public static int jacobi_symbol(int q, int p)
//****************************************************************************80
//
// Purpose:
//
// JACOBI_SYMBOL evaluates the Jacobi symbol (Q/P).
//
// Discussion:
//
// If P is prime, then
//
// Jacobi Symbol (Q/P) = Legendre Symbol (Q/P)
//
// Else
//
// let P have the prime factorization
//
// P = Product ( 1 <= I <= N ) P(I)^E(I)
//
// Jacobi Symbol (Q/P) =
//
// Product ( 1 <= I <= N ) Legendre Symbol (Q/P(I))^E(I)
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 June 2000
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Daniel Zwillinger,
// CRC Standard Mathematical Tables and Formulae,
// 30th Edition,
// CRC Press, 1996, pages 86-87.
//
// Parameters:
//
// Input, int Q, an integer whose Jacobi symbol with
// respect to P is desired.
//
// Input, int P, the number with respect to which the Jacobi
// symbol of Q is desired. P should be 2 or greater.
//
// Output, int JACOBI_SYMBOL, the Jacobi symbol (Q/P).
// Ordinarily, L will be -1, 0 or 1.
// If JACOBI_SYMBOL is -10, an error occurred.
//
{
const int FACTOR_MAX = 20;
int[] factor = new int[FACTOR_MAX];
int i;
int nfactor = 0;
int nleft = 0;
int[] power = new int[FACTOR_MAX];
switch (p)
{
//
// P must be greater than 1.
//
case <= 1:
Console.WriteLine("");
Console.WriteLine("JACOBI_SYMBOL - Fatal error!");
Console.WriteLine(" P must be greater than 1.");
return(1);
}
//
// Decompose P into factors of prime powers.
//
typeMethods.i4_factor(p, FACTOR_MAX, ref nfactor, ref factor, ref power, ref nleft);
if (nleft != 1)
{
Console.WriteLine("");
Console.WriteLine("JACOBI_SYMBOL - Fatal error!");
Console.WriteLine(" Not enough factorization space.");
return(1);
}
//
// Force Q to be nonnegative.
//
while (q < 0)
{
q += p;
}
//
// For each prime factor, compute the Legendre symbol, and
// multiply the Jacobi symbol by the appropriate factor.
//
int value = 1;
for (i = 0; i < nfactor; i++)
{
int l = Legendre.legendre_symbol(q, factor[i]);
switch (l)
{
case < -1:
Console.WriteLine("");
Console.WriteLine("JACOBI_SYMBOL - Fatal error!");
Console.WriteLine(" Error during Legendre symbol calculation.");
return(1);
default:
value *= (int)Math.Pow(l, power[i]);
break;
}
}
return(value);
}