var expr = new Expression("x");
expr = expr.subtract(3);
expr = expr.add("x");
console.log(expr.toString());
var eq = new Equation(expr, 4);
console.log(eq.toString());
var x = eq.solveFor("x");
console.log("x = " + x.toString());
Right Now
Chrome / OS X: Cmd + Option + J
Chrome / Windows: Ctrl + Shift + J
Firefox / OS X: Cmd + Option + K
Firefox / Windows: Ctrl + Shift + K
In the Browser
Download algebra.min.js.
<script src="algebra.min.js">
In Node
var algebra = require('algebra.js');
The main objects available are Fraction, Expression, and Equation.
var Fraction = algebra.Fraction;
var Expression = algebra.Expression;
var Equation = algebra.Equation;
Fractions
Add, subtract, multiply, and divide fractions by either integers or other fractions. Fractions are automatically
reduced.
var frac = new Fraction(1, 2);
console.log(frac.toString());
frac = frac.add(new Fraction(3, 4));
console.log(frac.toString());
frac = frac.subtract(2);
console.log(frac.toString());
frac = frac.multiply(new Fraction(4, 3));
console.log(frac.toString());
frac = frac.divide(5);
console.log(frac.toString());
Expressions
Initialize expressions with a variable name.
var x = new Expression("x");
Add / Subtract
Add or subtract integers, fractions, variables, or other expressions to or from expressions.
var x = new Expression("x");
x = x.add(3);
console.log(x.toString());
x = x.subtract(new Fraction(1, 3));
console.log(x.toString());
x = x.add("y");
console.log(x.toString());
var otherExp = new Expression("x").add(6);
x = x.add(otherExp);
console.log(x.toString());
x + 3
x + 8/3
x + y + 8/3
2x + y + 26/3
When adding / subtracting an expression to / from another expression, any like-terms will be combined.
Keep in mind the distributive property when subtracting expressions.
var expr1 = new Expression("a").add("b").add("c");
var expr2 = new Expression("c").subtract("b");
var expr3 = expr1.subtract(expr2);
console.log(expr1.toString() + " - (" + expr2.toString() + ") = " + expr3.toString());
a + b + c - (c - b) = a + 2b
Multiply
Multiply expressions by integers, fractions, variables, or other expressions.
var expr1 = new Expression("x");
expr1 = expr1.add(2);
expr1 = expr1.multiply(4);
var expr2 = new Expression("x");
expr2 = expr2.multiply("y");
expr2 = expr2.multiply(new Fraction(1, 3));
expr2 = expr2.add(4);
var expr3 = expr1.multiply(expr2);
console.log("(" + expr1.toString() + ")(" + expr2.toString() + ") = " + expr3.toString());
(4x + 8)(1/3xy + 4) = 4/3x^2y + 8/3xy + 16x + 32
Divide
Divide expressions by either integers or fractions.
var x = new Expression("x").divide(2).divide(new Fraction(1, 5));
console.log(x.toString());
Raise
Raise expressions to integer powers.
var exp = new Expression("x").add(2);
var exp3 = exp.pow(3);
console.log("(" + exp.toString() + ")^3 = " + exp3.toString());
(x + 2)^3 = x^3 + 6x^2 + 12x + 8
Evaluate
Evaluate expressions by substituting in fractions, integers, or other expressions for variables. Evaluating an expression for only some of its variables returns an expression object. Evaluating an expression for all of its variables returns a fraction object.
Integers and Fractions
var expr = new Expression("x");
expr = expr.multiply(2);
expr = expr.multiply("x");
expr = expr.add("y");
expr = expr.add(new Fraction(1, 3));
console.log(expr.toString());
var answer1 = expr.eval({x: 2});
var answer2 = expr.eval({x: 2, y: new Fraction(3, 4)});
console.log(answer1.toString());
console.log(answer2.toString());
2x^2 + y + 1/3
y + 25/3
109/12
Other Expressions
var expr = new Expression("x").add(2);
console.log(expr.toString());
var sub = new Expression("y").add(4);
var answer = expr.eval({x: sub});
console.log(answer.toString());
Equations
Build an Equation
Build an equation by setting an expression equal to another expression or to an integer or fraction.
var z = new Expression("z");
var eq1 = new Equation(z.subtract(4).divide(9), z.add(6));
console.log(eq1.toString());
var eq2 = new Equation(z.add(4).multiply(9), 6);
console.log(eq2.toString());
var eq3 = new Equation(z.divide(2).multiply(7), new Fraction(1, 4));
console.log(eq3.toString());
1/9z - 4/9 = z + 6
9z + 36 = 6
7/2z = 1/4
Solve Linear Equations
One Variable
If a linear equation only has one variable, solving for that variable will return a fraction object.
var x1 = new Expression("x");
x1 = x1.add(new Fraction(2, 3));
x1 = x1.divide(5);
var x2 = new Expression("x");
x2 = x2.divide(7);
x2 = x2.add(4);
var eq = new Equation(x1, x2);
console.log(eq.toString());
var answer = eq.solveFor("x");
console.log("x = " + answer.toString());
1/5x + 2/15 = 1/7x + 4
x = 203/3
Multiple Variables
If a linear equation has more than one variable, solving for a variable will return an expression.
var expr1 = new Expression("x");
expr1 = expr1.add(5);
expr1 = expr1.divide(4);
var expr2 = new Expression("y");
expr2 = expr2.subtract(new Fraction(4, 5));
expr2 = expr2.multiply(3);
var eq = new Equation(expr1, expr2);
console.log(eq.toString());
var xAnswer = eq.solveFor("x");
var yAnswer = eq.solveFor("y");
console.log("x = " + xAnswer.toString());
console.log("y = " + yAnswer.toString());
1/4x + 5/4 = 3y - 12/5
x = 12y - 73/5
y = 1/12x + 73/60
Solve Quadratic Equations
An equation is quadratic if it can be arranged into the form
$$ax^2 + bx + c = 0$$
where $a neq 0$.
A quadratic equation has at least one real root if its discriminant, $b^2 – 4ac$, is greater than or equal to 0.
Solving a quadratic equation with a discriminant that is greater than or equal to 0 returns an array of its real roots as either Fraction objects or numbers,
depending on if the roots are rational or irrational, respectively. Solving a quadratic equation with a discriminant that is less than 0 will return an empty array.
var n1 = new Expression("x").add(5);
var n2 = new Expression("x").subtract(new Fraction(3, 4));
var quad = new Equation(n1.multiply(n2), 0);
console.log(quad.toString());
var answers = quad.solveFor("x");
console.log("x = " + answers.toString());
x^2 + 17/4x - 15/4 = 0
x = -5,3/4
Solve Cubic Equations
An equation is cubic if it can be arranged into the form
$$ax^3 + bx^2 + cx + d = 0$$
where $a neq 0$.
All cubic equations have at least one real root. Solving a cubic equation returns an array of its real roots as either Fraction objects or numbers.
var n1 = new Expression("x").add(2);
var n2 = new Expression("x").add(3);
var n3 = new Expression("x").add(4);
var cubic = new Equation(n1.multiply(n2).multiply(n3), 0);
console.log(cubic.toString());
var answers = cubic.solveFor("x");
console.log("x = " + answers.toString());
x^3 + 9x^2 + 26x + 24 = 0
x = -4,-3,-2
Solve Quartic Equations
Coming soon.
Solve Anything Else
Equations will only be solved if there is an algebraic solution or if the variable being solved for can be isolated through arithmetic operations. Attempting to solve an equation that does not fit these criteria returns undefined.
var expr = new Expression("x");
expr = expr.multiply("x");
expr = expr.add("x");
expr = expr.add("y");
var eq = new Equation(expr, 3);
console.log(eq.toString());
var xAnswer = eq.solveFor("x");
var yAnswer = eq.solveFor("y");
console.log("x = " + xAnswer);
console.log("y = " + yAnswer.toString());
x^2 + x + y = 3
x = undefined
y = -x^2 - x + 3
Make things pretty with LaTeX. All classes have a .toTex() method for rendering LaTeX. Combining this with
KaTeX, for example, is easy.
Example
<div id="mySolution">
Good E-Reader has a piece announcing the imminent demise of the Sony Digital Paper notepad. The problem is, Sony’s current online store for the U.S. knows of no such plans. We talked to the store. The real news is that the e-commerce site is shutting down August 28—not the discontinuation of the reader. 
