/usr/include/CGAL/polynomial_utils.h is in libcgal-dev 4.5-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 | // Copyright (c) 2008 Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Author(s) : Michael Hemmer <hemmer@mpi-inf.mpg.de>
//
// ============================================================================
#include <CGAL/basic.h>
#include <CGAL/Polynomial_traits_d.h>
#ifndef CGAL_POLYNOMIAL_UTILS_H
#define CGAL_POLYNOMIAL_UTILS_H
#define CGAL_UNARY_POLY_FUNCTION(functor,function) \
template <typename Polynomial_d> inline \
typename Polynomial_traits_d<Polynomial_d>::functor::result_type \
function(const Polynomial_d& p){ \
typedef Polynomial_traits_d<Polynomial_d> PT; \
return typename PT::functor()(p); \
}
#define CGAL_UNARY_POLY_FUNCTION_INDEX(functor,function) \
CGAL_UNARY_POLY_FUNCTION(functor,function) \
template <typename Polynomial_d> inline \
typename Polynomial_traits_d<Polynomial_d>::functor::result_type \
function(const Polynomial_d& p, int index ){ \
typedef Polynomial_traits_d<Polynomial_d> PT; \
typename PT::functor fo; \
return fo(p,index); \
}
#define CGAL_BINARY_POLY_FUNCTION(functor,function) \
template <typename Polynomial_d> inline \
typename Polynomial_traits_d<Polynomial_d>::functor::result_type \
function(const Polynomial_d& p, \
const typename Polynomial_traits_d<Polynomial_d>:: \
functor::second_argument_type& second \
){ \
typedef Polynomial_traits_d<Polynomial_d> PT; \
return typename PT::functor()(p,second); \
}
#define CGAL_BINARY_POLY_FUNCTION_INDEX(functor,function) \
CGAL_BINARY_POLY_FUNCTION(functor,function) \
template <typename Polynomial_d> inline \
typename Polynomial_traits_d<Polynomial_d>::functor::result_type \
function(const Polynomial_d& p, \
const typename Polynomial_traits_d<Polynomial_d>:: \
functor::second_argument_type& second, \
int index \
){ \
typedef Polynomial_traits_d<Polynomial_d> PT; \
return typename PT::functor()(p,second,index); \
}
namespace CGAL {
// GetCoefficient
template <typename Polynomial_d> inline
typename Polynomial_traits_d<Polynomial_d>::Get_coefficient::result_type
get_coefficient(const Polynomial_d& p, int i){
typename Polynomial_traits_d<Polynomial_d>::Get_coefficient get_coefficient;
return get_coefficient(p,i);
}
// GetInnermostCoefficient
template <typename Polynomial_d> inline
typename Polynomial_traits_d<Polynomial_d>
::Get_innermost_coefficient::result_type
get_innermost_coefficient(const Polynomial_d& p, Exponent_vector ev){
typename Polynomial_traits_d<Polynomial_d>::Get_innermost_coefficient gic;
return gic(p,ev);
}
// ConstructCoefficientConstIteratorRange
// ConstructInnermostCoefficientConstIteratorRange
// Swap
template <typename Polynomial_d> inline
typename Polynomial_traits_d<Polynomial_d>::Swap::result_type
swap(const Polynomial_d& p, int i, int j){
typename Polynomial_traits_d<Polynomial_d>::Swap swap;
return swap(p,i,j);
}
// Move
template <typename Polynomial_d> inline
typename Polynomial_traits_d<Polynomial_d>::Move::result_type
move(const Polynomial_d& p, int i, int j){
typename Polynomial_traits_d<Polynomial_d>::Move move;
return move(p,i,j);
}
// Permute
template <typename Polynomial_d, typename Input_iterator> inline
typename Polynomial_traits_d<Polynomial_d>::Permute::result_type
permute(const Polynomial_d& p, Input_iterator begin, Input_iterator end){
typename Polynomial_traits_d<Polynomial_d>::Permute permute;
return permute(p,begin,end);
}
// Degree
CGAL_UNARY_POLY_FUNCTION_INDEX(Degree,degree)
// TotalDegree
CGAL_UNARY_POLY_FUNCTION(Total_degree,total_degree)
// DegreeVector
CGAL_UNARY_POLY_FUNCTION(Degree_vector,degree_vector)
// LeadingCoefficient
CGAL_UNARY_POLY_FUNCTION(Leading_coefficient,leading_coefficient)
// InnermostLeadingCoefficient
CGAL_UNARY_POLY_FUNCTION(
Innermost_leading_coefficient,
innermost_leading_coefficient)
// Canonicalize
CGAL_UNARY_POLY_FUNCTION(Canonicalize, canonicalize)
// Differentiate
CGAL_UNARY_POLY_FUNCTION_INDEX(Differentiate, differentiate)
// Evaluate
CGAL_BINARY_POLY_FUNCTION(Evaluate,evaluate)
// EvaluateHomogeneous
template <typename Polynomial_d, typename T> inline
typename Polynomial_traits_d<Polynomial_d>::Evaluate_homogeneous::result_type
evaluate_homogeneous(const Polynomial_d& p,const T& num, const T& den){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Evaluate_homogeneous()(p,num,den);
}
// Substitute
template <typename Polynomial_d, typename Input_iterator> inline
typename CGAL::Coercion_traits<
typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type,
typename std::iterator_traits<Input_iterator>::value_type>
::Type
substitute(const Polynomial_d& p,Input_iterator begin, Input_iterator end){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Substitute()(p,begin, end);
}
// IsZeroAt
template <typename Polynomial_d, typename Input_iterator> inline
typename Polynomial_traits_d<Polynomial_d>::Is_zero_at::result_type
is_zero_at(const Polynomial_d& p, Input_iterator begin, Input_iterator end){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Is_zero_at()(p,begin, end);
}
// SignAt
template <typename Polynomial_d, typename Input_iterator> inline
typename Polynomial_traits_d<Polynomial_d>::Sign_at::result_type
sign_at(const Polynomial_d& p, Input_iterator begin, Input_iterator end){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Sign_at()(p,begin, end);
}
// SubstituteHomogeneous
template <typename Polynomial_d, typename Input_iterator> inline
typename CGAL::Coercion_traits<
typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type,
typename std::iterator_traits<Input_iterator>::value_type>
::Type
substitute_homogeneous(
const Polynomial_d& p,Input_iterator begin, Input_iterator end){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Substitute_homogeneous()(p,begin, end);
}
// IsZeroAtHomogeneous
template <typename Polynomial_d, typename Input_iterator> inline
typename Polynomial_traits_d<Polynomial_d>::Is_zero_at_homogeneous::result_type
is_zero_at_homogeneous(
const Polynomial_d& p, Input_iterator begin, Input_iterator end){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Is_zero_at_homogeneous()(p,begin, end);
}
// SignAtHomogeneous
template <typename Polynomial_d, typename Input_iterator> inline
typename Polynomial_traits_d<Polynomial_d>::Sign_at_homogeneous::result_type
sign_at_homogeneous(
const Polynomial_d& p, Input_iterator begin, Input_iterator end){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Sign_at_homogeneous()(p,begin, end);
}
// Compare // provided by number_type utils
// CGAL_BINARY_POLY_FUNCTION(Compare,compare);
// UnivariateContent
CGAL_UNARY_POLY_FUNCTION(Univariate_content, univariate_content)
// MultivariateContent
CGAL_UNARY_POLY_FUNCTION(Multivariate_content, multivariate_content)
// SquareFreeFactorize
template <typename Polynomial_d, typename OutputIterator> inline
OutputIterator
square_free_factorize(const Polynomial_d& p, OutputIterator oi){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Square_free_factorize()(p,oi);
}
// MakeSquareFree
CGAL_UNARY_POLY_FUNCTION(Make_square_free, make_square_free)
// IsSquareFree
CGAL_UNARY_POLY_FUNCTION(Is_square_free, is_square_free)
// PseudoDivision
// PseudoDivisionQuotient
// PseudoDivisionRemainder
template <typename Polynomial_d> inline
void
pseudo_division(
const Polynomial_d& f, const Polynomial_d& g,
Polynomial_d& q, Polynomial_d& r,
typename Polynomial_traits_d<Polynomial_d>::Coefficient_type& D){
typedef Polynomial_traits_d<Polynomial_d> PT;
typename PT::Pseudo_division()(f,g,q,r,D);
return;
}
template <typename Polynomial_d> inline
typename Polynomial_traits_d<Polynomial_d>::Pseudo_division_quotient::result_type
pseudo_division_quotient(const Polynomial_d& f, const Polynomial_d& g){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Pseudo_division_quotient()(f,g);
}
template <typename Polynomial_d> inline
typename Polynomial_traits_d<Polynomial_d>::Pseudo_division_remainder::result_type
pseudo_division_remainder(const Polynomial_d& f, const Polynomial_d& g){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Pseudo_division_remainder()(f,g);
}
// GcdUpToConstantFactor
CGAL_BINARY_POLY_FUNCTION(
Gcd_up_to_constant_factor,
gcd_up_to_constant_factor)
// IntegralDivisionUpToConstantFactor
CGAL_BINARY_POLY_FUNCTION(
Integral_division_up_to_constant_factor,
integral_division_up_to_constant_factor)
// UnivariateContentUpToConstantFactor
CGAL_UNARY_POLY_FUNCTION(
Univariate_content_up_to_constant_factor,
univariate_content_up_to_constant_factor)
// SquareFreeFactorizeUpToConstantFactor
template <typename Polynomial_d, typename OutputIterator> inline
OutputIterator
square_free_factorize_up_to_constant_factor(
const Polynomial_d& p, OutputIterator oi){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Square_free_factorize_up_to_constant_factor()(p,oi);
}
// Shift
CGAL_BINARY_POLY_FUNCTION_INDEX(Shift,shift)
// Negate
CGAL_UNARY_POLY_FUNCTION_INDEX(Negate,negate)
// Invert
CGAL_UNARY_POLY_FUNCTION_INDEX(Invert,invert)
// Translate
CGAL_BINARY_POLY_FUNCTION_INDEX(Translate,translate)
// TranslateHomogeneous
template <typename Polynomial_d> inline
typename Polynomial_traits_d<Polynomial_d>::Translate_homogeneous::result_type
translate_homogeneous(const Polynomial_d& f,
const typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& num,
const typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& den){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Translate_homogeneous()(f,num,den);
}
template <typename Polynomial_d> inline
typename Polynomial_traits_d<Polynomial_d>::Translate_homogeneous::result_type
translate_homogeneous(const Polynomial_d& f,
const typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& num,
const typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& den,
int index ){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Translate_homogeneous()(f,num,den,index);
}
// Scale
CGAL_BINARY_POLY_FUNCTION_INDEX(Scale,scale)
// ScaleHomogeneous
template <typename Polynomial_d> inline
typename Polynomial_traits_d<Polynomial_d>::Scale_homogeneous::result_type
scale_homogeneous(const Polynomial_d& f,
const typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& num,
const typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& den){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Scale_homogeneous()(f,num,den);
}
template <typename Polynomial_d> inline
typename Polynomial_traits_d<Polynomial_d>::Scale_homogeneous::result_type
scale_homogeneous(const Polynomial_d& f,
const typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& num,
const typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& den,
int index ){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Scale_homogeneous()(f,num,den,index);
}
// Resultant
CGAL_BINARY_POLY_FUNCTION(Resultant,resultant)
template <typename Polynomial_d,typename OutputIterator> inline
OutputIterator polynomial_subresultants
(Polynomial_d p, Polynomial_d q, OutputIterator out) {
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Polynomial_subresultants() (p, q, out);
}
template <typename Polynomial_d,typename OutputIterator> inline
OutputIterator principal_subresultants
(Polynomial_d p, Polynomial_d q, OutputIterator out) {
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Principal_subresultants() (p, q, out);
}
template<typename Polynomial_d,
typename OutputIterator1,
typename OutputIterator2,
typename OutputIterator3> inline
OutputIterator1 polynomial_subresultants_with_cofactors
(Polynomial_d p,
Polynomial_d q,
OutputIterator1 sres_out,
OutputIterator2 coP_out,
OutputIterator3 coQ_out) {
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Polynomial_subresultants_with_cofactors()
(p, q, sres_out, coP_out, coQ_out);
}
template <typename Polynomial_d,typename OutputIterator> inline
OutputIterator
principal_sturm_habicht_sequence
(Polynomial_d f, OutputIterator out){
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Principal_sturm_habicht_sequence() (f, out);
}
template<typename Polynomial_d,typename OutputIterator> OutputIterator
sturm_habicht_sequence(Polynomial_d f,OutputIterator out) {
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Sturm_habicht_sequence() (f, out);
}
template<typename Polynomial_d,
typename OutputIterator1,
typename OutputIterator2,
typename OutputIterator3>
OutputIterator1
sturm_habicht_sequence_with_cofactors
(Polynomial_d f,
OutputIterator1 stha_out,
OutputIterator2 cof_out,
OutputIterator3 cofx_out) {
typedef Polynomial_traits_d<Polynomial_d> PT;
return typename PT::Sturm_habicht_sequence_with_cofactors()
(f, stha_out, cof_out, cofx_out);
}
// TODO: REMOVE function below ?
template<typename NT> inline
Polynomial<NT> scale_up(const Polynomial<NT>& p, const NT& a)
{ Polynomial<NT> q(p); q.scale_up(a); return q; }
template<typename NT> inline
Polynomial<NT> scale_down(const Polynomial<NT>& p, const NT& b)
{ Polynomial<NT> q(p); q.scale_down(b); return q; }
template<typename NT> inline
Polynomial<NT> translate_by_one(const Polynomial<NT>& p)
{ Polynomial<NT> q(p); q.translate_by_one(); return q; }
template<typename NT> inline
Polynomial<NT> reversal(const Polynomial<NT>& p)
{ Polynomial<NT> q(p); q.reversal(); return q; }
} //namespace CGAL
#undef CGAL_UNARY_POLY_FUNCTION
#undef CGAL_UNARY_POLY_FUNCTION_INDEX
#undef CGAL_BINARY_POLY_FUNCTION
#undef CGAL_BINARY_POLY_FUNCTION_INDEX
#endif // CGAL_POLYNOMIAL_UTILS_H
|