Exploiting chordal structure in polynomial ideals: a Gröbner bases approach
The paper contains a new elimination method for polynomial systems. The method is well suitable for systems with many equations and many variables, but there are only few variables in each equation. The idea is to use classical elimination (by Gröbner bases) for carefully chosen subsets of equations and variables in an iterative way. Algorithm 2 computes upper and lower bounds for elimination ideals. Theorem 3 gives sufficient conditions for these bounds being exact; hence in these cases, Algorithm 2 computes the precision ideals. Algorithm 3 computes a description of the ideal which has properties sumilar to a lexicographical Gröbner basis. In case of zero dimension, it is easy to compute all solutions when such a description is known.
scientific article; zbMATH DE number 6624158
scientific article