Construction of Real Algebraic Numbers in Coq

  • Cyril Cohen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7406)


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.


Arithmetic Operation Cauchy Sequence Algebraic Number Proof Assistant Polynomial Evaluation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Cyril Cohen
    • 1
    • 2
    • 3
  1. 1.INRIA Saclay–Île-de-FranceFrance
  2. 2.LIX École PolytechniqueFrance
  3. 3.Microsoft Research - INRIA Joint CentreFrance

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