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.