coredisc

Function: coredisc
Section: number_theoretical
C-Name: coredisc0
Prototype: GD0,L,
Help: coredisc(n,{flag=0}): discriminant of the quadratic field Q(sqrt(n)).
 If (optional) flag is nonzero, output a two-component row vector [d,f],
 where d is the discriminant of the quadratic field Q(sqrt(n)) and n=df^2. f
 may be a half integer.
Doc: a \emph{fundamental discriminant} is an integer of the form $t\equiv 1
 \mod 4$ or $4t \equiv 8,12 \mod 16$, with $t$ squarefree (i.e.~$1$ or the
 discriminant of a quadratic number field). Given a nonzero integer
 $n$, this routine returns the (unique) fundamental discriminant $d$
 such that $n=df^2$, $f$ a positive rational number. If $\fl$ is nonzero,
 returns the two-element row vector $[d,f]$. If $n$ is congruent to
 0 or 1 modulo 4, $f$ is an integer, and a half-integer otherwise.

 By convention, \kbd{coredisc(0, 1))} returns $[0,1]$.

 Note that \tet{quaddisc}$(n)$ returns the same value as \kbd{coredisc}$(n)$,
 and also works with rational inputs $n\in\Q^*$.
Variant: Also available are \fun{GEN}{coredisc}{GEN n} ($\fl = 0$) and
 \fun{GEN}{coredisc2}{GEN n} ($\fl = 1$)