rationalize.md (2601B)
1 <!-- Note: This file is automatically generated from source code comments. Changes made in this file will be overridden. --> 2 3 # Function rationalize 4 5 Transform a rationalizable expression in a rational fraction. 6 If rational fraction is one variable polynomial then converts 7 the numerator and denominator in canonical form, with decreasing 8 exponents, returning the coefficients of numerator. 9 10 11 ## Syntax 12 13 ```js 14 rationalize(expr) 15 rationalize(expr, detailed) 16 rationalize(expr, scope) 17 rationalize(expr, scope, detailed) 18 ``` 19 20 ### Parameters 21 22 Parameter | Type | Description 23 --------- | ---- | ----------- 24 `expr` | Node | string | The expression to check if is a polynomial expression 25 `optional` | Object | boolean | scope of expression or true for already evaluated rational expression at input 26 `detailed` | Boolean | optional True if return an object, false if return expression node (default) 27 28 ### Returns 29 30 Type | Description 31 ---- | ----------- 32 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 33 34 35 ### Throws 36 37 Type | Description 38 ---- | ----------- 39 40 41 ## Examples 42 43 ```js 44 math.rationalize('sin(x)+y') 45 // Error: There is an unsolved function call 46 math.rationalize('2x/y - y/(x+1)') 47 // (2*x^2-y^2+2*x)/(x*y+y) 48 math.rationalize('(2x+1)^6') 49 // 64*x^6+192*x^5+240*x^4+160*x^3+60*x^2+12*x+1 50 math.rationalize('2x/( (2x-1) / (3x+2) ) - 5x/ ( (3x+4) / (2x^2-5) ) + 3') 51 // -20*x^4+28*x^3+104*x^2+6*x-12)/(6*x^2+5*x-4) 52 math.rationalize('x/(1-x)/(x-2)/(x-3)/(x-4) + 2x/ ( (1-2x)/(2-3x) )/ ((3-4x)/(4-5x) )') = 53 // (-30*x^7+344*x^6-1506*x^5+3200*x^4-3472*x^3+1846*x^2-381*x)/ 54 // (-8*x^6+90*x^5-383*x^4+780*x^3-797*x^2+390*x-72) 55 56 math.rationalize('x+x+x+y',{y:1}) // 3*x+1 57 math.rationalize('x+x+x+y',{}) // 3*x+y 58 59 const ret = math.rationalize('x+x+x+y',{},true) 60 // ret.expression=3*x+y, ret.variables = ["x","y"] 61 const ret = math.rationalize('-2+5x^2',{},true) 62 // ret.expression=5*x^2-2, ret.variables = ["x"], ret.coefficients=[-2,0,5] 63 ``` 64 65 66 ## See also 67 68 [simplify](simplify.md)