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.
@article{urn:eudml:doc:44255,
title = {Multivariate Sturm-Habicht sequences: real root counting on n-rectangles and triangles.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {10},
year = {1997},
pages = {119-130},
zbl = {0999.12002},
mrnumber = {MR1485295},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44255}
}
González-Vega, Laureano; Trujillo, Guadalupe. Multivariate Sturm-Habicht sequences: real root counting on n-rectangles and triangles.. Revista Matemática de la Universidad Complutense de Madrid, Tome 10 (1997) pp. 119-130. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44255/