A Combination of Ritt-Wu''s Method and Collins'' Method
Shang Chou, Xiao Zhi Gao, Nicholas Freitag McPhee · 1989
We propose a method for the decision problem in real closed fields. The method is a combination of the Tarski-Seidenberg-Collins (TSC) method and the Ritt-Wu method. To decide whether a system of polynomial equations and inequations has common zeros (solutions) in a real closed field, we first apply Ritt-Wu''s decomposition method to delete those components that do not have common zeros in an algebraically closed field. Then we apply the TSC method to the remaining components to complete the solution. Many non-trivial examples have been solved by this method.