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Add Rational Expressions #95

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Add Rational Expressions #95

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3fd30cd
Fix bug where variable of degree zero wouldnt be combined with constants
IsaMorphic Dec 12, 2018
98a20e2
totally broken probably, but begin adding rational statments
IsaMorphic Dec 14, 2018
502ea59
Added main functionality to rationals, and fixed a few bugs.
IsaMorphic Dec 14, 2018
9399915
Add solving functionality with rationals
IsaMorphic Dec 14, 2018
686238c
Fix a few strange and tricky bugs
IsaMorphic Dec 15, 2018
82fb9f6
Make code compatible with uglify
IsaMorphic Dec 15, 2018
21ed031
fix changes made by replace all I did at one point
IsaMorphic Mar 11, 2019
a811182
A couple of fixes
IsaMorphic Mar 11, 2019
d6dd9e8
Fix formatting (including inconsistencies)
IsaMorphic Apr 22, 2019
9f19724
Fix problems with all existing tests
IsaMorphic Apr 23, 2019
c5c2b64
Add the ability to solve equations that contain cross-products
IsaMorphic Apr 23, 2019
90238cf
Add semicolon
IsaMorphic Apr 24, 2019
872845b
Respect order of operations, parse exponents before mul/div
IsaMorphic Apr 24, 2019
c28679c
Improved functionality and added tests for rationals
IsaMorphic Apr 24, 2019
66f0c2b
fix some issues with expression division (again)
IsaMorphic Apr 24, 2019
26b6443
Fix more bugs
IsaMorphic Apr 25, 2019
7ec7161
Adjust role of Rationals, remove ability to use them as terms.
IsaMorphic Apr 25, 2019
63919da
Restore old monomial division functionality and fix resulting bugs.
IsaMorphic Apr 25, 2019
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2 changes: 2 additions & 0 deletions algebra.js
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Original file line number Diff line number Diff line change
@@ -1,5 +1,6 @@
var Fraction = require('./src/fractions');
var Expression = require('./src/expressions').Expression;
var Rational = require('./src/expressions').Rational;
var Equation = require('./src/equations');
var Parser = require('./src/parser');

Expand Down Expand Up @@ -30,6 +31,7 @@ var toTex = function(input) {

module.exports = {
Fraction: Fraction,
Rational: Rational,
Expression: Expression,
Equation: Equation,
parse: parse,
Expand Down
259 changes: 132 additions & 127 deletions src/equations.js
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Original file line number Diff line number Diff line change
@@ -1,30 +1,44 @@
var Expression = require('./expressions').Expression;
var Rational = require('./expressions').Rational;
var Variable = require('./expressions').Variable;
var Term = require('./expressions').Term;
var Fraction = require('./fractions');
var isInt = require('./helper').isInt;

var Equation = function(lhs, rhs) {
if (lhs instanceof Expression) {
this.lhs = lhs;

if (rhs instanceof Expression) {
this.rhs = rhs;
} else if (rhs instanceof Fraction || isInt(rhs)) {
this.rhs = new Expression(rhs);
} else {
throw new TypeError("Invalid Argument (" + rhs.toString() + "): Right-hand side must be of type Expression, Fraction or Integer.");
}
if (lhs instanceof Rational) {
this.lhs = lhs.copy();
} else if (lhs instanceof Expression) {
this.lhs = new Rational(lhs);
} else if (lhs instanceof Fraction || isInt(lhs)) {
this.lhs = new Rational(lhs);
} else {
throw new TypeError("Invalid Argument (" + lhs.toString() + "): Left-hand side must be of type Expression.");
}
if (rhs instanceof Rational) {
this.rhs = rhs.copy();
} else if (rhs instanceof Expression) {
this.rhs = new Rational(rhs);
} else if (rhs instanceof Fraction || isInt(rhs)) {
this.rhs = new Rational(rhs);
} else {
throw new TypeError("Invalid Argument (" + rhs.toString() + "): Right-hand side must be of type Expression, Fraction or Integer.");
}
this._crossMultiply();
};

Equation.prototype._crossMultiply = function() {
var newLhs = this.lhs.copy();
var newRhs = this.rhs.copy();
// Both sides should now be rationals and we are ready to cross-multiply
this.lhs = newLhs.numer.multiply(newRhs.denom);
this.rhs = newLhs.denom.multiply(newRhs.numer);
};

Equation.prototype.solveFor = function(variable) {
if (!this.lhs._hasVariable(variable) && !this.rhs._hasVariable(variable)) {
throw new TypeError("Invalid Argument (" + variable.toString() + "): Variable does not exist in the equation.");
}

// If the equation is linear and the variable in question can be isolated through arithmetic, solve.
if (this._isLinear() || this._variableCanBeIsolated(variable)) {
var solvingFor = new Term(new Variable(variable));
Expand All @@ -34,7 +48,7 @@ Equation.prototype.solveFor = function(variable) {
for (var i = 0; i < this.rhs.terms.length; i++) {
var term = this.rhs.terms[i];

if (term.canBeCombinedWith(solvingFor)) {
if (term.hasVariable(variable)) {
newLhs = newLhs.subtract(term);
} else {
newRhs = newRhs.add(term);
Expand All @@ -44,34 +58,32 @@ Equation.prototype.solveFor = function(variable) {
for (var i = 0; i < this.lhs.terms.length; i++) {
var term = this.lhs.terms[i];

if (term.canBeCombinedWith(solvingFor)) {
if (term.hasVariable(variable)) {
newLhs = newLhs.add(term);
} else {
newRhs = newRhs.subtract(term);
}
}

newRhs = newRhs.subtract(this.lhs.constant());
newRhs = newRhs.add(this.rhs.constant());

if (newLhs.terms.length === 0) {
if (newLhs._maxDegree() == 0) {
if (newLhs.constant().equalTo(newRhs.constant())) {
return new Fraction(1, 1);
} else {
throw new EvalError("No Solution");
}
}

newRhs = newRhs.divide(newLhs.terms[0].coefficient());
var isolated = newLhs.divide(solvingFor);
var divisor = new Rational(isolated);
newRhs = newRhs.divide(divisor);

if (newRhs.terms.length === 0) {
if (newRhs._maxDegree() == 0) {
return newRhs.constant().reduce();
}

newRhs._sort();
return newRhs;

// Otherwise, move everything to the LHS.
// Otherwise, move everything to the LHS.
} else {
var newLhs = this.lhs.copy();
newLhs = newLhs.subtract(this.rhs);
Expand All @@ -85,7 +97,7 @@ Equation.prototype.solveFor = function(variable) {
throw new EvalError("No Solution");
}

// Otherwise, check degree and solve.
// Otherwise, check degree and solve.
} else if (this._isQuadratic(variable)) {
var coefs = newLhs._quadraticCoefficients();

Expand Down Expand Up @@ -120,8 +132,8 @@ Equation.prototype.solveFor = function(variable) {
a = a.valueOf();
b = b.valueOf();

var root1 = (-b - squareRootDiscriminant) / (2*a);
var root2 = (-b + squareRootDiscriminant) / (2*a);
var root1 = (-b - squareRootDiscriminant) / (2 * a);
var root2 = (-b + squareRootDiscriminant) / (2 * a);
return [root1, root2];
}
}
Expand All @@ -137,6 +149,9 @@ Equation.prototype.solveFor = function(variable) {
var c = coefs.c;
var d = coefs.d;

if (a == undefined)
throw new Error("No Solution");

// Calculate D and D0.
var D = a.multiply(b).multiply(c).multiply(d).multiply(18);
D = D.subtract(b.pow(3).multiply(d).multiply(4));
Expand All @@ -147,9 +162,9 @@ Equation.prototype.solveFor = function(variable) {
var D0 = b.pow(2).subtract(a.multiply(c).multiply(3));

// Check for special cases when D = 0.

if (D.valueOf() === 0) {

// If D = D0 = 0, there is one distinct real root, -b / 3a.
if (D0.valueOf() === 0) {
var root1 = b.multiply(-1).divide(a.multiply(3));
Expand All @@ -171,106 +186,96 @@ Equation.prototype.solveFor = function(variable) {

// Otherwise, use a different method for solving.
} else {
var f = ((3*(c/a)) - ((Math.pow(b, 2))/(Math.pow(a, 2))))/3;
var g = (2*(Math.pow(b, 3))/(Math.pow(a, 3)));
g = g - (9*b*c/(Math.pow(a, 2)));
g = g + (27*d)/a;
g = g/27;
var h = (Math.pow(g, 2)/4) + (Math.pow(f, 3)/27);

/*
if f = g = h = 0 then roots are equal (has been already taken care of!)
if h>0, only one real root
if h<=0, all three roots are real
*/

if(h>0)
{

var R = -(g/2) + Math.sqrt(h);
var S = Math.cbrt(R);
var T = -(g/2) - Math.sqrt(h);
var U = Math.cbrt(T);
var root1 = (S+U) - (b/(3*a));
/* Round off the roots if the difference between absolute value of ceil and number is < e-15*/
if(root1<0)
{
var Croot1 = Math.floor(root1);
if(root1 - Croot1 < 1e-15)
root1 = Croot1;
}
else if(root1>0)
{
var Croot1 = Math.ceil(root1);
if(Croot1 - root1 < 1e-15)
root1 = Croot1;
}

return [root1];
}
else
{
var i = Math.sqrt(((Math.pow(g, 2)/4) - h));
var j = Math.cbrt(i);

var k = Math.acos(-(g/(2*i)));
var L = -j;
var M = Math.cos(k/3);
var N = Math.sqrt(3) * Math.sin(k/3);
var P = -(b/(3*a));

var root1 = 2*j*Math.cos(k/3) - (b/(3*a));
var root2 = L*(M+N) + P;
var root3 = L*(M-N) + P;


/* Round off the roots if the difference between absolute value of ceil and number is < e-15*/
if(root1<0)
{
var Croot1 = Math.floor(root1);
if(root1 - Croot1 < 1e-15)
root1 = Croot1;
}
else if(root1>0)
{
var Croot1 = Math.ceil(root1);
if(Croot1 - root1 < 1e-15)
root1 = Croot1;
}

if(root2<0)
{
var Croot2 = Math.floor(root2);
if(root2 - Croot2 < 1e-15)
root2 = Croot2;
}
else if(root2>0)
{
var Croot2 = Math.ceil(root2);
if(Croot2 - root2 < 1e-15)
root2 = Croot2;
}

if(root1<0)
{
var Croot3 = Math.floor(root3);
if(root3 - Croot3 < 1e-15)
root3 = Croot3;
}
else if(root3>0)
{
var Croot3 = Math.ceil(root3);
if(Croot3 - root3 < 1e-15)
root3 = Croot3;
}

var roots = [root1, root2, root3];
roots.sort(function(a, b){return a-b;}); // roots in ascending order

return [roots[0], roots[1], roots[2]];

}

var f = ((3 * (c / a)) - ((Math.pow(b, 2)) / (Math.pow(a, 2)))) / 3;
var g = (2 * (Math.pow(b, 3)) / (Math.pow(a, 3)));
g = g - (9 * b * c / (Math.pow(a, 2)));
g = g + (27 * d) / a;
g = g / 27;
var h = (Math.pow(g, 2) / 4) + (Math.pow(f, 3) / 27);

/*
if f = g = h = 0 then roots are equal (has been already taken care of!)
if h>0, only one real root
if h<=0, all three roots are real
*/

if (h > 0) {

var R = -(g / 2) + Math.sqrt(h);
var S = Math.cbrt(R);
var T = -(g / 2) - Math.sqrt(h);
var U = Math.cbrt(T);
var root1 = (S + U) - (b / (3 * a));
/* Round off the roots if the difference between absolute value of ceil and number is < e-15*/
if (root1 < 0) {
var Croot1 = Math.floor(root1);
if (root1 - Croot1 < 1e-15)
root1 = Croot1;
}
else if (root1 > 0) {
var Croot1 = Math.ceil(root1);
if (Croot1 - root1 < 1e-15)
root1 = Croot1;
}

return [root1];
}
else {
var i = Math.sqrt(((Math.pow(g, 2) / 4) - h));
var j = Math.cbrt(i);

var k = Math.acos(-(g / (2 * i)));
var L = -j;
var M = Math.cos(k / 3);
var N = Math.sqrt(3) * Math.sin(k / 3);
var P = -(b / (3 * a));

var root1 = 2 * j * Math.cos(k / 3) - (b / (3 * a));
var root2 = L * (M + N) + P;
var root3 = L * (M - N) + P;


/* Round off the roots if the difference between absolute value of ceil and number is < e-15*/
if (root1 < 0) {
var Croot1 = Math.floor(root1);
if (root1 - Croot1 < 1e-15)
root1 = Croot1;
}
else if (root1 > 0) {
var Croot1 = Math.ceil(root1);
if (Croot1 - root1 < 1e-15)
root1 = Croot1;
}

if (root2 < 0) {
var Croot2 = Math.floor(root2);
if (root2 - Croot2 < 1e-15)
root2 = Croot2;
}
else if (root2 > 0) {
var Croot2 = Math.ceil(root2);
if (Croot2 - root2 < 1e-15)
root2 = Croot2;
}

if (root1 < 0) {
var Croot3 = Math.floor(root3);
if (root3 - Croot3 < 1e-15)
root3 = Croot3;
}
else if (root3 > 0) {
var Croot3 = Math.ceil(root3);
if (Croot3 - root3 < 1e-15)
root3 = Croot3;
}

var roots = [root1, root2, root3];
roots.sort(function(a, b) { return a - b; }); // roots in ascending order

return [roots[0], roots[1], roots[2]];

}

}
}
}
Expand Down Expand Up @@ -299,7 +304,7 @@ Equation.prototype._maxDegreeOfVariable = function(variable) {
};

Equation.prototype._variableCanBeIsolated = function(variable) {
return this._maxDegreeOfVariable(variable) === 1 && this._noCrossProductsWithVariable(variable);
return this._maxDegreeOfVariable(variable) === 1;
};

Equation.prototype._noCrossProductsWithVariable = function(variable) {
Expand Down
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