69 lines
2.5 KiB
Markdown
69 lines
2.5 KiB
Markdown
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<!-- Note: This file is automatically generated from source code comments. Changes made in this file will be overridden. -->
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# Function rationalize
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Transform a rationalizable expression in a rational fraction.
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If rational fraction is one variable polynomial then converts
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the numerator and denominator in canonical form, with decreasing
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exponents, returning the coefficients of numerator.
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## Syntax
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```js
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rationalize(expr)
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rationalize(expr, detailed)
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rationalize(expr, scope)
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rationalize(expr, scope, detailed)
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```
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### Parameters
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Parameter | Type | Description
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--------- | ---- | -----------
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`expr` | Node | string | The expression to check if is a polynomial expression
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`optional` | Object | boolean | scope of expression or true for already evaluated rational expression at input
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`detailed` | Boolean | optional True if return an object, false if return expression node (default)
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### Returns
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Type | Description
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---- | -----------
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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
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### Throws
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Type | Description
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---- | -----------
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## Examples
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```js
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math.rationalize('sin(x)+y')
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// Error: There is an unsolved function call
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math.rationalize('2x/y - y/(x+1)')
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// (2*x^2-y^2+2*x)/(x*y+y)
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math.rationalize('(2x+1)^6')
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// 64*x^6+192*x^5+240*x^4+160*x^3+60*x^2+12*x+1
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math.rationalize('2x/( (2x-1) / (3x+2) ) - 5x/ ( (3x+4) / (2x^2-5) ) + 3')
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// -20*x^4+28*x^3+104*x^2+6*x-12)/(6*x^2+5*x-4)
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math.rationalize('x/(1-x)/(x-2)/(x-3)/(x-4) + 2x/ ( (1-2x)/(2-3x) )/ ((3-4x)/(4-5x) )') =
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// (-30*x^7+344*x^6-1506*x^5+3200*x^4-3472*x^3+1846*x^2-381*x)/
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// (-8*x^6+90*x^5-383*x^4+780*x^3-797*x^2+390*x-72)
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math.rationalize('x+x+x+y',{y:1}) // 3*x+1
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math.rationalize('x+x+x+y',{}) // 3*x+y
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const ret = math.rationalize('x+x+x+y',{},true)
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// ret.expression=3*x+y, ret.variables = ["x","y"]
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const ret = math.rationalize('-2+5x^2',{},true)
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// ret.expression=5*x^2-2, ret.variables = ["x"], ret.coefficients=[-2,0,5]
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```
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## See also
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[simplify](simplify.md)
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