Discrete weighted transforms and large-integer arithmetic
Mathematics of Computation
Formal and efficient primality proofs by use of computer algebra oracles
Journal of Symbolic Computation - Special issue on computer algebra and mechanized reasoning: selected St. Andrews' ISSAC/Calculemus 2000 contributions
A compiled implementation of strong reduction
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
A Skeptic’s Approach to Combining HOL and Maple
Journal of Automated Reasoning
Autarkic Computations in Formal Proofs
Journal of Automated Reasoning
Journal of Automated Reasoning
Using Reflection to Build Efficient and Certified Decision Procedures
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
A computational approach to pocklington certificates in type theory
FLOPS'06 Proceedings of the 8th international conference on Functional and Logic Programming
Implementing the cylindrical algebraic decomposition within the Coq system
Mathematical Structures in Computer Science
Proving Bounds on Real-Valued Functions with Computations
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Certified exact real arithmetic using co-induction in arbitrary integer base
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Primality proving with elliptic curves
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Proving formally the implementation of an efficient gcd algorithm for polynomials
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Floating-point arithmetic in the Coq system
Information and Computation
Rigorous polynomial approximation using taylor models in Coq
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
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Computing efficiently with numbers can be crucial for some theorem proving applications. In this paper, we present a library of modular arithmetic that has been developed within the Coq proof assistant. The library proposes the usual operations that have all been proved correct. The library is purely functional but can also be used on top of some native modular arithmetic. With this library, we have been capable of certifying the primality of numbers with more than 13000 digits.