adding factoring support

lib/ChangeTypes.js

@@ -3,114 +3,147 @@
 module.exports = {
   NO_CHANGE: 'NO_CHANGE',
 
-  // e.g. |-3| -> 3
-  ABSOLUTE_VALUE: 'ABSOLUTE_VALUE',
+  // ARITHMETIC
+
+  // e.g. 2 + 2 -> 4 or 2 * 2 -> 4
+  SIMPLIFY_ARITHMETIC: 'SIMPLIFY_ARITHMETIC',
+
+  // BASICS
+
+  // e.g. 2/-1 -> -2
+  DIVISION_BY_NEGATIVE_ONE: 'DIVISION_BY_NEGATIVE_ONE',
+  // e.g. 2/1 -> 2
+  DIVISION_BY_ONE: 'DIVISION_BY_ONE',
+  // e.g. x * 0 -> 0
+  MULTIPLY_BY_ZERO: 'MULTIPLY_BY_ZERO',
+  // e.g. x * 2 -> 2x
+  REARRANGE_COEFF: 'REARRANGE_COEFF',
+  // e.g. x ^ 0 -> 1
+  REDUCE_EXPONENT_BY_ZERO: 'REDUCE_EXPONENT_BY_ZERO',
+  // e.g. 0/1 -> 0
+  REDUCE_ZERO_NUMERATOR: 'REDUCE_ZERO_NUMERATOR',
+  // e.g. 2 + 0 -> 2
+  REMOVE_ADDING_ZERO: 'REMOVE_ADDING_ZERO',
+  // e.g. x ^ 1 -> x
+  REMOVE_EXPONENT_BY_ONE: 'REMOVE_EXPONENT_BY_ONE',
+  // e.g. 1 ^ x -> 1
+  REMOVE_EXPONENT_BASE_ONE: 'REMOVE_EXPONENT_BASE_ONE',
+  // e.g. x * -1 -> -x
+  REMOVE_MULTIPLYING_BY_NEGATIVE_ONE: 'REMOVE_MULTIPLYING_BY_NEGATIVE_ONE',
+  // e.g. x * 1 -> x
+  REMOVE_MULTIPLYING_BY_ONE: 'REMOVE_MULTIPLYING_BY_ONE',
+  // e.g. 2 - - 3 -> 2 + 3
+  RESOLVE_DOUBLE_MINUS: 'RESOLVE_DOUBLE_MINUS',
+
+  // COLLECT AND COMBINE
+
+  // e.g. 2 + x + 3 + x -> 5 + 2x
+  COLLECT_AND_COMBINE_LIKE_TERMS: 'COLLECT_AND_COMBINE_LIKE_TERMS',
+  // e.g. x + 2 + x^2 + x + 4 -> x^2 + (x + x) + (4 + 2)
+  COLLECT_LIKE_TERMS: 'COLLECT_LIKE_TERMS',
+
+  // ADDING POLYNOMIALS
+
   // e.g. 2x + x -> 2x + 1x
   ADD_COEFFICIENT_OF_ONE: 'ADD_COEFFICIENT_OF_ONE',
-  // e.g. x^2 * x -> x^2 * x^1
-  ADD_EXPONENT_OF_ONE: 'ADD_EXPONENT_OF_ONE',
-  // e.g. 1/2 + 1/3 -> 5/6
-  ADD_FRACTIONS: 'ADD_FRACTIONS',
-  // e.g. (1 + 2)/3 -> 3/3
-  ADD_NUMERATORS: 'ADD_NUMERATORS',
   // e.g. x^2 + x^2 -> 2x^2
   ADD_POLYNOMIAL_TERMS: 'ADD_POLYNOMIAL_TERMS',
+  // e.g. 2x^2 + 3x^2 + 5x^2 -> (2+3+5)x^2
+  GROUP_COEFFICIENTS: 'GROUP_COEFFICIENTS',
+  // e.g. -x + 2x => -1*x + 2x
+  UNARY_MINUS_TO_NEGATIVE_ONE: 'UNARY_MINUS_TO_NEGATIVE_ONE',
+
+  // MULTIPLYING POLYNOMIALS
+
+  // e.g. x^2 * x -> x^2 * x^1
+  ADD_EXPONENT_OF_ONE: 'ADD_EXPONENT_OF_ONE',
+  // e.g. x^2 * x^3 * x^1 -> x^(2 + 3 + 1)
+  COLLECT_EXPONENTS: 'COLLECT_EXPONENTS',
+  // e.g. 2x * 3x -> (2 * 3)(x * x)
+  MULTIPLY_COEFFICIENTS: 'MULTIPLY_COEFFICIENTS',
+  // e.g. 2x * x -> 2x ^ 2
+  MULTIPLY_POLYNOMIAL_TERMS: 'MULTIPLY_POLYNOMIAL_TERMS',
+
+  // FRACTIONS
+
   // e.g. (x + 2)/2 -> x/2 + 2/2
   BREAK_UP_FRACTION: 'BREAK_UP_FRACTION',
-  // e.g. nthRoot(x ^ 2, 4) -> nthRoot(x, 2)
-  CANCEL_EXPONENT: 'CANCEL_EXPONENT',
-  // e.g. nthRoot(x ^ 2, 2) -> x
-  CANCEL_EXPONENT_AND_ROOT: 'CANCEL_EXPONENT_AND_ROOT',
   // e.g. -2/-3 => 2/3
   CANCEL_MINUSES: 'CANCEL_MINUSES',
   // e.g. 2x/2 -> x
   CANCEL_TERMS: 'CANCEL_TERMS',
-  // e.g. nthRoot(x ^ 4, 2) -> x ^ 2
-  CANCEL_ROOT: 'CANCEL_ROOT',
-  // e.g. 2 + x + 3 + x -> 5 + 2x
-  COLLECT_AND_COMBINE_LIKE_TERMS: 'COLLECT_AND_COMBINE_LIKE_TERMS',
-  // e.g. x^2 * x^3 * x^1 -> x^(2 + 3 + 1)
-  COLLECT_EXPONENTS: 'COLLECT_EXPONENTS',
-  // e.g. x + 2 + x^2 + x + 4 -> x^2 + (x + x) + (4 + 2)
-  COLLECT_LIKE_TERMS: 'COLLECT_LIKE_TERMS',
-  // e.g. 2/6 + 1/4 -> (2*2)/(6*2) + (1*3)/(4*3)
-  COMMON_DENOMINATOR: 'COMMON_DENOMINATOR',
+  // e.g. 2/6 -> 1/3
+  SIMPLIFY_FRACTION: 'SIMPLIFY_FRACTION',
+  // e.g. 2/-3 -> -2/3
+  SIMPLIFY_SIGNS: 'SIMPLIFY_SIGNS',
+
+  // ADDING FRACTIONS
+
+  // e.g. 1/2 + 1/3 -> 5/6
+  ADD_FRACTIONS: 'ADD_FRACTIONS',
+  // e.g. (1 + 2)/3 -> 3/3
+  ADD_NUMERATORS: 'ADD_NUMERATORS',
   // e.g. (2+1)/5
   COMBINE_NUMERATORS: 'COMBINE_NUMERATORS',
-  // e.g. nthRoot(2, 2) * nthRoot(3, 2) -> nthRoot(2 * 3, 2)
-  COMBINE_UNDER_ROOT: 'COMBINE_UNDER_ROOT',
+  // e.g. 2/6 + 1/4 -> (2*2)/(6*2) + (1*3)/(4*3)
+  COMMON_DENOMINATOR: 'COMMON_DENOMINATOR',
   // e.g. 3 + 1/2 -> 6/2 + 1/2 (for addition)
   CONVERT_INTEGER_TO_FRACTION: 'CONVERT_INTEGER_TO_FRACTION',
-  // e.g. 2 * 2 * 2 -> 2 ^ 3
-  CONVERT_MULTIPLICATION_TO_EXPONENT: 'CONVERT_MULTIPLICATION_TO_EXPONENT',
+  // e.g. 1.2 + 1/2 -> 1.2 + 0.5
+  DIVIDE_FRACTION_FOR_ADDITION: 'DIVIDE_FRACTION_FOR_ADDITION',
+  // e.g. (2*2)/(6*2) + (1*3)/(4*3) -> (2*2)/12 + (1*3)/12
+  MULTIPLY_DENOMINATORS: 'MULTIPLY_DENOMINATORS',
+  // e.g. (2*2)/12 + (1*3)/12 -> 4/12 + 3/12
+  MULTIPLY_NUMERATORS: 'MULTIPLY_NUMERATORS',
+
+  // MULTIPLYING FRACTIONS
+
+  // e.g. 1/2 * 2/3 -> 2/6
+  MULTIPLY_FRACTIONS: 'MULTIPLY_FRACTIONS',
+
+  // DIVISION
+
+  // e.g. 2/3/4 -> 2/(3*4)
+  SIMPLIFY_DIVISION: 'SIMPLIFY_DIVISION',
+  // e.g. x/(2/3) -> x * 3/2
+  MULTIPLY_BY_INVERSE: 'MULTIPLY_BY_INVERSE',
+
+  // DISTRIBUTION
+
   // e.g. 2(x + y) -> 2x + 2y
   DISTRIBUTE: 'DISTRIBUTE',
   // e.g. -(2 + x) -> -2 - x
   DISTRIBUTE_NEGATIVE_ONE: 'DISTRIBUTE_NEGATIVE_ONE',
+  // e.g. 2 * 4x + 2*5 --> 8x + 10 (as part of distribution)
+  SIMPLIFY_TERMS: 'SIMPLIFY_TERMS',
+
+  // ABSOLUTE
+  // e.g. |-3| -> 3
+  ABSOLUTE_VALUE: 'ABSOLUTE_VALUE',
+
+  // ROOTS
+  // e.g. nthRoot(x ^ 2, 4) -> nthRoot(x, 2)
+  CANCEL_EXPONENT: 'CANCEL_EXPONENT',
+  // e.g. nthRoot(x ^ 2, 2) -> x
+  CANCEL_EXPONENT_AND_ROOT: 'CANCEL_EXPONENT_AND_ROOT',
+  // e.g. nthRoot(x ^ 4, 2) -> x ^ 2
+  CANCEL_ROOT: 'CANCEL_ROOT',
+  // e.g. nthRoot(2, 2) * nthRoot(3, 2) -> nthRoot(2 * 3, 2)
+  COMBINE_UNDER_ROOT: 'COMBINE_UNDER_ROOT',
+  // e.g. 2 * 2 * 2 -> 2 ^ 3
+  CONVERT_MULTIPLICATION_TO_EXPONENT: 'CONVERT_MULTIPLICATION_TO_EXPONENT',
   // e.g. nthRoot(2 * x) -> nthRoot(2) * nthRoot(x)
   DISTRIBUTE_NTH_ROOT: 'DISTRIBUTE_NTH_ROOT',
-  // e.g. 1.2 + 1/2 -> 1.2 + 0.5
-  DIVIDE_FRACTION_FOR_ADDITION: 'DIVIDE_FRACTION_FOR_ADDITION',
-  // e.g. 2/-1 -> -2
-  DIVISION_BY_NEGATIVE_ONE: 'DIVISION_BY_NEGATIVE_ONE',
-  // e.g. 2/1 -> 2
-  DIVISION_BY_ONE: 'DIVISION_BY_ONE',
   // e.g. nthRoot(4) * nthRoot(x^2) -> 2 * x
   EVALUATE_DISTRIBUTED_NTH_ROOT: 'EVALUATE_DISTRIBUTED_NTH_ROOT',
   // e.g. 12 -> 2 * 2 * 3
   FACTOR_INTO_PRIMES: 'FACTOR_INTO_PRIMES',
-  // e.g. 2x^2 + 3x^2 + 5x^2 -> (2+3+5)x^2
-  GROUP_COEFFICIENTS: 'GROUP_COEFFICIENTS',
   // e.g. nthRoot(2 * 2 * 2, 2) -> nthRoot((2 * 2) * 2)
   GROUP_TERMS_BY_ROOT: 'GROUP_TERMS_BY_ROOT',
-  // e.g. x/(2/3) -> x * 3/2
-  MULTIPLY_BY_INVERSE: 'MULTIPLY_BY_INVERSE',
-  // e.g. x * 0 -> 0
-  MULTIPLY_BY_ZERO: 'MULTIPLY_BY_ZERO',
-  // e.g. 2x * 3x -> (2 * 3)(x * x)
-  MULTIPLY_COEFFICIENTS: 'MULTIPLY_COEFFICIENTS',
-  // e.g. 1/2 * 2/3 -> 2/6
-  MULTIPLY_FRACTIONS: 'MULTIPLY_FRACTIONS',
-  // e.g. (2*2)/(6*2) + (1*3)/(4*3) -> (2*2)/12 + (1*3)/12
-  MULTIPLY_DENOMINATORS: 'MULTIPLY_DENOMINATORS',
-  // e.g. (2*2)/12 + (1*3)/12 -> 4/12 + 3/12
-  MULTIPLY_NUMERATORS: 'MULTIPLY_NUMERATORS',
-  // e.g. 2x * x -> 2x ^ 2
-  MULTIPLY_POLYNOMIAL_TERMS: 'MULTIPLY_POLYNOMIAL_TERMS',
   // e.g. nthRoot(4) -> 2
   NTH_ROOT_VALUE: 'NTH_ROOT_VALUE',
-  // e.g. x * 2 -> 2x
-  REARRANGE_COEFF: 'REARRANGE_COEFF',
-  // e.g. 2 + 0 -> 2
-  REMOVE_ADDING_ZERO: 'REMOVE_ADDING_ZERO',
-  // e.g. x ^ 1 -> x
-  REMOVE_EXPONENT_BY_ONE: 'REMOVE_EXPONENT_BY_ONE',
-  // e.g. 1 ^ x -> 1
-  REMOVE_EXPONENT_BASE_ONE: 'REMOVE_EXPONENT_BASE_ONE',
-  // e.g. x * -1 -> -x
-  REMOVE_MULTIPLYING_BY_NEGATIVE_ONE: 'REMOVE_MULTIPLYING_BY_NEGATIVE_ONE',
-  // e.g. x * 1 -> x
-  REMOVE_MULTIPLYING_BY_ONE: 'REMOVE_MULTIPLYING_BY_ONE',
-  // e.g. x ^ 0 -> 1
-  REDUCE_EXPONENT_BY_ZERO: 'REDUCE_EXPONENT_BY_ZERO',
-  // e.g. 0/1 -> 0
-  REDUCE_ZERO_NUMERATOR: 'REDUCE_ZERO_NUMERATOR',
-  // e.g. 2 - - 3 -> 2 + 3
-  RESOLVE_DOUBLE_MINUS: 'RESOLVE_DOUBLE_MINUS',
-  // e.g. 2 + 2 -> 4 or 2 * 2 -> 4
-  SIMPLIFY_ARITHMETIC: 'SIMPLIFY_ARITHMETIC',
-  // e.g. 2/3/4 -> 2/(3*4)
-  SIMPLIFY_DIVISION: 'SIMPLIFY_DIVISION',
-  // e.g. 2/6 -> 1/3
-  SIMPLIFY_FRACTION: 'SIMPLIFY_FRACTION',
-  // e.g. 2/-3 -> -2/3
-  SIMPLIFY_SIGNS: 'SIMPLIFY_SIGNS',
-  // e.g. 2 * 4x + 2*5 --> 8x + 10 (as part of distribution)
-  SIMPLIFY_TERMS: 'SIMPLIFY_TERMS',
-  // e.g. -x + 2x => -1*x + 2x
-  UNARY_MINUS_TO_NEGATIVE_ONE: 'UNARY_MINUS_TO_NEGATIVE_ONE',
 
-  // Expression change types:
+  // SOLVING FOR A VARIABLE
 
   // e.g. x - 3 = 2 -> x - 3 + 3 = 2 + 3
   ADD_TO_BOTH_SIDES: 'ADD_TO_BOTH_SIDES',
@@ -131,8 +164,21 @@ module.exports = {
   // e.g. 2 = x -> x = 2
   SWAP_SIDES: 'SWAP_SIDES',
 
+  // CONSTANT EQUATION
+
   // e.g. 2 = 2
   STATEMENT_IS_TRUE: 'STATEMENT_IS_TRUE',
   // e.g. 2 = 3
   STATEMENT_IS_FALSE: 'STATEMENT_IS_FALSE',
+
+  // FACTORING
+
+  // e.g. x^2 - 4x -> x(x - 4)
+  FACTOR_SYMBOL: 'FACTOR_SYMBOL',
+  // e.g. x^2 - 4 -> (x - 2)(x + 2)
+  FACTOR_DIFFERENCE_OF_SQUARES: 'FACTOR_DIFFERENCE_OF_SQUARES',
+  // e.g. x^2 + 2x + 1 -> (x + 1)^2
+  FACTOR_PERFECT_SQUARE: 'FACTOR_PERFECT_SQUARE',
+  // e.g. x^2 + 3x + 2 -> (x + 1)(x + 2)
+  FACTOR_SUM_PRODUCT_RULE: 'FACTOR_SUM_PRODUCT_RULE',
 };

lib/checks/index.js

@@ -3,6 +3,7 @@ const canMultiplyLikeTermPolynomialNodes = require('./canMultiplyLikeTermPolynom
 const canRearrangeCoefficient = require('./canRearrangeCoefficient');
 const canSimplifyPolynomialTerms = require('./canSimplifyPolynomialTerms');
 const hasUnsupportedNodes = require('./hasUnsupportedNodes');
+const isQuadratic = require('./isQuadratic');
 const resolvesToConstant = require('./resolvesToConstant');
 
 module.exports = {
@@ -11,5 +12,6 @@ module.exports = {
   canRearrangeCoefficient,
   canSimplifyPolynomialTerms,
   hasUnsupportedNodes,
+  isQuadratic,
   resolvesToConstant,
 };

lib/checks/isQuadratic.js

@@ -0,0 +1,54 @@
+const Node = require('../node');
+const Symbols = require('../Symbols');
+
+// Given a node, will determine if the expression is in the form of a quadratic
+// e.g. `x^2 + 2x + 1` OR `x^2 - 1` but not `x^3 + x^2 + x + 1`
+function isQuadratic(node) {
+  if (!Node.Type.isOperator(node, '+')) {
+    return false;
+  }
+
+  if (node.args.length > 3) {
+    return false;
+  }
+
+  // make sure only one symbol appears in the expression
+  const symbolSet = Symbols.getSymbolsInExpression(node);
+  if (symbolSet.size !== 1) {
+    return false;
+  }
+
+  const secondDegreeTerms = node.args.filter(isPolynomialTermOfDegree(2));
+  const firstDegreeTerms = node.args.filter(isPolynomialTermOfDegree(1));
+  const constantTerms = node.args.filter(Node.Type.isConstant);
+
+  // Check that there is one second degree term and at most one first degree
+  // term and at most one constant term
+  if (secondDegreeTerms.length !== 1 || firstDegreeTerms.length > 1 ||
+    constantTerms.length > 1) {
+    return false;
+  }
+
+  // check that there are no terms that don't fall into these groups
+  if ((secondDegreeTerms.length + firstDegreeTerms.length +
+      constantTerms.length) !== node.args.length) {
+    return false;
+  }
+
+  return true;
+}
+
+// Given a degree, returns a function that checks if a node
+// is a polynomial term of the given degree.
+function isPolynomialTermOfDegree(degree) {
+  return function(node) {
+    if (Node.PolynomialTerm.isPolynomialTerm(node)) {
+      const polyTerm = new Node.PolynomialTerm(node);
+      const exponent = polyTerm.getExponentNode(true);
+      return exponent && parseFloat(exponent.value) === degree;
+    }
+    return false;
+  };
+}
+
+module.exports = isQuadratic;

lib/factor/ConstantFactors.js

@@ -41,8 +41,11 @@ ConstantFactors.getPrimeFactors = function(number){
 ConstantFactors.getFactorPairs = function(number){
   const factors = [];
 
-  const root = Math.sqrt(number);
-  for (var divisor = 1; divisor <= root; divisor++) {
+  const bound = Math.floor(Math.sqrt(Math.abs(number)));
+  for (var divisor = -bound; divisor <= bound; divisor++) {
+    if (divisor === 0) {
+      continue;
+    }
     if (number % divisor === 0) {
       const quotient = number / divisor;
       factors.push([divisor, quotient]);