Characteristic set method for differential-difference polynomial systems. (English) Zbl 1169.13019
Summary: We present a characteristic set method for mixed differential and difference polynomial systems. We introduce the concepts of coherent, regular, proper irreducible, and strongly irreducible ascending chains and study their properties. We give an algorithm which can be used to decompose the zero set for a finitely generated differential and difference polynomial sets into the union of the zero sets of regular and consistent ascending chains. As a consequence, we solve the perfect ideal membership problem for differential and difference polynomials.
MSC:
| 13P99 | Computational aspects and applications of commutative rings |
| 13N15 | Derivations and commutative rings |
| 68W30 | Symbolic computation and algebraic computation |
Keywords:
characteristic set; differential and difference polynomial; regular ascending chain; irreducible ascending chain; zero decomposition algorithm; perfect ideal membership problemReferences:
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