Algosim documentation: KroneckerSymbol

KroneckerSymbol

The Kronecker symbol.

Syntax

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