polynomium

polynomium

Library for symbolically representing and working with polynomials.

Package Installation and Usage

The package is available on npm:

npm install polynomium

The library can be imported in the usual ways:

var polynomium = require('polynomium');

The library also supports standalone usage in browsers:

<script src="https://lapets.github.io/polynomium/lib/polynomium.js"></script>

Examples

The library supports the creation of objects that represent polynomials of zero or more variables:

var x = polynomium.v('x');
var y = polynomium.v('y');
var a = polynomium.c(2);
var b = polynomium.c(3);
var c = polynomium.c(5);
var p = (y.mul(x.add(b)));
var q = (y.mul(x.add(b))).mul(a);
var r = (y.mul(x.add(b))).mul((y.mul(x.add(b))));

Given the polynomials above, it is possible to display them in a human-readable way:

> x.toString()
'x'
> b.toString()
'3'
> (y.add(x.add(b))).toString()
'y + x + 3'
> p.toString()
'x*y + 3y'
> q.toString()
'2x*y + 6y'
> q.maxCoefficients(p).toString()
'2x*y + 6y'
> r.toString()
'x^2*y^2 + 6x*y^2 + 9y^2'

When possible, the operator functions will convert arguments that are numeric constants and valid variable names into polynomium objects:

> (y.add(x.add(5))).toString()
'y + x + 5'
> (y.add('x')).toString()
'y + x'

By default, the terms in the outer sum are in order of descending significance (where a term's significance is the sum of its exponents across its factors). The individual variables within factors are in ascending alphabetical order.

It is also possible to evaluate a polynomial by supplying an object that binds explicit values to each variable:

> r.evaluate({"x":2, "y":5})
625
> r({"x":2, "y":5})
625

In some cases, function objects cannot be used within data structures (such as when converting to JSON). A method is included for such scenarios:

> var o = r.toObject()
> o
{ polynomium: true,
  terms: 
   { 'y': { '2': 9 }, 
     'x,y': { '1,2': 6, '2,2': 1 } } }
> polynomium.add(o, o).toObject()
{ polynomium: true,
  terms: 
   { 'y': { '2': 18 }, 
     'x,y': { '1,2': 12, '2,2': 2 } } }

Testing

Unit tests are included in test/test.js. They can be run using Mocha:

npm test