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Computing the topological degree of polynomial maps
| Content Provider | Scilit |
|---|---|
| Author | Sakkalis, Takis Ligatsikas, Zenon |
| Copyright Year | 1997 |
| Description | Let C be a cube in $R^{n+1}$ and let F = $(f_{1}$, …, $f_{n+1}$) be a polynomial vector field. In this note we propose a recursive algorithm for the computation of the degree of F on C. The main idea of the algorithm is that the degree of F is equal to the algebraic sum of the degrees of the map $(f_{1}$, $f_{2}$, …, $f_{i−1}$, $f_{i}$, $f_{i+1}$, …, $f_{n+1}$) over all sides of C, thereby reducing an (n + 1)–dimensional problem to an n–dimensional one. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/8F65BE1A3FAED6A3057EA52371D40BDA/S0004972700030768a.pdf/div-class-title-computing-the-topological-degree-of-polynomial-maps-div.pdf |
| Ending Page | 94 |
| Page Count | 8 |
| Starting Page | 87 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700030768 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 1 |
| Volume Number | 56 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1997-08-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Applied Mathematics Polynomial Maps Topological Degree |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
