Top
Back: Conti and Traverso
Forward: Hosten and Sturmfels
FastBack: Gauss-Manin connection
FastForward: Buchberger algorithm
Up: Algorithms
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

C.6.2.2 The algorithm of Pottier

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 ( system). The ideal corresponding to the lattice basis vectors

$\displaystyle I_1=<x^{v_i^+}-x^{v_i^-}\vert 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 $t$.
Top Back: Conti and Traverso Forward: Hosten and Sturmfels FastBack: Gauss-Manin connection FastForward: Buchberger algorithm Up: Algorithms Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4.4.1, 2025, generated by texi2html.