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Dinca, George
and
Mawhin, Jean
2021.
Brouwer Degree.
Vol. 95,
Issue. ,
p.
325.
Published online by Cambridge University Press: 17 April 2009
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.