/usr/include/CGAL/Polynomial_traits_d.h is in libcgal-dev 4.7-4.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 | // 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@informatik.uni-mainz.de>
// Sebastian Limbach <slimbach@mpi-inf.mpg.de>
//
// ============================================================================
#ifndef CGAL_POLYNOMIAL_TRAITS_D_H
#define CGAL_POLYNOMIAL_TRAITS_D_H
#include <CGAL/basic.h>
#include <functional>
#include <list>
#include <vector>
#include <utility>
#include <CGAL/Polynomial/fwd.h>
#include <CGAL/Polynomial/misc.h>
#include <CGAL/Polynomial/Polynomial_type.h>
#include <CGAL/Polynomial/Monomial_representation.h>
#include <CGAL/Polynomial/Degree.h>
#include <CGAL/polynomial_utils.h>
#include <CGAL/Polynomial/square_free_factorize.h>
#include <CGAL/Polynomial/modular_filter.h>
#include <CGAL/extended_euclidean_algorithm.h>
#include <CGAL/Polynomial/resultant.h>
#include <CGAL/Polynomial/subresultants.h>
#include <CGAL/Polynomial/sturm_habicht_sequence.h>
#include <boost/iterator/transform_iterator.hpp>
#define CGAL_POLYNOMIAL_TRAITS_D_BASE_TYPEDEFS \
private: \
typedef Polynomial_traits_d< Polynomial< Coefficient_type_ > > PT; \
typedef Polynomial_traits_d< Coefficient_type_ > PTC; \
\
typedef Polynomial<Coefficient_type_> Polynomial_d; \
typedef Coefficient_type_ Coefficient_type; \
\
typedef typename Innermost_coefficient_type<Polynomial_d>::Type \
Innermost_coefficient_type; \
static const int d = Dimension<Polynomial_d>::value; \
\
\
typedef std::pair< Exponent_vector, Innermost_coefficient_type > \
Exponents_coeff_pair; \
typedef std::vector< Exponents_coeff_pair > Monom_rep; \
\
typedef CGAL::Recursive_const_flattening< d-1, \
typename CGAL::Polynomial<Coefficient_type>::const_iterator > \
Coefficient_const_flattening; \
\
typedef typename \
Coefficient_const_flattening::Recursive_flattening_iterator \
Innermost_coefficient_const_iterator; \
\
typedef typename Polynomial_d::const_iterator \
Coefficient_const_iterator; \
\
typedef std::pair<Innermost_coefficient_const_iterator, \
Innermost_coefficient_const_iterator> \
Innermost_coefficient_const_iterator_range; \
\
typedef std::pair<Coefficient_const_iterator, \
Coefficient_const_iterator> \
Coefficient_const_iterator_range; \
namespace CGAL {
namespace internal {
// Base class for functors depending on the algebraic category of the
// innermost coefficient
template< class Coefficient_type_, class ICoeffAlgebraicCategory >
class Polynomial_traits_d_base_icoeff_algebraic_category {
public:
typedef Null_functor Multivariate_content;
};
// Specializations
template< class Coefficient_type_ >
class Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Integral_domain_without_division_tag >
: public Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Null_tag > {};
template< class Coefficient_type_ >
class Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Integral_domain_tag >
: public Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Integral_domain_without_division_tag > {};
template< class Coefficient_type_ >
class Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Unique_factorization_domain_tag >
: public Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Integral_domain_tag > {
CGAL_POLYNOMIAL_TRAITS_D_BASE_TYPEDEFS
public:
struct Multivariate_content
: public std::unary_function< Polynomial_d , Innermost_coefficient_type >{
Innermost_coefficient_type
operator()(const Polynomial_d& p) const {
typedef Innermost_coefficient_const_iterator IT;
Innermost_coefficient_type content(0);
typename PT::Construct_innermost_coefficient_const_iterator_range range;
for (IT it = range(p).first; it != range(p).second; it++){
content = CGAL::gcd(content, *it);
if(CGAL::is_one(content)) break;
}
return content;
}
};
};
template< class Coefficient_type_ >
class Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Euclidean_ring_tag >
: public Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Unique_factorization_domain_tag >
{};
template< class Coefficient_type_ >
class Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Field_tag >
: public Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Integral_domain_tag > {
CGAL_POLYNOMIAL_TRAITS_D_BASE_TYPEDEFS
public:
// Multivariate_content;
struct Multivariate_content
: public std::unary_function< Polynomial_d , Innermost_coefficient_type >{
Innermost_coefficient_type operator()(const Polynomial_d& p) const {
if( CGAL::is_zero(p) )
return Innermost_coefficient_type(0);
else
return Innermost_coefficient_type(1);
}
};
};
template< class Coefficient_type_ >
class Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Field_with_sqrt_tag >
: public Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Field_tag > {};
template< class Coefficient_type_ >
class Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Field_with_kth_root_tag >
: public Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Field_with_sqrt_tag > {};
template< class Coefficient_type_ >
class Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Field_with_root_of_tag >
: public Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, Field_with_kth_root_tag > {};
// Base class for functors depending on the algebraic category of the
// Polynomial type
template< class Coefficient_type_, class PolynomialAlgebraicCategory >
class Polynomial_traits_d_base_polynomial_algebraic_category {
public:
typedef Null_functor Univariate_content;
typedef Null_functor Square_free_factorize;
};
// Specializations
template< class Coefficient_type_ >
class Polynomial_traits_d_base_polynomial_algebraic_category<
Polynomial< Coefficient_type_ >, Integral_domain_without_division_tag >
: public Polynomial_traits_d_base_polynomial_algebraic_category<
Polynomial< Coefficient_type_ >, Null_tag > {};
template< class Coefficient_type_ >
class Polynomial_traits_d_base_polynomial_algebraic_category<
Polynomial< Coefficient_type_ >, Integral_domain_tag >
: public Polynomial_traits_d_base_polynomial_algebraic_category<
Polynomial< Coefficient_type_ >, Integral_domain_without_division_tag > {};
template< class Coefficient_type_ >
class Polynomial_traits_d_base_polynomial_algebraic_category<
Polynomial< Coefficient_type_ >, Unique_factorization_domain_tag >
: public Polynomial_traits_d_base_polynomial_algebraic_category<
Polynomial< Coefficient_type_ >, Integral_domain_tag > {
CGAL_POLYNOMIAL_TRAITS_D_BASE_TYPEDEFS
public:
// Univariate_content
struct Univariate_content
: public std::unary_function< Polynomial_d , Coefficient_type>{
Coefficient_type operator()(const Polynomial_d& p) const {
return p.content();
}
};
// Square_free_factorize;
struct Square_free_factorize{
template < class OutputIterator >
OutputIterator operator()( const Polynomial_d& p, OutputIterator oi) const {
std::vector<Polynomial_d> factors;
std::vector<int> mults;
square_free_factorize
( p, std::back_inserter(factors), std::back_inserter(mults) );
CGAL_postcondition( factors.size() == mults.size() );
for(unsigned int i = 0; i < factors.size(); i++){
*oi++=std::make_pair(factors[i],mults[i]);
}
return oi;
}
template< class OutputIterator >
OutputIterator operator()(
const Polynomial_d& p ,
OutputIterator oi,
Innermost_coefficient_type& a ) const {
if( CGAL::is_zero(p) ) {
a = Innermost_coefficient_type(0);
return oi;
}
typedef Polynomial_traits_d< Polynomial_d > PT;
typename PT::Innermost_leading_coefficient ilcoeff;
typename PT::Multivariate_content mcontent;
a = CGAL::unit_part( ilcoeff( p ) ) * mcontent( p );
return (*this)( p/Polynomial_d(a), oi);
}
};
};
template< class Coefficient_type_ >
class Polynomial_traits_d_base_polynomial_algebraic_category<
Polynomial< Coefficient_type_ >, Euclidean_ring_tag >
: public Polynomial_traits_d_base_polynomial_algebraic_category<
Polynomial< Coefficient_type_ >, Unique_factorization_domain_tag > {};
// Polynomial_traits_d_base class connecting the two base classes which depend
// on the algebraic category of the innermost coefficient type and the poly-
// nomial type.
// First the general base class for the innermost coefficient
template< class InnermostCoefficient_type,
class ICoeffAlgebraicCategory, class PolynomialAlgebraicCategory >
class Polynomial_traits_d_base {
typedef InnermostCoefficient_type ICoeff;
public:
static const int d = 0;
typedef ICoeff Polynomial_d;
typedef ICoeff Coefficient_type;
typedef ICoeff Innermost_coefficient_type;
struct Degree
: public std::unary_function< ICoeff , int > {
int operator()(const ICoeff&) const { return 0; }
};
struct Total_degree
: public std::unary_function< ICoeff , int > {
int operator()(const ICoeff&) const { return 0; }
};
typedef Null_functor Construct_polynomial;
typedef Null_functor Get_coefficient;
typedef Null_functor Leading_coefficient;
typedef Null_functor Univariate_content;
typedef Null_functor Multivariate_content;
typedef Null_functor Shift;
typedef Null_functor Negate;
typedef Null_functor Invert;
typedef Null_functor Translate;
typedef Null_functor Translate_homogeneous;
typedef Null_functor Scale_homogeneous;
typedef Null_functor Differentiate;
struct Is_square_free
: public std::unary_function< ICoeff, bool > {
bool operator()( const ICoeff& ) const {
return true;
}
};
struct Make_square_free
: public std::unary_function< ICoeff, ICoeff>{
ICoeff operator()( const ICoeff& x ) const {
if (CGAL::is_zero(x)) return x ;
else return ICoeff(1);
}
};
typedef Null_functor Square_free_factorize;
typedef Null_functor Pseudo_division;
typedef Null_functor Pseudo_division_remainder;
typedef Null_functor Pseudo_division_quotient;
struct Gcd_up_to_constant_factor
: public std::binary_function< ICoeff, ICoeff, ICoeff >{
ICoeff operator()(const ICoeff& x, const ICoeff& y) const {
if (CGAL::is_zero(x) && CGAL::is_zero(y))
return ICoeff(0);
else
return ICoeff(1);
}
};
typedef Null_functor Integral_division_up_to_constant_factor;
struct Univariate_content_up_to_constant_factor
: public std::unary_function< ICoeff, ICoeff >{
ICoeff operator()(const ICoeff& ) const {
// TODO: Why not return 0 if argument is 0 ?
return ICoeff(1);
}
};
typedef Null_functor Square_free_factorize_up_to_constant_factor;
typedef Null_functor Resultant;
typedef Null_functor Canonicalize;
typedef Null_functor Evaluate_homogeneous;
struct Innermost_leading_coefficient
:public std::unary_function <ICoeff, ICoeff>{
const ICoeff& operator()(const ICoeff& x){return x;}
};
struct Degree_vector{
typedef Exponent_vector result_type;
typedef Coefficient_type argument_type;
// returns the exponent vector of inner_most_lcoeff.
result_type operator()(const Coefficient_type&) const{
return Exponent_vector();
}
};
struct Get_innermost_coefficient
: public std::binary_function< ICoeff, Polynomial_d, Exponent_vector > {
const ICoeff& operator()( const Polynomial_d& p, Exponent_vector ) {
return p;
}
};
typedef Null_functor Evaluate ;
struct Substitute{
public:
template <class Input_iterator>
typename
CGAL::Coercion_traits<
typename std::iterator_traits<Input_iterator>::value_type,
Innermost_coefficient_type>::Type
operator()(
const Innermost_coefficient_type& p,
Input_iterator CGAL_precondition_code(begin),
Input_iterator CGAL_precondition_code(end) ) const {
CGAL_precondition(end == begin);
typedef typename std::iterator_traits<Input_iterator>::value_type
value_type;
typedef CGAL::Coercion_traits<Innermost_coefficient_type,value_type> CT;
return typename CT::Cast()(p);
}
};
struct Substitute_homogeneous{
public:
// this is the end of the recursion
// begin contains the homogeneous variabel
// hdegree is the remaining degree
template <class Input_iterator>
typename
CGAL::Coercion_traits<
typename std::iterator_traits<Input_iterator>::value_type,
Innermost_coefficient_type>::Type
operator()(
const Innermost_coefficient_type& p,
Input_iterator begin,
Input_iterator CGAL_precondition_code(end),
int hdegree) const {
typedef typename std::iterator_traits<Input_iterator>::value_type
value_type;
typedef CGAL::Coercion_traits<Innermost_coefficient_type,value_type> CT;
typename CT::Type result =
typename CT::Cast()(CGAL::ipower(*begin++,hdegree))
* typename CT::Cast()(p);
CGAL_precondition(end == begin);
CGAL_precondition(hdegree >= 0);
return result;
}
};
};
// Now the version for the polynomials with all functors provided by all
// polynomials
template< class Coefficient_type_,
class ICoeffAlgebraicCategory, class PolynomialAlgebraicCategory >
class Polynomial_traits_d_base< Polynomial< Coefficient_type_ >,
ICoeffAlgebraicCategory, PolynomialAlgebraicCategory >
: public Polynomial_traits_d_base_icoeff_algebraic_category<
Polynomial< Coefficient_type_ >, ICoeffAlgebraicCategory >,
public Polynomial_traits_d_base_polynomial_algebraic_category<
Polynomial< Coefficient_type_ >, PolynomialAlgebraicCategory > {
typedef Polynomial_traits_d< Polynomial< Coefficient_type_ > > PT;
typedef Polynomial_traits_d< Coefficient_type_ > PTC;
public:
typedef Polynomial<Coefficient_type_> Polynomial_d;
typedef Coefficient_type_ Coefficient_type;
typedef typename internal::Innermost_coefficient_type<Polynomial_d>::Type
Innermost_coefficient_type;
static const int d = Dimension<Polynomial_d>::value;
private:
typedef std::pair< Exponent_vector, Innermost_coefficient_type >
Exponents_coeff_pair;
typedef std::vector< Exponents_coeff_pair > Monom_rep;
typedef CGAL::Recursive_const_flattening< d-1,
typename CGAL::Polynomial<Coefficient_type>::const_iterator >
Coefficient_const_flattening;
public:
typedef typename Coefficient_const_flattening::Recursive_flattening_iterator
Innermost_coefficient_const_iterator;
typedef typename Polynomial_d::const_iterator Coefficient_const_iterator;
typedef std::pair<Innermost_coefficient_const_iterator,
Innermost_coefficient_const_iterator>
Innermost_coefficient_const_iterator_range;
typedef std::pair<Coefficient_const_iterator,
Coefficient_const_iterator>
Coefficient_const_iterator_range;
// We use our own Strict Weak Ordering predicate in order to avoid
// problems when calling sort for a Exponents_coeff_pair where the
// coeff type has no comparison operators available.
private:
struct Compare_exponents_coeff_pair
: public std::binary_function<
std::pair< Exponent_vector, Innermost_coefficient_type >,
std::pair< Exponent_vector, Innermost_coefficient_type >,
bool >
{
bool operator()(
const std::pair< Exponent_vector, Innermost_coefficient_type >& p1,
const std::pair< Exponent_vector, Innermost_coefficient_type >& p2 ) const {
// TODO: Precondition leads to an error within test_translate in
// Polynomial_traits_d test
// CGAL_precondition( p1.first != p2.first );
return p1.first < p2.first;
}
};
public:
//
// Functors as defined in the reference manual
// (with sometimes slightly extended functionality)
// Construct_polynomial;
struct Construct_polynomial {
typedef Polynomial_d result_type;
Polynomial_d operator()() const {
return Polynomial_d(0);
}
template <class T>
Polynomial_d operator()( T a ) const {
return Polynomial_d(a);
}
//! construct the constant polynomial a0
Polynomial_d operator() (const Coefficient_type& a0) const
{return Polynomial_d(a0);}
//! construct the polynomial a0 + a1*x
Polynomial_d operator() (
const Coefficient_type& a0, const Coefficient_type& a1) const
{return Polynomial_d(a0,a1);}
//! construct the polynomial a0 + a1*x + a2*x^2
Polynomial_d operator() (
const Coefficient_type& a0, const Coefficient_type& a1,
const Coefficient_type& a2) const
{return Polynomial_d(a0,a1,a2);}
//! construct the polynomial a0 + a1*x + ... + a3*x^3
Polynomial_d operator() (
const Coefficient_type& a0, const Coefficient_type& a1,
const Coefficient_type& a2, const Coefficient_type& a3) const
{return Polynomial_d(a0,a1,a2,a3);}
//! construct the polynomial a0 + a1*x + ... + a4*x^4
Polynomial_d operator() (
const Coefficient_type& a0, const Coefficient_type& a1,
const Coefficient_type& a2, const Coefficient_type& a3,
const Coefficient_type& a4) const
{return Polynomial_d(a0,a1,a2,a3,a4);}
//! construct the polynomial a0 + a1*x + ... + a5*x^5
Polynomial_d operator() (
const Coefficient_type& a0, const Coefficient_type& a1,
const Coefficient_type& a2, const Coefficient_type& a3,
const Coefficient_type& a4, const Coefficient_type& a5) const
{return Polynomial_d(a0,a1,a2,a3,a4,a5);}
//! construct the polynomial a0 + a1*x + ... + a6*x^6
Polynomial_d operator() (
const Coefficient_type& a0, const Coefficient_type& a1,
const Coefficient_type& a2, const Coefficient_type& a3,
const Coefficient_type& a4, const Coefficient_type& a5,
const Coefficient_type& a6) const
{return Polynomial_d(a0,a1,a2,a3,a4,a5,a6);}
//! construct the polynomial a0 + a1*x + ... + a7*x^7
Polynomial_d operator() (
const Coefficient_type& a0, const Coefficient_type& a1,
const Coefficient_type& a2, const Coefficient_type& a3,
const Coefficient_type& a4, const Coefficient_type& a5,
const Coefficient_type& a6, const Coefficient_type& a7) const
{return Polynomial_d(a0,a1,a2,a3,a4,a5,a6,a7);}
//! construct the polynomial a0 + a1*x + ... + a8*x^8
Polynomial_d operator() (
const Coefficient_type& a0, const Coefficient_type& a1,
const Coefficient_type& a2, const Coefficient_type& a3,
const Coefficient_type& a4, const Coefficient_type& a5,
const Coefficient_type& a6, const Coefficient_type& a7,
const Coefficient_type& a8) const
{return Polynomial_d(a0,a1,a2,a3,a4,a5,a6,a7,a8);}
#if 1
private:
template <class Input_iterator, class NT> Polynomial_d
construct_value_type(Input_iterator begin, Input_iterator end, NT) const {
typedef CGAL::Coercion_traits<NT,Coefficient_type> CT;
CGAL_static_assertion((boost::is_same<typename CT::Type,Coefficient_type>::value));
typename CT::Cast cast;
return Polynomial_d(
boost::make_transform_iterator(begin,cast),
boost::make_transform_iterator(end,cast));
}
template <class Input_iterator, class NT> Polynomial_d
construct_value_type(Input_iterator begin, Input_iterator end, std::pair<Exponent_vector,NT>) const {
return (*this)(begin,end,false);// construct from non sorted monom rep
}
public:
template< class Input_iterator >
Polynomial_d operator()( Input_iterator begin, Input_iterator end) const {
if(begin == end ) return Polynomial_d(0);
typedef typename std::iterator_traits<Input_iterator>::value_type value_type;
return construct_value_type(begin,end,value_type());
}
template< class Input_iterator >
Polynomial_d operator()( Input_iterator begin, Input_iterator end, bool is_sorted) const {
// Avoid compiler warning
(void)is_sorted;
if(begin == end ) return Polynomial_d(0);
Monom_rep monom_rep(begin,end);
// if(!is_sorted)
std::sort(monom_rep.begin(),monom_rep.end(),Compare_exponents_coeff_pair());
return Create_polynomial_from_monom_rep<Coefficient_type>()(monom_rep.begin(),monom_rep.end());
}
#else
// Construct from Coefficient type
template< class Input_iterator >
inline Polynomial_d
construct( Input_iterator begin, Input_iterator end, Tag_true) const {
if(begin == end ) return Polynomial_d(0);
return Polynomial_d(begin,end);
}
// Construct from momom rep
template< class Input_iterator >
inline Polynomial_d
construct( Input_iterator begin, Input_iterator end, Tag_false) const {
// construct from non sorted monom rep
return (*this)(begin,end,false);
}
template< class Input_iterator >
Polynomial_d
operator()( Input_iterator begin, Input_iterator end ) const {
if(begin == end ) return Polynomial_d(0);
typedef typename std::iterator_traits<Input_iterator>::value_type value_type;
typedef Boolean_tag<boost::is_same<value_type,Coefficient_type>::value>
Is_coeff;
std::vector<value_type> vec(begin,end);
return construct(vec.begin(),vec.end(),Is_coeff());
}
template< class Input_iterator >
Polynomial_d
operator()(Input_iterator begin, Input_iterator end , bool is_sorted) const{
if(!is_sorted)
std::sort(begin,end,Compare_exponents_coeff_pair());
return Create_polynomial_from_monom_rep< Coefficient_type >()(begin,end);
}
#endif
public:
template< class T >
class Create_polynomial_from_monom_rep {
public:
template <class Monom_rep_iterator>
Polynomial_d operator()(
Monom_rep_iterator begin,
Monom_rep_iterator end) const {
Innermost_coefficient_type zero(0);
std::vector< Innermost_coefficient_type > coefficients;
for(Monom_rep_iterator it = begin; it != end; it++){
int current_exp = it->first[0];
if((int) coefficients.size() < current_exp)
coefficients.resize(current_exp,zero);
coefficients.push_back(it->second);
}
return Polynomial_d(coefficients.begin(),coefficients.end());
}
};
template< class T >
class Create_polynomial_from_monom_rep< Polynomial < T > > {
public:
template <class Monom_rep_iterator>
Polynomial_d operator()(
Monom_rep_iterator begin,
Monom_rep_iterator end) const {
typedef Polynomial_traits_d<Coefficient_type> PT;
typename PT::Construct_polynomial construct;
CGAL_static_assertion(PT::d != 0); // Coefficient_type is a Polynomial
std::vector<Coefficient_type> coefficients;
Coefficient_type zero(0);
while(begin != end){
int current_exp = begin->first[PT::d];
// fill up with zeros until current exp is reached
if((int) coefficients.size() < current_exp)
coefficients.resize(current_exp,zero);
// select range for coefficient of current exponent
Monom_rep_iterator coeff_end = begin;
while( coeff_end != end && coeff_end->first[PT::d] == current_exp ){
++coeff_end;
}
coefficients.push_back(construct(begin, coeff_end));
begin = coeff_end;
}
return Polynomial_d(coefficients.begin(),coefficients.end());
}
};
};
// Get_coefficient;
struct Get_coefficient
: public std::binary_function<Polynomial_d, int, Coefficient_type > {
const Coefficient_type& operator()( const Polynomial_d& p, int i) const {
static const Coefficient_type zero = Coefficient_type(0);
CGAL_precondition( i >= 0 );
typename PT::Degree degree;
if( i > degree(p) )
return zero;
return p[i];
}
};
// Get_innermost_coefficient;
struct Get_innermost_coefficient
: public
std::binary_function< Polynomial_d, Exponent_vector, Innermost_coefficient_type >
{
const Innermost_coefficient_type&
operator()( const Polynomial_d& p, Exponent_vector ev ) const {
CGAL_precondition( !ev.empty() );
typename PTC::Get_innermost_coefficient gic;
typename PT::Get_coefficient gc;
int exponent = ev.back();
ev.pop_back();
return gic( gc( p, exponent ), ev );
};
};
// Swap variable x_i with x_j
struct Swap {
typedef Polynomial_d result_type;
typedef Polynomial_d first_argument_type;
typedef int second_argument_type;
typedef int third_argument_type;
public:
Polynomial_d operator()(const Polynomial_d& p, int i, int j ) const {
CGAL_precondition(0 <= i && i < d);
CGAL_precondition(0 <= j && j < d);
typedef std::pair< Exponent_vector, Innermost_coefficient_type >
Exponents_coeff_pair;
Monomial_representation gmr;
Construct_polynomial construct;
typedef std::vector< Exponents_coeff_pair > Monom_vector;
typedef typename Monom_vector::iterator MVIterator;
Monom_vector monoms;
gmr( p, std::back_inserter( monoms ) );
for( MVIterator it = monoms.begin(); it != monoms.end(); ++it ) {
std::swap(it->first[i],it->first[j]);
}
// sort only once !
std::sort(monoms.begin(), monoms.end(),Compare_exponents_coeff_pair());
return construct(monoms.begin(), monoms.end(),true);
}
};
// Move;
// move variable x_i to position of x_j
// order of other variables remains
// default j = d makes x_i the othermost variable
struct Move {
typedef Polynomial_d result_type;
typedef Polynomial_d first_argument_type;
typedef int second_argument_type;
typedef int third_argument_type;
Polynomial_d
operator()(const Polynomial_d& p, int i, int j = (d-1) ) const {
CGAL_precondition(0 <= i && i < d);
CGAL_precondition(0 <= j && j < d);
typedef std::pair< Exponent_vector, Innermost_coefficient_type >
Exponents_coeff_pair;
typedef std::vector< Exponents_coeff_pair > Monom_rep;
Monomial_representation gmr;
Construct_polynomial construct;
Monom_rep mon_rep;
gmr( p, std::back_inserter( mon_rep ) );
for( typename Monom_rep::iterator it = mon_rep.begin();
it != mon_rep.end();
++it ) {
// this is as good as std::rotate since it uses swap also
if (i < j)
for( int k = i; k < j; k++ )
std::swap(it->first[k],it->first[k+1]);
else
for( int k = i; k > j; k-- )
std::swap(it->first[k],it->first[k-1]);
}
return construct( mon_rep.begin(), mon_rep.end() );
}
};
struct Permute {
typedef Polynomial_d result_type;
template <typename Input_iterator> Polynomial_d operator()
(const Polynomial_d& p, Input_iterator first, Input_iterator last) const {
Construct_polynomial construct;
Monomial_representation gmr;
Monom_rep mon_rep;
gmr( p, std::back_inserter( mon_rep ));
std::vector<int> on_place, number_is;
int i= 0;
for (Input_iterator iter = first ; iter != last ; ++iter)
number_is.push_back (i++);
on_place = number_is;
int rem_place = 0, rem_number = i= 0;
for(Input_iterator iter = first ; iter != last ; ++iter){
for( typename Monom_rep::iterator it = mon_rep.begin(); it !=
mon_rep.end(); ++it )
std::swap(it->first[number_is[i]],it->first[(*iter)]);
rem_place= number_is[i];
rem_number= on_place[(*iter)];
on_place[(*iter)] = i;
on_place[rem_place]=rem_number;
number_is[rem_number]=rem_place;
number_is[i++]= (*iter);
}
return construct( mon_rep.begin(), mon_rep.end() );
}
};
//Degree;
typedef CGAL::internal::Degree<Polynomial_d> Degree;
// Total_degree;
struct Total_degree : public std::unary_function< Polynomial_d , int >{
int operator()(const Polynomial_d& p) const {
typedef Polynomial_traits_d<Coefficient_type> COEFF_POLY_TRAITS;
typename COEFF_POLY_TRAITS::Total_degree total_degree;
Degree degree;
CGAL_precondition( degree(p) >= 0);
int result = 0;
for(int i = 0; i <= degree(p) ; i++){
if( ! CGAL::is_zero( p[i]) )
result = (std::max)(result , total_degree(p[i]) + i );
}
return result;
}
};
// Leading_coefficient;
struct Leading_coefficient
: public std::unary_function< Polynomial_d , Coefficient_type>{
const Coefficient_type& operator()(const Polynomial_d& p) const {
return p.lcoeff();
}
};
// Innermost_leading_coefficient;
struct Innermost_leading_coefficient
: public std::unary_function< Polynomial_d , Innermost_coefficient_type>{
const Innermost_coefficient_type&
operator()(const Polynomial_d& p) const {
typename PTC::Innermost_leading_coefficient ilcoeff;
typename PT::Leading_coefficient lcoeff;
return ilcoeff(lcoeff(p));
}
};
//return a canonical representative of all constant multiples.
struct Canonicalize
: public std::unary_function<Polynomial_d, Polynomial_d>{
private:
inline Polynomial_d canonicalize_(Polynomial_d p, CGAL::Tag_true) const
{
typedef typename Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type IC;
typename Polynomial_traits_d<Polynomial_d>::Innermost_leading_coefficient ilcoeff;
typename Algebraic_extension_traits<IC>::Normalization_factor nfac;
IC tmp = nfac(ilcoeff(p));
if(tmp != IC(1)){
p *= Polynomial_d(tmp);
}
remove_scalar_factor(p);
p /= p.unit_part();
p.simplify_coefficients();
CGAL_postcondition(nfac(ilcoeff(p)) == IC(1));
return p;
};
inline Polynomial_d canonicalize_(Polynomial_d p, CGAL::Tag_false) const
{
remove_scalar_factor(p);
p /= p.unit_part();
p.simplify_coefficients();
return p;
};
public:
Polynomial_d
operator()( const Polynomial_d& p ) const {
if (CGAL::is_zero(p)) return p;
typedef Innermost_coefficient_type IC;
typedef typename Algebraic_extension_traits<IC>::Is_extended Is_extended;
return canonicalize_(p, Is_extended());
}
};
// Differentiate;
struct Differentiate
: public std::unary_function<Polynomial_d, Polynomial_d>{
Polynomial_d
operator()(Polynomial_d p, int i = (d-1)) const {
if (i == (d-1) ){
p.diff();
}else{
Swap swap;
p = swap(p,i,d-1);
p.diff();
p = swap(p,i,d-1);
}
return p;
}
};
// Evaluate;
struct Evaluate
:public std::binary_function<Polynomial_d,Coefficient_type,Coefficient_type>{
// Evaluate with respect to one variable
Coefficient_type
operator()(const Polynomial_d& p, const Coefficient_type& x) const {
return p.evaluate(x);
}
#define ICOEFF typename First_if_different<Innermost_coefficient_type, Coefficient_type>::Type
Coefficient_type operator()
( const Polynomial_d& p, const ICOEFF& x) const
{
return p.evaluate(x);
}
#undef ICOEFF
};
// Evaluate_homogeneous;
struct Evaluate_homogeneous{
typedef Coefficient_type result_type;
typedef Polynomial_d first_argument_type;
typedef Coefficient_type second_argument_type;
typedef Coefficient_type third_argument_type;
Coefficient_type operator()(
const Polynomial_d& p, const Coefficient_type& a, const Coefficient_type& b) const
{
return p.evaluate_homogeneous(a,b);
}
#define ICOEFF typename First_if_different<Innermost_coefficient_type, Coefficient_type>::Type
Coefficient_type operator()
( const Polynomial_d& p, const ICOEFF& a, const ICOEFF& b) const
{
return p.evaluate_homogeneous(a,b);
}
#undef ICOEFF
};
// Is_zero_at;
struct Is_zero_at {
private:
typedef Algebraic_structure_traits<Innermost_coefficient_type> AST;
typedef typename AST::Is_zero::result_type BOOL;
public:
typedef BOOL result_type;
template< class Input_iterator >
BOOL operator()(
const Polynomial_d& p,
Input_iterator begin,
Input_iterator end ) const {
typename PT::Substitute substitute;
return( CGAL::is_zero( substitute( p, begin, end ) ) );
}
};
// Is_zero_at_homogeneous;
struct Is_zero_at_homogeneous {
private:
typedef Algebraic_structure_traits<Innermost_coefficient_type> AST;
typedef typename AST::Is_zero::result_type BOOL;
public:
typedef BOOL result_type;
template< class Input_iterator >
BOOL operator()
( const Polynomial_d& p, Input_iterator begin, Input_iterator end ) const
{
typename PT::Substitute_homogeneous substitute_homogeneous;
return( CGAL::is_zero( substitute_homogeneous( p, begin, end ) ) );
}
};
// Sign_at, Sign_at_homogeneous, Compare
// define XXX_ even though ICoeff may not be Real_embeddable
// select propoer XXX among XXX_ or Null_functor using ::boost::mpl::if_
private:
struct Sign_at_ {
private:
typedef Real_embeddable_traits<Innermost_coefficient_type> RT;
public:
typedef typename RT::Sign result_type;
template< class Input_iterator >
result_type operator()(
const Polynomial_d& p,
Input_iterator begin,
Input_iterator end ) const
{
typename PT::Substitute substitute;
return CGAL::sign( substitute( p, begin, end ) );
}
};
struct Sign_at_homogeneous_ {
typedef Real_embeddable_traits<Innermost_coefficient_type> RT;
public:
typedef typename RT::Sign result_type;
template< class Input_iterator >
result_type operator()(
const Polynomial_d& p,
Input_iterator begin,
Input_iterator end) const {
typename PT::Substitute_homogeneous substitute_homogeneous;
return CGAL::sign( substitute_homogeneous( p, begin, end ) );
}
};
typedef Real_embeddable_traits<Innermost_coefficient_type> RET_IC;
typedef typename RET_IC::Is_real_embeddable IC_is_real_embeddable;
public:
typedef typename ::boost::mpl::if_<IC_is_real_embeddable,Sign_at_,Null_functor>::type Sign_at;
typedef typename ::boost::mpl::if_<IC_is_real_embeddable,Sign_at_homogeneous_,Null_functor>::type Sign_at_homogeneous;
typedef typename Real_embeddable_traits<Polynomial_d>::Compare Compare;
struct Construct_coefficient_const_iterator_range
: public std::unary_function< Polynomial_d,
Coefficient_const_iterator_range> {
Coefficient_const_iterator_range
operator () (const Polynomial_d& p) const {
return std::make_pair( p.begin(), p.end() );
}
};
struct Construct_innermost_coefficient_const_iterator_range
: public std::unary_function< Polynomial_d,
Innermost_coefficient_const_iterator_range> {
Innermost_coefficient_const_iterator_range
operator () (const Polynomial_d& p) const {
return std::make_pair(
typename Coefficient_const_flattening::Flatten()(p.end(),p.begin()),
typename Coefficient_const_flattening::Flatten()(p.end(),p.end()));
}
};
struct Is_square_free
: public std::unary_function< Polynomial_d, bool >{
bool operator()( const Polynomial_d& p ) const {
if( !internal::may_have_multiple_factor( p ) )
return true;
Gcd_up_to_constant_factor gcd_utcf;
Univariate_content_up_to_constant_factor ucontent_utcf;
Integral_division_up_to_constant_factor idiv_utcf;
Differentiate diff;
Coefficient_type content = ucontent_utcf( p );
typename PTC::Is_square_free isf;
if( !isf( content ) )
return false;
Polynomial_d regular_part = idiv_utcf( p, Polynomial_d( content ) );
Polynomial_d g = gcd_utcf(regular_part,diff(regular_part));
return ( g.degree() == 0 );
}
};
struct Make_square_free
: public std::unary_function< Polynomial_d, Polynomial_d >{
Polynomial_d
operator()(const Polynomial_d& p) const {
if (CGAL::is_zero(p)) return p;
Gcd_up_to_constant_factor gcd_utcf;
Univariate_content_up_to_constant_factor ucontent_utcf;
Integral_division_up_to_constant_factor idiv_utcf;
Differentiate diff;
typename PTC::Make_square_free msf;
Coefficient_type content = ucontent_utcf(p);
Polynomial_d result = Polynomial_d(msf(content));
Polynomial_d regular_part = idiv_utcf(p,Polynomial_d(content));
Polynomial_d g = gcd_utcf(regular_part,diff(regular_part));
result *= idiv_utcf(regular_part,g);
return Canonicalize()(result);
}
};
// Pseudo_division;
struct Pseudo_division {
typedef Polynomial_d result_type;
void
operator()(
const Polynomial_d& f, const Polynomial_d& g,
Polynomial_d& q, Polynomial_d& r, Coefficient_type& D) const {
Polynomial_d::pseudo_division(f,g,q,r,D);
}
};
struct Pseudo_division_quotient
:public std::binary_function<Polynomial_d, Polynomial_d, Polynomial_d> {
Polynomial_d
operator()(const Polynomial_d& f, const Polynomial_d& g) const {
Polynomial_d q,r;
Coefficient_type D;
Polynomial_d::pseudo_division(f,g,q,r,D);
return q;
}
};
struct Pseudo_division_remainder
:public std::binary_function<Polynomial_d, Polynomial_d, Polynomial_d> {
Polynomial_d
operator()(const Polynomial_d& f, const Polynomial_d& g) const {
Polynomial_d q,r;
Coefficient_type D;
Polynomial_d::pseudo_division(f,g,q,r,D);
return r;
}
};
struct Gcd_up_to_constant_factor
:public std::binary_function<Polynomial_d, Polynomial_d, Polynomial_d> {
Polynomial_d
operator()(const Polynomial_d& p, const Polynomial_d& q) const {
if(p==q) return CGAL::canonicalize(p);
if (CGAL::is_zero(p) && CGAL::is_zero(q)){
return Polynomial_d(0);
}
// apply modular filter first
if (internal::may_have_common_factor(p,q)){
return internal::gcd_utcf_(p,q);
}else{
return Polynomial_d(1);
}
}
};
struct Integral_division_up_to_constant_factor
:public std::binary_function<Polynomial_d, Polynomial_d, Polynomial_d> {
Polynomial_d
operator()(const Polynomial_d& p, const Polynomial_d& q) const {
typedef Innermost_coefficient_type IC;
typename PT::Construct_polynomial construct;
typename PT::Innermost_leading_coefficient ilcoeff;
typename PT::Construct_innermost_coefficient_const_iterator_range range;
typedef Algebraic_extension_traits<Innermost_coefficient_type> AET;
typename AET::Denominator_for_algebraic_integers dfai;
typename AET::Normalization_factor nfac;
IC ilcoeff_q = ilcoeff(q);
// this factor is needed in case IC is an Algebraic extension
IC dfai_q = dfai(range(q).first, range(q).second);
// make dfai_q a 'scalar'
ilcoeff_q *= dfai_q * nfac(dfai_q);
Polynomial_d result = (p * construct(ilcoeff_q)) / q;
return Canonicalize()(result);
}
};
struct Univariate_content_up_to_constant_factor
:public std::unary_function<Polynomial_d, Coefficient_type> {
Coefficient_type
operator()(const Polynomial_d& p) const {
typename PTC::Gcd_up_to_constant_factor gcd_utcf;
if(CGAL::is_zero(p)) return Coefficient_type(0);
if(PT::d == 1) return Coefficient_type(1);
Coefficient_type result(0);
for(typename Polynomial_d::const_iterator it = p.begin();
it != p.end();
it++){
result = gcd_utcf(*it,result);
}
return result;
}
};
struct Square_free_factorize_up_to_constant_factor {
private:
typedef Coefficient_type Coeff;
typedef Innermost_coefficient_type ICoeff;
// rsqff_utcf computes the sqff recursively for Coeff
// end of recursion: ICoeff
template < class OutputIterator >
OutputIterator rsqff_utcf ( ICoeff , OutputIterator oi) const{
return oi;
}
template < class OutputIterator >
OutputIterator rsqff_utcf (
typename First_if_different<Coeff,ICoeff>::Type c,
OutputIterator oi) const {
typename PTC::Square_free_factorize_up_to_constant_factor sqff;
std::vector<std::pair<Coefficient_type,int> > fac_mul_pairs;
sqff(c,std::back_inserter(fac_mul_pairs));
for(unsigned int i = 0; i < fac_mul_pairs.size(); i++){
Polynomial_d factor(fac_mul_pairs[i].first);
int mult = fac_mul_pairs[i].second;
*oi++=std::make_pair(factor,mult);
}
return oi;
}
public:
template < class OutputIterator>
OutputIterator
operator()(Polynomial_d p, OutputIterator oi) const {
if (CGAL::is_zero(p)) return oi;
Univariate_content_up_to_constant_factor ucontent_utcf;
Integral_division_up_to_constant_factor idiv_utcf;
Coefficient_type c = ucontent_utcf(p);
p = idiv_utcf( p , Polynomial_d(c));
std::vector<Polynomial_d> factors;
std::vector<int> mults;
square_free_factorize_utcf(
p, std::back_inserter(factors), std::back_inserter(mults));
for(unsigned int i = 0; i < factors.size() ; i++){
*oi++=std::make_pair(factors[i],mults[i]);
}
if (CGAL::total_degree(c) == 0)
return oi;
else
return rsqff_utcf(c,oi);
}
};
struct Shift
: public std::binary_function< Polynomial_d,int,Polynomial_d >{
Polynomial_d
operator()(const Polynomial_d& p, int e, int i = (d-1)) const {
Construct_polynomial construct;
Monomial_representation gmr;
Monom_rep monom_rep;
gmr(p,std::back_inserter(monom_rep));
for(typename Monom_rep::iterator it = monom_rep.begin();
it != monom_rep.end();
it++){
it->first[i]+=e;
}
return construct(monom_rep.begin(), monom_rep.end());
}
};
struct Negate
: public std::unary_function< Polynomial_d, Polynomial_d >{
Polynomial_d operator()(const Polynomial_d& p, int i = (d-1)) const {
Construct_polynomial construct;
Monomial_representation gmr;
Monom_rep monom_rep;
gmr(p,std::back_inserter(monom_rep));
for(typename Monom_rep::iterator it = monom_rep.begin();
it != monom_rep.end();
it++){
if (it->first[i] % 2 != 0)
it->second = - it->second;
}
return construct(monom_rep.begin(), monom_rep.end());
}
};
struct Invert
: public std::unary_function< Polynomial_d , Polynomial_d >{
Polynomial_d operator()(Polynomial_d p, int i = (PT::d-1)) const {
if (i == (d-1)){
p.reversal();
}else{
p = Swap()(p,i,PT::d-1);
p.reversal();
p = Swap()(p,i,PT::d-1);
}
return p ;
}
};
struct Translate
: public std::binary_function< Polynomial_d , Innermost_coefficient_type,
Polynomial_d >{
Polynomial_d
operator()(
Polynomial_d p,
const Innermost_coefficient_type& c,
int i = (d-1))
const {
if (i == (d-1) ){
p.translate(Coefficient_type(c));
}else{
Swap swap;
p = swap(p,i,d-1);
p.translate(Coefficient_type(c));
p = swap(p,i,d-1);
}
return p;
}
};
struct Translate_homogeneous{
typedef Polynomial_d result_type;
typedef Polynomial_d first_argument_type;
typedef Innermost_coefficient_type second_argument_type;
typedef Innermost_coefficient_type third_argument_type;
Polynomial_d
operator()(Polynomial_d p,
const Innermost_coefficient_type& a,
const Innermost_coefficient_type& b,
int i = (d-1) ) const {
if (i == (d-1) ){
p.translate(Coefficient_type(a),Coefficient_type(b));
}else{
Swap swap;
p = swap(p,i,d-1);
p.translate(Coefficient_type(a),Coefficient_type(b));
p = swap(p,i,d-1);
}
return p;
}
};
struct Scale
: public
std::binary_function< Polynomial_d, Innermost_coefficient_type, Polynomial_d > {
Polynomial_d operator()( Polynomial_d p, const Innermost_coefficient_type& c,
int i = (PT::d-1) ) const {
CGAL_precondition( i <= d-1 );
CGAL_precondition( i >= 0 );
typename PT::Scale_homogeneous scale_homogeneous;
return scale_homogeneous( p, c, Innermost_coefficient_type(1), i );
}
};
struct Scale_homogeneous{
typedef Polynomial_d result_type;
typedef Polynomial_d first_argument_type;
typedef Innermost_coefficient_type second_argument_type;
typedef Innermost_coefficient_type third_argument_type;
Polynomial_d
operator()(
Polynomial_d p,
const Innermost_coefficient_type& a,
const Innermost_coefficient_type& b,
int i = (d-1) ) const {
CGAL_precondition( ! CGAL::is_zero(b) );
CGAL_precondition( i <= d-1 );
CGAL_precondition( i >= 0 );
if (i != (d-1) ) p = Swap()(p,i,d-1);
if(CGAL::is_one(b))
p.scale_up(Coefficient_type(a));
else
if(CGAL::is_one(a))
p.scale_down(Coefficient_type(b));
else
p.scale(Coefficient_type(a),Coefficient_type(b));
if (i != (d-1) ) p = Swap()(p,i,d-1);
return p;
}
};
struct Resultant
: public std::binary_function<Polynomial_d, Polynomial_d, Coefficient_type>{
Coefficient_type
operator()(
const Polynomial_d& p,
const Polynomial_d& q) const {
return internal::resultant(p,q);
}
};
// Polynomial subresultants (aka subresultant polynomials)
struct Polynomial_subresultants {
template<typename OutputIterator>
OutputIterator operator()(
const Polynomial_d& p,
const Polynomial_d& q,
OutputIterator out,
int i = (d-1) ) const {
if(i == (d-1) )
return CGAL::internal::polynomial_subresultants<PT>(p,q,out);
else
return CGAL::internal::polynomial_subresultants<PT>(Move()(p,i),
Move()(q,i),
out);
}
};
// principal subresultants (aka scalar subresultants)
struct Principal_subresultants {
template<typename OutputIterator>
OutputIterator operator()(
const Polynomial_d& p,
const Polynomial_d& q,
OutputIterator out,
int i = (d-1) ) const {
if(i == (d-1) )
return CGAL::internal::principal_subresultants<PT>(p,q,out);
else
return CGAL::internal::principal_subresultants<PT>(Move()(p,i),
Move()(q,i),
out);
}
};
// Subresultants with cofactors
struct Polynomial_subresultants_with_cofactors {
template<typename OutputIterator1,
typename OutputIterator2,
typename OutputIterator3>
OutputIterator1 operator()(
const Polynomial_d& p,
const Polynomial_d& q,
OutputIterator1 out_sres,
OutputIterator2 out_co_p,
OutputIterator3 out_co_q,
int i = (d-1) ) const {
if(i == (d-1) )
return CGAL::internal::polynomial_subresultants_with_cofactors<PT>
(p,q,out_sres,out_co_p,out_co_q);
else
return CGAL::internal::polynomial_subresultants_with_cofactors<PT>
(Move()(p,i),Move()(q,i),out_sres,out_co_p,out_co_q);
}
};
// Sturm-Habicht sequence (aka signed subresultant sequence)
struct Sturm_habicht_sequence {
template<typename OutputIterator>
OutputIterator operator()(
const Polynomial_d& p,
OutputIterator out,
int i = (d-1) ) const {
if(i == (d-1) )
return CGAL::internal::sturm_habicht_sequence<PT>(p,out);
else
return CGAL::internal::sturm_habicht_sequence<PT>(Move()(p,i),
out);
}
};
// Sturm-Habicht sequence with cofactors
struct Sturm_habicht_sequence_with_cofactors {
template<typename OutputIterator1,
typename OutputIterator2,
typename OutputIterator3>
OutputIterator1 operator()(
const Polynomial_d& p,
OutputIterator1 out_stha,
OutputIterator2 out_f,
OutputIterator3 out_fx,
int i = (d-1) ) const {
if(i == (d-1) )
return CGAL::internal::sturm_habicht_sequence_with_cofactors<PT>
(p,out_stha,out_f,out_fx);
else
return CGAL::internal::sturm_habicht_sequence_with_cofactors<PT>
(Move()(p,i),out_stha,out_f,out_fx);
}
};
// Principal Sturm-Habicht sequence (formal leading coefficients
// of Sturm-Habicht sequence)
struct Principal_sturm_habicht_sequence {
template<typename OutputIterator>
OutputIterator operator()(
const Polynomial_d& p,
OutputIterator out,
int i = (d-1) ) const {
if(i == (d-1) )
return CGAL::internal::principal_sturm_habicht_sequence<PT>(p,out);
else
return CGAL::internal::principal_sturm_habicht_sequence<PT>
(Move()(p,i),out);
}
};
typedef
CGAL::internal::Monomial_representation<Polynomial_d>
Monomial_representation;
// returns the Exponten_vector of the innermost leading coefficient
struct Degree_vector{
typedef Exponent_vector result_type;
typedef Polynomial_d argument_type;
// returns the exponent vector of inner_most_lcoeff.
result_type operator()(const Polynomial_d& polynomial) const{
typename PTC::Degree_vector degree_vector;
Exponent_vector result = degree_vector(polynomial.lcoeff());
result.push_back(polynomial.degree());
return result;
}
};
// substitute every variable by its new value in the iterator range
// begin refers to the innermost/first variable
struct Substitute{
public:
template <class Input_iterator>
typename CGAL::Coercion_traits<
typename std::iterator_traits<Input_iterator>::value_type,
Innermost_coefficient_type
>::Type
operator()(
const Polynomial_d& p,
Input_iterator begin,
Input_iterator end) const {
typedef typename std::iterator_traits<Input_iterator> ITT;
typedef typename ITT::iterator_category Category;
return (*this)(p,begin,end,Category());
}
template <class Input_iterator>
typename CGAL::Coercion_traits<
typename std::iterator_traits<Input_iterator>::value_type,
Innermost_coefficient_type
>::Type
operator()(
const Polynomial_d& p,
Input_iterator begin,
Input_iterator end,
std::forward_iterator_tag) const {
typedef typename std::iterator_traits<Input_iterator> ITT;
std::list<typename ITT::value_type> list(begin,end);
return (*this)(p,list.begin(),list.end());
}
template <class Input_iterator>
typename
CGAL::Coercion_traits
<typename std::iterator_traits<Input_iterator>::value_type,
Innermost_coefficient_type>::Type
operator()(
const Polynomial_d& p,
Input_iterator begin,
Input_iterator end,
std::bidirectional_iterator_tag) const {
typedef typename std::iterator_traits<Input_iterator>::value_type
value_type;
typedef CGAL::Coercion_traits<Innermost_coefficient_type,value_type> CT;
typename PTC::Substitute subs;
typename CT::Type x = typename CT::Cast()(*(--end));
int i = Degree()(p);
typename CT::Type y =
subs(Get_coefficient()(p,i),begin,end);
while (--i >= 0){
y *= x;
y += subs(Get_coefficient()(p,i),begin,end);
}
return y;
}
}; // substitute every variable by its new value in the iterator range
// begin refers to the innermost/first variable
struct Substitute_homogeneous{
template<typename Input_iterator>
struct Result_type{
typedef std::iterator_traits<Input_iterator> ITT;
typedef typename ITT::value_type value_type;
typedef Coercion_traits<value_type, Innermost_coefficient_type> CT;
typedef typename CT::Type Type;
};
public:
template <class Input_iterator>
typename Result_type<Input_iterator>::Type
operator()( const Polynomial_d& p, Input_iterator begin, Input_iterator end) const{
int hdegree = Total_degree()(p);
typedef std::iterator_traits<Input_iterator> ITT;
std::list<typename ITT::value_type> list(begin,end);
// make the homogeneous variable the first in the list
list.push_front(list.back());
list.pop_back();
// reverse and begin with the outermost variable
return (*this)(p, list.rbegin(), list.rend(), hdegree);
}
// this operator is undcoumented and for internal use:
// the iterator range starts with the outermost variable
// and ends with the homogeneous variable
template <class Input_iterator>
typename Result_type<Input_iterator>::Type
operator()(
const Polynomial_d& p,
Input_iterator begin,
Input_iterator end,
int hdegree) const{
typedef std::iterator_traits<Input_iterator> ITT;
typedef typename ITT::value_type value_type;
typedef Coercion_traits<value_type, Innermost_coefficient_type> CT;
typename PTC::Substitute_homogeneous subsh;
typename CT::Type x = typename CT::Cast()(*begin++);
int i = Degree()(p);
typename CT::Type y = subsh(Get_coefficient()(p,i),begin,end, hdegree-i);
while (--i >= 0){
y *= x;
y += subsh(Get_coefficient()(p,i),begin,end,hdegree-i);
}
return y;
}
};
};
} // namespace internal
// Definition of Polynomial_traits_d
//
// In order to determine the algebraic category of the innermost coefficient,
// the Polynomial_traits_d_base class with "Null_tag" is used.
template< class Polynomial >
class Polynomial_traits_d
: public internal::Polynomial_traits_d_base< Polynomial,
typename Algebraic_structure_traits<
typename internal::Innermost_coefficient_type<Polynomial>::Type >::Algebraic_category,
typename Algebraic_structure_traits< Polynomial >::Algebraic_category > ,
public Algebraic_structure_traits<Polynomial>{
//------------ Rebind -----------
private:
template <class T, int d>
struct Gen_polynomial_type{
typedef CGAL::Polynomial<typename Gen_polynomial_type<T,d-1>::Type> Type;
};
template <class T>
struct Gen_polynomial_type<T,0>{ typedef T Type; };
public:
template <class T, int d>
struct Rebind{
typedef Polynomial_traits_d<typename Gen_polynomial_type<T,d>::Type> Other;
};
//------------ Rebind -----------
};
} //namespace CGAL
#endif // CGAL_POLYNOMIAL_TRAITS_D_H
|