mathjs/src/function/combinatorics/bellNumbers.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

'use strict'

function factory (type, config, load, typed) {
  const add = load(require('../arithmetic/add'))
  const stirlingS2 = load(require('./stirlingS2'))
  const isNegative = load(require('../utils/isNegative'))
  const isInteger = load(require('../utils/isInteger'))

  /**
   * The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S.
   * bellNumbers only takes integer arguments.
   * The following condition must be enforced: n >= 0
   *
   * Syntax:
   *
   *   math.bellNumbers(n)
   *
   * Examples:
   *
   *    math.bellNumbers(3) // returns 5
   *    math.bellNumbers(8) // returns 4140
   *
   * See also:
   *
   *    stirlingS2
   *
   * @param {Number | BigNumber} n    Total number of objects in the set
   * @return {Number | BigNumber}     B(n)
   */
  const bellNumbers = typed('bellNumbers', {
    'number | BigNumber': function (n) {
      if (!isInteger(n) || isNegative(n)) {
        throw new TypeError('Non-negative integer value expected in function bellNumbers')
      }

      // Sum (k=0, n) S(n,k).
      let result = 0
      for (let i = 0; i <= n; i++) {
        result = add(result, stirlingS2(n, i))
      }

      return result
    }
  })

  bellNumbers.toTex = { 1: `\\mathrm{B}_{\${args[0]}}` }

  return bellNumbers
}

exports.name = 'bellNumbers'
exports.factory = factory