Topic
Regular chain
About: Regular chain is a research topic. Over the lifetime, 66 publications have been published within this topic receiving 2019 citations.
Papers published on a yearly basis
Papers
TL;DR: The main result is that four different existing notions of good triangular sets are equivalent, and the relationship between these notions is studied.
322 citations
1 Apr 1985
TL;DR: • The other method cons is t s in fac tor iz ing PI(X) in ~[X] , then P2( X) in~(C~l)[X] where ~(Ctl) = ~(X] / I I I (X) , for each reducible factor II 1 of P1 ' and so on.
Abstract: • The other method cons is t s in fac tor iz ing PI(X) in ~[X] , then P2(X) in ~(C~l)[X] where ~(Ctl) = ~[X] / I I I (X) , for each i r reducible factor II 1 of P1 ' and so on, in o rde r to de te rmine al l the fields on which one has to compute. But a lgor i thms for factor izing a re heavy tools , and they requi re the knowledge of pr imi t ive e lements for Q(c~,cc 2) ..... ~(c~ 1 ..... a~_l).
170 citations
TL;DR: An overview of the key ideas which have led to either better implementation techniques or a better understanding of the underlying theory and new techniques that are essential to the recent success and for future research directions in the development of triangular decomposition methods.
87 citations
TL;DR: The properties and computation of the non-properness locus of the canonical projection restricted at a parametric regular chain or at its saturated ideal at the border polynomial and discriminant variety systems are investigated.
Abstract: Border polynomial and discriminant variety are two important notions related to parametric polynomial system solving, in particular, for partitioning the parameter space into regions where the solutions of the system depend continuously on the parameter values. In this paper, we study the relations between those notions in the case of parametric triangular systems. We also investigate the properties and computation of the non-properness locus of the canonical projection restricted at a parametric regular chain or at its saturated ideal.
68 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 3 |
| 2019 | 2 |
| 2017 | 1 |
| 2016 | 2 |
| 2015 | 4 |