Polynomial expressions for non-binomial structures.

Abstract Following recent paper of the author about polynomial expressions with respect to binomial ideals, the current paper is devoted to the non-binomial case. Beside the established facts in the underlying theory, the correctness and termination of the algorithms are addressed. From the collection of examples, the main large-scale non-binomial one is of particular importance. Application of the new algorithms for the cases of moderately large binomial like cyclic 16-roots and cyclic 18-roots is discussed. A combinatorial analysis for complexity of the proposed algorithms is shown to be at least O (log ⁡ (log ⁡ n) n 2 (log ⁡ n) 2). [ABSTRACT FROM AUTHOR]