Function: idealdiv
Section: number_fields
C-Name: idealdiv0
Prototype: GGGD0,L,
Help: idealdiv(nf,x,y,{flag=0}): quotient x/y of two ideals x and y in HNF
 in the number field nf. If (optional) flag is nonzero, the quotient is
 supposed to be an integral ideal (slightly faster).
Description:
 (gen, gen, gen, ?0):gen        idealdiv($1, $2, $3)
 (gen, gen, gen, 1):gen         idealdivexact($1, $2, $3)
 (gen, gen, gen, #small):gen    $"invalid flag in idealdiv"
 (gen, gen, gen, small):gen     idealdiv0($1, $2, $3, $4)
Doc: quotient $x\cdot y^{-1}$ of the two ideals $x$ and $y$ in the number
 field $\var{nf}$. The result is given in HNF.

 If $\fl$ is nonzero, the quotient $x \cdot y^{-1}$ is assumed to be an
 integral ideal. This can be much faster when the norm of the quotient is
 small even though the norms of $x$ and $y$ are large. More precisely,
 the algorithm cheaply removes all maximal ideals above rational
 primes such that $v_{p}(Nx) = v_{p}(Ny)$.
Variant: Also available are \fun{GEN}{idealdiv}{GEN nf, GEN x, GEN y}
 ($\fl=0$) and \fun{GEN}{idealdivexact}{GEN nf, GEN x, GEN y} ($\fl=1$).
