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numtheory(deprecated)

  

jacobi

  

Jacobi symbol

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

jacobi(a, b)

Parameters

a

-

integer

b

-

non-negative integer

Description

• 

Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[KroneckerSymbol], NumberTheory[JacobiSymbol] instead.

• 

The function jacobi will compute the Jacobi symbol Jab of a and b.  If the factorization of b is p1k1...psks, then jacobi(a, b) = legendre(a, p1)^k1 * ... * legendre(a, ps)^ks, where legendrea,p is the Legendre symbol of a and p.

• 

Note that jacobi returns unevaluated if given algebraic arguments not of the types specified above.

• 

The command with(numtheory,jacobi) allows the use of the abbreviated form of this command.

Examples

Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[KroneckerSymbol], NumberTheory[JacobiSymbol] instead.

withnumtheory:

jacobi12,3

0

(1)

jacobi28,21

0

(2)

jacobi6,11

−1

(3)

legendre6,11

−1

(4)

jacobi226,135

1

(5)

jacobi26,35

−1

(6)

jacobi286,4272943

1

(7)

jacobi104,997

−1

(8)

jacobi888,1999

−1

(9)

jacobia,b

jacobia,b

(10)

See Also

NumberTheory[JacobiSymbol]

NumberTheory[KroneckerSymbol]

numtheory(deprecated)[legendre]