].numberValue === 0) {
      this.update(this.children[1]);
      this.negateHere();
    }
    if (this.children[1].numberValue === 0) {
      this.update(this.children[0]);
    }
  }
}

/**
 * Represents the types which a Node can represent. The nodes can only be
 * operators, constants, functions or variables. Each one of this node types
 * have their own features that distinguish them from the others.
 */
export enum NodeType {
  Operator, // +, * ...
  Constant, // 1, 23, 32.1, -1
  Function, // log(1), sin(pi)
  Variable  // x, y, a...
}

/**
 * Builds a tree using node as a root.
 * @param node The root for the new tree.
 * @param pieces The pieces from where to build node.
 */
function buildTree(node: Node, pieces: string[]) {
  let flag;
  if (pieces.length === 2 && pieces[0] === '-') {
    flag = pieces.shift();
  }
// Checking the expression actually is atomic
  if (pieces.length === 1) {
    pieces = breakPieces(pieces[0]);
  }
// In case is atomic
  if (pieces.length === 1) {
    switch (node.type = detectNodeType(pieces[0])) {
      case NodeType.Variable:
        node.value = pieces[0].match(symbolRegex)[0];
        break;
      case NodeType.Function:
        node.value = pieces[0].match(symbolRegex)[0];
        node.children = [
          new Node(pieces[0].replace(node.value, ''), node)
        ];
        break;
      case NodeType.Constant:
        node.value = Number(pieces[0]);
        node.rationalize();
        break;
      default:
        throw new InputError('Something unexpected happened.');
    }
  } else {
    let priorI = -1;
    for (let i = 1; i < pieces.length; i++) {
// This if checks if pieces[i] is an operator and checks that
// pieces[i - 1] is not an operator. If its and operator it
// probably is -. Then checks the priority of the operator so it
// keeps the record about where to cut the expression to keep
// building this tree.
      if (Node.operators[pieces[i]] !== undefined &&
        Node.operators[pieces[i - 1]] === undefined &&
        (priorI < 0 || Node.operators[pieces[i]].priority <
          Node.operators[pieces[priorI]].priority)) {
        priorI = i;
      }
    }
// TODO: FACTORIAL! ---> ! operator exception
// TODO: Exponents in exponent meant space!
    if ((node.value = pieces[priorI]) !== '^^') {
      node.type = NodeType.Operator;
      node.children.push(new Node(undefined, node));
      buildTree(node.children[0], pieces.slice(0, priorI));
      node.children.push(new Node(undefined, node));
      buildTree(node.children[1], pieces.slice(priorI + 1));
    }
  }

  if (flag === '-') {
    node.positive = false;
  }
}

/**
 * Detects which kind of node the expression corresponds.
 * @param exp The expression to detect.
 * @return The type of node the expression is.
 */
function detectNodeType(exp: string): NodeType {
  let s;
  if (numberRegex.test(exp) && exp.match(numberRegex)[0] === exp) {
    return NodeType.Constant;
  }

  if (s = exp.match(symbolRegex)[0]) {
    if (exp.indexOf(s) === 0 && exp[s.length] === '(') {
      return NodeType.Function;
    }
    return NodeType.Variable;
  }

  return undefined;
}

/**
 * Splits the expression into the different nodes this expression will be
 * composed.
 * @param exp The expression to split.
 * @return The splitted expression.
 */
function breakPieces(exp: string): string[] {
  const parts: string[] = [];
  let part: string;

  for (let i = 0; i < exp.length; i++) {
    if (exp[i] === '(') {
      part = getBracketExp(exp.substring(i, exp.length));
      parts.push(part);
      i += part.length + 1;
    } else if (isNumeric(exp[i]) || exp[i] === '.') {
      part = exp.substring(i, exp.length).match(numberRegex)[0];
      parts.push(part);
      i += part.length - 1;
    } else if (isAlpha(exp[i])) {
      part = exp.substring(i, exp.length).match(symbolRegex)[0];
      if (exp[i + part.length] === '(') {
        part += '(' +
          getBracketExp(exp.substring(i + part.length, exp.length))
          + ')';
      }
      parts.push(part);
      i += part.length - 1;
    } else if (Node.operators[exp[i]] !== undefined) {
      parts.push(exp[i]);
    } else if (exp[i] === ')') {
      throw new InputError({
        message: 'There is an extra closing bracket',
        input: exp
      });
    }
  }

  return parts;
}

/**
 * Get the content from the first brackets on the expression given.
 * @param exp From where to get the expression.
 * @return The expression inside the first pair of brackets the expression has.
 */
function getBracketExp(exp: string): string {
  if (exp[0] !== '(') {
    throw new InputError({
      message: 'The expression does not start with a bracket.',
      input: exp
    });
  }

  let k, i;
  for (k = i = 1; k !== 0 && i < exp.length; i++) {
    if (exp[i] === ')') {
      k--;
    } else if (exp[i] === '(') {
      k++;
    }
  }
  if (k !== 0) {
    throw new InputError({
      message: 'Expression with extra open bracket.',
      input: exp
    });
  }

  return exp.substring(1, i - 1);
}

/**
 * Checks if a string or a number is a number.
 * @param n The value to be tested.
 * @return True if n is a number even being a string.
 */
function isNumber(n: any): boolean {
  if (typeof n === 'string') {
    const strictNumberRegex = /^-?(((\d+)(\.\d+)?)|(\.\d+))$/;
    return typeof n === 'number' || strictNumberRegex.test(n);
  }

  return typeof n === 'number';
}

/**
 * Checks if a char is alpha.
 * @param c The character to check, this is a string with length 1.
 * @return Whether c is or is not alpha.
 */
function isAlpha(c: string): boolean {
  return c.length === 1 && c.search(/[a-z]|[A-Z]/i) === 0;
}

/**
 * Checks if a char is numeric.
 * @param c The character to check, this is a string with length 1.
 * @return Whether c is or is not a number.
 */
function isNumeric(c: string): boolean {
  return c.length === 1 && c.search(/[0-9]/i) >= 0;
}

/**
 * Checks if a char is alphanumeric.
 * @param c The character to check, this is a string with length 1.
 * @return Whether c is or is not alpha or a number.
 */
function isAlphaNumeric(c: string): boolean {
  return c.length === 1 && c.search(/\w/i) >= 0;
}

/**
 * Formats an expression given in order to be processable by node constructor.
 * @param exp The expression to be formatted.
 * @return The expression formatted.
 */
function formatString(exp: string): string {
// This two turns expressions like: ( exp ), ( exp), (exp ) into (exp).
  exp = exp
    .replace(/ +/g, '')
    .replace(/ *\( */g, '(')
    .replace(/ *\) */g, ')')
    .replace(/ *\+ */g, '+')
    .replace(/ *\* */g, '*')
    .replace(/ *- */g, '-')
    .replace(/ *\/ */g, '/')
    .replace(/ *\^ */g, '^');
// Checks if there are empty expressions on input
  if (exp.length === 0 || exp.search(/\( *\)/) >= 0) {
    throw new InputError('There cannot be empty expressions on input.');
  }
// Checks there are no errors on input
  const errorPattern =
    /(([*+\/^])([*+\/^])+)|(\(([*+\/^])+)|(([*+\/^])+\))/;
  if (exp.search(errorPattern) >= 0) {
    throw new Error('There are two operators that does not suppose' +
      ' to be together: ' + exp + '.');
  }

  return exp;
}