math.function

Function to work with mathemathic concepts.

Javascript function does not have useful properties like domain and image. This package solves it creating a constructor that returns a function with this properties.

Version

0.1.0

Install

npm install math.function

Usage

var MFunction = require('math.function')
var MSet = require('math.set')

var sum = new MFunction(intervalSum)

sum.domain // returns [new MSet('-Infinity, Infinity'), new MSet('-Infinity, Infinity')]
sum.image // returns (-Infinity, Infinity) instance of math.set

sum(5, 6) // returns 11

sum.domain = ['(2, 3] U {4}', '(1, 2) U {3}']
sum.domain // returns [new MSet('(2, 3] U {4}'), new MSet('(1, 2) U {3}')]
sum.image // returns new MSet('(3, 5) U (5, 6] U {7}')

sum(2, 3) // throws an error (2 does not belongs to domain)

function intervalSum (a, b) {
    return [{
        value: a[0].value + b[0].value,
        limit: a[0].limit || b[0].limit
    }, {
        value: a[1].value + b[1].value,
        limit: a[1].limit || b[1].limit
    }]
}

API

Function

constructor(intervalFunction, domain)

Constructor creates an instance of javascript Function based on a function parameter intervalFunction. intervalFunction function defines the behaviour of the created function when it is applied to intervals with this data structure.

For example, in sum operation, given intervals (a, b] and [c, d), the result is the interval (a + c, b + d). Investigating a bit, it is posible to deduce that the function that given two intervals returns the interval that represents the sum of intervals is:

function intervalSum (interval1, interval2) {
    return [{
        value: interval1[0].value + interval2[0].value,
        limit: interval1[0].limit || interval2[0].limit
    }, {
        value: interval1[1].value + interval2[1].value,
        limit: interval1[1].limit || interval2[1].limit
    }]
}

Then, passing this function as parameter the sum function is created:

var MFunction = require('math.function')
var sum = new MFunction(intervalSum)
sum(2, 6) // returns 8
sum(5, 5) // returns 10

intervalFunction (...intervals)

This parameter function has the same arity as function created by constructor. It must receive interval parameters and return a SetCastable value that represents the image function that created function when is applied to these intervals.

domain

domain is an optional parameter. It is an array of SetCastable values that defines the domain of created function.

.domain

domain property is an array of instances of math.set. The length of array corresponds with the number of parameters of function instance. The domain property is an array of Real sets by default:

var MFunction = require('math.function')
var MSet = require('math.set')

var sum = new MFunction(intervalSum)
sum.domain // it returns default value new [new MSet('(-Infinity, Infinity)'), new MSet('(-Infinity, Infinity)')]

Besides, if domain is set with an array of SetCastable values, it return a set that represents this value:

sum.domain = ['(2, 4)', '{3, 4, 5} U [0, 1)']
sum.domain // now it returns [new MSet('(2, 4)'), new MSet('{3, 4, 5} U [0, 1)')]

.image

image property is an instance of math.set that depends on the domain of function instance and intervalFunction constructor parameter. For example:

var MFunction = require('math.function')
var MSet = require('math.set')

var sum = MFunction(intervalSum)

sum.domain = ['[2, 3]'), '{5}']
sum.image // returns new MSet('[7, 8]')

sum.domain = ['(2, 3] U {4}', '(1, 2) U {3}']
sum.image // returns new MSet('(3, 5) U (5, 6] U {7}')

LICENSE

MIT