## Computing Elimination Ideals and Discriminants of Likelihood Equations. (arXiv:1810.05620v1 [cs.SC])

We develop a probabilistic algorithm for computing elimination ideals of
likelihood equations, which is for larger models by far more efficient than
directly computing Groebner bases or the interpolation method proposed in the
first author's previous work. The efficiency is improved by a theoretical
result showing that the sum of data variables appears in most coefficients of
the generator polynomial of elimination ideal. Furthermore, applying the known
structures of Newton polytopes of discriminants, we can also efficiently deduce
discriminants of the elimination ideals. For instance, the discriminants of 3
by 3 matrix model and one Jukes-Cantor model in phylogenetics (with sizes over
30 GB and 8 GB text files, respectively) can be computed by our methods.查看全文