C.6.2.5 The algorithm of Bigatti, La Scala and Robbiano
The algorithm of Bigatti, La Scala and Robbiano (see [BLR98]) combines the ideas of
the algorithms of Pottier and of Hosten and Sturmfels. The
computations are performed on a graded ideal with one auxiliary
variable u and one supplementary generator x1 ⋅… ⋅ xn − u (instead of the generator
t ⋅ x1 ⋅… ⋅ xn − 1 in the algorithm of Pottier). The algorithm uses a quite unusual technique to get rid of the
variable u again.
There is another algorithm of the authors which tries to parallelize
the computations (but which is not implemented in this library).
|