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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
is
saturated – as in the algorithm of Conti and Traverso – by inversion of all variables: One adds an auxiliary variable t
and the generator t⋅x1 ⋅…⋅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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