Resolution
Global GMS
ES Strata
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
Common Transversals and Tangents: Second Approach
Study the curve in P1P1 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.

KL, 06/03 http://www.singular.uni-kl.de