Computer Algebra Scripts Verifying Claims made in Section 3 of Paper

For the main proof in Section 3, we use a Singular computation in order to factor an ideal.
This singular program which is explained in detail in the appendix can be found here.
Its output can be found here.

Moreover, in the appendix one of the six factors of the main factorization (resulting as output of the factorizing Gröbner basis algorithm) is analyzed by hand. Although the other components look somewhat similar, they also have to be analyzed in the same way.

For completeness, in the text file which can be found here we carry out this analysis for all six factors. Every factor describes two plane conics. By symmetry, it suffices to consider one of the two conics in each factor.
In fact, the text file is a Singular program. Although the main steps in the analysis are done by hand, it was convenient to put all these calculations into a Singular file. Namely, several Singular steps serve to do some routine calculations and also to serve for verification purposes.