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Update roots
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@jiggzson
jiggzson committed Dec 31, 2019
1 parent 2b4e4a8 commit 4b9992a
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92 changes: 77 additions & 15 deletions nerdamer.core.js
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Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,7 @@
* Source : https://github.com/jiggzson/nerdamer
*/

/* global trig, trigh, Infinity, define, arguments2Array, NaN, evaluate */
/* global trig, trigh, Infinity, define, arguments2Array, NaN */
//externals ====================================================================
/* BigInterger.js v1.6.40 https://github.com/peterolson/BigInteger.js/blob/master/LICENSE */
//var nerdamerBigInt = typeof nerdamerBigInt !== 'undefined' ? nerdamerBigInt : require("big-integer");
Expand Down Expand Up @@ -709,7 +709,7 @@ var nerdamer = (function (imports) {
return retval;
};

/**
/**
* Gets nth roots of a number
* @param {Symbol} symbol
* @returns {Vector}
Expand All @@ -726,11 +726,13 @@ var nerdamer = (function (imports) {
b = _.parse(symbol.power);
}

if(a && b && (a.group === N || a.group === CP) && b.group === N) {
if(a && b && (a.group === N) && b.group === N && a.multiplier.isNegative()) {
var _roots = [];

var parts = Symbol.toPolarFormArray(evaluate(symbol));

var r = parts[0];

//var r = _.parse(a).abs().toString();

//https://en.wikipedia.org/wiki/De_Moivre%27s_formula
var x = _.arg(a);
Expand All @@ -756,14 +758,15 @@ var nerdamer = (function (imports) {
_roots = _roots.map(function(x) {
return _.multiply(x, Symbol.imaginary());
});

}
else {
_roots = [_.parse(symbol)];
}

return Vector.fromArray(_roots);
};

/**
* Sorts and array given 2 parameters
* @param {String} a
Expand Down Expand Up @@ -3174,6 +3177,7 @@ var nerdamer = (function (imports) {
Symbol.toPolarFormArray = function (symbol) {
var re, im, r, theta;
re = symbol.realpart();
im = symbol.imagpart();
r = Symbol.hyp(re, im);
theta = re.equals(0) ? _.parse('pi/2') : _.trig.atan(_.divide(im, re));
return [r, theta];
Expand Down Expand Up @@ -7008,6 +7012,52 @@ var nerdamer = (function (imports) {
return _.parse(format('({0})*180/pi', symbol));
}

function nroots(symbol) {
var a, b;
if(symbol.group === FN && symbol.fname === '') {
a = Symbol.unwrapPARENS(_.parse(symbol).toLinear());
b = _.parse(symbol.power);
}
else if(symbol.group === P) {
a = _.parse(symbol.value);
b = _.parse(symbol.power);
}

if(a && b && a.group === N && b.group === N) {
var _roots = [];
var parts = Symbol.toPolarFormArray(symbol);
var r = _.parse(a).abs().toString();
//https://en.wikipedia.org/wiki/De_Moivre%27s_formula
var x = arg(a).toString();
var n = b.multiplier.den.toString();
var p = b.multiplier.num.toString();

var formula = "(({0})^({1})*(cos({3})+({2})*sin({3})))^({4})";
for(var i=0; i<n; i++) {
var t = evaluate(_.parse(format("(({0})+2*pi*({1}))/({2})", x, i, n))).multiplier.toDecimal();
_roots.push(evaluate(_.parse(format(formula, r, n, Settings.IMAGINARY, t, p))));
}
return Vector.fromArray(_roots);
}
else if(symbol.isConstant(true)) {
var sign = symbol.sign();
var x = evaluate(symbol.abs());
var root = _.sqrt(x);

var _roots = [root.clone(), root.negate()];

if(sign < 0)
_roots = _roots.map(function(x) {
return _.multiply(x, Symbol.imaginary());
});
}
else {
_roots = [_.parse(symbol)];
}

return Vector.fromArray(_roots);
}

/**
* The square root function
* @param {Symbol} symbol
Expand Down Expand Up @@ -7260,6 +7310,19 @@ var nerdamer = (function (imports) {
return _.add(re, _.multiply(im.negate(), Symbol.imaginary()));
}

/**
* Returns the arugment of a complex number
* @param {Symbol} symbol
* @returns {Symbol}
*/
function arg(symbol) {
var re = symbol.realpart();
var im = symbol.imagpart();
if (re.isConstant() && im.isConstant())
return new Symbol(Math.atan2(im, re));
return _.symfunction('atan2', [im, re]);
}

/**
* Returns the arugment of a complex number
* @param {Symbol} symbol
Expand All @@ -7269,15 +7332,15 @@ var nerdamer = (function (imports) {
var re = symbol.realpart();
var im = symbol.imagpart();
if (re.isConstant() && im.isConstant()) {
// if(im.equals(0) && re.equals(-1)) {
// return _.parse('pi');
// }
// else if(im.equals(1) && re.equals(0)) {
// return _.parse('pi/2');
// }
// else if(im.equals(1) && re.equals(1)) {
// return _.parse('pi/4');
// }
if(im.equals(0) && re.equals(-1)) {
return _.parse('pi');
}
else if(im.equals(1) && re.equals(0)) {
return _.parse('pi/2');
}
else if(im.equals(1) && re.equals(1)) {
return _.parse('pi/4');
}
return new Symbol(Math.atan2(im, re));
}
return _.symfunction('atan2', [im, re]);
Expand Down Expand Up @@ -8085,7 +8148,6 @@ var nerdamer = (function (imports) {
this.conjugate = conjugate;
this.imagpart = imagpart;
this.realpart = realpart;


//Parser.methods ===============================================================
this.addPreprocessor = function (name, action, order, shift_cells) {
Expand Down
5 changes: 5 additions & 0 deletions spec/algebra.spec.js
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Original file line number Diff line number Diff line change
Expand Up @@ -753,4 +753,9 @@ describe('Algebra', function () {
expect(result.toString()).toEqual(testCases[i].expected);
}
});

it('should calculate nth roots correctly', function() {
expect(nerdamer('roots((-1)^(1/5))').evaluate().text()).toEqual('[0.5877852522924731*i+0.8090169943749475,-0.3090169943749474+0.9510565162951536*i,-1+1.2246467991473532e-16*i,-0.30901699437494756-0.9510565162951535*i,-0.5877852522924734*i+0.8090169943749473]');
expect(nerdamer('roots((2)^(1/3))').evaluate().text()).toEqual('[1.1224620483093812,-1.1224620483093812]');
});
});

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