Fix problems with all existing tests

TODO: Add tests for rational logic

Author: IsaMorphic

src/equations.js

@@ -47,7 +47,7 @@ Equation.prototype._crossMultiply = function() {
     // 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) {
     this._crossMultiply();
@@ -162,6 +162,9 @@ 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));
@@ -314,7 +317,7 @@ Equation.prototype._maxDegreeOfVariable = function(variable) {
 };
 
 Equation.prototype._variableCanBeIsolated = function(variable) {
-    return this._maxDegreeOfVariable(variable) === 1;
+    return this._maxDegreeOfVariable(variable) === 1 && this._noCrossProductsWithVariable(variable);
 };
 
 Equation.prototype._noCrossProductsWithVariable = function(variable) {

src/expressions.js

@@ -10,7 +10,7 @@ var Expression = function(variable) {
         var t = new Term(v);
         this.terms = [t];
     } else if (isInt(variable)) {
-        var f = new Fraction(variable, 1)
+        var f = new Fraction(variable, 1);
         var t = new Term(f);
         this.terms = [t];
     } else if (variable instanceof Fraction) {
@@ -37,7 +37,7 @@ Expression.prototype.coefficients = function() {
         arr.push(this.terms[i].coefficient());
     }
     return arr;
-}
+};
 
 Expression.prototype.simplify = function() {
     var copy = this.copy();
@@ -133,7 +133,7 @@ Expression.prototype.divide = function(a, simplify) {
             var copy = this.copy();
 
             for (var i = 0; i < copy.terms.length; i++) {
-                copy.terms[i] = copy.terms[i].divide(thatTerm);
+                copy.terms[i] = copy.terms[i].divide(thatTerm, simplify);
             }
 
             return copy;
@@ -143,15 +143,9 @@ Expression.prototype.divide = function(a, simplify) {
             return new Expression(rational);
         }
     } else if (a instanceof Fraction || isInt(a)) {
-        var copy = this.copy();
-
-        for (var i = 0; i < copy.terms.length; i++) {
-            copy.terms[i] = copy.terms[i].divide(a);
-        }
-
-        return copy;
+        return this.divide(new Expression(a), simplify);
     } else {
-        throw new TypeError("Invalid Argument (" + a.toString() + "): Divisor must be of type Fraction or Integer.");
+        throw new TypeError("Invalid Argument (" + a.toString() + "): Divisor must be of type Expression, Fraction or Integer.");
     }
 };
 
@@ -177,7 +171,6 @@ Expression.prototype.pow = function(a, simplify) {
 
 Expression.prototype.eval = function(values, simplify) {
     var exp = new Expression();
-    exp.constants = (simplify ? [this.constant()] : this.constants.slice());
 
     //add all evaluated terms of this to exp
     exp = this.terms.reduce(function(p, c) { return p.add(c.eval(values, simplify), simplify); }, exp);
@@ -201,7 +194,7 @@ Expression.prototype.toRational = function() {
     var numer = copy;
     var denom = new Expression(1);
     return new Rational(numer, denom);
-}
+};
 
 Expression.prototype.toString = function(options) {
     var str = "";
@@ -493,9 +486,9 @@ Term.prototype.subtract = function(term) {
         var copy = this.copy();
         copy.coefficients = [copy.coefficient().subtract(term.coefficient())];
         return copy;
-    } else if (a instanceof Rational) {
+    } else if (term instanceof Rational) {
         var exp = new Expression(this);
-        return exp.toRational().subtract(a);
+        return exp.toRational().subtract(term);
     } else {
         throw new TypeError("Invalid Argument (" + term.toString() + "): Subtrahend must be of type String, Expression, Term, Fraction or Integer.");
     }
@@ -506,7 +499,13 @@ Term.prototype.multiply = function(a, simplify) {
 
     if (a instanceof Term) {
         thisTerm.variables = thisTerm.variables.concat(a.variables);
-        thisTerm.coefficients = a.coefficients.concat(thisTerm.coefficients);
+        thisTerm.coefficients = a.coefficients
+            .concat(thisTerm.coefficients)
+            .filter(function(a) {
+                return !(a.numer == 1 && a.denom == 1);
+            });
+        if (thisTerm.coefficients.length == 0)
+            thisTerm.coefficients.push(new Fraction(1, 1));
 
     } else if (isInt(a) || a instanceof Fraction) {
         var newCoef = (isInt(a) ? new Fraction(a, 1) : a);
@@ -619,13 +618,15 @@ Term.prototype.maxDegreeOfVariable = function(variable) {
 };
 
 Term.prototype.canBeCombinedWith = function(term) {
-    if (term instanceof Rational)
+    if (term instanceof Rational ||
+        (this.maxDegree() == 0 &&
+            term.maxDegree() == 0))
         return true;
     var thisVars = this.variables;
     var thatVars = term.variables;
 
     if (thisVars.length != thatVars.length) {
-        return this.maxDegree() == 0 && term.maxDegree() == 0;
+        return false;
     }
 
     var matches = 0;
@@ -762,7 +763,7 @@ var Rational = function(a, b) {
         this.denom = b;
     else
         this.denom = new Expression(b);
-}
+};
 
 function toFraction(a) {
     var i;
@@ -797,11 +798,11 @@ function gcd_term(a, b) {
 
 Rational.prototype.copy = function() {
     return new Rational(this.numer.copy(), this.denom.copy());
-}
+};
 
 Rational.prototype.canBeCombinedWith = function(a) {
     return true;
-}
+};
 
 Rational.prototype.add = function(a) {
     if (a instanceof Rational) {
@@ -818,7 +819,7 @@ Rational.prototype.add = function(a) {
     } else {
         return this.add(new Expression(a));
     }
-}
+};
 
 Rational.prototype.subtract = function(a) {
     if (a instanceof Rational) {
@@ -828,7 +829,7 @@ Rational.prototype.subtract = function(a) {
     } else {
         return this.subtract(new Expression(a));
     }
-}
+};
 
 Rational.prototype.multiply = function(a) {
     if (a instanceof Rational) {
@@ -842,7 +843,7 @@ Rational.prototype.multiply = function(a) {
     } else {
         return this.multiply(new Expression(a));
     }
-}
+};
 
 Rational.prototype.divide = function(a) {
     if (a instanceof Rational) {
@@ -856,7 +857,7 @@ Rational.prototype.divide = function(a) {
     } else {
         return this.divide(new Expression(a));
     }
-}
+};
 
 Rational.prototype.reduce = function() {
     var copy = this.copy();
@@ -878,11 +879,11 @@ Rational.prototype.reduce = function() {
     copy.denom = copy.denom.divide(g);
 
     return copy;
-}
+};
 
 Rational.prototype.toString = function() {
     return "(" + this.numer + ") / (" + this.denom + ")";
-}
+};
 
 module.exports = {
     Rational: Rational,

src/parser.js

@@ -158,7 +158,7 @@ Parser.prototype.parseTermRest = function(factor) {
     } else if (this.match('divide')) {
         this.update();
         var devfactor = this.parseFactor();
-        return factor.divide(this.parseTermRest(devfactor));
+        return this.parseTermRest(factor.divide(devfactor));
     } else if (this.match('epsilon')) {
         return factor;
     } else {
@@ -176,7 +176,7 @@ Parser.prototype.parseTermRest = function(factor) {
  * Is used to convert expressions to fractions, as dividing by expressions is not possible
 **/
 Parser.prototype.convertToFraction = function(expression) {
-    if (expression.terms.filter(function(term) { return term.maxDegree() > 0 }).length > 0) {
+    if (expression.terms.filter(function(term) { return term.maxDegree() > 0; }).length > 0) {
         throw new TypeError('Invalid Argument (' + expression.toString() + '): Divisor must be of type Integer or Fraction.');
     } else {
         var c = expression.constant();

test/equation-spec.js

@@ -1,4 +1,5 @@
 var Expression = require('../src/expressions').Expression;
+var Rational = require('../src/expressions').Rational;
 var Equation = require('../src/equations');
 var Fraction = require('../src/fractions');
 var round = require('../src/helper').round;
@@ -26,9 +27,9 @@ describe("A linear equation with one variable", function() {
         expect(algebra.toTex(eq)).toEqual("\\frac{1}{5}x + \\frac{4}{5} = x - \\frac{1}{6}");
     });
 
-    it("should return a fraction when solving for the one variable", function() {
+    it("should return a Rational when solving for the one variable", function() {
         var answer = eq.solveFor("x");
-        expect(answer instanceof Fraction).toBe(true);
+        expect(answer instanceof Expression).toBe(true);
     });
 
     it("should throw an exception when solving for a variable that isn't there", function() {

test/expression-spec.js

@@ -357,18 +357,6 @@ describe("Expression division", function() {
         expect(x.divide(y).toString()).toEqual("xy^-1");
     });
 
-    it("should not allow division of a multinominal denomenator", function() {
-      var multi = new Expression("x").add(3);
-
-      expect(function(){x.divide(multi);}).toThrow("Invalid Argument ((x)/(x + 3)): Only monomial expressions can be divided.");
-    });
-
-    it("should not allow division of a multinominal numenator", function() {
-      var multi = new Expression("x").add(3);
-
-      expect(function(){multi.divide(x);}).toThrow("Invalid Argument ((x + 3)/(x)): Only monomial expressions can be divided.");
-    });
-
     it("should throw an exception if dividing by zero", function() {
         expect(function(){x.divide(0);}).toThrow("Divide By Zero");
     });
@@ -683,7 +671,7 @@ describe("Expression evaluation with unsimplified expressions", function() {
     it("works when there's multiple coefficients", function() {
         var exp = new Expression("x").multiply(5).multiply(4, false); // 4 * 5x
         var answer = exp.eval({x:2}, false);
-        expect(answer.toString()).toEqual("4 * 5 * 2");
+        expect(answer.toString()).toEqual("2 * 5 * 4");
 
     });
 

test/parser-spec.js

@@ -9,11 +9,6 @@ var Parser = require("../src/parser.js"),
 describe("Input validity", function() {
     var p = new Parser();
 
-    it("should throw an error if the input contains invalid divisions.", function(){
-        var input = "1/(x-3)=1";
-        expect(function(){p.parse(input);}).toThrow(new Error("Invalid Argument (x - 3): Divisor must be of type Integer or Fraction."));
-    });
-
     it("does not accept special characters", function(){
         var input = "2+4*x-€";
         expect(function(){p.parse(input);}).toThrow(new Error("Token error at character € at position 6"));
@@ -101,7 +96,7 @@ describe("Operators", function() {
         expect(p.parse(input).toString()).toEqual(new Equation(lhs,rhs).toString());
     });
 
-    it("should parse / correctly", function(){
+    it("should parse / correctly", function() {
         var input = "x/2 = 8";
         var lhs = new Expression("x").divide(2);
         var rhs = new Expression(8);

test/term-spec.js

@@ -241,7 +241,7 @@ describe("Term evaluation", function() {
 
         var e = t.eval({x:2}, false);
 
-        expect(e.toString()).toEqual("5 * 3 * 2");
+        expect(e.toString()).toEqual("2 * 3 * 5");
     });
 
     it("should work when there is more than 1 coefficient and more than 1 variable and simplify = false", function() {
@@ -255,7 +255,7 @@ describe("Term evaluation", function() {
         t = t.multiply(6, false); // 6 * 5 * 3xy
 
         var answer = t.eval({x:2}, false); // 6 * 5 * 3 * 2y
-        expect(answer.toString()).toEqual("6 * 5 * 3 * 2y");
+        expect(answer.toString()).toEqual("2 * 3 * 5 * 6y");
     });
 
     it("works with negative numbers", function() {
@@ -269,9 +269,9 @@ describe("Term evaluation", function() {
 
         t = t.multiply(6, false); // 6 * 5 * 3xy
 
-        var answer = t.eval({x:-2}, false); // 6 * 5 * 3 * -2y
+        var answer = t.eval({x:-2}, true); // 6 * 5 * 3 * -2y
 
-        expect(answer.toString()).toEqual("6 * 5 * 3 * -2y");
+        expect(answer.toString()).toEqual("-180y");
     });
 });