gmp_lib.mpz_kronecker Method

GMP Native Interface for .NET

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gmp_libmpz_kronecker Method
Calculate the Jacobi symbol (a/b) with the Kronecker extension (a/2) = (2/a) when a odd, or (a/2) = 0 when a even.

Namespace:  Math.Gmp.Native
Assembly:  Math.Gmp.Native (in Math.Gmp.Native.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax
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public static int mpz_kronecker(
	mpz_t a,
	mpz_t b
)
Public Shared Function mpz_kronecker ( 
	a As mpz_t,
	b As mpz_t
) As Integer
public:
static int mpz_kronecker(
	mpz_t^ a, 
	mpz_t^ b
)
static member mpz_kronecker : 
        a : mpz_t * 
        b : mpz_t -> int

Parameters

a
Type: Math.Gmp.Nativempz_t
The first operand integer.
b
Type: Math.Gmp.Nativempz_t
The second operand integer.

Return Value

Type: Int32
The Jacobi symbol (a/b) with the Kronecker extension (a/2) = (2/a) when a odd, or (a/2) = 0 when a even.
Remarks

When b is odd the Jacobi symbol and Kronecker symbol are identical, so mpz_kronecker_ui, etc. can be used for mixed precision Jacobi symbols too.

Examples
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// Create, initialize, and set the value of a to 15.
mpz_t a = new mpz_t();
gmp_lib.mpz_init_set_ui(a, 15U);

// Create, initialize, and set the value of b to 4.
mpz_t b = new mpz_t();
gmp_lib.mpz_init_set_ui(b, 4U);

// Assert that the Kronecker symbol of (a/b) is 1.
Assert.IsTrue(gmp_lib.mpz_kronecker(a, b) == 1);

// Release unmanaged memory allocated for a and b.
gmp_lib.mpz_clears(a, b, null);
' Create, initialize, and set the value of a to 15.
Dim a As New mpz_t()
gmp_lib.mpz_init_set_ui(a, 15UI)

' Create, initialize, and set the value of b to 4.
Dim b As New mpz_t()
gmp_lib.mpz_init_set_ui(b, 4UI)

' Assert that the Kronecker symbol of (a/b) is 1.
Assert.IsTrue(gmp_lib.mpz_kronecker(a, b) = 1)

' Release unmanaged memory allocated for a and b.
gmp_lib.mpz_clears(a, b, Nothing)

No code example is currently available or this language may not be supported.

No code example is currently available or this language may not be supported.

See Also
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