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adding factoring support #104

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merged 8 commits into from
Feb 10, 2017
Merged

adding factoring support #104

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d9633f4
adding factoring support
aelnaiem Jan 27, 2017
988b98e
removing extra line
aelnaiem Jan 30, 2017
a527552
Merge branch 'master' into ae_quadratic
aelnaiem Feb 6, 2017
93adba6
more tests, more functionality and code cleanup for factoring quadratics
aelnaiem Feb 6, 2017
d71c753
linting
aelnaiem Feb 6, 2017
f7ee0de
looping through factoring functions and adding more tests
aelnaiem Feb 8, 2017
ce97fc3
organizing change types by the type of change they are associated with
aelnaiem Feb 8, 2017
915f539
factoring out the gcd when factoring a symbol and adding tests for ne…
aelnaiem Feb 10, 2017
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195 changes: 115 additions & 80 deletions lib/ChangeTypes.js
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Original file line number Diff line number Diff line change
Expand Up @@ -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',
Expand All @@ -131,12 +164,14 @@ 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 change types:
// FACTORING

// e.g. x^2 - 4x -> x(x - 4)
FACTOR_SYMBOL: 'FACTOR_SYMBOL',
Expand Down
12 changes: 8 additions & 4 deletions lib/checks/isQuadratic.js
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Expand Up @@ -12,13 +12,14 @@ function isQuadratic(node) {
return false;
}

// get the number of symbols in the expression and ensure there's only one
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sorry I'm being really picky now so you don't have to change this but

I think this comment is pretty close to what the code is doing, I meant more like
"make sure only one symbol appears in the expression, i.e. just x and not both x and y"

the point of confusion for people could be that it's a set (which you show in the var name which is helpful, so it's probably fine) and there can be multiple symbol terms (multiple symbols) as long as they're of the same symbol name

const symbolSet = Symbols.getSymbolsInExpression(node);
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I think this might be confusing to an outsider - add a comment explaining what this is checking?

if (symbolSet.size !== 1) {
return false;
}

const secondDegreeTerms = node.args.filter(isPolynomialTermOfDegree('2'));
const firstDegreeTerms = node.args.filter(isPolynomialTermOfDegree('1'));
const secondDegreeTerms = node.args.filter(isPolynomialTermOfDegree(2));
const firstDegreeTerms = node.args.filter(isPolynomialTermOfDegree(1));
const constantTerms = node.args.filter(Node.Type.isConstant);
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what if there are other args that don't fall into one of these buckets? we should return false right? so I guess check that the length of each of these add up to the number of args


// Check that there is one second degree term and at most one first degree
Expand All @@ -29,19 +30,22 @@ function isQuadratic(node) {
}

// check that there are no terms that don't fall into these groups
if (secondDegreeTerms.length + firstDegreeTerms.length + constantTerms.length !== node.args.length) {
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) {
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add a docstring that also makes it clear we have to pass a string as the degree (which is unfortunate :p)

return function(node) {
if (Node.PolynomialTerm.isPolynomialTerm(node)) {
const polyTerm = new Node.PolynomialTerm(node);
const exponent = polyTerm.getExponentNode(true);
return exponent && exponent.value === degree;
return exponent && parseFloat(exponent.value) === degree;
}
return false;
};
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