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C.6.2.2 The algorithm of Pottier

The algorithm of Pottier (see [Pot94]) starts by computing a lattice basis v1,,vr for the integer kernel of A using the LLL-algorithm. The ideal corresponding to the lattice basis vectors

        +    −
I1 =< xvi − xvi |i = 1,...,r >
is saturated – as in the algorithm of Conti and Traverso – by inversion of all variables: One adds an auxiliary variable t and the generator tx1 xn 1 to obtain an ideal I2 in K[t,x1,,xn] from which one computes IA by elimination of t.


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