The Cauchy Index (continued)
Preliminaries
- A : a rectangle defined by [ 1, 2] x [ 3, 4] which encloses a zero.
- F = (p,q) does not vanish on the boundary of A,
- is not zero at each vertex of A.
- Let
-
-
Then, we set (for counterclockwise traversal of )
Proposition*
IAF is an even integer and the multiplicity
* T. Sakkalis, “The Euclidean Algorithm and the Degree of the Gauss Map”, SIAM J. Computing. Vol. 19, No. 3, 1990.