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Computing the topological degree of polynomial maps

Published online by Cambridge University Press:  17 April 2009

Takis Sakkalis  and
Zenon Ligatsikas
Takis Sakkalis
Affiliation:
Department of MathematicsAgricultural University of AthensAthens 118 55Greece e-mail: [email protected]
Zenon Ligatsikas
Affiliation:
Department of MathematicsAgricultural University of AthensAthens 118 55Greece e-mail: [email protected]
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Abstract

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Let C be a cube in Rn+1 and let F = (f1, …, fn+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 (f1, f2, …, fi−1, fi, fi+1, …, fn+1) over all sides of C, thereby reducing an (n + 1)–dimensional problem to an n–dimensional one.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 1 , August 1997 , pp. 87 - 94
Copyright
Copyright © Australian Mathematical Society 1997

References

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