Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Polynomial systems of equations are a central object of study in computer algebra. Among the many existing algorithms for solving polynomial systems, perhaps the most successful numerical ones are the homotopy algorithms. The number of operations that these algorithms perform depends on the condition number of the roots of the polynomial system. Roughly speaking the condition number expresses the sensitivity of the roots with respect to small perturbation of the input coefficients. A natural question to ask is how can  bound, in the worst case, the condition number when the input polynomials have integer coefficients?  address this problem and  provide effective bounds that depend on the number of variables, the degree and the maximum coefficient bitsize of the input polynomials. Such bounds allows to estimate the bit complexity of the algorithms that depend on the separation bound, like the homotopy algorithms, for solving polynomial systems.
['Aaron Herman', 'Elias P. Tsigaridas']
I am writing a research paper on a idea Bounds for the Condition Number of Polynomials Systems with Integer Coefficients (Invited Talk)
[{"from": "human", "value": "I am writing a research paper on a idea Bounds for the Condition Number of Polynomials Systems with Integer Coefficients (Invited Talk)"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Polynomial systems of equations are a central object of study in computer algebra. Among the many existing algorithms for solving polynomial systems, perhaps the most successful numerical ones are the homotopy algorithms. The number of operations that these algorithms perform depends on the condition number of the roots of the polynomial system. Roughly speaking the condition number expresses the sensitivity of the roots with respect to small perturbation of the input coefficients. A natural question to ask is how can  bound, in the worst case, the condition number when the input polynomials have integer coefficients?  address this problem and  provide effective bounds that depend on the number of variables, the degree and the maximum coefficient bitsize of the input polynomials. Such bounds allows to estimate the bit complexity of the algorithms that depend on the separation bound, like the homotopy algorithms, for solving polynomial systems."}]