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A.2.3 slim Groebner bases

The command slimgb calls an implementation of an algorithm to compute Groebner bases which is designed for keeping the polynomials slim (short with small coefficients) during a Groebner basis computation. It provides, in particular, a fast algorithm for computing Groebner bases over function fields or over the rational numbers, but also in several other cases. The algorithm which is still under developement was developed in the diploma thesis of Michael Brickenstein. It has been published as http://www.mathematik.uni-kl.de/~zca/Reports_on_ca/35/paper_35_full.ps.gz.

In the example below (Groebner basis with respect to degree reverse lexicographic ordering over function field) slimgb is much faster than the std command.

ring r=(32003,u1, u2, u3, u4),(x1, x2, x3, x4, x5, x6, x7),dp;
ideal i=

For detailed information and limitations see slimgb.