NAME    jacobi - Jacobi symbol functionSYNOPSIS    jacobi(x, y)TYPES    x		integer    y		integer    return	1, -1, or 0DESCRIPTION    If y is a positive odd prime and x is an integer not divisible    by y, jacobi(x,y) returns the Legendre symbol function, usually    denoted by (x/y) as if x/y were a fraction; this has the value    1 or -1 according as x is or is not a quadratic residue modulo y.    x is a quadratic residue modulo y if for some integer u,    x = u^2 (mod y); if for all integers u, x != u^2 (mod y), x    is said to be a quadratic nonresidue modulo y.    If y is a positive odd prime and x is divisible by y, jacobi(x,y)    returns the value 1.  (This differs from the zero value usually    given in number theory books for (x/y) when x and y    are not relatively prime.)    assigned to (x/y) O    If y is an odd positive integer equal to p_1 * p_2 * ... * p_k,    where the p_i are primes, not necessarily distinct, the    jacobi symbol function is given by		jacobi(x,y)  =	(x/p_1) * (x/p_2) * ... * (x/p_k).    where the functions on the right are Legendre symbol functions.    This is also often usually by (x/y).    If jacobi(x,y) = -1, then x is a quadratic nonresidue modulo y.    Equivalently, if x is a quadratic residue modulo y, then    jacobi(x,y) = 1.    If jacobi(x,y) = 1 and y is composite, x may be either a quadratic    residue or a quadratic nonresidue modulo y.    If y is even or negative, jacobi(x,y) as defined by calc returns    the value 0.EXAMPLE    ; print jacobi(2,3), jacobi(2,5), jacobi(2,15)    -1 -1 1    ; print jacobi(80,199)    1LIMITS    noneLINK LIBRARY    NUMBER *qjacobi(NUMBER *x, NUMBER *y)    FLAG zjacobi(ZVALUE z1, ZVALUE z2)SEE ALSO## Copyright (C) 1999  Landon Curt Noll#### Calc is open software; you can redistribute it and/or modify it under## the terms of the version 2.1 of the GNU Lesser General Public License## as published by the Free Software Foundation.#### Calc is distributed in the hope that it will be useful, but WITHOUT## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General## Public License for more details.#### A copy of version 2.1 of the GNU Lesser General Public License is## distributed with calc under the filename COPYING-LGPL.  You should have## received a copy with calc; if not, write to Free Software Foundation, Inc.## 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.#### @(#) $Revision: 29.3 $## @(#) $Id: jacobi,v 29.3 2006/05/07 07:25:46 chongo Exp $## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/jacobi,v $#### Under source code control:	1995/12/18 12:34:57## File existed as early as:	1995#### chongo <was here> /\oo/\	http://www.isthe.com/chongo/## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/