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Merge pull request #515 from jiggzson/dev
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Update v. 1.1.1
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@jiggzson
jiggzson authored Dec 31, 2019
2 parents d36da8f + 4b9992a commit 536c583
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Showing 4 changed files with 171 additions and 22 deletions.
6 changes: 5 additions & 1 deletion Algebra.js
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Original file line number Diff line number Diff line change
Expand Up @@ -1787,6 +1787,10 @@ if((typeof module) !== 'undefined') {
}
},
roots: function(symbol) {

if(symbol.isConstant(true, true)) {
return core.Utils.nroots(symbol);
}
var roots = __.proots(symbol).map(function(x) {
return _.parse(x);
});
Expand Down Expand Up @@ -3924,4 +3928,4 @@ if((typeof module) !== 'undefined') {
}
]);
nerdamer.api();
})();
})();
180 changes: 160 additions & 20 deletions nerdamer.core.js
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Original file line number Diff line number Diff line change
Expand Up @@ -709,6 +709,63 @@ var nerdamer = (function (imports) {
return retval;
};

/**
* Gets nth roots of a number
* @param {Symbol} symbol
* @returns {Vector}
*/
var nroots = function(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 && 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);
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, 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);
};

/**
* Sorts and array given 2 parameters
Expand Down Expand Up @@ -1133,7 +1190,10 @@ var nerdamer = (function (imports) {
//Big ==========================================================================
var Big = {
cos: function (x) {
return new Symbol(bigDec.cos(x.toString()));
return new Symbol(bigDec.cos(x.multiplier.toDecimal()));
},
sin: function (x) {
return new Symbol(bigDec.sin(x.multiplier.toDecimal()));
}
};
//Math2 ========================================================================
Expand Down Expand Up @@ -3109,10 +3169,8 @@ var nerdamer = (function (imports) {
return symbol;
};
Symbol.hyp = function (a, b) {
if (a.equals(0))
return b.clone();
if (b.equals(0))
return a.clone();
a = a || new Symbol(0);
b = b || new Symbol(0);
return _.sqrt(_.add(_.pow(a.clone(), new Symbol(2)), _.pow(b.clone(), new Symbol(2))));
};
//converts to polar form array
Expand Down Expand Up @@ -3512,9 +3570,17 @@ var nerdamer = (function (imports) {
isSQRT: function () {
return this.fname === SQRT;
},
isConstant: function (check_all) {
isConstant: function (check_all, check_symbols) {
if(check_symbols && this.group === CB) {
for(var x in this.symbols) {
if(this.symbols[x].isConstant(true))
return true;
}
}

if (check_all === 'all' && (this.isPi() || this.isE()))
return true;

if (check_all && this.group === FN) {
for (var i = 0; i < this.args.length; i++) {
if (!this.args[i].isConstant(check_all))
Expand Down Expand Up @@ -6945,7 +7011,53 @@ var nerdamer = (function (imports) {
function degrees(symbol) {
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 @@ -7211,6 +7323,29 @@ var nerdamer = (function (imports) {
return _.symfunction('atan2', [im, re]);
}

/**
* 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()) {
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]);
}

/**
* Returns the polarform of a complex number
* @param {Symbol} symbol
Expand Down Expand Up @@ -8009,6 +8144,10 @@ var nerdamer = (function (imports) {
this.sqrt = sqrt;
this.log = log;
this.nthroot = nthroot;
this.arg = arg;
this.conjugate = conjugate;
this.imagpart = imagpart;
this.realpart = realpart;

//Parser.methods ===============================================================
this.addPreprocessor = function (name, action, order, shift_cells) {
Expand Down Expand Up @@ -8983,19 +9122,19 @@ var nerdamer = (function (imports) {
result = _.multiply(_.pow(a, b), i);
}
else {
if(a.equals(-1)) {
var theta = _.multiply(b, _.parse('pi'));
result = evaluate(_.add(trig.cos(theta), _.multiply(Symbol.imaginary(), trig.sin(theta))));
}
else {
var aa = a.clone();
aa.multiplier.negate();
result = _.pow(_.symfunction(PARENTHESIS, [new Symbol(sign)]), b.clone());
var _a = _.pow(new Symbol(aa.multiplier.num), b.clone());
var _b = _.pow(new Symbol(aa.multiplier.den), b.clone());
var r = _.divide(_a, _b);
result = _.multiply(result, r);
}
// if(a.equals(-1)) {
// var theta = _.multiply(b, _.parse('pi'));
// result = evaluate(_.add(trig.cos(theta), _.multiply(Symbol.imaginary(), trig.sin(theta))));
// }
// else {
var aa = a.clone();
aa.multiplier.negate();
result = _.pow(_.symfunction(PARENTHESIS, [new Symbol(sign)]), b.clone());
var _a = _.pow(new Symbol(aa.multiplier.num), b.clone());
var _b = _.pow(new Symbol(aa.multiplier.den), b.clone());
var r = _.divide(_a, _b);
result = _.multiply(result, r);
// }
}
}
else if (Settings.PARSE2NUMBER && b.isImaginary()) {
Expand Down Expand Up @@ -10974,6 +11113,7 @@ var nerdamer = (function (imports) {
isVariableSymbol: isVariableSymbol,
isVector: isVector,
keys: keys,
nroots: nroots,
remove: remove,
reserveNames: reserveNames,
range: range,
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]');
});
});
2 changes: 1 addition & 1 deletion spec/core.spec.js
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Original file line number Diff line number Diff line change
Expand Up @@ -191,7 +191,7 @@ describe('Nerdamer core', function () {
},
{
given: '(-1)^(3/4)',
expected: '(93222358/131836323)*i-93222358/131836323'
expected: '(-1)^(3/4)'
}
];

Expand Down

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