Unmixed-dimensional Decomposition of a Finitely Generated Perfect Differential Ideal
✍ Scribed by Driss Bouziane; Abdelilah Kandri Rody; Hamid Maârouf
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 345 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0747-7171
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✦ Synopsis
We present an algorithm that computes an unmixed-dimensional decomposition of a finitely generated perfect differential ideal I. Each I i in the decomposition I = I 1 ∩ • • • ∩ I k is given by its characteristic set. This decomposition is a generalization of the differential case of Kalkbrener's decomposition. We use a different approach. The basic operation in our algorithm is the computation of the inverse of an algebraic polynomial with respect to a finite set of algebraic polynomials. No factorization is needed. Some of the main problems in polynomial ideal theory can be solved by means of this decomposition: we show how the radical membership can be decided, a characteristic set of a prime differential ideal can be selected, and the differential dimension with a parametric set of a differential ideal can be read. The algorithm has been implemented in the computer algebra system MAPLE and has been tested successfully on many examples.