KroneckerSymbol

The Kronecker symbol.

Syntax

• KroneckerSymbol(a, n)

  • a is an integer

  • n is an integer

Description

The Kronecker symbol is an extension of the Jacobi symbol to all integers n. Hence, it is also an extension of the Legendre symbol.

Examples

matrix(compute(KroneckerSymbol(a, n), n, 1, 20, a, 1, 20))

⎛ 1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1⎞
⎜ 1   0  −1   0  −1   0   1   0   1   0  −1   0  −1   0   1   0   1   0  −1   0⎟
⎜ 1  −1   0   1  −1   0   1  −1   0   1  −1   0   1  −1   0   1  −1   0   1  −1⎟
⎜ 1   0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1   0⎟
⎜ 1  −1  −1   1   0   1  −1  −1   1   0   1  −1  −1   1   0   1  −1  −1   1   0⎟
⎜ 1   0   0   0   1   0   1   0   0   0   1   0  −1   0   0   0  −1   0  −1   0⎟
⎜ 1   1  −1   1  −1  −1   0   1   1  −1   1  −1  −1   0   1   1  −1   1  −1  −1⎟
⎜ 1   0  −1   0  −1   0   1   0   1   0  −1   0  −1   0   1   0   1   0  −1   0⎟
⎜ 1   1   0   1   1   0   1   1   0   1   1   0   1   1   0   1   1   0   1   1⎟
⎜ 1   0   1   0   0   0  −1   0   1   0  −1   0   1   0   0   0  −1   0  −1   0⎟
⎜ 1  −1   1   1   1  −1  −1  −1   1  −1   0   1  −1   1   1   1  −1  −1  −1   1⎟
⎜ 1   0   0   0  −1   0   1   0   0   0  −1   0   1   0   0   0  −1   0   1   0⎟
⎜ 1  −1   1   1  −1  −1  −1  −1   1   1  −1   1   0   1  −1   1   1  −1  −1  −1⎟
⎜ 1   0   1   0   1   0   0   0   1   0  −1   0   1   0   1   0  −1   0   1   0⎟
⎜ 1   1   0   1   0   0  −1   1   0   0  −1   0  −1  −1   0   1   1   0   1   0⎟
⎜ 1   0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1   0⎟
⎜ 1   1  −1   1  −1  −1  −1   1   1  −1  −1  −1   1  −1   1   1   0   1   1  −1⎟
⎜ 1   0   0   0  −1   0   1   0   0   0  −1   0  −1   0   0   0   1   0  −1   0⎟
⎜ 1  −1  −1   1   1   1   1  −1   1  −1   1  −1  −1  −1  −1   1   1  −1   0   1⎟
⎝ 1   0  −1   0   0   0  −1   0   1   0   1   0  −1   0   0   0  −1   0   1   0⎠

∑(ans)

65

See also

• LegendreSymbol

• JacobiSymbol