Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present methods for the computation of roots of univariate and bivariate nonlinear polynomial systems as ll as the identification of their multiplicity.  first present an algorithm, called the TDB algorithm, which computes the values and the multiplicities of roots of a univariate polynomial. The procedure is based on the concept of the degree of a certain Gauss map, which is deduced from the polynomial itself. In the bivariate case,  use a combination of resultants and our procedure for the univariate case, as the basis for developing an algorithm for locating the roots and computing their multiplicities. Our methods are robust and global in nature. Complexity analysis of the proposed methods is included together with comparison with standard subdivision methods. Examples illustrate our techniques.
['Kwang Hee Ko', 'Takis Sakkalis', 'Nicholas M. Patrikalakis']
I am writing a research paper on a idea Nonlinear polynomial systems: multiple roots and their multiplicities
[{"from": "human", "value": "I am writing a research paper on a idea Nonlinear polynomial systems: multiple roots and their multiplicities"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present methods for the computation of roots of univariate and bivariate nonlinear polynomial systems as ll as the identification of their multiplicity.  first present an algorithm, called the TDB algorithm, which computes the values and the multiplicities of roots of a univariate polynomial. The procedure is based on the concept of the degree of a certain Gauss map, which is deduced from the polynomial itself. In the bivariate case,  use a combination of resultants and our procedure for the univariate case, as the basis for developing an algorithm for locating the roots and computing their multiplicities. Our methods are robust and global in nature. Complexity analysis of the proposed methods is included together with comparison with standard subdivision methods. Examples illustrate our techniques."}]