-- | -- Module: Math.NumberTheory.Primes.Testing.Certificates -- Copyright: (c) 2011 Daniel Fischer -- Licence: MIT -- Maintainer: Daniel Fischer <daniel.is.fischer@googlemail.com> -- -- Certificates for primality or compositeness. module Math.NumberTheory.Primes.Testing.Certificates ( -- * Certificates Certificate(..) , argueCertificate , CompositenessProof , composite , PrimalityProof , cprime -- * Arguments , CompositenessArgument(..) , PrimalityArgument(..) -- ** Weaken proofs to arguments , arguePrimality , argueCompositeness -- ** Prove valid arguments , verifyPrimalityArgument , verifyCompositenessArgument -- * Determine and prove whether a number is prime or composite , certify -- ** Checks for the paranoid , checkCertificate , checkCompositenessProof , checkPrimalityProof ) where import Math.NumberTheory.Primes.Testing.Certificates.Internal