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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 $x_1\cdot\ldots\cdot x_n - u$ (instead of the generator $t\cdot x_1\cdot\ldots\cdot x_n -1$ 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).