- * Use: Computes the Jacobi symbol. If @n@ is prime, this is the
- * Legendre symbol and is equal to 1 if and only if @a@ is a
- * quadratic residue mod @n@. The result is zero if and only if
- * @a@ and @n@ have a common factor greater than one.
+ * Use: Computes the Kronecker symbol %$\jacobi{a}{n}$%. If @n@ is
+ * prime, this is the Legendre symbol and is equal to 1 if and
+ * only if @a@ is a quadratic residue mod @n@. The result is
+ * zero if and only if @a@ and @n@ have a common factor greater
+ * than one.
+ *
+ * If @n@ is composite, then this computes the Kronecker symbol
+ *
+ * %$\jacobi{a}{n}=\jacobi{a}{u}\prod_i\jacobi{a}{p_i}^{e_i}$%
+ *
+ * where %$n = u p_0^{e_0} \ldots p_{n-1}^{e_{n-1}}$% is the
+ * prime factorization of %$n$%. The missing bits are:
+ *
+ * * %$\jacobi{a}{1} = 1$%;
+ * * %$\jacobi{a}{-1} = 1$% if @a@ is negative, or 1 if
+ * positive;
+ * * %$\jacobi{a}{0} = 0$%;
+ * * %$\jacobi{a}{2}$ is 0 if @a@ is even, 1 if @a@ is
+ * congruent to 1 or 7 (mod 8), or %$-1$% otherwise.
+ *
+ * If %$n$% is positive and odd, then this is the Jacobi
+ * symbol. (The Kronecker symbol is a consistant domain
+ * extension; the Jacobi symbol was implemented first, and the
+ * name stuck.)