(random nodalPlaneCurve)(d,delta,R)
The procedure starts by choosing
\ \ \ 1) an ideal I of delta random points in $\PP^2$, and then returns
\ \ \ 2) the principal ideal generated by an random element in the saturated square J=saturate(I^2) of degree d.
If the procedure fails, for example if J_d=0, then the null is returned.
Under the option Certified=>true, the result is certified by establishing that
\ \ \ 1) the points are distinct nodes, and that
\ \ \ 2) the curve has ordinary nodes at these points
by using the Jacobian criterion applied to the singular locus of the curve.
Under the option Attempts=>n, the program makes n attempts in both steps to achieve the desired goal. Here n can be infinity. The default value is n=1.






Over very small fields the curves are often singular:


The object nodalPlaneCurve is an instance of the type RandomObject.