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Multivariate Sturm-Habicht sequences: real root counting on n-rectangles and triangles.

Laureano González-Vega, Guadalupe Trujillo (1997)

Revista Matemática de la Universidad Complutense de Madrid

The main purpose of this note is to show how Sturm-Habicht Sequence can be generalized to the multivariate case and used to compute the number of real solutions of a polynomial system of equations with a finite number of complex solutions. Using the same techniques, some formulae counting the number of real solutions of such polynomial systems of equations inside n-dimensional rectangles or triangles in the plane are presented.

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