Function: kronecker
Section: number_theoretical
C-Name: kronecker
Prototype: lGG
Help: kronecker(x,y): kronecker symbol (x/y).
Description:
(small, small):small kross($1, $2)
(int, small):small krois($1, $2)
(small, int):small krosi($1, $2)
(gen, gen):small kronecker($1, $2)
Doc:
\idx{Kronecker symbol} $(x|y)$, where $x$ and $y$ must be of type integer. By
definition, this is the extension of \idx{Legendre symbol} to $\Z \times \Z$
by total multiplicativity in both arguments with the following special rules
for $y = 0, -1$ or $2$:
\item $(x|0) = 1$ if $|x| = 1$ and $0$ otherwise.
\item $(x|-1) = 1$ if $x \geq 0$ and $-1$ otherwise.
\item $(x|2) = 0$ if $x$ is even and $1$ if $x = 1,-1 \mod 8$ and $-1$
if $x=3,-3 \mod 8$.