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// Copyright (c) 2002-2008 Max-Planck-Institute Saarbruecken (Germany) // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Polynomial/include/CGAL/Polynomial/modular_gcd_utcf_algorithm_M.h $ // $Id: include/CGAL/Polynomial/modular_gcd_utcf_algorithm_M.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Dominik Huelse // Michael Hemmer // // ============================================================================ /*! \file CGAL/Polynomial/modular_gcd_utcf_algorithm_M.h provides gcd for Polynomials, based on Modular arithmetic. */ #ifndef CGAL_POLYNOMIAL_MODULAR_GCD_UTCF_ALGORITHM_M_H #define CGAL_POLYNOMIAL_MODULAR_GCD_UTCF_ALGORITHM_M_H 1 #include #include #include #include #include #include #include #include #include // algorithm M for integer polynomials, without denominator bound namespace CGAL { namespace internal{ template Polynomial gcd_utcf_UFD(Polynomial,Polynomial); template Polynomial< Polynomial > modular_gcd_utcf_algorithm_M( const Polynomial< Polynomial >& FF1 , const Polynomial< Polynomial >& FF2 ){ return gcd_utcf_UFD(FF1, FF2); } template Polynomial modular_gcd_utcf_algorithm_M( const Polynomial& FF1 , const Polynomial& FF2 ){ // Enforce IEEE double precision and to nearest before using modular arithmetic CGAL::Protect_FPU_rounding pfr(CGAL_FE_TONEAREST); // std::cout << "start modular_gcd_utcf_algorithm_M " << std::endl; #ifdef CGAL_MODULAR_GCD_TIMER timer_init.start(); #endif typedef Polynomial Poly; // will play the role of content typedef typename CGAL::Scalar_factor_traits::Scalar Scalar; typedef typename CGAL::Modular_traits::Residue_type MPoly; typedef typename CGAL::Modular_traits::Residue_type MScalar; typedef Chinese_remainder_traits CRT; typename CRT::Chinese_remainder chinese_remainder; CGAL::Real_timer timer; if(FF1.is_zero()){ if(FF2.is_zero()){ return Poly(1);// TODO: return 0 for CGAL } else{ // std::cout<<"\nFF1 is zero"<= 2000){ std::cerr<<"primes in the array exhausted"< degree_e); if( mG_.degree() < degree_e ){ if( n != 0 ) std::cout << "UNLUCKY PRIME !!"<< std::endl; // restart chinese remainder // ignore previous unlucky primes n=1; degree_e= mG_.degree(); }else{ CGAL_postcondition( mG_.degree() == degree_e); n++; // increase number of lucky primes } // -------------------------------------- // try chinese remainder // std::cout <<" chinese remainder round :" << n << std::endl; typename CGAL::Modular_traits::Modular_image_representative inv_map; if(n == 1){ // init chinese remainder q = CGAL::Residue::get_current_prime(); // implicit ! Gs_old = Gs = inv_map(mG_); //H1s_old = H1s = inv_map(mH1); //H2s_old = H2s = inv_map(mH2); }else{ // continue chinese remainder p = CGAL::Residue::get_current_prime(); // implicit! Gs_old = Gs ; //H1s_old = H1s ; //H2s_old = H2s ; #ifdef CGAL_MODULAR_GCD_TIMER timer_CR.start(); #endif // chinese_remainder(q,Gs ,p,inv_map(mG_),pq,Gs); // cached_extended_euclidean_algorithm(q,p,s,t); internal::Cached_extended_euclidean_algorithm ceea; ceea(q,p,s,t); pq =p*q; chinese_remainder(q,p,pq,s,t,Gs,inv_map(mG_),Gs); #ifdef CGAL_MODULAR_GCD_TIMER timer_CR.stop(); #endif q=pq; } try{ if( n != 1 && Gs == Gs_old ){ Poly r1,r2; #ifdef CGAL_MODULAR_GCD_TIMER timer_division.start(); #endif typedef CGAL::Algebraic_structure_traits< Poly > ASTE_Poly; typename ASTE_Poly::Divides divides; bool div1=divides(Gs,g_*F1,H1s); bool div2=divides(Gs,g_*F2,H2s); if (div1 && div2){ solved = true; } // this is the old code // NT dummy; // Poly::euclidean_division(g_*F1,Gs,H1s,r1); // Poly::euclidean_division(g_*F2,Gs,H2s,r2); // if (r1.is_zero() && r2.is_zero()) // solved = true; #ifdef CGAL_MODULAR_GCD_TIMER timer_division.stop(); #endif // std::cout << "number of primes used : "<< n << std::endl; } // end while }catch(...){} } //TODO CGAL: change this to multivariat content // Scalar scalar_content_f1 = scalar_factor(FF1); // Scalar scalar_content_f2 = scalar_factor(FF2); // Scalar scalar_content_gcd = CGAL::gcd(scalar_content_f1,scalar_content_f2); // Poly result = CGAL::canonicalize(Gs)*Poly(scalar_content_gcd); // return result; return CGAL::canonicalize(Gs); } } // namespace internal } // namespace CGAL #endif // CGAL_POLYNOMIAL_MODULAR_GCD_UTCF_ALGORITHM_M_H