Expressions with polynomials divided by polynomials are now simplified (

#231)

* Expressions with polynomials divided by polynomials are now simplified

* minor naming/style changes

* minor thought fail fix

lib/simplifyExpression/fractionsSearch/cancelLikeTerms.js

@@ -240,7 +240,6 @@ function cancelTerms(numerator, denominator) {
   if (print.ascii(numerator) === print.ascii(denominator)) {
     return new CancelOutStatus(null, null, true);
   }
-
   // case 2: they're both exponent nodes with the same base
   // e.g. (2x+5)^8 and (2x+5)^2
   if (Node.Type.isOperator(numerator, '^') &&
@@ -257,16 +256,25 @@ function cancelTerms(numerator, denominator) {
     numerator.args[1] = newExponent;
     return new CancelOutStatus(numerator, null, true);
   }
-
   // case 3: they're both polynomial terms, check if they have the same symbol
   // e.g. 4x^2 / 5x^2 => 4 / 5
   // e.g. 4x^3 / 5x^2 => 4x^(3-2) / 5
+  // case 3.1: they're both polynomial terms with different symbols but with coefficients
+  // e.g 20x / 40y => x / 2y
+  // e.g 60x / 40y => 3x / 2y
+  // e.g 4x / 2y => 2x / y
   if (Node.PolynomialTerm.isPolynomialTerm(numerator) &&
       Node.PolynomialTerm.isPolynomialTerm(denominator)) {
     const numeratorTerm = new Node.PolynomialTerm(numerator);
     const denominatorTerm = new Node.PolynomialTerm(denominator);
     if (numeratorTerm.getSymbolName() !== denominatorTerm.getSymbolName()) {
-      return new CancelOutStatus(numerator, denominator);
+      if (Node.Type.isOperator(numerator, '*') && Node.Type.isOperator(denominator, '*')) {
+        // case 3.1
+        return cancelCoeffs(numerator, denominator);
+      }
+      else {
+        return new CancelOutStatus(numerator, denominator);
+      }
     }
     const numeratorExponent = numeratorTerm.getExponentNode(true);
     let denominatorExponent =  denominatorTerm.getExponentNode(true);
@@ -294,7 +302,6 @@ function cancelTerms(numerator, denominator) {
   // or is multiplication node
   // e.g. 2 / 4x -> 1 / 2x
   // e.g. ignore cases like:  2 / a and 2 / x^2
-
   if (Node.Type.isConstant(numerator)
       && Node.Type.isOperator(denominator, '*')
       && Node.PolynomialTerm.isPolynomialTerm(denominator)) {
@@ -330,7 +337,6 @@ function cancelTerms(numerator, denominator) {
 
   // case 5: both numerator and denominator are numbers within a more complicated fraction
   // e.g. (35 * nthRoot (7)) / (5 * nthRoot(5)) -> (7 * nthRoot(7)) / nthRoot(5)
-
   if (Node.Type.isConstant(numerator) && Node.Type.isConstant(denominator)) {
     const frac = Node.Creator.operator('/', [numerator, denominator]);
     const reduceStatus = divideByGCD(frac);
@@ -371,4 +377,42 @@ function isMultiplicationOfTerms(node) {
           !Node.PolynomialTerm.isPolynomialTerm(node));
 }
 
+function cancelCoeffs(numerator, denominator){
+  const denominatorTerm = new Node.PolynomialTerm(denominator);
+  const numeratorTerm = new Node.PolynomialTerm(numerator);
+
+  const denominatorCoeff = denominatorTerm.getCoeffNode();
+  const denominatorVariable = denominatorTerm.getSymbolNode();
+  const denominatorExponent = denominatorTerm.getExponentNode();
+
+  const numeratorCoeff = numeratorTerm.getCoeffNode();
+  const numeratorVariable = numeratorTerm.getSymbolNode();
+  const numeratorExponent = numeratorTerm.getExponentNode();
+
+  // simplify a constant fraction (e.g 2 / 4)
+  const frac = Node.Creator.operator('/', [numeratorCoeff, denominatorCoeff]);
+
+  const reduceStatus = divideByGCD(frac);
+
+  if (!reduceStatus.hasChanged()) {
+    return new CancelOutStatus(numerator, denominator, false);
+  }
+
+  // Sometimes the fraction reduces to a constant e.g. 6 / 2 -> 3,
+  // in which case the denominator coefficient should be null
+  let newDenominatorCoeff = null;
+  let newNumerator = null;
+  if (Node.Type.isConstant(reduceStatus.newNode)) {
+    newNumerator = Node.Creator.polynomialTerm(numeratorVariable, numeratorExponent, reduceStatus.newNode);
+    newDenominatorCoeff = null;
+  }
+  else {
+    newNumerator = Node.Creator.polynomialTerm(numeratorVariable, numeratorExponent, reduceStatus.newNode.args[0]);
+    newDenominatorCoeff = reduceStatus.newNode.args[1];
+  }
+  const newDenominator = Node.Creator.polynomialTerm(denominatorVariable, denominatorExponent, newDenominatorCoeff);
+
+  return new CancelOutStatus(newNumerator, newDenominator, true);
+}
+
 module.exports = cancelLikeTerms;

test/simplifyExpression/fractionsSearch/cancelLikeTerms.test.js

@@ -24,9 +24,14 @@ describe('cancel like terms', function () {
     ['2/ (4x)', '1 / (2x)'],
     ['2/ (4x^2)', '1 / (2x^2)'],
     ['2 a / a', '2'],
-    ['(35 * nthRoot (7)) / (5 * nthRoot(5))','(7 * nthRoot(7)) / nthRoot(5)'],
+    ['(35 * nthRoot (7)) / (5 * nthRoot(5))', '(7 * nthRoot(7)) / nthRoot(5)'],
     ['3/(9r^2)', '1 / (3r^2)'],
-    ['6/(2x)', '3 / (x)']
+    ['6/(2x)', '3 / (x)'],
+    ['(40 * x) / (20 * y)', '(2x) / (y)'],
+    ['(20 * x) / (40 * y)', '(x) / (2y)'],
+    ['20x / (40y)', 'x / (2y)'],
+    ['60x / (40y)', '3x / (2y)'],
+    ['4x / (2y)', '2x / (y)']
   ];
 
   tests.forEach(t => testCancelLikeTerms(t[0], t[1]));

test/simplifyExpression/simplify.test.js

@@ -51,6 +51,11 @@ describe('can simplify with division', function () {
     ['2x/x', '2'],
     ['2x/4/3', '1/6 x'],
     ['((2+x)(3+x))/(2+x)', '3 + x'],
+    ['(20 * x) / (5 * (40 * y))', 'x / (10y)'],
+    ['400 * z / ((20 * x) / (5 * (40 * y)))', '(4000y * z) / x'],
+    ['20x / (40y)', 'x / (2y)'],
+    ['60x / (40y)', '3x / (2y)'],
+    ['4x / (2y)', '2x / y']
   ];
   tests.forEach(t => testSimplify(t[0], t[1], t[2]));
   // TODO: factor the numerator to cancel out with denominator