Abstract
This paper shows a construction in Coq of the set of real algebraic numbers, together with a formal proof that this set has a structure of discrete Archimedean real closed field. This construction hence implements an interface of real closed field. Instances of such an interface immediately enjoy quantifier elimination thanks to a previous work. This work also intends to be a basis for the construction of complex algebraic numbers and to be a reference implementation for the certification of numerous algorithms relying on algebraic numbers in computer algebra.
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Cohen, C. (2012). Construction of Real Algebraic Numbers in Coq . In: Beringer, L., Felty, A. (eds) Interactive Theorem Proving. ITP 2012. Lecture Notes in Computer Science, vol 7406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32347-8_6
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DOI: https://doi.org/10.1007/978-3-642-32347-8_6
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