In order to check the interference with high efficiency in NC(Numerical Control) turning,two types of methods,called interaction arithmetic of implicit equation and parameter equation respectively,are put forward and compared in computational accuracy and efficiency.

Aiming at linkage mechanism,this paper has put forward a method of solution of implicit equations by using simulation.

In this paper, we give an introduction to the development of mathematics mech-anization: constructive algebraic geometry, constructive differential algebraic geometry, construc-tive real algebraic geometry, methods of equation solving, and automated geometric reasoning.

By introducing theories and methods of quadratic equation solving in both eastern and western countries and regions in multicultural viewpoint,this paper showed cultural pluralism of equation solving from multicultural point of view,then excavates including educational values and gave some suggestion on equation teaching.