Resolvent systems of difference polynomial ideals

ABSTRACT

In this paper, a new theory of resolvent systems is developed for prime difference ideals and difference ideals defined by coherent and proper irreducible ascending chains. Algorithms to compute such resolvent systems are also given. As a consequence, we prove that any irreducible difference variety is birationally equivalent to an irreducible difference variety of codimension one. As a preparation to the resolvent theory, we also prove that the saturation ideal of a coherent and proper ascending chain is unmixed in the sense that all its prime components have the same dimension and order.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Algebraic algorithms

General Terms:
Algorithms, Theory

Keywords:
difference ascending chain, difference polynomial, difference variety, resolvent, unmixed decomposition