An improved method for counting distinct real roots of polynomial system in a triangle

A piecewise algebraic curve is defined by a bivariate spline function. It is important to study the number of real intersection points of the piecewise algebraic curves. In 2002, Renhong Wang et al. proposed a lower bound of the number of distinct real intersection points of two piecewise algebraic curves whose common points are finite in a triangle by using the method of rotation degree of vector field. Using Strum´s theorem, we improve this method (by costructing an adaptive root isolating algorithm) to be more effective and practicable.