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numtheory[jacobi] - Jacobi symbol

Calling Sequence

jacobi(a, b)

Parameters

a

-

integer

b

-

non-negative integer

Description

• 

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

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

numtheory:-jacobia,b

(10)

See Also

numtheory[legendre]


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