Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The theorem of three circles in real algebraic geometry guarantees the termination and correctness of an algorithm of isolating real roots of a univariate polynomial. The main idea of its proof is to consider polynomials whose roots belong to a certain area of the complex plane delimited by straight lines. After applying a transformation involving inversion this area is mapped to an area delimited by circles.  provide a formalisation of this rather geometric proof in Ssreflect, an extension of the proof assistant Coq, that supports a variety of algebraic tools. They allow us to formalise the proof from an algebraic point of view.
['Julianna Zsidó']
I am writing a research paper on a idea Theorem of Three Circles in Coq
[{"from": "human", "value": "I am writing a research paper on a idea Theorem of Three Circles in Coq"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The theorem of three circles in real algebraic geometry guarantees the termination and correctness of an algorithm of isolating real roots of a univariate polynomial. The main idea of its proof is to consider polynomials whose roots belong to a certain area of the complex plane delimited by straight lines. After applying a transformation involving inversion this area is mapped to an area delimited by circles.  provide a formalisation of this rather geometric proof in Ssreflect, an extension of the proof assistant Coq, that supports a variety of algebraic tools. They allow us to formalise the proof from an algebraic point of view."}]