A modular, efficient formalisation of real algebraic numbers

Wenda Li, Lawrence C. Paulson
2016 Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2016  
This paper presents a construction of the real algebraic numbers with executable arithmetic operations in Isabelle/HOL. Instead of verified resultants, arithmetic operations on real algebraic numbers are based on a decision procedure to decide the sign of a bivariate polynomial (with rational coefficients) at a real algebraic point. The modular design allows the safe use of fast external code. This work can be the basis for decision procedures that rely on real algebraic numbers.
doi:10.1145/2854065.2854074 dblp:conf/cpp/LiP16 fatcat:df2xm27wc5dhpoikym3xdur5f4