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 ImplicitHypersurface

implicitization of hypersurface

 Syntax
 ```ImplicitHypersurface(ParamDescr: LIST): RINGELEM ImplicitHypersurface(ParamDescr: LIST, Algo: STRING): RINGELEM ImplicitHypersurface(P: RING, ParamDescr: LIST): RINGELEM ImplicitHypersurface(P: RING, ParamDescr: LIST, Algo: STRING): RINGELEM```

 Description
This function returns the implicitization of the hypersurface parametrically described by the list ParamDescr . From version CoCoA-5.2.2 it works also for rational parametrization.

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

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

Verbosity: 20-80-90.

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

 Example
 ```/**/ 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 /**/ -- Parametrization by rational functions /**/ K := NewFractionField(RingQQt(1)); /**/ use K; /**/ ParamDescr := [ (1-t^2)/(1+t^2), 2*t/(1+t^2) ]; /**/ ImplicitHypersurface(ParamDescr); x^2 +x^2 -1 ```