SINGULAR                             /
 A Computer Algebra System for Polynomial Computations   /   version 1-3-8
                                                       0<
     by: G.-M. Greuel, G. Pfister, H. Schoenemann        \   May 2000
FB Mathematik der Universitaet, D-67653 Kaiserslautern    \
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//
//  This calculation proceeds in positive characteristic, rather than
//  characteristic zero.  Since we do find that the eliminant has degree
//  320, the Shape Lemma holds and so the ideal is reduced if and only
//  if the eliminant has no repeated factors.  We show that it does not.
//
//  Our conclusion for characteristic zero uses the contrapositive of
//    {Multiple solutions of an ideal in characteristic zero}
//             ====>
//    {Multiple solutions in any reduction of that ideal}
//
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//
//  We set up the rings and the ideal
//
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//
//  We compute the Groebner basis of the this ideal
//
//  The ideal has degree 320 and dimension 0
// codimension = 6
// dimension   = 0
// degree      = 320
//  This is the time for the first Groebner basis calculation
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//  Now we compute an eliminant using fglm, it will be H[1]
//  The eliminant has degree 320
// codimension = 1
// dimension   = 5
// degree      = 320
//  We compute the ideal of the eliminant and its first derivative
//  Since this is the unit ideal, the eliminant has no repeated factors
//  and thus the original ideal is reduced.
_[1]=1
//  This is the time for the full calculation
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Auf Wiedersehen.