Function: hyperellratpoints
Section: elliptic_curves
C-Name: hyperellratpoints
Prototype: GGD0,L,
Help: hyperellratpoints(X,h,{flag=0}): X being a non-singular hyperelliptic
 curve given by an integral model, return a vector containing the affine rational points on the curve
 of naive height less than h.
 If fl=1, stop as soon as a point is found.
 X can be given either by a squarefree polynomial P such that
 X:y^2=P(x) or by a vector [P,Q] such that X:y^2+Q(x)y=P(x) and Q^2+4P is
 squarefree.
Doc: $X$ being a non-singular hyperelliptic curve given by an integral model,
 return a vector containing the affine rational points on the curve of naive height less than $h$.
 If $\fl=1$, stop as soon as a point is found; return either an empty vector or a vector containing a single point.

 $X$ is given either by a squarefree polynomial $P$ such that $X: y^2=P(x)$
 or by a vector $[P,Q]$ such that $X: y^2+Q(x)\*y=P(x)$ and $Q^2+4\*P$ is
 squarefree.

 \noindent The parameter $h$ can be

 \item an integer $H$: find the points $[n/d,y]$ whose abscissas $x = n/d$ have
 naive height (= $\max(|n|, d)$) less than $H$;

 \item a vector $[N,D]$ with $D\leq N$: find the points $[n/d,y]$ with
 $|n| \leq N$, $d \leq D$.

 \item a vector $[N,[D_1,D_2]]$ with $D_1<D_2\leq N$  find the points
 $[n/d,y]$ with $|n| \leq N$ and $D_1 \leq d \leq D_2$.