Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In particular, the notion of connected components of semialgebraic sets is not used.
['Daniel Perrucci', 'Marie-Françoise Roy']
I am writing a research paper on a idea Elementary recursive quantifier elimination based on Thom encoding and sign determination
[{"from": "human", "value": "I am writing a research paper on a idea Elementary recursive quantifier elimination based on Thom encoding and sign determination"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In particular, the notion of connected components of semialgebraic sets is not used."}]