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