A lightweight JavaScript CAS for comparing expressions and equations.
npm install @khanacademy/kasA lightweight JavaScript CAS (Computer Algebra System) for comparing expressions and equations.
It is used throughout Khan Academy's interactive exercises.
It can parse plain text math, LaTeX, or a mix of both:
``js`
var expr = KAS.parse("3x \\frac{42}{42} sin^2y").expr;
expr.print();
// "3x42/42*sin(y)^(2)"
It can evaluate expressions:
`js`
var expr = KAS.parse("(x^2+y^2)^.5").expr;
expr.eval({x: 3, y: 4});
// 5
It can compare expressions and equations:
`js
var expr1 = KAS.parse("(1-x)(-1-6x)").expr;
var expr2 = KAS.parse("(6x+1)(x-1)").expr;
KAS.compare(expr1, expr2).equal;
// true
var eq1 = KAS.parse("2w+50/w=25").expr;
var eq2 = KAS.parse("w(12.5-w)=25").expr;
KAS.compare(eq1, eq2).equal;
// true
`
It can perform basic transforms that always simplify an expression:
`js
var expr = KAS.parse("1+1+x+x+x+y").expr;
expr.collect().print();
// "2+3*x+y"
var expr = KAS.parse("b^(2ylog_b x)").expr;
expr.collect().print();
// "x^(2*y)"
`
It can perform non-simplifying transforms on an expression:
`js`
var expr = KAS.parse("ab(c+d)e^f").expr;
expr.print();
// "ab(c+d)*e^(f)"
expr.expand().print();
// "abe^(f)c+abe^(f)d"
expr.expand().factor().print();
// "abe^(f)*(c+d)"
It can combine the above abilities to perform powerful simplification:
`js
var expr = KAS.parse("((nx^5)^5)/(n^-2x^2)^-3").expr;
expr.print();
// "(nx^(5))^(5)(n^(-2)x^(2))^(-1-3)"
expr.simplify().print();
// "n^(-1)*x^(31)"
var expr = KAS.parse("(15np-25mp)/(15p^2-5p)+(20mp+10p^2)/(15p^2-5p)").expr;
expr.print();
// "(15np+-25mp)(15p^(2)+-5p)^(-1)+(20mp+10p^(2))(15p^(2)+-5*p)^(-1)"
expr.simplify().print();
// "(-1+3p)^(-1)(3n+-1m+2*p)"
`
pnpm install
pnpm build:parser