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%body SINGULAR - A Computer Algebra System for Polynomial Computations Overview Objects Functionality Libraries Examples Applications Availability History Contributors Future %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
SINGULAR Examples Build. Blocks Comb. Appl. HCA Proving
Arrangements Branches Classify Coding Deformations Equidim Part Existence Finite Groups Flatness Genus Hilbert Series Membership Nonnormal Locus Normalization Primdec Puiseux Plane Curves Saturation Solving Space Curves Spectrum %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
SINGULAR Applications Robotics Circuit Design Medicine Glass Melting %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
Study the curve in P1x P1 defined by the tangency condition more closely. There are two main cases of which we will only consider the so-called asymmetric case here:

In this case, the ideal I is generated by   el-g2, ek-gf, ak-dc, ah-c2   and the 2-minors of the matrix
where
.
Computational Task: Remove excess components E1, E2 and E3 from I by saturation! The ring in which these computations need to be done only contains 2 parameters now:
.
The Ei do not involve s and t, so we can harmlessly treat s and t as variables - as long as we interpret the result carefully afterwards. The Subsequent Computational Task.
The SINGULAR computation.