Function rationalize #

Transform a rationalizable expression in a rational fraction. If rational fraction is one variable polynomial then converts the numerator and denominator in canonical form, with decreasing exponents, returning the coefficients of numerator.

Syntax #

rationalize(expr)
rationalize(expr, detailed)
rationalize(expr, scope)
rationalize(expr, scope, detailed)

Parameters #

Parameter	Type	Description
`expr`	Node \| string	The expression to check if is a polynomial expression
`optional`	Object \| boolean	scope of expression or true for already evaluated rational expression at input
`detailed`	Boolean	optional True if return an object, false if return expression node (default)

Returns #

Type Description

Object | Node The rational polynomial of expr or an object {expression, numerator, denominator, variables, coefficients}, where expression is a Node with the node simplified expression, numerator is a Node with the simplified numerator of expression, denominator is a Node or boolean with the simplified denominator or false (if there is no denominator), variables is an array with variable names, and coefficients is an array with coefficients of numerator sorted by increased exponent {Expression Node} node simplified expression

Type	Description
Object \| Node	The rational polynomial of `expr` or an object `{expression, numerator, denominator, variables, coefficients}`, where `expression` is a `Node` with the node simplified expression, `numerator` is a `Node` with the simplified numerator of expression, `denominator` is a `Node` or `boolean` with the simplified denominator or `false` (if there is no denominator), `variables` is an array with variable names, and `coefficients` is an array with coefficients of numerator sorted by increased exponent {Expression Node} node simplified expression

Throws #

Type | Description —- | ———–

Examples #

math.rationalize('sin(x)+y')
              //  Error: There is an unsolved function call
math.rationalize('2x/y - y/(x+1)')
              // (2*x^2-y^2+2*x)/(x*y+y)
math.rationalize('(2x+1)^6')
              // 64*x^6+192*x^5+240*x^4+160*x^3+60*x^2+12*x+1
math.rationalize('2x/( (2x-1) / (3x+2) ) - 5x/ ( (3x+4) / (2x^2-5) ) + 3')
              // -20*x^4+28*x^3+104*x^2+6*x-12)/(6*x^2+5*x-4)
math.rationalize('x/(1-x)/(x-2)/(x-3)/(x-4) + 2x/ ( (1-2x)/(2-3x) )/ ((3-4x)/(4-5x) )') =
              // (-30*x^7+344*x^6-1506*x^5+3200*x^4-3472*x^3+1846*x^2-381*x)/
              //     (-8*x^6+90*x^5-383*x^4+780*x^3-797*x^2+390*x-72)

math.rationalize('x+x+x+y',{y:1}) // 3*x+1
math.rationalize('x+x+x+y',{})    // 3*x+y

const ret = math.rationalize('x+x+x+y',{},true)
              // ret.expression=3*x+y, ret.variables = ["x","y"]
const ret = math.rationalize('-2+5x^2',{},true)
              // ret.expression=5*x^2-2, ret.variables = ["x"], ret.coefficients=[-2,0,5]