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https://github.com/infusion/Polynomial.js

A JavaScript library to work with polynomials
https://github.com/infusion/Polynomial.js

Last synced: 26 days ago
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A JavaScript library to work with polynomials

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README 

        
# Polynomial.js



[![NPM Package](https://img.shields.io/npm/v/polynomial.svg?style=flat)](https://npmjs.org/package/polynomial "View this project on npm")

[![Build Status](https://travis-ci.org/infusion/Polynomial.js.svg?branch=master)](https://travis-ci.org/infusion/Polynomial.js)

[![MIT license](http://img.shields.io/badge/license-MIT-brightgreen.svg)](http://opensource.org/licenses/MIT)



Polynomials are defined as the sum of variables with increasing integer power and their coefficients in a certain field. For example the following might be still known from school:



```

P(x) = x^2 + 4x + 3

```



Examples

===



Adding two polynomials

---

```javascript

var p = new Polynomial("3x^2").add("-x^2"); // 2x^2

```



Second derivative of polynomial

---

```javascript

var p = new Polynomial("5+3x^3+6x^5").derive(2); // 120x^3+18x

```



Parser

===



Any function (see below) as well as the constructor of the *Polynomial* class parses its input like this.



You can pass either Objects, Doubles or Strings. Make sure strings don't contain any white-spaces or brackets. The parser doesn't analyse the string recursively.



Objects

---

```javascript

new Polynomial({'3': 4, '5': '9'}); // 9x^5+4x^3

new Polynomial([1,2,3]); //3x^2+2x+1

```



Doubles

---

```javascript

new Polynomial(55); // 55x^0

```



Strings

---

```javascript

new Polynomial("98x^2+4+23x^4");

```

The string parser passes every coefficient directly to the field parser, which allows to pass complex and rational coefficients as well:



```javascript

// Example with complex numbers

Polynomial.setField("C");

new Polynomial("98x^2+i+23ix^4");



// Example with rational numbers

Polynomial.setField("Q");

new Polynomial("5/3x^3+4/3x");

```



Fields

===



Polynomial.js is held general in order to operate on various fields. [Fraction.js](https://github.com/infusion/Fraction.js) and [Complex.js](https://github.com/infusion/Complex.js) build the perfect base to extend polynomials to rational and complex numbers.



* ℚ: Rational numbers supported by [Fraction.js](https://github.com/infusion/Fraction.js) 

* ℂ: Complex numbers supported by [Complex.js](https://github.com/infusion/Complex.js)

* ℍ: Quaternions supported by [Quaternion.js](https://github.com/infusion/Quaternion.js)

* ℤp: Field of integers mod p, with p prime

* ℝ: Field of real numbers



Examples

---

```javascript

Polynomial.setField("Q");

Polynomial("3/2x^2-4x").mod("5x"); // 0



Polynomial.setField("Z11");

Polynomial("3x^2+x+7").gcd("3x^2+x+7"); // x^2+4x+6



Polynomial.setField("Z7");

Polynomial("9x^2+4").pow(3); // x^6+6x^4+5x^2+1



Polynomial.setField("R");

Polynomial("3x^3-1").mul(4); // 12x^3-4



// Derivative of polynomial

Polynomial.setField("Q");

Polynomial("5+3x^3+6x^5").derive(); // 30x^4+9x^2



// Integrated polynomial

Polynomial.setField("Q");

Polynomial("3x^2").integrate(); // x^3

```



Functions

===



Polynomial add(n)

---

Returns the sum of the actual polynomial and the parameter n



Polynomial sub(n)

---

Returns the difference of the actual polynomial and the parameter n



Polynomial mul(n)

---

Returns the product of the actual polynomial and the parameter n



Polynomial addmul(x, y)

---

Adds the product of x and y to the actual number



Polynomial div(n)

---

Returns the quotient of the actual polynomial and the parameter n



There is a global variable to enable division tracing like this, if you want to output details:



```javascript

Polynomial.trace = true;

new Polynomial("x^4+3x^3+2x^2+6x")

        .div("x+3");

console.log(Polynomial.trace.map(x => x.toString())); // ["x^4+3x^3", "2x^2+6x", "0"]

```



Polynomial neg(n)

---

Returns the negated polynomial



Polynomial reciprocal(n)

---

Returns the [reciprocal polynomial](https://en.wikipedia.org/wiki/Reciprocal_polynomial)



Polynomial lc()

---

Gets the leading coefficient



Polynomial lm()

---

Gets the leading monomial



Polynomial monic()

---

Divide all coefficients of the polynomial by lc()



Polynomial derive(n)

---

Returns the n-th derivative of the polynomial



Polynomial integrate(n)

---

Returns the n-th integration of the polynomial



mixed eval(x)

---

Evaluate the polynomial at point x, using [Horner's method](https://en.wikipedia.org/wiki/Horner%27s_method). Type for x must be a valid value for the given field.



mixed result(x)

---

(Deprecated) Alias for `eval`.



Polynomial pow(exp)

---

Returns the power of the actual polynomial, raised to an integer exponent.



Polynomial mod(n)

---

Returns the modulus (rest of the division) of the actual polynomial and n (this % n).



Polynomial gcd(n)

---

Returns the greatest common divisor of two polynomials



Number degree()

---

Returns the degree of the polynomial



String toString()

---

Generates a string representation of the actual polynomial. This makes use of the `toString()` function of the field.



String toLatex()

---

Generates a LaTeX representation of the actual polynomial.



String toHorner()

---

Formats the actual polynomial to a [Horner Scheme](https://en.wikipedia.org/wiki/Horner's_method)



Polynomial clone()

---

Creates a copy of the actual Polynomial object



Polynomial Polynomial::fromRoots(roots)

---

Creates a new (monic) Polynomial whose roots lie at the values provided in the array `roots`



Polynomial::setField(x)

---

Sets the field globally. Choose one of the following strings for `x`:



- "R": real numbers

- "Q": rational numbers

- "H": quaternions

- "C": complex numbers

- "Zp": with p a prime number, like "Z7"

- or an object with the field operators. See examples folders for bigint



Exceptions

===

If a really hard error occurs (parsing error, division by zero), *polynomial.js* throws exceptions! Please make sure you handle them correctly.



Installation

===

Installing polynomial.js is as easy as cloning this repo or use one of the following commands:



```

bower install polynomial.js

```

or



```

npm install polynomial

```



Using Polynomial.js with the browser

===

```html

 

 



Polynomial.setField("C")

console.log(Polynomial("4x+3i"));



```



Using Polynomial.js with require.js

===

```html



requirejs(['polynomial.js'],

function(Polynomial) {

console.log(Polynomial("4x+3i"));

});



```



Coding Style

===

As every library I publish, polynomial.js is also built to be as small as possible after compressing it with Google Closure Compiler in advanced mode. Thus the coding style orientates a little on maxing-out the compression rate. Please make sure you keep this style if you plan to extend the library.



Testing

===

If you plan to enhance the library, make sure you add test cases and all the previous tests are passing. You can test the library with



```

npm test

```



Copyright and licensing

===

Copyright (c) 2015, [Robert Eisele](http://www.xarg.org/)

Dual licensed under the MIT or GPL Version 2 licenses.