D.5.11.10 testParametrization

Usage:

testParametrization(f, rTT); f poly, rTT ring

Assume:

The assumptions on the basering and the polynomial f are as required by paraPlaneCurve. The ring rTT has two variables and contains an ideal PARA (such as the ring obtained by applying paraPlaneCurve to f).

Return:

int which is 1 if PARA defines a parametrization of the curve {f=0} and 0, otherwise.

Theory:

We compute the polynomial defining the image of PARA
and compare it with f.

LIB "paraplanecurves.lib";
ring R = 0,(x,y,z),dp;
poly f = y^8-x^3*(z+x)^5;
def RP1 = paraPlaneCurve(f);
==> // 'paraPlaneCurve' created a ring together with an ideal PARA.
==> // Supposing you typed, say,  def RP1 = paraPlaneCurve(f);
==> // you may access the ideal by typing
==> //      setring RP1; PARA;
testParametrization(f, RP1);
==> 1