Re: jacobi symbol

[Nicolas Mascot <mascotn@maths.tcd.ie>]

Good evening!

There is a command for the Kronecker symbol. I often confuse it with the Jacobi symbol, but if I am not mistaken, the Kronecker symbol generalises the Jacobi symbol. To be safe, here is what the documentation says:

kronecker(x,y):

Kronecker symbol (x|y), where x and y must be of type integer. By definition, this is the extension of Legendre symbol to Z x Z by total multiplicativity in both arguments with the following special rules for y = 0, -1 or 2:

* (x|0) = 1 if |x|= 1 and 0 otherwise.

* (x|-1) = 1 if x >= 0 and -1 otherwise.

* (x|2) = 0 if x is even and 1 if x = 1,-1 mod 8 and -1 if x = 3,-3 mod 8.

Best regards,

Nicolas

On 16/02/2021 20:59, jean-pierre Cherdieu wrote:

hi every body,

does someone know if there is a command to compute the jacobi symbol.

sincerely,

--

Jean-Pierre Cherdieu