﻿ KroneckerSymbol – Algosim documentation
Algosim documentation: KroneckerSymbol

# 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`