00001
00002 #include <basix/double.hpp>
00003 #include <basix/int.hpp>
00004 #include <basix/vector.hpp>
00005 #include <basix/port.hpp>
00006 #include <basix/literal.hpp>
00007 #include <numerix/integer.hpp>
00008 #include <numerix/modular.hpp>
00009 #include <numerix/modular_integer.hpp>
00010 #include <numerix/rational.hpp>
00011 #include <numerix/complex.hpp>
00012 #include <numerix/complex_double.hpp>
00013 #include <numerix/ball.hpp>
00014 #include <numerix/ball_complex.hpp>
00015 #include <algebramix/vector_unrolled.hpp>
00016 #include <algebramix/vector_simd.hpp>
00017 #include <algebramix/vector_modular.hpp>
00018 #include <analyziz/vector_double.hpp>
00019 #include <analyziz/vector_ball.hpp>
00020 #include <basix/compound.hpp>
00021 #include <basix/mmx_syntax.hpp>
00022 #include <basix/lisp_syntax.hpp>
00023 #include <basix/cpp_syntax.hpp>
00024 #include <basix/syntactic.hpp>
00025 #include <algebramix/polynomial.hpp>
00026 #include <algebramix/polynomial_polynomial.hpp>
00027 #include <algebramix/polynomial_integer.hpp>
00028 #include <algebramix/polynomial_rational.hpp>
00029 #include <algebramix/polynomial_modular.hpp>
00030 #include <algebramix/polynomial_modular_integer.hpp>
00031 #include <algebramix/polynomial_complex.hpp>
00032 #include <algebramix/polynomial_schonhage.hpp>
00033 #include <analyziz/polynomial_numeric.hpp>
00034 #include <analyziz/polynomial_double.hpp>
00035 #include <analyziz/polynomial_ball.hpp>
00036 #include <analyziz/solver.hpp>
00037 #include <analyziz/solver_aberth.hpp>
00038 #include <analyziz/solver_ball.hpp>
00039 #include <algebramix/permutation.hpp>
00040 #include <basix/row_tuple.hpp>
00041 #include <algebramix/matrix.hpp>
00042 #include <algebramix/matrix_ring_naive.hpp>
00043 #include <algebramix/matrix_integer.hpp>
00044 #include <algebramix/matrix_modular_integer.hpp>
00045 #include <algebramix/matrix_quotient.hpp>
00046 #include <algebramix/matrix_complex.hpp>
00047 #include <analyziz/matrix_jacobian.hpp>
00048 #include <analyziz/matrix_double.hpp>
00049 #include <analyziz/matrix_ball.hpp>
00050 #include <analyziz/matrix_numeric.hpp>
00051 #include <analyziz/eigen.hpp>
00052 #include <analyziz/eigen_homotopy.hpp>
00053 #include <analyziz/eigen_ball.hpp>
00054 #include <multimix/multivariate_coordinates.hpp>
00055 #include <multimix/multivariate_monomial.hpp>
00056 #include <multimix/multivariate_polynomial.hpp>
00057 #include <multimix/sparse_polynomial_integer.hpp>
00058 #include <multimix/sparse_polynomial_rational.hpp>
00059 #include <multimix/sparse_polynomial_modular.hpp>
00060 #include <multimix/sparse_polynomial_modular_integer.hpp>
00061 #include <numerix/floating.hpp>
00062 #include <continewz/homotopy_euler.hpp>
00063 #include <continewz/homotopy_floating.hpp>
00064 #include <continewz/homotopy_post_certify.hpp>
00065 #include <basix/routine.hpp>
00066 #include <basix/alias.hpp>
00067 #include <basix/glue.hpp>
00068
00069 #define double_literal(x) as_double (as_string (x))
00070 #define int_literal(x) as_int (as_string (x))
00071 #define is_generic_literal is<literal>
00072 #define gen_literal_apply(f,v) gen (as<generic> (f), v)
00073 #define gen_literal_access(f,v) access (as<generic> (f), v)
00074 #define is_generic_compound is<compound>
00075 #define compound_arguments(x) cdr (as_vector (x))
00076 #define gen_compound_apply(f,v) gen (as<generic> (f), v)
00077 namespace mmx {
00078 template<typename C> polynomial<C>
00079 polynomial_reverse (const vector<C>& v) {
00080 return polynomial<C> (reverse (v)); }
00081
00082 template<typename C> polynomial<modular<modulus<C>, modular_local> >
00083 as_polynomial_modular (const polynomial<C>& f, const modulus<C>& p) {
00084 modular<modulus<C>, modular_local>::set_modulus (p);
00085 return as<polynomial<modular<modulus<C>, modular_local> > > (f); }
00086
00087 template<typename C> vector<generic>
00088 wrap_subresultants (const polynomial<C>& f, const polynomial<C>& g) {
00089 return as<vector<generic> > (subresultants (f, g)); }
00090
00091 }
00092 namespace mmx { POLYNOMIAL_GENERIC_USES_SCHONHAGE }
00093 #define identity_matrix_integer identity_matrix<integer>
00094 #define hilbert_matrix_rational hilbert_matrix<rational>
00095
00096 namespace mmx {
00097 template<typename C> matrix<C>
00098 matrix_new (const vector<row_tuple<C> >& t) {
00099 if (N(t) == 0) return matrix<C> ();
00100 nat i, j, rows= N(t), cols= N(t[0]);
00101 C dummy= zero_cst<C> ();
00102 matrix<C> r (dummy, rows, cols);
00103 for (i=0; i<rows; i++) {
00104 ASSERT (N(t[i]) == cols, "unequal row lengths");
00105 for (j=0; j<cols; j++)
00106 r(i,j)= t[i][j];
00107 }
00108 return r;
00109 }
00110
00111 template<typename C> matrix<C>
00112 matrix_new (const vector<C>& t) {
00113 nat j, rows= 1, cols= N(t);
00114 C dummy= zero_cst<C> ();
00115 matrix<C> r (dummy, rows, cols);
00116 for (j=0; j<cols; j++)
00117 r(0,j)= t[j];
00118 return r;
00119 }
00120
00121 template<typename C> vector<generic>
00122 wrap_column_reduced_echelon_with_permutation (const matrix<C>& m) {
00123 permutation permut;
00124 generic tp=as<generic> (column_reduced_echelon (m, permut));
00125 return vec (tp, as<generic> (permut));
00126 }
00127
00128 template<typename C> vector<generic>
00129 wrap_column_reduced_echelon_with_transform (const matrix<C>& m) {
00130 matrix<C> k;
00131 generic tp=as<generic> (column_reduced_echelon (m, k));
00132 return vec (tp, as<generic> (k));
00133 }
00134
00135 template<typename C> vector<generic>
00136 wrap_row_reduced_echelon_with_transform (const matrix<C>& m) {
00137 matrix<C> k;
00138 generic tp=as<generic> (row_reduced_echelon (m, k));
00139 return vec (tp, as<generic> (k));
00140 }
00141 }
00142
00143 #define mmx_coordinate multivariate_coordinate<>
00144 #define mmx_coordinates multivariate_coordinates<>
00145 #define mv_monomial multivariate<monomial<> >
00146
00147 #define mv_polynomial(C) multivariate<sparse_polynomial<C> >
00148
00149
00150 namespace mmx {
00151 #define Polynomial \
00152 multivariate<sparse_polynomial<modular<modulus<C>, modular_local> > >
00153 template<typename C> Polynomial
00154 as_mv_polynomial_modular (const mv_polynomial(C)& f, const modulus<C>& p) {
00155 modular<modulus<C>, modular_local>::set_modulus (p);
00156 return as<Polynomial> (f); }
00157 #undef Polynomial
00158 }
00159
00160 namespace mmx {
00161 static vector<integer>
00162 GLUE_1 (const vector<int> &arg_1) {
00163 return as<vector<integer> > (arg_1);
00164 }
00165
00166 static vector<rational>
00167 GLUE_2 (const vector<int> &arg_1) {
00168 return as<vector<rational> > (arg_1);
00169 }
00170
00171 static vector<complex<rational> >
00172 GLUE_3 (const vector<int> &arg_1) {
00173 return as<vector<complex<rational> > > (arg_1);
00174 }
00175
00176 static vector<int>
00177 GLUE_4 (const vector<integer> &arg_1) {
00178 return as<vector<int> > (arg_1);
00179 }
00180
00181 static vector<mmx_ball(double, double) >
00182 GLUE_5 (const vector<integer> &arg_1) {
00183 return as<vector<mmx_ball(double, double) > > (arg_1);
00184 }
00185
00186 static vector<mmx_ball(double, complex<double> ) >
00187 GLUE_6 (const vector<integer> &arg_1) {
00188 return as<vector<mmx_ball(double, complex<double> ) > > (arg_1);
00189 }
00190
00191 static vector<mmx_ball(double, complex<double> ) >
00192 GLUE_7 (const vector<mv_polynomial(rational) > &arg_1, const vector<mmx_coordinate> &arg_2, const vector<mmx_ball(double, complex<double> ) > &arg_3, const mmx_coordinate &arg_4, const mmx_ball(double, complex<double> ) &arg_5) {
00193 return homotopy (arg_1, arg_2, arg_3, arg_4, arg_5);
00194 }
00195
00196 static vector<mmx_ball(double, complex<double> ) >
00197 GLUE_8 (const vector<mv_polynomial(rational) > &arg_1, const vector<mmx_coordinate> &arg_2, const vector<mmx_ball(double, complex<double> ) > &arg_3, const mmx_coordinate &arg_4, const vector<mmx_ball(double, complex<double> ) > &arg_5) {
00198 return homotopy (arg_1, arg_2, arg_3, arg_4, arg_5);
00199 }
00200
00201 static matrix<mmx_ball(double, complex<double> ) >
00202 GLUE_9 (const vector<mv_polynomial(rational) > &arg_1, const vector<mmx_coordinate> &arg_2, const matrix<mmx_ball(double, complex<double> ) > &arg_3, const mmx_coordinate &arg_4, const mmx_ball(double, complex<double> ) &arg_5) {
00203 return homotopy (arg_1, arg_2, arg_3, arg_4, arg_5);
00204 }
00205
00206 static matrix<mmx_ball(double, complex<double> ) >
00207 GLUE_10 (const vector<mv_polynomial(rational) > &arg_1, const vector<mmx_coordinate> &arg_2, const matrix<mmx_ball(double, complex<double> ) > &arg_3, const mmx_coordinate &arg_4, const vector<mmx_ball(double, complex<double> ) > &arg_5) {
00208 return homotopy (arg_1, arg_2, arg_3, arg_4, arg_5);
00209 }
00210
00211 static vector<mmx_ball(double, double) >
00212 GLUE_11 (const vector<rational> &arg_1) {
00213 return as<vector<mmx_ball(double, double) > > (arg_1);
00214 }
00215
00216 static vector<mmx_ball(double, complex<double> ) >
00217 GLUE_12 (const vector<rational> &arg_1) {
00218 return as<vector<mmx_ball(double, complex<double> ) > > (arg_1);
00219 }
00220
00221 static vector<mmx_ball(double, complex<double> ) >
00222 GLUE_13 (const vector<complex<rational> > &arg_1) {
00223 return as<vector<mmx_ball(double, complex<double> ) > > (arg_1);
00224 }
00225
00226 void
00227 glue_homotopy_ball_double () {
00228 static bool done = false;
00229 if (done) return;
00230 done = true;
00231 call_glue (string ("glue_matrix_ball_double"));
00232 call_glue (string ("glue_mvpolynomial_rational"));
00233 static alias<int> mmx_significant_digits_alias = global_alias (((int&) mmx_significant_digits));
00234 define_constant<alias<int> > ("significant_digits", mmx_significant_digits_alias);
00235 static alias<int> mmx_bit_precision_alias = global_alias (((int&) mmx_bit_precision));
00236 define_constant<alias<int> > ("bit_precision", mmx_bit_precision_alias);
00237 static alias<int> mmx_discrepancy_alias = global_alias (((int&) mmx_discrepancy));
00238 define_constant<alias<int> > ("discrepancy", mmx_discrepancy_alias);
00239 static alias<bool> mmx_pretty_exponents_alias = global_alias (((bool&) mmx_pretty_exponents));
00240 define_constant<alias<bool> > ("pretty_exponents", mmx_pretty_exponents_alias);
00241 define_converter (":>", GLUE_1, PENALTY_INCLUSION);
00242 define_converter (":>", GLUE_2, PENALTY_INCLUSION);
00243 define_converter (":>", GLUE_3, PENALTY_HOMOMORPHISM);
00244 define_converter (":>", GLUE_4, PENALTY_INCLUSION);
00245 define_converter (":>", GLUE_5, PENALTY_INCLUSION);
00246 define_converter (":>", GLUE_6, PENALTY_HOMOMORPHISM);
00247 define ("homotopy", GLUE_7);
00248 define ("homotopy", GLUE_8);
00249 define ("homotopy", GLUE_9);
00250 define ("homotopy", GLUE_10);
00251 define_converter (":>", GLUE_11, PENALTY_INCLUSION);
00252 define_converter (":>", GLUE_12, PENALTY_HOMOMORPHISM);
00253 define_converter (":>", GLUE_13, PENALTY_INCLUSION);
00254 }
00255 }
