Implementation of discrete summations

src/factoriesAny.js

@@ -53,6 +53,7 @@ export { createSign } from './function/arithmetic/sign.js'
 export { createSqrt } from './function/arithmetic/sqrt.js'
 export { createSquare } from './function/arithmetic/square.js'
 export { createSubtract } from './function/arithmetic/subtract.js'
+export { createSummation } from './function/arithmetic/summation.js'
 export { createXgcd } from './function/arithmetic/xgcd.js'
 export { createInvmod } from './function/arithmetic/invmod.js'
 export { createDotMultiply } from './function/arithmetic/dotMultiply.js'

src/factoriesNumber.js

@@ -122,6 +122,7 @@ export const createSign = /* #__PURE__ */ createNumberFactory('sign', signNumber
 export const createSqrt = /* #__PURE__ */ createNumberFactory('sqrt', sqrtNumber)
 export const createSquare = /* #__PURE__ */ createNumberFactory('square', squareNumber)
 export const createSubtract = /* #__PURE__ */ createNumberFactory('subtract', subtractNumber)
+export { createSummation } from './function/arithmetic/summation.js'
 export const createXgcd = /* #__PURE__ */ createNumberFactory('xgcd', xgcdNumber)
 export const createDivideScalar = /* #__PURE__ */ createNumberFactory('divideScalar', divideNumber)
 export const createPow = /* #__PURE__ */ createNumberFactory('pow', powNumber)

src/function/arithmetic/summation.js

@@ -0,0 +1,45 @@
+import { isInteger } from '../../utils/number.js'
+import { factory } from '../../utils/factory.js'
+
+const name = 'summation'
+const dependencies = ['typed', 'numeric']
+
+export const createSummation = /* #__PURE__ */ factory(name, dependencies, ({ typed, numeric }) => {
+  /**
+    * Takes two integer values start, and end, and a functrion.
+    * Calculates the summation of the function over the start to end range.
+    *
+    * Syntax:
+    *
+    *   math.summation(start, end, func))
+    *
+    * Examples:
+    *
+    *   // Summation of squares from 1 to 5: 1^2 + 2^2 + 3^2 + 4^2 + 5^2
+    *   math.sum(1, 5, x => x ** 2)       // returns 55
+    *
+    * This function does not support collections (Array or Matrix).
+    *
+    * @param  {number} start                                       Start
+    * @param  {number} end                                         Denominator
+    * @param  {function} func                                      f(n)
+    * @return {number | BigNumber | Fraction}                      Sum of f(n) for n from [start, end]
+    */
+  return typed(name, {
+    'number, number, function': function (start, end, func) {
+      if (!isInteger(start) || !isInteger(end)) {
+        throw new Error('For summations, start and end must be integers')
+      }
+      if (start > end) {
+        throw new Error('For summations, start must be greater than, or equal to end')
+      }
+
+      let sum = 0
+      for (let i = start; i <= end; i++) {
+        sum += func(i)
+      }
+
+      return sum
+    }
+  })
+})

test/unit-tests/function/arithmetic/summation.test.js

@@ -0,0 +1,22 @@
+import assert from 'assert'
+
+import math from '../../../../src/defaultInstance.js'
+
+const summation = math.summation
+
+describe('summation', function () {
+  it('should produce the sum of a function over a range from start to end', function () {
+    assert.deepEqual(summation(1, 5, x => x ** 2), 55)
+    assert.deepEqual(summation(1, 4, x => x ** 3, 100))
+  })
+
+  it('should throw an error if start or end are not integers', function () {
+    assert.throws(function () { summation(1.1, 2.2, x => x ** 2) })
+    assert.throws(function () { summation(1.1, 2, x => x ** 2) })
+    assert.throws(function () { summation(1, 2.4, x => x ** 2) })
+  })
+
+  it('should throw an error if end is less than start', function () {
+    assert.throws(function () { summation(2, 1, x => x ** 2) })
+  })
+})