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Why Mathsteps

Mathsteps aims to provide step-by-step instructions like a tutor would give them to a student.

Requirements

Mathsteps requires Node version > 6.0.0

Usage Example

To install mathsteps using npm:

(Coming)

npm install @taskbase/mathsteps

const mathsteps = require('mathsteps');

const steps = mathsteps.simplifyExpression('2x + 2x + x + x');

steps.forEach(step => {
	console.log("before change: " + step.oldNode.toString());   // before change: 2 x + 2 x + x + x
	console.log("change: " + step.changeType);                  // change: ADD_POLYNOMIAL_TERMS
	console.log("after change: " + step.newNode.toString());    // after change: 6 x
	console.log("# of substeps: " + step.substeps.length);      // # of substeps: 3
});

To solve an equation:

const steps = mathsteps.solveEquation('2x + 3x = 35');

steps.forEach(step => {
    console.log("before change: " + step.oldEquation.ascii());  // e.g. before change: 2x + 3x = 35
    console.log("change: " + step.changeType);                  // e.g. change: SIMPLIFY_LEFT_SIDE
    console.log("after change: " + step.newEquation.ascii());   // e.g. after change: 5x = 35
    console.log("# of substeps: " + step.substeps.length);      // e.g. # of substeps: 2
});

To see all the change types:

const changes = mathsteps.ChangeTypes;

Which syntax is mathsteps expecting?

Asciimath

Simplify Expression

Simplifying Expressions

What can mathsteps simplifyExpression do?

  • arithmetic simplification: ["(2+2)*5", "20"]
  • collect and combines like terms: ["x^2 + 3x*(-4x) + 5x^3 + 3x^2 + 6", "5x^3 - 8x^2 + 6"]
  • simplify with division: ["(20 * x) / (5 * (40 * y))", "x / (10y)"]
  • deal with fractions: ["2(x+3)/3", "2x / 3 + 2"]
  • cancelling out: ["(1+2a)/a", "1 / a + 2"]
  • deal with absolute values: ["(x^3*y)/x^2 + abs(-5)", "x * y + 5"]
  • deal with nth roots: ["x * nthRoot(x^4, 2)", "x^3"]

unsure:

  • deal with higher order polynomials: ?

What can't mathsteps simplifyExpression do?

Solve Equation

Solving equations.

What can solveEquation do?

  • Solve linear equations with one variable
  • Solve for y in linear equations with x and y as variables.
  • Solve binomic equation
  • Some inequalities (e.g. "x + 2 > 3" to "x > 1")
  • Constant comparison (e.g. "1 = 2" to ChangeTypes.STATEMENT_IS_FALSE)

What can't solveEquation do?

  • Expressions with multiple variables other than y and x
  • Some inequalities (e.g. "( x )/( 2x + 7) >= 4")
  • Calculate square root of x^2, so result will stay e.g. x^2=2

Build

First clone the project from github:

git clone https://github.com/taskbase/mathsteps.git
cd mathsteps

Install the project dependencies:

npm ci
cd lib && npm ci && cd ..
cd example-consumer && npm ci && cd ..

Publish version

See scripts in package.json.

Test

To execute tests for the library, install the project dependencies:

npm ci

Then, the tests can be executed:

npm test

TODOs

  • Fix usage of factoring for simplification
  • Throw error instead of returning empty array?

Done (compared to https://github.com/google/mathsteps)

  • Port to TypeScript!

Attribution

Based on google/mathsteps