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implicitization of hypersurface

ImplicitHypersurface(ParamDescr: LIST): RINGELEM
ImplicitHypersurface(ParamDescr: LIST, Algo: STRING): RINGELEM
ImplicitHypersurface(R: RING, ParamDescr: LIST): RINGELEM
ImplicitHypersurface(R: RING, ParamDescr: LIST, Algo: STRING): RINGELEM

This function returns the implicitization of the hypersurface parametrically described by the list ParamDescr .

The algorithms are described in the paper Abbott, Bigatti, Robbiano Implicitization of Hypersurfaces

If provided with a ring R , the result is in R , otherwise it is in a newly created ring.

NOTE: it assumes the input is a correct parametric description of a hypersurface in K^(len(ParamDescr)+1) !!

/**/ P ::= QQ[x,y,z];
/**/ Use S ::= QQ[s,t];
/**/ ImplicitHypersurface(P, [s^2, s*t, t^2]);
y^2 -x*z
/**/ ImplicitHypersurface(P, [s^2, s*t, t^2], "Direct");
y^2 -x*z
/**/ ImplicitHypersurface(P, [s^2, s*t, t^2], "ElimTH");
y^2 -x*z

See Also