X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/45c0fd363937c6e9b05da04a9167e9912c05ca0c..6ec3a4cf4aaa7cd375e1aa18f85861986259b8e5:/mp.h

diff --git a/mp.h b/mp.h
index 99ed098..13f97d1 100644
--- a/mp.h
+++ b/mp.h
@@ -941,15 +941,35 @@ extern mp *mp_modinv(mp */*d*/, mp */*x*/, mp */*p*/);
 
 /* --- @mp_jacobi@ --- *
  *
- * Arguments:	@mp *a@ = an integer less than @n@
- *		@mp *n@ = an odd integer
+ * Arguments:	@mp *a@ = an integer
+ *		@mp *n@ = another integer
  *
  * Returns:	@-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%.
  *
- * 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.)
  */
 
 extern int mp_jacobi(mp */*a*/, mp */*n*/);