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Exploiting chordal structure in polynomial ideals: a Gröbner bases approach. (English) Zbl 1353.13033
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.

##### MSC:
 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 68W30 Symbolic computation and algebraic computation
##### Software:
Chordal; COLAMD; PolyBoRi; SageMath; SINGULAR
Full Text:
##### References:
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