From 2aa2f29e2b287799b20e3d99a15aa6a0033b1fbc Mon Sep 17 00:00:00 2001
From: Devan Patel <devanp92@ufl.edu>
Date: Mon, 27 Apr 2015 12:41:04 -0400
Subject: [PATCH] Adding support for Bell Numbers in Combinatorics Module.

---
 lib/function/combinatorics/bellNumbers.js     | 69 +++++++++++++++++++
 lib/math.js                                   |  1 +
 lib/util/latex.js                             |  1 +
 .../combinatorics/bellNumbers.test.js         | 37 ++++++++++
 4 files changed, 108 insertions(+)
 create mode 100644 lib/function/combinatorics/bellNumbers.js
 create mode 100644 test/function/combinatorics/bellNumbers.test.js

diff --git a/lib/function/combinatorics/bellNumbers.js b/lib/function/combinatorics/bellNumbers.js
new file mode 100644
index 000000000..3c02f2be8
--- /dev/null
+++ b/lib/function/combinatorics/bellNumbers.js
@@ -0,0 +1,69 @@
+'use strict';
+
+module.exports = function (math) {
+  var util = require('../../util/index'),
+
+  BigNumber = math.type.BigNumber,
+  collection = math.collection,
+
+  isNumber = util.number.isNumber,
+  isInteger = util.number.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 take integer arguments.
+  * The following condition must be enforced: n >= 0
+  *
+  * Syntax:
+  *
+  *   math.bellNumbers(n)
+  *
+  * Examples:
+  *
+  *    math.bellNumbers(4, 3); //returns 10
+  *
+  *
+  * @param {Number | BigNumber} n    Total number of objects in the set
+  * @return {Number | BigNumber}     B(n)
+  */
+
+  math.bellNumbers = function bellNumbers (n) {
+    var result = 0;
+    var arity = arguments.length;
+    if (arity != 1) {
+      throw new math.error.ArgumentsError('bellNumbers', arguments.length, 1);
+    }
+
+    if (isNumber(n)) {
+      if (!isInteger(n) || n < 0) {
+        throw new TypeError('Positive integer value expected in function bellNumbers');
+      }
+      // Sum (k=0, n) S(n,k).
+      for(var i = 0; i <= n; i++) {
+        var stirlingS2 = math.stirlingS2(n,i);
+        result += stirlingS2;
+      }
+      return result;
+   //  } else if (n instanceof BigNumber) {
+   //   result = new BigNumber(0);
+   //   for (var i = new BigNumber(1); i.lte(n); i = i.plus(1)) {
+   //     result += (math.stirlingS2(n, i));
+   //   }
+   //   return result;
+   // } else{
+     throw new math.error.UnsupportedTypeError('bellNumbersg', math['typeof'](n));
+   }
+ };
+
+
+
+  /**
+   * Test whether BigNumber n is a positive integer
+   * @param {BigNumber} n
+   * @returns {boolean} isPositiveInteger
+   */
+   var isPositiveInteger = function(n) {
+     return n.isInteger() && n.gte(0);
+   };
+ };
diff --git a/lib/math.js b/lib/math.js
index b1c3f3934..4dc8e7a15 100644
--- a/lib/math.js
+++ b/lib/math.js
@@ -270,6 +270,7 @@ function create (config) {
 
   //functions - combinatorics
   require('./function/combinatorics/stirlingS2')(math, _config);
+  require('./function/combinatorics/bellNumbers')(math, _config);
 
   // functions - complex
   require('./function/complex/arg')(math, _config);
diff --git a/lib/util/latex.js b/lib/util/latex.js
index 98bc967ac..3deac3845 100644
--- a/lib/util/latex.js
+++ b/lib/util/latex.js
@@ -169,6 +169,7 @@ var functions = {
 
   //combinatorics
   'stirlingS2': '\\mathrm{S}\\left(%0%,%1%\\right)',
+  'bellNumbers': '\\mathrm{B}_{%0%}',
 
   //construction
   'bignumber': {
diff --git a/test/function/combinatorics/bellNumbers.test.js b/test/function/combinatorics/bellNumbers.test.js
new file mode 100644
index 000000000..e383e3a0f
--- /dev/null
+++ b/test/function/combinatorics/bellNumbers.test.js
@@ -0,0 +1,37 @@
+var assert = require('assert'),
+error = require('../../../lib/error/index'),
+math = require('../../../index'),
+bellNumbers = math.bellNumbers;
+
+describe('bellNumbers', function() {
+
+  it('should calculate the number of partitions of a set', function() {
+    assert.equal(bellNumbers(3), 5);
+    assert.equal(bellNumbers(0), 1);
+    assert.equal(bellNumbers(8), 4140);
+  });
+
+  // it('should calculate the bellNumbers of n items with BigNumbers', function(){
+  //   assert.deepEqual(bellNumbers(math.bignumber(2)), math.bignumber(2));
+  // //   assert.deepEqual(bellNumbers(math.bignumber(10), math.bignumber(4)),math.bignumber(34105));
+  // //   assert.deepEqual(bellNumbers(math.bignumber(8), math.bignumber(6)),math.bignumber(266));
+  // });
+
+  it('should not work with non-integer and negative input', function() {
+    assert.throws(function() {bellNumbers(0.5)}, TypeError);
+    assert.throws(function() {bellNumbers(-1)}, TypeError);
+    // assert.throws(function() {bellNumbers(math.bignumber(-3))}, TypeError);
+    // assert.throws(function() {bellNumbers(math.bignumber(3.5))}, TypeError);
+  });
+
+  it('should not work with the wrong number or type of arguments', function() {
+    assert.throws(function() {bellNumbers(5, 3, 2)});
+    assert.throws(function() {bellNumbers(true, "hello world")});
+  });
+
+  it('should LaTeX bellNumbers', function () {
+    var expression = math.parse('bellNumbers(3)');
+    assert.equal(expression.toTex(), '\\mathrm{B}_{3}');
+  });
+
+});