Based On Weak Non-degenerate Algebraic Variety Of Non-hybrid Decomposition Conditions Improved Algorithm

Decomposing an algebraic variety into irreducible or equidimensional compone- nts is a fundamental task in classic algebraic geometry and has various applications in modern geometry engineering, which is a hotspot of international research because of its important value of theory and application.The article introduces the background of algebraic variety decomposition, present status of international research. Then it explains basic concepts and knowledge of algebraic variety decomposition, such as Wu's characteristic, Grobnerbasis and so on. As we know, initial set is the foundation and mail tool of many decomposition algorithm. And it is one of the most frequent concepts in zero decomposition area. Actually, we need think about problems in this area in some analytic method. In the use of triangulation methods of decomposition of algebraic varieties, the initial set is also an inevitable. Based on the U-set, we improve the computation of the algebraic variety of a saturated ideal.This article is based on U-set, the main priorities are set to replace the use of initial set. The main result of this paper1. Perfecting the definition of U-set and making it more concise.2. Improving the computation of the algebraic variety of a saturated ideal.3. Improving the unmixed decomposition of an algebraic variety. By our imp- rovement we can remove some branch without computeG basis, and simplify the computation of the algebraic variety of a saturated ideal. robnerCompared with the existing program, these new algorithms are better. This can be found from many examples.