The function jacobi will compute the Jacobi symbol  of a and b.  If the factorization of b is , then jacobi(a, b) = legendre(a, p1)^k1 * ... * legendre(a, ps)^ks, where  is the Legendre symbol of a and p.

Note that jacobi returns unevaluated if given algebraic arguments not of the types specified above.

The command with(numtheory,jacobi) allows the use of the abbreviated form of this command.