Name
Abstract | ||
|---|---|---|
If n points B_1,---,B_n$ in the standard simplex \Delta_n are affinely independent, then they can span an (n-1)-simplex denoted by \Lambda=Con(B_1,---,B_n). Here \Lambda corresponds to an n*n matrix [\Lambda] whose columns are B_1,---,B_n. In this paper, we firstly proved that if \Lambda of diameter sufficiently small contains a point $P$, and f(P)>0 (<0) for a form f in R[X], then the coefficients of f([\Lambda] X) are all positive (negative). Next, as an application of this result, a necessary and sufficient condition for determining the real zeros on \Delta_n of a system of homogeneous algebraic equations with integral coefficients is established. |
Year | Venue | Field |
|---|---|---|
2012 | CoRR | Discrete mathematics,Matrix (mathematics),Mathematical analysis,Homogeneous,Algebraic equation,Simplex,Mathematics |
DocType | Volume | Citations |
Journal | abs/1209.3080 | 0 |
PageRank | References | Authors |
0.34 | 1 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yong Yao | 1 | 0 | 0.34 |
| Jia Xu | 2 | 298 | 36.94 |
| Jing-Zhong Zhang | 3 | 137 | 16.54 |