Studying The Real Branches Of Algebraic Curves In The Approximate Singular Points Using Puiseux Expansion

In this paper, we will study how we find the number of the reals branches of algebraic curve which pass by the approximate singular points using the expansion of Puiseux , the approximating calculations , the Newton's polygon , Gap theory and TestCriterion in the formal series field . Then we will find a good Algorithm .

Studying Theory Resultant and some applications

Theory Resultant are considered as one of the new mathematical tools that motivate the researchers in all mathematical domains.They use in solving many of mathematical problems.