numbers.js

numbers.js is a client-side javascript library that adds some advanced mathematics functionality to the standard Math library.

Library Contents

• README.md: This file.
• numbers-x.y.z.js: Version x.y.z of the numbers library, suitable for development.
• numbers-x.y.z-min.js: Version x.y.z of the numbers library, suitable for production.

Reference

Metadata

• ver (or version): The current version of the numbers library.

  console.log(F.ver); // > 0.1.0

Arithmetic and Number Theory Functions

• sum: Find the sum of a set of numbers.

  var s = F.sum([1,2,3,4]);
  console.log(s); // > 10

• product: Find the product of a set of numbers.

  var p = F.product([1,2,3,4]);
  console.log(p); // > 24

• nFac (or factorial): Find the factorial (n!) of a number n.

  var f1 = F.nFac(5);
  var f2 = F.factorial(5);
  console.log(f1); // > 120
  console.log(f2); // > 120

• gcd (or greatestCommonDivisor): Find the greatest common divisor of a set of numbers.

  var d1 = F.gcd([2,4,6]);
  var d2 = F.greatestCommonDivisor([2,4,6]);
  console.log(d1); // > 2
  console.log(d2); // > 2

• lcm (or leastCommonMultiple): Find the least common multiple of a set of numbers.

  var m1 = F.lcm([3,6,9,12]);
  var m2 = F.leastCommonMulitple([3,6,9,12]);
  console.log(m1); // > 36
  console.log(m2); // > 36

• isPrime: Determine whether a number n (less than 2⁵³) is prime using a combination of sieve and trial division.

  console.log(F.isPrime(21)); // > false
  console.log(F.isPrime(31)); // > true

• isRelativelyPrime: Determine whether two numbers are relatively prime to one another.

  console.log(F.isRelativelyPrime(6,9)); // > false
  console.log(F.isRelativelyPrime(4,9)); // > true

• isCongruent: Determine whether two numbers are congruent to one another by some modulus.

  console.log(F.isCongruent(6,2,3)); // > false
  console.log(F.isCongruent(5,2,3)); // > true

Statistical Functions

• mean (or avg): Find the arithmetic mean of a set of numbers.

  console.log(F.mean([2,3,4,5])); // > 3.5
  console.log(F.avg([2,3,4,5])); // > 3.5

• variance: Find the variance of a set of numbers.

  console.log(F.variance([2,3,4,5])); // > 1.25

• stdev (or standardDeviation): Find the standard deviation of a set of numbers.

  console.log(F.stdev([2,3,4,5])); // > 1.118033988749895
  console.log(F.standardDeviation([2,3,4,5])); // > 1.118033988749895

• sem (or standardErrorOfMean): Find the standard error of the mean of a set of numbers.

• covariance: Find the covariance of two sets of numbers.

• z (or zValue): Given a mean and standard deviation, find the z-value of a number n.

Combinatorial Functions

• nPr (or permutations): Find the number of ordered sets of r items that can be selected from a set of n items.

  console.log(F.nPr(20,2)); // > 380
  console.log(F.permutations(20,2)); // > 380

• nCr (or combinations): Find the number of unordered sets of r items that can be selected from a set of n items.

  console.log(F.nCr(10,5)); // > 252
  console.log(F.combinations(10,5)); // > 252

Vector Calculus and Linear Algebra Functions

• dotProduct: Find the inner product of two vectors.

  console.log(F.dotProduct([1,1], [5,7])); // > 12

• isOrthogonal: Determine whether two vectors are orthogonal to one another.

  console.log(F.isOrthogonal([-5,1],[1,5])); // > true
  console.log(F.isOrthogonal([-9,6,2],[4,7,5]); // > false

• magnitude: Determine the magnitude of a vector.

  console.log(F.magnitude([0,1])); // > 1 (unit vector)
  console.log(F.magnitude([3,4,5])); // > 7.071067811865475

• normalize: Normalize a vector.

  console.log(F.normalize([0,8])); // > [0,1]
  console.log(F.normalize([3,4])); // > [0.6,0.8]

Conversion Functions

• rebase: Convert a number from one base to another. If no value is given for the input base, decimal (base 10) is assumed.

  console.log(F.rebase(42,2)); // > 101010
  console.log(F.rebase(101010,10,2)); // > 42

• deg2rad: Convert an angle in degrees to an angle in radians.

  console.log(F.deg2rad(45)); // > 0.7853981633974483

• rad2deg: Convert an angle in radians to an angle in degrees.

  console.log(F.rad2deg(Math.PI/2); // > 90

• rect2pol: Convert a point described in cartesian coordinates (x,y) to a point described in polar coordinates (r,t). Returns an object with properties r and t, with t measured in radians from -Math.PI to Math.PI.

  var p = F.rect2pol(0,1);
  console.log(p.r); // > 1
  console.log(p.t); // > 1.5707963267948966

• pol2rect: Convert a point described in polar coordinates (r,t) to a point described in cartesian coordinates (x,y). Returns an object with properties x and y.

  var p = F.pol2rect(1,3*Math.PI/4);
  console.log(p.x); // > -0.7071067811865475
  console.log(p.y); // > 0.7071067811865476

Other Functions

• noConflict: Run numbers.js in no-conflict mode, optionally aliasing the library to a different variable. Has no effect on global F variable if there is no conflict.

  Example 1: Reassign value of F

  <script>
    window.F = { foo: function() { return "Hello, world!"; } };
  </script>
  <script src="numbers-0.1.0-min.js"></script>
  <script>
    console.log(F.foo()); // > undefined
    G = numbers.noConflict();
    console.log(F.foo()); // > Hello, world!
    console.log(G.avg([1,2,3,4])); > 2.5
  </script>

  Example 2: Use global numbers variable

  <script>
    window.F = { foo: function() { return "Hello, world!"; } };
  </script>
  <script src="numbers-0.1.0-min.js"></script>
  <script>
    console.log(F.foo()); // > undefined
    numbers.noConflict();
    console.log(F.foo()); // > Hello, world!
    console.log(numbers.avg([1,2,3,4])); > 2.5
  </script>

  Example 3: Do nothing if there is no conflict

  <script src="numbers-0.1.0-min.js"></script>
  <script>
    console.log(F.avg([1,2,3,4])); // > 2.5
    numbers.noConflict();
    console.log(F.avg([1,2,3,4])); // > 2.5
  </script>