fix: allow zero values in multinomial

HISTORY.md

@@ -2,6 +2,9 @@
 
 # unpublished changes since 15.2.0
 
+- Fix: `multinomial` threw a `TypeError` on arrays containing a zero, like
+  `multinomial([2, 0, 1])`. Zero is a valid count (`0! = 1`), consistent with
+  `combinations` and `factorial`.
 - Docs: fix the browser example `rocket_trajectory_optimization.html` (#3654).
   Thanks @dvd101x.
 

src/function/probability/multinomial.js

@@ -2,14 +2,14 @@ import { deepForEach } from '../../utils/collection.js'
 import { factory } from '../../utils/factory.js'
 
 const name = 'multinomial'
-const dependencies = ['typed', 'add', 'divide', 'multiply', 'factorial', 'isInteger', 'isPositive']
+const dependencies = ['typed', 'add', 'divide', 'multiply', 'factorial', 'isInteger', 'isNegative']
 
-export const createMultinomial = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, divide, multiply, factorial, isInteger, isPositive }) => {
+export const createMultinomial = /* #__PURE__ */ factory(name, dependencies, ({ typed, add, divide, multiply, factorial, isInteger, isNegative }) => {
   /**
    * Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities.
    *
    * multinomial takes one array of integers as an argument.
-   * The following condition must be enforced: every ai <= 0
+   * The following condition must be enforced: every ai >= 0
    *
    * Syntax:
    *
@@ -32,7 +32,7 @@ export const createMultinomial = /* #__PURE__ */ factory(name, dependencies, ({
       let denom = 1
 
       deepForEach(a, function (ai) {
-        if (!isInteger(ai) || !isPositive(ai)) {
+        if (!isInteger(ai) || isNegative(ai)) {
           throw new TypeError('Positive integer value expected in function multinomial')
         }
         sum = add(sum, ai)

test/unit-tests/function/probability/multinomial.test.js

@@ -15,6 +15,16 @@ describe('multinomial', function () {
     assert.deepStrictEqual(multinomial([math.bignumber(10), math.bignumber(1), math.bignumber(2)]), math.bignumber(858))
   })
 
+  it('should allow zero values (0! = 1), consistent with combinations', function () {
+    assert.strictEqual(multinomial([0]), 1)
+    assert.strictEqual(multinomial([3, 0]), 1)
+    assert.strictEqual(multinomial([2, 0, 1]), 3)
+    assert.strictEqual(multinomial([0, 4, 4]), 70)
+    // multinomial([k, n - k]) must agree with combinations(n, k)
+    assert.strictEqual(multinomial([5, 0]), math.combinations(5, 5))
+    assert.deepStrictEqual(multinomial([math.bignumber(3), math.bignumber(0)]), math.bignumber(1))
+  })
+
   it('should not work with non-integer and negative input', function () {
     assert.throws(function () { multinomial([0.5, 3]) }, TypeError)
     assert.throws(function () { multinomial([math.bignumber(3), math.bignumber(0.5)]) }, TypeError)