A decision method for certain algebraic geometry problems (Q752130)

Wu Wen-tsün's method of mechanical theorem proving in geometry is complete for certain elementary geometry problems involving equality only. For the corresponding algebraic geometry problem, the method is complete for problems with an algebraically closed field as the associated field. The authors present a theorem to extend some theoretical property of Wu's method from algebraically closed fields to arbitrary fields. The theorem implies a decision method for the membership of the set of all polynomials which fix a certain type of algebraic variety denoted by \(V^*\) by Wu Wen-tsün.