
C.6.2.2 The algorithm of Pottier
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The algorithm of Pottier (see [Pot94]) starts by computing a lattice
basis $v_1,\ldots,v_r$ for the integer kernel of $A$ using the
LLL-algorithm. The ideal corresponding to the lattice basis vectors
$$ I_1=<x^{v_i^+}-x^{v_i^-}|i=1,\ldots,r> $$
is saturated -- as in the algorithm of Conti and Traverso -- by
inversion of all variables: One adds an auxiliary variable $t$ and the
generator $t\cdot x_1\cdot\ldots\cdot x_n -1$ to obtain an ideal $I_2$
in $K[t,x_1,\ldots,x_n]$ from which one computes $I_A$ by elimination of
$t$.


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