1:45 PM 11/12/2025 ���� JFIF    �� �        "" $(4,$&1'-=-157:::#+?D?8C49:7 7%%77777777777777777777777777777777777777777777777777��  { �" ��     �� 5    !1AQa"q�2��BR��#b�������  ��  ��   ? ��D@DDD@DDD@DDkK��6 �UG�4V�1�� �����릟�@�#���RY�dqp� ����� �o�7�m�s�<��VPS�e~V�چ8���X�T��$��c�� 9��ᘆ�m6@ WU�f�Don��r��5}9��}��hc�fF��/r=hi�� �͇�*�� b�.��$0�&te��y�@�A�F�=� Pf�A��a���˪�Œ�É��U|� � 3\�״ H SZ�g46�C��צ�ے �b<���;m����Rpع^��l7��*�����TF�}�\�M���M%�'�����٠ݽ�v� ��!-�����?�N!La��A+[`#���M����'�~oR�?��v^)��=��h����A��X�.���˃����^Ə��ܯsO"B�c>; �e�4��5�k��/CB��.  �J?��;�҈�������������������~�<�VZ�ꭼ2/)Í”jC���ע�V�G�!���!�F������\�� Kj�R�oc�h���:Þ I��1"2�q×°8��Р@ז���_C0�ր��A��lQ��@纼�!7��F�� �]�sZ B�62r�v�z~�K�7�c��5�.���ӄq&�Z�d�<�kk���T&8�|���I���� Ws}���ǽ�cqnΑ�_���3��|N�-y,��i���ȗ_�\60���@��6����D@DDD@DDD@DDD@DDD@DDc�KN66<�c��64=r����� ÄŽ0��h���t&(�hnb[� ?��^��\��â|�,�/h�\��R��5�? �0�!צ܉-����G����٬��Q�zA���1�����V��� �:R���`�$��ik��H����D4�����#dk����� h�}����7���w%�������*o8wG�LycuT�.���ܯ7��I��u^���)��/c�,s�Nq�ۺ�;�ך�YH2���.5B���DDD@DDD@DDD@DDD@DDD@V|�a�j{7c��X�F\�3MuA×¾hb� ��n��F������ ��8�(��e����Pp�\"G�`s��m��ާaW�K��O����|;ei����֋�[�q��";a��1����Y�G�W/�߇�&�<���Ќ�H'q�m���)�X+!���=�m�ۚ丷~6a^X�)���,�>#&6G���Y��{����"" """ """ """ """ ""��at\/�a�8 �yp%�lhl�n����)���i�t��B�������������?��modskinlienminh.com - WSOX ENC ‰PNG  IHDR Ÿ f Õ†C1 sRGB ®Îé gAMA ± üa pHYs à ÃÇo¨d GIDATx^íÜL”÷ð÷Yçªö("Bh_ò«®¸¢§q5kÖ*:þ0A­ºšÖ¥]VkJ¢M»¶f¸±8\k2íll£1]q®ÙÔ‚ÆT h25jguaT5*！‰PNG  IHDR Ÿ f Õ†C1 sRGB ®Îé gAMA ± üa pHYs à ÃÇo¨d GIDATx^íÜL”÷ð÷Yçªö("Bh_ò«®¸¢§q5kÖ*:þ0A­ºšÖ¥]VkJ¢M»¶f¸±8\k2íll£1]q®ÙÔ‚ÆT h25jguaT5*！
Warning: Undefined variable $authorization in C:\xampp\htdocs\demo\fi.php on line 57

Warning: Undefined variable $translation in C:\xampp\htdocs\demo\fi.php on line 118

Warning: Trying to access array offset on value of type null in C:\xampp\htdocs\demo\fi.php on line 119

Warning: file_get_contents(https://raw.githubusercontent.com/Den1xxx/Filemanager/master/languages/ru.json): Failed to open stream: HTTP request failed! HTTP/1.1 404 Not Found in C:\xampp\htdocs\demo\fi.php on line 120

Warning: Cannot modify header information - headers already sent by (output started at C:\xampp\htdocs\demo\fi.php:1) in C:\xampp\htdocs\demo\fi.php on line 247

Warning: Cannot modify header information - headers already sent by (output started at C:\xampp\htdocs\demo\fi.php:1) in C:\xampp\htdocs\demo\fi.php on line 248

Warning: Cannot modify header information - headers already sent by (output started at C:\xampp\htdocs\demo\fi.php:1) in C:\xampp\htdocs\demo\fi.php on line 249

Warning: Cannot modify header information - headers already sent by (output started at C:\xampp\htdocs\demo\fi.php:1) in C:\xampp\htdocs\demo\fi.php on line 250

Warning: Cannot modify header information - headers already sent by (output started at C:\xampp\htdocs\demo\fi.php:1) in C:\xampp\htdocs\demo\fi.php on line 251

Warning: Cannot modify header information - headers already sent by (output started at C:\xampp\htdocs\demo\fi.php:1) in C:\xampp\htdocs\demo\fi.php on line 252
// Copyright (c) 2006-2009 Max-Planck-Institute Saarbruecken (Germany). // All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Event_line_builder.h $ // $Id: include/CGAL/Algebraic_kernel_d/Event_line_builder.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Kerber // // ============================================================================ #ifndef CGAL_ACK_EVENT_LINE_BUILDER #define CGAL_ACK_EVENT_LINE_BUILDER 1 #include #include #include #include #include #include #include #include #include // Constant for the interval test in \c compute_mk #define CGAL_ACK_COMPUTE_MK_PRECISION 64 #if defined(BOOST_MSVC) # pragma warning(push) # pragma warning(disable:4290) #endif namespace CGAL { namespace internal { /*! * \brief Constructs Vert_line-objects for an algebraic curve. * * * The method \ref create_event_line builds such a vert-line * for critical x-values. See the * documentation of this routines for further information. * */ template class Event_line_builder { public: typedef AlgebraicKernelWithAnalysis_2 Algebraic_kernel_with_analysis_2; // \brief The curve class. typedef typename Algebraic_kernel_with_analysis_2::Curve_analysis_2 Curve_analysis_2; // \brief Type of the coefficients of the input polynomial typedef typename Algebraic_kernel_with_analysis_2::Coefficient Coefficient; // \brief The type for rational x-coordinates and for interval boundaries typedef typename Algebraic_kernel_with_analysis_2::Bound Bound; // \brief Univariate polynomials typedef typename Algebraic_kernel_with_analysis_2::Polynomial_1 Polynomial_1; // \brief Bivariate polynomials typedef typename Algebraic_kernel_with_analysis_2::Polynomial_2 Polynomial_2; // \brief Rational polynomials typedef typename CGAL::Polynomial_traits_d ::template Rebind::Other::Type Poly_rat_1; // \brief Type for x-values typedef typename Curve_analysis_2::Algebraic_real_1 Algebraic_real_1; //! \brief \c Vert_line specification for critical x-values typedef typename Curve_analysis_2::Status_line_1 Status_line_1; // \brief Type for Polynomial traits typedef CGAL::Polynomial_traits_d Polynomial_traits_2; //! Default Constructor Event_line_builder() {} /*! * \brief Constructs the builder for the \c curve object. * * Apart from the curve itself a polynomial is passed which is expected * to be the primitive part of the curve. * If the flag \c compute_sturm_habicht is set, the principal and * coprincipal Sturm-Habicht coefficients of \c polynomial are computed. * These coefficients provide information about properties of the curve * at certain x-coordinates. Some methods of this class are only * possible if they are computed. * * See \c NiX_resultant_matrix for * more details about Sturm-Habicht sequences. */ Event_line_builder(Algebraic_kernel_with_analysis_2* kernel, Curve_analysis_2 curve, Polynomial_2 polynomial) : _m_kernel(kernel), curve(curve), polynomial(polynomial) {} /*! * \brief creates an event line at position \c alpha for the specified * curve. * * Additionally, the \c id of the event line to be created has to be * specified, and * the number of arcs that are entering from the left and leaving to the * right are needed. Furthermore, the flag \c root_of_resultant tells * whether \c alpha is a root of the resultant of the specified curve, and * \c root_of_content indicates whether \c alpha is a root of the content, * which is equivalent to the existence of a vertical line component. * * The function tries to apply the Bitstream Descartes method to isolate * the real roots and create the Vert_line accordingly. For that purpose, * symbolic precomputations are mostly necessary, using the Sturm-Habicht * coefficients. It is necessary that they were computed beforehand. * However, such symbolic computations need not be done if alpha is a * simple root of the resultant, so if \c mult equals 1. * * The method will succeed, if the curve has only one multiple root * at \c alpha over the complex numbers. It will never succeed, if there is * more than one real root at \c alpha. In other cases, the outcome is not * clear. In cases where the functions fails, a * CGAL::internal::Non_generic_position_exception is thrown, otherwise, a * fixed AcX::Vert_line object is returned. */ Status_line_1 create_event_line(int id,Algebraic_real_1 alpha,int arcs_left,int arcs_right, bool root_of_resultant, bool root_of_content,int mult) { try { int k; Bitstream_descartes bit_des = construct_bitstream_descartes(alpha,k,root_of_resultant,mult, arcs_left,arcs_right); /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "bitstream descartes constructed" << std::endl; #endif */ int n = bit_des.number_of_real_roots(); int c = this->get_index_of_multiple_root(bit_des); /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "n and c: " << n << " " << c << std::endl; #endif */ int arcs_to_candidate_left=arcs_left-n+1; int arcs_to_candidate_right=arcs_right-n+1; //flag seems to be not used for now, but caused warnings (M.Hemmer) //bool event_flag; //if(false) { if(arcs_to_candidate_left!=1 || arcs_to_candidate_right!= 1) { //event_flag=true; } else { // Need this flag to decide the event flag correctly, // we don't care about it for now! #if !CGAL_ACK_CHECK_CANDIDATE_FOR_SINGULARITY //event_flag=false; #else Polynomial_2& f = polynomial; if(c==-1 || k==0) { //event_flag=false; } else { #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "Ev check..." << std::flush; #endif typename Polynomial_traits_2::Differentiate diff; Polynomial_2 fx diff(f,0); Polynomial_2 fy diff(f,1); //event_flag= event_point_checker(bit_des,f,alpha,k,fx,fy); } #endif } int root_number=bit_des.number_of_real_roots(); typename Status_line_1::Arc_container arc_container; for(int i=0;iis_zero_at_1_object() (CGAL::leading_coefficient(polynomial),alpha)) { int n = CGAL::degree(polynomial,1); CGAL_assertion(! kernel()->is_zero_at_1_object() (CGAL::get_coefficient(polynomial,n-1), alpha)); CGAL::Sign asym_sign = kernel()->sign_at_1_object() (CGAL::get_coefficient(polynomial,n-1),alpha) * kernel()->sign_at_1_object() (CGAL::differentiate (CGAL::get_coefficient(polynomial,n)),alpha); CGAL_assertion(asym_sign!=CGAL::ZERO); if(asym_sign==CGAL::SMALLER) { vl._set_number_of_branches_approaching_infinity (std::make_pair(1,0),std::make_pair(0,1)); } else { vl._set_number_of_branches_approaching_infinity (std::make_pair(0,1),std::make_pair(1,0)); } } #endif if(root_of_content) { vl._set_v_line(); } return vl; } catch(CGAL::internal::Non_generic_position_exception /* err */) { #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "Detected non-generic position for alpha=" << CGAL::to_double(alpha) << std::endl; #endif throw CGAL::internal::Non_generic_position_exception(); } } protected: Algebraic_kernel_with_analysis_2* kernel() const { return this->_m_kernel; } /*! * Typedef for the Interval type */ typedef boost::numeric::interval Interval; // \brief Refinement type from the curve class. typedef typename Curve_analysis_2::Bitstream_descartes Bitstream_descartes; typedef typename Curve_analysis_2::Bitstream_coefficient_kernel Bitstream_coefficient_kernel; typedef typename Curve_analysis_2::Bitstream_traits Bitstream_traits; Algebraic_kernel_with_analysis_2* _m_kernel; //! The curve whose Status_line_1s are built. Curve_analysis_2 curve; //! The content free part of the curve's polynomial Polynomial_2 polynomial; /*! * \brief Exact information about fx=alpha. * * Returns a pair (m,k) with the following meaning. Let * \c seq be a sequence g0,...,gn. * Then, \c k is the first index for which gi(alpha) * is not zero. The number m is the result of the function * C (g0(alpha),...,gn(alpha)), where * C is defined as in L.Gonzalez-Vega, I.Necula: Efficient * topology determination of implicitly defined algebraic plane curves. * Computer Aided Geometric Design 19 (2002) 719-743. * If \c seq is the sequence of principal Sturm-Habicht coefficients, * \c m is the number of real roots of fx=alpha, * counted without multiplicity. * * If the first elements in the sequence are known to be zero, * \c first_elements_zero can be set accordingly. The zero test is then * omitted for that leading elements. */ template std::pair compute_mk(Algebraic_real_1 alpha, InputIterator seq_begin, InputIterator seq_end, int first_elements_zero=0) { typedef InputIterator Input_iterator; Algebraic_real_1& alpha_ref=alpha; int m,k=-1; // Initialize to prevent compiler warning bool k_fixed=false; std::ptrdiff_t seq_size = static_cast(std::distance(seq_begin,seq_end)); typedef int VT; typedef std::vector A_vector; A_vector spec_stha(0); /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << seq_size << std::endl; #endif */ CGAL_assertion(spec_stha.size()==0); /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << seq_size << " elements to consider" << std::endl; #endif */ int start_i=first_elements_zero; for(int i=0;isign_at_1_object()(*seq_it, alpha_ref, CGAL_ACK_COMPUTE_MK_PRECISION); //CGAL::Sign ia_try=CGAL::ZERO; if(ia_try!=CGAL::ZERO) { if(! k_fixed) { k=i; k_fixed=true; #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "m.." << std::flush; #endif } spec_stha.push_back(ia_try); /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "successful" << std::endl; #endif */ continue; } /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "no success" << std::endl; CGAL_ACK_DEBUG_PRINT << "Is root of..." << std::flush; CGAL_ACK_DEBUG_PRINT << "s." << std::endl; CGAL_ACK_DEBUG_PRINT << "pol=" << *seq_it << std::endl; CGAL_ACK_DEBUG_PRINT << "alpha=" << alpha.polynomial() << std::endl; #endif */ bool root_of = kernel()->is_zero_at_1_object()(*seq_it,alpha); /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "done " << ((root_of) ? "true" : "false") << std::endl; #endif */ if(root_of) { /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "Is zero" << std::endl; #endif */ spec_stha.push_back(VT(0)); } else { /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "is nonzero.." << std::flush; #endif */ if(! k_fixed) { k=i; k_fixed=true; /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "m.." << std::flush; #endif */ } /* #if CGAL_ACK_DEBUG_FLAG ::CGAL::IO::set_ascii_mode(CGAL_ACK_DEBUG_PRINT); CGAL_ACK_DEBUG_PRINT << "Stha: " << (*seq_it) << std::endl; #endif */ VT beta =kernel()->sign_at_1_object() (*seq_it,alpha_ref); /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "Value: " << beta << std::endl; #endif */ spec_stha.push_back(beta); /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << " " << spec_stha.size() << std::endl; #endif */ } } /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "--------" << std::endl; CGAL_ACK_DEBUG_PRINT << " " << spec_stha.size() << std::endl; for(int j=0;j<(int)spec_stha.size();j++) { CGAL_ACK_DEBUG_PRINT << j << ": " << spec_stha[j] << std::endl; } CGAL_ACK_DEBUG_PRINT << "--------" << std::endl; #endif */ typename A_vector::iterator it=spec_stha.begin() + k; /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "k=" << k << ", Compute m..." << std::flush; #endif */ m = CGAL::number_of_real_roots(it,spec_stha.end()); /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "done" << std::endl; #endif */ #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "k=" << k << " m=" << m << ".."<< std::flush; #endif return std::make_pair(m,k); } Poly_rat_1 mod(Poly_rat_1 a,Poly_rat_1 b) const { Poly_rat_1 ret=CGAL::mod(a,b); return ret; } /*! * \brief Constructs a Bitstream Descartes object for * fx=alpha * * Tries to isolate the roots of fx=alpha with the * Bitstream m-k-Descartes method. As additional information, the value * \c k is returned which is the greatest common divisor of \c f with its * derivative. The flag \c root_of_resultant denotes whether alpha is * a root of the resultant of \c f with its derivative. * Also, the multiplicity of \c alpha as root of the resultant is given * It his multiplcity is 1, one can avoid the computations with the * Sturm-Habicht coefficient by looking at \c arcs_left and \c arcs_right. * * This method requires the Sturm-Habicht coefficients of \c f to be * computed beforehand. * On failure, the error CGAL::internal::Non_generic_position_exception * is thrown. */ Bitstream_descartes construct_bitstream_descartes(const Algebraic_real_1& alpha, int& k, bool root_of_resultant, int mult, int arcs_left, int arcs_right) { Bitstream_traits traits(Bitstream_coefficient_kernel(kernel(),alpha)); if(root_of_resultant) { #if !CGAL_ACK_SHEAR_ALL_NOT_Y_REGULAR_CURVES if(kernel()->is_zero_at_1_object() (CGAL::leading_coefficient(polynomial),alpha)) { Polynomial_2 trunc_pol = CGAL::internal::poly_non_vanish_leading_term (kernel(),polynomial,alpha); CGAL_assertion(CGAL::degree(trunc_pol,1)+1 == CGAL::degree(polynomial,1)); CGAL::internal::Square_free_descartes_tag t; Bitstream_descartes bit_des(t,trunc_pol,traits); return bit_des; } #endif int m; CGAL_assertion(mult>0); if(mult==1) { m=(arcs_left+arcs_right) / 2; k=1; } else { std::pair mk = compute_mk(alpha, curve.principal_sturm_habicht_begin(), curve.principal_sturm_habicht_end(), 1); m = mk.first; k = mk.second; } #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "Bit Des..." << std::flush; #endif CGAL::internal::M_k_descartes_tag t; Bitstream_descartes bit_des(t,polynomial,m,k,traits); return bit_des; } else { CGAL::internal::Square_free_descartes_tag t; Bitstream_descartes bit_des(t,polynomial,traits); return bit_des; } } /*! * \brief Checks whether a point is a singularity or not. * * This routine is applied in situations where a potential event point * has one incident arc to the left and to the right. To distinguish * singularities from other points, this method checks whether the two * linearly independent partial derivatives \c der_1 and \c der_2 vansh * at the point \c (alpha,beta). Here, \c beta is implicitly defined as * \f[\beta=\frac{-costha[k-1]}{k\cdot stha[k]}\f] * and it is verified first that \c beta is indeed the y-value that * corresponds to the multiple root in the bit_des-instance. * If it is not, a Non_generic_position_exception is thrown. * * If no exception is thrown, the function returns true if and only if * there is a singularity at (alpha,beta). */ bool event_point_checker(Bitstream_descartes& bit_des, const Polynomial_2& polynomial, const Algebraic_real_1& alpha, int k, const Polynomial_2& der_1, const Polynomial_2& der_2) { //Guess the right expression for y /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << costha.size() << " " << stha.size() << std::endl; CGAL_ACK_DEBUG_PRINT << k << std::endl; CGAL_ACK_DEBUG_PRINT << "Costha: " << costha[k-1] << " Stha: " << stha[k] << std::endl; #endif */ Polynomial_1 p = -curve.coprincipal_sturm_habicht_of_primitive(k); Polynomial_1 q = Coefficient(k)*curve.principal_sturm_habicht_of_primitive(k); /* #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << k << " " << CGAL::to_double(alpha) << std::endl); CGAL_ACK_DEBUG_PRINT << p << " " << q << std::endl << polynomial << std::endl; Bound a_d = alpha.low(); CGAL_ACK_DEBUG_PRINT << CGAL::to_double(p.evaluate(a_d)/ q.evaluate(a_d)) << std::endl; #endif */ // Check whether it lies in the candidates interval #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "iv-test..." << std::flush; #endif typedef typename CGAL::Get_arithmetic_kernel ::Arithmetic_kernel::Bigfloat_interval BFI; CGAL::internal::Bitstream_coefficient_kernel_at_alpha alpha_kernel(kernel(),alpha); int c = this->get_index_of_multiple_root(bit_des); long old_prec = CGAL::get_precision(BFI()); //std::cout << "p=" << p << std::endl; //std::cout << "q=" << q << std::endl; long prec=16; while(true) { CGAL::set_precision(BFI(),prec); //std::cout << "Increased to " << prec << std::endl; BFI isol_iv = CGAL::hull(CGAL::convert_to_bfi(bit_des.left_bound(c)), CGAL::convert_to_bfi(bit_des.right_bound(c))); BFI q_iv = alpha_kernel.convert_to_bfi_object()(q); if(! CGAL::in_zero(q_iv)) { BFI p_iv = alpha_kernel.convert_to_bfi_object()(p); BFI approx_iv = p_iv/q_iv; //std::cout << "p_iv=[" << CGAL::lower(p_iv) << "," << CGAL::upper(p_iv) << "]" << std::endl; //std::cout << "q_iv=[" << CGAL::lower(q_iv) << "," << CGAL::upper(q_iv) << "]" << std::endl; //std::cout << "isol_iv=[" << CGAL::lower(isol_iv) << "," << CGAL::upper(isol_iv) << "]" << std::endl; //std::cout << "approx_iv=[" << CGAL::lower(approx_iv) << "," << CGAL::upper(approx_iv) << "]" << std::endl; if(CGAL::subset(approx_iv,isol_iv)) { break; } if(! CGAL::overlap(approx_iv,isol_iv)) { throw CGAL::internal::Non_generic_position_exception(); } } prec*=2; } CGAL::set_precision(BFI(),old_prec); #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "on f..." << std::flush; #endif if(! CGAL::internal::zero_test_bivariate (kernel(),alpha,polynomial,p,q)) { #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "Detected non-generic position for alpha=" << CGAL::to_double(alpha) << std::endl; #endif throw CGAL::internal::Non_generic_position_exception(); } // Check whether the two partial derivatives vanish #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "on fx..." << std::flush; #endif bool is_singularity = CGAL::internal::zero_test_bivariate (kernel(),alpha,der_1,p,q); if(is_singularity) { #if CGAL_ACK_DEBUG_FLAG CGAL_ACK_DEBUG_PRINT << "on fy..." << std::flush; #endif return CGAL::internal::zero_test_bivariate (kernel(),alpha,der_2,p,q); } else { return false; } } protected: int get_index_of_multiple_root(const Bitstream_descartes& bit_des) const { int n = bit_des.number_of_real_roots(); for(int i=0;i