/usr/include/singular/singular/polys/monomials/p_polys.h is in libsingular4-dev-common 1:4.1.0-p3+ds-2build1.
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 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 | /****************************************
* Computer Algebra System SINGULAR *
****************************************/
/***************************************************************
* File: p_polys.h
* Purpose: declaration of poly stuf which are independent of
* currRing
* Author: obachman (Olaf Bachmann)
* Created: 9/00
*******************************************************************/
/***************************************************************
* Purpose: implementation of poly procs which iter over ExpVector
* Author: obachman (Olaf Bachmann)
* Created: 8/00
*******************************************************************/
#ifndef P_POLYS_H
#define P_POLYS_H
#include <omalloc/omalloc.h>
#include <misc/mylimits.h>
#include <misc/intvec.h>
#include <coeffs/coeffs.h>
#include <polys/monomials/monomials.h>
#include <polys/monomials/ring.h>
#include <polys/templates/p_MemAdd.h>
#include <polys/templates/p_MemCmp.h>
#include <polys/templates/p_Procs.h>
#include <polys/sbuckets.h>
#ifdef HAVE_PLURAL
#include <polys/nc/nc.h>
#endif
poly p_Farey(poly p, number N, const ring r);
/*
* xx,q: arrays of length 0..rl-1
* xx[i]: SB mod q[i]
* assume: char=0
* assume: q[i]!=0
* destroys xx
*/
poly p_ChineseRemainder(poly *xx, number *x,number *q, int rl, CFArray &inv_cache, const ring R);
/***************************************************************
*
* Divisiblity tests, args must be != NULL, except for
* pDivisbleBy
*
***************************************************************/
unsigned long p_GetShortExpVector(const poly a, const ring r);
/// p_GetShortExpVector of p * pp
unsigned long p_GetShortExpVector(const poly p, const poly pp, const ring r);
#ifdef HAVE_RINGS
/*! divisibility check over ground ring (which may contain zero divisors);
TRUE iff LT(f) divides LT(g), i.e., LT(f)*c*m = LT(g), for some
coefficient c and some monomial m;
does not take components into account
*/
BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r);
#endif
/***************************************************************
*
* Misc things on polys
*
***************************************************************/
poly p_One(const ring r);
int p_MinDeg(poly p,intvec *w, const ring R);
long p_DegW(poly p, const short *w, const ring R);
/// return TRUE if all monoms have the same component
BOOLEAN p_OneComp(poly p, const ring r);
/// return i, if head depends only on var(i)
int p_IsPurePower(const poly p, const ring r);
/// return i, if poly depends only on var(i)
int p_IsUnivariate(poly p, const ring r);
/// set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0
/// return #(e[i]>0)
int p_GetVariables(poly p, int * e, const ring r);
/// returns the poly representing the integer i
poly p_ISet(long i, const ring r);
/// returns the poly representing the number n, destroys n
poly p_NSet(number n, const ring r);
void p_Vec2Polys(poly v, poly**p, int *len, const ring r);
/***************************************************************
*
* Copying/Deletion of polys: args may be NULL
*
***************************************************************/
// simply deletes monomials, does not free coeffs
void p_ShallowDelete(poly *p, const ring r);
/***************************************************************
*
* Copying/Deleteion of polys: args may be NULL
* - p/q as arg mean a poly
* - m a monomial
* - n a number
* - pp (resp. qq, mm, nn) means arg is constant
* - p (resp, q, m, n) means arg is destroyed
*
***************************************************************/
poly p_Sub(poly a, poly b, const ring r);
poly p_Power(poly p, int i, const ring r);
/***************************************************************
*
* PDEBUG stuff
*
***************************************************************/
#ifdef PDEBUG
// Returns TRUE if m is monom of p, FALSE otherwise
BOOLEAN pIsMonomOf(poly p, poly m);
// Returns TRUE if p and q have common monoms
BOOLEAN pHaveCommonMonoms(poly p, poly q);
// p_Check* routines return TRUE if everything is ok,
// else, they report error message and return false
// check if Lm(p) is from ring r
BOOLEAN p_LmCheckIsFromRing(poly p, ring r);
// check if Lm(p) != NULL, r != NULL and initialized && Lm(p) is from r
BOOLEAN p_LmCheckPolyRing(poly p, ring r);
// check if all monoms of p are from ring r
BOOLEAN p_CheckIsFromRing(poly p, ring r);
// check r != NULL and initialized && all monoms of p are from r
BOOLEAN p_CheckPolyRing(poly p, ring r);
// check if r != NULL and initialized
BOOLEAN p_CheckRing(ring r);
// only do check if cond
#define pIfThen(cond, check) do {if (cond) {check;}} while (0)
BOOLEAN _p_Test(poly p, ring r, int level);
BOOLEAN _p_LmTest(poly p, ring r, int level);
BOOLEAN _pp_Test(poly p, ring lmRing, ring tailRing, int level);
#define p_Test(p,r) _p_Test(p, r, PDEBUG)
#define p_LmTest(p,r) _p_LmTest(p, r, PDEBUG)
#define pp_Test(p, lmRing, tailRing) _pp_Test(p, lmRing, tailRing, PDEBUG)
#else // ! PDEBUG
#define pIsMonomOf(p, q) (TRUE)
#define pHaveCommonMonoms(p, q) (TRUE)
#define p_LmCheckIsFromRing(p,r) (TRUE)
#define p_LmCheckPolyRing(p,r) (TRUE)
#define p_CheckIsFromRing(p,r) (TRUE)
#define p_CheckPolyRing(p,r) (TRUE)
#define p_CheckRing(r) (TRUE)
#define P_CheckIf(cond, check) (TRUE)
#define p_Test(p,r) (TRUE)
#define p_LmTest(p,r) (TRUE)
#define pp_Test(p, lmRing, tailRing) (TRUE)
#endif
/***************************************************************
*
* Misc stuff
*
***************************************************************/
/*2
* returns the length of a polynomial (numbers of monomials)
*/
static inline unsigned pLength(poly a)
{
unsigned l = 0;
while (a!=NULL)
{
pIter(a);
l++;
}
return l;
}
// returns the length of a polynomial (numbers of monomials) and the last mon.
// respect syzComp
poly p_Last(const poly a, int &l, const ring r);
/*----------------------------------------------------*/
void p_Norm(poly p1, const ring r);
void p_Normalize(poly p,const ring r);
void p_ProjectiveUnique(poly p,const ring r);
void p_Content(poly p, const ring r);
#if 1
// currently only used by Singular/janet
void p_SimpleContent(poly p, int s, const ring r);
#endif
poly p_Cleardenom(poly p, const ring r);
void p_Cleardenom_n(poly p, const ring r,number &c);
//number p_GetAllDenom(poly ph, const ring r);// unused
int p_Size( poly p, const ring r );
// homogenizes p by multiplying certain powers of the varnum-th variable
poly p_Homogen (poly p, int varnum, const ring r);
BOOLEAN p_IsHomogeneous (poly p, const ring r);
// Setm
static inline void p_Setm(poly p, const ring r)
{
p_CheckRing2(r);
r->p_Setm(p, r);
}
p_SetmProc p_GetSetmProc(const ring r);
poly p_Subst(poly p, int n, poly e, const ring r);
// TODO:
#define p_SetmComp p_Setm
// component
static inline unsigned long p_SetComp(poly p, unsigned long c, ring r)
{
p_LmCheckPolyRing2(p, r);
if (r->pCompIndex>=0) __p_GetComp(p,r) = c;
return c;
}
// sets component of poly a to i
static inline void p_SetCompP(poly p, int i, ring r)
{
if (p != NULL)
{
p_Test(p, r);
if (rOrd_SetCompRequiresSetm(r))
{
do
{
p_SetComp(p, i, r);
p_SetmComp(p, r);
pIter(p);
}
while (p != NULL);
}
else
{
do
{
p_SetComp(p, i, r);
pIter(p);
}
while(p != NULL);
}
}
}
static inline void p_SetCompP(poly p, int i, ring lmRing, ring tailRing)
{
if (p != NULL)
{
p_SetComp(p, i, lmRing);
p_SetmComp(p, lmRing);
p_SetCompP(pNext(p), i, tailRing);
}
}
// returns maximal column number in the modul element a (or 0)
static inline long p_MaxComp(poly p, ring lmRing, ring tailRing)
{
long result,i;
if(p==NULL) return 0;
result = p_GetComp(p, lmRing);
if (result != 0)
{
loop
{
pIter(p);
if(p==NULL) break;
i = p_GetComp(p, tailRing);
if (i>result) result = i;
}
}
return result;
}
static inline long p_MaxComp(poly p,ring lmRing) {return p_MaxComp(p,lmRing,lmRing);}
static inline long p_MinComp(poly p, ring lmRing, ring tailRing)
{
long result,i;
if(p==NULL) return 0;
result = p_GetComp(p,lmRing);
if (result != 0)
{
loop
{
pIter(p);
if(p==NULL) break;
i = p_GetComp(p,tailRing);
if (i<result) result = i;
}
}
return result;
}
static inline long p_MinComp(poly p,ring lmRing) {return p_MinComp(p,lmRing,lmRing);}
static inline poly pReverse(poly p)
{
if (p == NULL || pNext(p) == NULL) return p;
poly q = pNext(p), // == pNext(p)
qn;
pNext(p) = NULL;
do
{
qn = pNext(q);
pNext(q) = p;
p = q;
q = qn;
}
while (qn != NULL);
return p;
}
void pEnlargeSet(poly**p, int length, int increment);
/***************************************************************
*
* I/O
*
***************************************************************/
/// print p according to ShortOut in lmRing & tailRing
void p_String0(poly p, ring lmRing, ring tailRing);
char* p_String(poly p, ring lmRing, ring tailRing);
void p_Write(poly p, ring lmRing, ring tailRing);
void p_Write0(poly p, ring lmRing, ring tailRing);
void p_wrp(poly p, ring lmRing, ring tailRing);
/// print p in a short way, if possible
void p_String0Short(const poly p, ring lmRing, ring tailRing);
/// print p in a long way
void p_String0Long(const poly p, ring lmRing, ring tailRing);
/***************************************************************
*
* Degree stuff -- see p_polys.cc for explainations
*
***************************************************************/
static inline long p_FDeg(const poly p, const ring r) { return r->pFDeg(p,r); }
static inline long p_LDeg(const poly p, int *l, const ring r) { return r->pLDeg(p,l,r); }
long p_WFirstTotalDegree(poly p, ring r);
long p_WTotaldegree(poly p, const ring r);
long p_WDegree(poly p,const ring r);
long pLDeg0(poly p,int *l, ring r);
long pLDeg0c(poly p,int *l, ring r);
long pLDegb(poly p,int *l, ring r);
long pLDeg1(poly p,int *l, ring r);
long pLDeg1c(poly p,int *l, ring r);
long pLDeg1_Deg(poly p,int *l, ring r);
long pLDeg1c_Deg(poly p,int *l, ring r);
long pLDeg1_Totaldegree(poly p,int *l, ring r);
long pLDeg1c_Totaldegree(poly p,int *l, ring r);
long pLDeg1_WFirstTotalDegree(poly p,int *l, ring r);
long pLDeg1c_WFirstTotalDegree(poly p,int *l, ring r);
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r);
/// same as the usual p_EqualPolys for polys belonging to *equal* rings
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r1, const ring r2);
long p_Deg(poly a, const ring r);
/***************************************************************
*
* Primitives for accessing and setting fields of a poly
*
***************************************************************/
static inline number p_SetCoeff(poly p, number n, ring r)
{
p_LmCheckPolyRing2(p, r);
n_Delete(&(p->coef), r->cf);
(p)->coef=n;
return n;
}
// order
static inline long p_GetOrder(poly p, ring r)
{
p_LmCheckPolyRing2(p, r);
if (r->typ==NULL) return ((p)->exp[r->pOrdIndex]);
int i=0;
loop
{
switch(r->typ[i].ord_typ)
{
case ro_am:
case ro_wp_neg:
return ((p->exp[r->pOrdIndex])-POLY_NEGWEIGHT_OFFSET);
case ro_syzcomp:
case ro_syz:
case ro_cp:
i++;
break;
//case ro_dp:
//case ro_wp:
default:
return ((p)->exp[r->pOrdIndex]);
}
}
}
static inline unsigned long p_AddComp(poly p, unsigned long v, ring r)
{
p_LmCheckPolyRing2(p, r);
pAssume2(rRing_has_Comp(r));
return __p_GetComp(p,r) += v;
}
static inline unsigned long p_SubComp(poly p, unsigned long v, ring r)
{
p_LmCheckPolyRing2(p, r);
pAssume2(rRing_has_Comp(r));
_pPolyAssume2(__p_GetComp(p,r) >= v,p,r);
return __p_GetComp(p,r) -= v;
}
#ifndef HAVE_EXPSIZES
/// get a single variable exponent
/// @Note:
/// the integer VarOffset encodes:
/// 1. the position of a variable in the exponent vector p->exp (lower 24 bits)
/// 2. number of bits to shift to the right in the upper 8 bits (which takes at most 6 bits for 64 bit)
/// Thus VarOffset always has 2 zero higher bits!
static inline long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
{
pAssume2((VarOffset >> (24 + 6)) == 0);
#if 0
int pos=(VarOffset & 0xffffff);
int bitpos=(VarOffset >> 24);
unsigned long exp=(p->exp[pos] >> bitmask) & iBitmask;
return exp;
#else
return (long)
((p->exp[(VarOffset & 0xffffff)] >> (VarOffset >> 24))
& iBitmask);
#endif
}
/// set a single variable exponent
/// @Note:
/// VarOffset encodes the position in p->exp @see p_GetExp
static inline unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
{
pAssume2(e>=0);
pAssume2(e<=iBitmask);
pAssume2((VarOffset >> (24 + 6)) == 0);
// shift e to the left:
register int shift = VarOffset >> 24;
unsigned long ee = e << shift /*(VarOffset >> 24)*/;
// find the bits in the exponent vector
register int offset = (VarOffset & 0xffffff);
// clear the bits in the exponent vector:
p->exp[offset] &= ~( iBitmask << shift );
// insert e with |
p->exp[ offset ] |= ee;
return e;
}
#else // #ifdef HAVE_EXPSIZES // EXPERIMENTAL!!!
static inline unsigned long BitMask(unsigned long bitmask, int twobits)
{
// bitmask = 00000111111111111
// 0 must give bitmask!
// 1, 2, 3 - anything like 00011..11
pAssume2((twobits >> 2) == 0);
static const unsigned long _bitmasks[4] = {-1, 0x7fff, 0x7f, 0x3};
return bitmask & _bitmasks[twobits];
}
/// @Note: we may add some more info (6 ) into VarOffset and thus encode
static inline long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
{
int pos =(VarOffset & 0xffffff);
int hbyte= (VarOffset >> 24); // the highest byte
int bitpos = hbyte & 0x3f; // last 6 bits
long bitmask = BitMask(iBitmask, hbyte >> 6);
long exp=(p->exp[pos] >> bitpos) & bitmask;
return exp;
}
static inline long p_SetExp(poly p, const long e, const unsigned long iBitmask, const int VarOffset)
{
pAssume2(e>=0);
pAssume2(e <= BitMask(iBitmask, VarOffset >> 30));
// shift e to the left:
register int hbyte = VarOffset >> 24;
int bitmask = BitMask(iBitmask, hbyte >> 6);
register int shift = hbyte & 0x3f;
long ee = e << shift;
// find the bits in the exponent vector
register int offset = (VarOffset & 0xffffff);
// clear the bits in the exponent vector:
p->exp[offset] &= ~( bitmask << shift );
// insert e with |
p->exp[ offset ] |= ee;
return e;
}
#endif // #ifndef HAVE_EXPSIZES
static inline long p_GetExp(const poly p, const ring r, const int VarOffset)
{
p_LmCheckPolyRing2(p, r);
pAssume2(VarOffset != -1);
return p_GetExp(p, r->bitmask, VarOffset);
}
static inline long p_SetExp(poly p, const long e, const ring r, const int VarOffset)
{
p_LmCheckPolyRing2(p, r);
pAssume2(VarOffset != -1);
return p_SetExp(p, e, r->bitmask, VarOffset);
}
/// get v^th exponent for a monomial
static inline long p_GetExp(const poly p, const int v, const ring r)
{
p_LmCheckPolyRing2(p, r);
pAssume2(v>0 && v <= r->N);
pAssume2(r->VarOffset[v] != -1);
return p_GetExp(p, r->bitmask, r->VarOffset[v]);
}
/// set v^th exponent for a monomial
static inline long p_SetExp(poly p, const int v, const long e, const ring r)
{
p_LmCheckPolyRing2(p, r);
pAssume2(v>0 && v <= r->N);
pAssume2(r->VarOffset[v] != -1);
return p_SetExp(p, e, r->bitmask, r->VarOffset[v]);
}
// the following should be implemented more efficiently
static inline long p_IncrExp(poly p, int v, ring r)
{
p_LmCheckPolyRing2(p, r);
int e = p_GetExp(p,v,r);
e++;
return p_SetExp(p,v,e,r);
}
static inline long p_DecrExp(poly p, int v, ring r)
{
p_LmCheckPolyRing2(p, r);
int e = p_GetExp(p,v,r);
pAssume2(e > 0);
e--;
return p_SetExp(p,v,e,r);
}
static inline long p_AddExp(poly p, int v, long ee, ring r)
{
p_LmCheckPolyRing2(p, r);
int e = p_GetExp(p,v,r);
e += ee;
return p_SetExp(p,v,e,r);
}
static inline long p_SubExp(poly p, int v, long ee, ring r)
{
p_LmCheckPolyRing2(p, r);
long e = p_GetExp(p,v,r);
pAssume2(e >= ee);
e -= ee;
return p_SetExp(p,v,e,r);
}
static inline long p_MultExp(poly p, int v, long ee, ring r)
{
p_LmCheckPolyRing2(p, r);
long e = p_GetExp(p,v,r);
e *= ee;
return p_SetExp(p,v,e,r);
}
static inline long p_GetExpSum(poly p1, poly p2, int i, ring r)
{
p_LmCheckPolyRing2(p1, r);
p_LmCheckPolyRing2(p2, r);
return p_GetExp(p1,i,r) + p_GetExp(p2,i,r);
}
static inline long p_GetExpDiff(poly p1, poly p2, int i, ring r)
{
return p_GetExp(p1,i,r) - p_GetExp(p2,i,r);
}
static inline int p_Comp_k_n(poly a, poly b, int k, ring r)
{
if ((a==NULL) || (b==NULL) ) return FALSE;
p_LmCheckPolyRing2(a, r);
p_LmCheckPolyRing2(b, r);
pAssume2(k > 0 && k <= r->N);
int i=k;
for(;i<=r->N;i++)
{
if (p_GetExp(a,i,r) != p_GetExp(b,i,r)) return FALSE;
// if (a->exp[(r->VarOffset[i] & 0xffffff)] != b->exp[(r->VarOffset[i] & 0xffffff)]) return FALSE;
}
return TRUE;
}
/***************************************************************
*
* Allocation/Initalization/Deletion
*
***************************************************************/
#if (OM_TRACK > 2) && defined(OM_TRACK_CUSTOM)
static inline poly p_New(const ring r, omBin bin)
#else
static inline poly p_New(const ring /*r*/, omBin bin)
#endif
{
p_CheckRing2(r);
pAssume2(bin != NULL && omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
poly p;
omTypeAllocBin(poly, p, bin);
p_SetRingOfLm(p, r);
return p;
}
static inline poly p_New(ring r)
{
return p_New(r, r->PolyBin);
}
#if PDEBUG > 2
static inline void p_LmFree(poly p, ring r)
#else
static inline void p_LmFree(poly p, ring)
#endif
{
p_LmCheckPolyRing2(p, r);
omFreeBinAddr(p);
}
#if PDEBUG > 2
static inline void p_LmFree(poly *p, ring r)
#else
static inline void p_LmFree(poly *p, ring)
#endif
{
p_LmCheckPolyRing2(*p, r);
poly h = *p;
*p = pNext(h);
omFreeBinAddr(h);
}
#if PDEBUG > 2
static inline poly p_LmFreeAndNext(poly p, ring r)
#else
static inline poly p_LmFreeAndNext(poly p, ring)
#endif
{
p_LmCheckPolyRing2(p, r);
poly pnext = pNext(p);
omFreeBinAddr(p);
return pnext;
}
static inline void p_LmDelete(poly p, const ring r)
{
p_LmCheckPolyRing2(p, r);
n_Delete(&pGetCoeff(p), r->cf);
omFreeBinAddr(p);
}
static inline void p_LmDelete(poly *p, const ring r)
{
p_LmCheckPolyRing2(*p, r);
poly h = *p;
*p = pNext(h);
n_Delete(&pGetCoeff(h), r->cf);
omFreeBinAddr(h);
}
static inline poly p_LmDeleteAndNext(poly p, const ring r)
{
p_LmCheckPolyRing2(p, r);
poly pnext = pNext(p);
n_Delete(&pGetCoeff(p), r->cf);
omFreeBinAddr(p);
return pnext;
}
/***************************************************************
*
* Misc routines
*
***************************************************************/
/// return the maximal exponent of p in form of the maximal long var
unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max = 0);
/// return monomial r such that GetExp(r,i) is maximum of all
/// monomials in p; coeff == 0, next == NULL, ord is not set
poly p_GetMaxExpP(poly p, ring r);
static inline unsigned long p_GetMaxExp(const unsigned long l, const ring r)
{
unsigned long bitmask = r->bitmask;
unsigned long max = (l & bitmask);
unsigned long j = r->ExpPerLong - 1;
if (j > 0)
{
unsigned long i = r->BitsPerExp;
long e;
loop
{
e = ((l >> i) & bitmask);
if ((unsigned long) e > max)
max = e;
j--;
if (j==0) break;
i += r->BitsPerExp;
}
}
return max;
}
static inline unsigned long p_GetMaxExp(const poly p, const ring r)
{
return p_GetMaxExp(p_GetMaxExpL(p, r), r);
}
static inline unsigned long
p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps)
{
const unsigned long bitmask = r->bitmask;
unsigned long sum = (l & bitmask);
unsigned long j = number_of_exps - 1;
if (j > 0)
{
unsigned long i = r->BitsPerExp;
loop
{
sum += ((l >> i) & bitmask);
j--;
if (j==0) break;
i += r->BitsPerExp;
}
}
return sum;
}
/***************************************************************
*
* Dispatcher to r->p_Procs, they do the tests/checks
*
***************************************************************/
/// returns a copy of p (without any additional testing)
static inline poly p_Copy_noCheck(poly p, const ring r)
{
assume(r != NULL); assume(r->p_Procs != NULL); assume(r->p_Procs->p_Copy != NULL);
return r->p_Procs->p_Copy(p, r);
}
/// returns a copy of p
static inline poly p_Copy(poly p, const ring r)
{
p_Test(p,r);
const poly pp = p_Copy_noCheck(p, r);
p_Test(pp,r);
return pp;
}
static inline poly p_Head(poly p, const ring r)
{
if (p == NULL) return NULL;
p_LmCheckPolyRing1(p, r);
poly np;
omTypeAllocBin(poly, np, r->PolyBin);
p_SetRingOfLm(np, r);
memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
pNext(np) = NULL;
pSetCoeff0(np, n_Copy(pGetCoeff(p), r->cf));
return np;
}
// returns a copy of p with Lm(p) from lmRing and Tail(p) from tailRing
static inline poly p_Copy(poly p, const ring lmRing, const ring tailRing)
{
if (p != NULL)
{
#ifndef PDEBUG
if (tailRing == lmRing)
return p_Copy_noCheck(p, tailRing);
#endif
poly pres = p_Head(p, lmRing);
pNext(pres) = p_Copy_noCheck(pNext(p), tailRing);
return pres;
}
else
return NULL;
}
// deletes *p, and sets *p to NULL
static inline void p_Delete(poly *p, const ring r)
{
assume( p!= NULL );
r->p_Procs->p_Delete(p, r);
}
static inline void p_Delete(poly *p, const ring lmRing, const ring tailRing)
{
assume( p!= NULL );
if (*p != NULL)
{
#ifndef PDEBUG
if (tailRing == lmRing)
{
p_Delete(p, tailRing);
return;
}
#endif
if (pNext(*p) != NULL)
p_Delete(&pNext(*p), tailRing);
p_LmDelete(p, lmRing);
}
}
// copys monomials of p, allocates new monomials from bin,
// deletes monomoals of p
static inline poly p_ShallowCopyDelete(poly p, const ring r, omBin bin)
{
p_LmCheckPolyRing2(p, r);
pAssume2(omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
return r->p_Procs->p_ShallowCopyDelete(p, r, bin);
}
// returns p+q, destroys p and q
static inline poly p_Add_q(poly p, poly q, const ring r)
{
assume( (p != q) || (p == NULL && q == NULL) );
int shorter;
return r->p_Procs->p_Add_q(p, q, shorter, r);
}
/// like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq) then lp == pLength(p+q)
static inline poly p_Add_q(poly p, poly q, int &lp, int lq, const ring r)
{
assume( (p != q) || (p == NULL && q == NULL) );
int shorter;
poly res = r->p_Procs->p_Add_q(p, q, shorter, r);
lp = (lp + lq) - shorter;
return res;
}
// returns p*n, destroys p
static inline poly p_Mult_nn(poly p, number n, const ring r)
{
if (n_IsOne(n, r->cf))
return p;
else if (n_IsZero(n, r->cf))
{
r->p_Procs->p_Delete(&p, r); // NOTE: without p_Delete - memory leak!
return NULL;
} else
return r->p_Procs->p_Mult_nn(p, n, r);
}
static inline poly p_Mult_nn(poly p, number n, const ring lmRing,
const ring tailRing)
{
#ifndef PDEBUG
if (lmRing == tailRing)
return p_Mult_nn(p, n, tailRing);
#endif
poly pnext = pNext(p);
pNext(p) = NULL;
p = lmRing->p_Procs->p_Mult_nn(p, n, lmRing);
pNext(p) = tailRing->p_Procs->p_Mult_nn(pnext, n, tailRing);
return p;
}
// returns p*n, does not destroy p
static inline poly pp_Mult_nn(poly p, number n, const ring r)
{
if (n_IsOne(n, r->cf))
return p_Copy(p, r);
else
return r->p_Procs->pp_Mult_nn(p, n, r);
}
// test if the monomial is a constant as a vector component
// i.e., test if all exponents are zero
static inline BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
{
//p_LmCheckPolyRing(p, r);
int i = r->VarL_Size - 1;
do
{
if (p->exp[r->VarL_Offset[i]] != 0)
return FALSE;
i--;
}
while (i >= 0);
return TRUE;
}
// test if monomial is a constant, i.e. if all exponents and the component
// is zero
static inline BOOLEAN p_LmIsConstant(const poly p, const ring r)
{
if (p_LmIsConstantComp(p, r))
return (p_GetComp(p, r) == 0);
return FALSE;
}
// returns Copy(p)*m, does neither destroy p nor m
static inline poly pp_Mult_mm(poly p, poly m, const ring r)
{
if (p_LmIsConstant(m, r))
return pp_Mult_nn(p, pGetCoeff(m), r);
else
{
return r->p_Procs->pp_Mult_mm(p, m, r);
}
}
// returns p*m, destroys p, const: m
static inline poly p_Mult_mm(poly p, poly m, const ring r)
{
if (p_LmIsConstant(m, r))
return p_Mult_nn(p, pGetCoeff(m), r);
else
return r->p_Procs->p_Mult_mm(p, m, r);
}
static inline poly p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, int lq,
const poly spNoether, const ring r)
{
int shorter;
const poly res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, spNoether, r);
lp += lq - shorter;
// assume( lp == pLength(res) );
return res;
}
// return p - m*Copy(q), destroys p; const: p,m
static inline poly p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, const ring r)
{
int shorter;
return r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r);
}
// returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r)
{
int shorter;
return r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r);
}
// returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
// if lp is length of p on input then lp is length of returned poly on output
static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, int &lp, const poly m, const ring r)
{
int shorter;
poly pp = r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r);
lp -= shorter;
return pp;
}
// returns -p, destroys p
static inline poly p_Neg(poly p, const ring r)
{
return r->p_Procs->p_Neg(p, r);
}
extern poly _p_Mult_q(poly p, poly q, const int copy, const ring r);
// returns p*q, destroys p and q
static inline poly p_Mult_q(poly p, poly q, const ring r)
{
assume( (p != q) || (p == NULL && q == NULL) );
if (p == NULL)
{
r->p_Procs->p_Delete(&q, r);
return NULL;
}
if (q == NULL)
{
r->p_Procs->p_Delete(&p, r);
return NULL;
}
if (pNext(p) == NULL)
{
#ifdef HAVE_PLURAL
if (rIsPluralRing(r))
q = nc_mm_Mult_p(p, q, r);
else
#endif /* HAVE_PLURAL */
q = r->p_Procs->p_Mult_mm(q, p, r);
r->p_Procs->p_Delete(&p, r);
return q;
}
if (pNext(q) == NULL)
{
// NEEDED
#ifdef HAVE_PLURAL
/* if (rIsPluralRing(r))
p = gnc_p_Mult_mm(p, q, r); // ???
else*/
#endif /* HAVE_PLURAL */
p = r->p_Procs->p_Mult_mm(p, q, r);
r->p_Procs->p_Delete(&q, r);
return p;
}
#ifdef HAVE_PLURAL
if (rIsPluralRing(r))
return _nc_p_Mult_q(p, q, r);
else
#endif
return _p_Mult_q(p, q, 0, r);
}
// returns p*q, does neither destroy p nor q
static inline poly pp_Mult_qq(poly p, poly q, const ring r)
{
if (p == NULL || q == NULL) return NULL;
if (pNext(p) == NULL)
{
#ifdef HAVE_PLURAL
if (rIsPluralRing(r))
return nc_mm_Mult_pp(p, q, r);
#endif
return r->p_Procs->pp_Mult_mm(q, p, r);
}
if (pNext(q) == NULL)
{
return r->p_Procs->pp_Mult_mm(p, q, r);
}
poly qq = q;
if (p == q)
qq = p_Copy(q, r);
poly res;
#ifdef HAVE_PLURAL
if (rIsPluralRing(r))
res = _nc_pp_Mult_qq(p, qq, r);
else
#endif
res = _p_Mult_q(p, qq, 1, r);
if (qq != q)
p_Delete(&qq, r);
return res;
}
// returns p + m*q destroys p, const: q, m
static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq,
const ring r)
{
#ifdef HAVE_PLURAL
if (rIsPluralRing(r))
return nc_p_Plus_mm_Mult_qq(p, m, q, lp, lq, r);
#endif
// this should be implemented more efficiently
poly res;
int shorter;
number n_old = pGetCoeff(m);
number n_neg = n_Copy(n_old, r->cf);
n_neg = n_InpNeg(n_neg, r->cf);
pSetCoeff0(m, n_neg);
res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r);
lp = (lp + lq) - shorter;
pSetCoeff0(m, n_old);
n_Delete(&n_neg, r->cf);
return res;
}
static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, const ring r)
{
int lp = 0, lq = 0;
return p_Plus_mm_Mult_qq(p, m, q, lp, lq, r);
}
// returns merged p and q, assumes p and q have no monomials which are equal
static inline poly p_Merge_q(poly p, poly q, const ring r)
{
assume( (p != q) || (p == NULL && q == NULL) );
return r->p_Procs->p_Merge_q(p, q, r);
}
// like p_SortMerge, except that p may have equal monimals
static inline poly p_SortAdd(poly p, const ring r, BOOLEAN revert= FALSE)
{
if (revert) p = pReverse(p);
return sBucketSortAdd(p, r);
}
// sorts p using bucket sort: returns sorted poly
// assumes that monomials of p are all different
// reverses it first, if revert == TRUE, use this if input p is "almost" sorted
// correctly
static inline poly p_SortMerge(poly p, const ring r, BOOLEAN revert= FALSE)
{
if (revert) p = pReverse(p);
return sBucketSortMerge(p, r);
}
/***************************************************************
*
* I/O
*
***************************************************************/
static inline char* p_String(poly p, ring p_ring)
{
return p_String(p, p_ring, p_ring);
}
static inline void p_String0(poly p, ring p_ring)
{
p_String0(p, p_ring, p_ring);
}
static inline void p_Write(poly p, ring p_ring)
{
p_Write(p, p_ring, p_ring);
}
static inline void p_Write0(poly p, ring p_ring)
{
p_Write0(p, p_ring, p_ring);
}
static inline void p_wrp(poly p, ring p_ring)
{
p_wrp(p, p_ring, p_ring);
}
#if PDEBUG > 0
#define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
do \
{ \
int _cmp = p_LmCmp(p,q,r); \
if (_cmp == 0) actionE; \
if (_cmp == 1) actionG; \
actionS; \
} \
while(0)
#else
#define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
p_MemCmp_LengthGeneral_OrdGeneral(p->exp, q->exp, r->CmpL_Size, r->ordsgn, \
actionE, actionG, actionS)
#endif
#define pDivAssume(x) do {} while (0)
/***************************************************************
*
* Allocation/Initalization/Deletion
*
***************************************************************/
// adjustments for negative weights
static inline void p_MemAdd_NegWeightAdjust(poly p, const ring r)
{
if (r->NegWeightL_Offset != NULL)
{
for (int i=r->NegWeightL_Size-1; i>=0; i--)
{
p->exp[r->NegWeightL_Offset[i]] -= POLY_NEGWEIGHT_OFFSET;
}
}
}
static inline void p_MemSub_NegWeightAdjust(poly p, const ring r)
{
if (r->NegWeightL_Offset != NULL)
{
for (int i=r->NegWeightL_Size-1; i>=0; i--)
{
p->exp[r->NegWeightL_Offset[i]] += POLY_NEGWEIGHT_OFFSET;
}
}
}
// ExpVextor(d_p) = ExpVector(s_p)
static inline void p_ExpVectorCopy(poly d_p, poly s_p, const ring r)
{
p_LmCheckPolyRing1(d_p, r);
p_LmCheckPolyRing1(s_p, r);
memcpy(d_p->exp, s_p->exp, r->ExpL_Size*sizeof(long));
}
static inline poly p_Init(const ring r, omBin bin)
{
p_CheckRing1(r);
pAssume1(bin != NULL && omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
poly p;
omTypeAlloc0Bin(poly, p, bin);
p_MemAdd_NegWeightAdjust(p, r);
p_SetRingOfLm(p, r);
return p;
}
static inline poly p_Init(const ring r)
{
return p_Init(r, r->PolyBin);
}
static inline poly p_LmInit(poly p, const ring r)
{
p_LmCheckPolyRing1(p, r);
poly np;
omTypeAllocBin(poly, np, r->PolyBin);
p_SetRingOfLm(np, r);
memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
pNext(np) = NULL;
pSetCoeff0(np, NULL);
return np;
}
static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r, omBin d_bin)
{
p_LmCheckPolyRing1(s_p, s_r);
p_CheckRing(d_r);
pAssume1(d_r->N <= s_r->N);
poly d_p = p_Init(d_r, d_bin);
for (unsigned i=d_r->N; i!=0; i--)
{
p_SetExp(d_p, i, p_GetExp(s_p, i,s_r), d_r);
}
if (rRing_has_Comp(d_r))
{
p_SetComp(d_p, p_GetComp(s_p,s_r), d_r);
}
p_Setm(d_p, d_r);
return d_p;
}
static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r)
{
pAssume1(d_r != NULL);
return p_LmInit(s_p, s_r, d_r, d_r->PolyBin);
}
// set all exponents l..k to 0, assume exp. k+1..n and 1..l-1 are in
// different blocks
// set coeff to 1
static inline poly p_GetExp_k_n(poly p, int l, int k, const ring r)
{
if (p == NULL) return NULL;
p_LmCheckPolyRing1(p, r);
poly np;
omTypeAllocBin(poly, np, r->PolyBin);
p_SetRingOfLm(np, r);
memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
pNext(np) = NULL;
pSetCoeff0(np, n_Init(1, r->cf));
int i;
for(i=l;i<=k;i++)
{
//np->exp[(r->VarOffset[i] & 0xffffff)] =0;
p_SetExp(np,i,0,r);
}
p_Setm(np,r);
return np;
}
// simialar to p_ShallowCopyDelete but does it only for leading monomial
static inline poly p_LmShallowCopyDelete(poly p, const ring r)
{
p_LmCheckPolyRing1(p, r);
pAssume1(omSizeWOfBin(bin) == omSizeWOfBin(r->PolyBin));
poly new_p = p_New(r);
memcpy(new_p->exp, p->exp, r->ExpL_Size*sizeof(long));
pSetCoeff0(new_p, pGetCoeff(p));
pNext(new_p) = pNext(p);
omFreeBinAddr(p);
return new_p;
}
/***************************************************************
*
* Operation on ExpVectors
*
***************************************************************/
// ExpVector(p1) += ExpVector(p2)
static inline void p_ExpVectorAdd(poly p1, poly p2, const ring r)
{
p_LmCheckPolyRing1(p1, r);
p_LmCheckPolyRing1(p2, r);
#if PDEBUG >= 1
for (int i=1; i<=r->N; i++)
pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask);
pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0);
#endif
p_MemAdd_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size);
p_MemAdd_NegWeightAdjust(p1, r);
}
// ExpVector(pr) = ExpVector(p1) + ExpVector(p2)
static inline void p_ExpVectorSum(poly pr, poly p1, poly p2, const ring r)
{
p_LmCheckPolyRing1(p1, r);
p_LmCheckPolyRing1(p2, r);
p_LmCheckPolyRing1(pr, r);
#if PDEBUG >= 1
for (int i=1; i<=r->N; i++)
pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask);
pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0);
#endif
p_MemSum_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size);
p_MemAdd_NegWeightAdjust(pr, r);
}
// ExpVector(p1) -= ExpVector(p2)
static inline void p_ExpVectorSub(poly p1, poly p2, const ring r)
{
p_LmCheckPolyRing1(p1, r);
p_LmCheckPolyRing1(p2, r);
#if PDEBUG >= 1
for (int i=1; i<=r->N; i++)
pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r));
pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0 ||
p_GetComp(p1, r) == p_GetComp(p2, r));
#endif
p_MemSub_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size);
p_MemSub_NegWeightAdjust(p1, r);
}
// ExpVector(p1) += ExpVector(p2) - ExpVector(p3)
static inline void p_ExpVectorAddSub(poly p1, poly p2, poly p3, const ring r)
{
p_LmCheckPolyRing1(p1, r);
p_LmCheckPolyRing1(p2, r);
p_LmCheckPolyRing1(p3, r);
#if PDEBUG >= 1
for (int i=1; i<=r->N; i++)
pAssume1(p_GetExp(p1, i, r) + p_GetExp(p2, i, r) >= p_GetExp(p3, i, r));
pAssume1(p_GetComp(p1, r) == 0 ||
(p_GetComp(p2, r) - p_GetComp(p3, r) == 0) ||
(p_GetComp(p1, r) == p_GetComp(p2, r) - p_GetComp(p3, r)));
#endif
p_MemAddSub_LengthGeneral(p1->exp, p2->exp, p3->exp, r->ExpL_Size);
// no need to adjust in case of NegWeights
}
// ExpVector(pr) = ExpVector(p1) - ExpVector(p2)
static inline void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r)
{
p_LmCheckPolyRing1(p1, r);
p_LmCheckPolyRing1(p2, r);
p_LmCheckPolyRing1(pr, r);
#if PDEBUG >= 2
for (int i=1; i<=r->N; i++)
pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r));
pAssume1(!rRing_has_Comp(r) || p_GetComp(p1, r) == p_GetComp(p2, r));
#endif
p_MemDiff_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size);
p_MemSub_NegWeightAdjust(pr, r);
}
static inline BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r)
{
p_LmCheckPolyRing1(p1, r);
p_LmCheckPolyRing1(p2, r);
unsigned i = r->ExpL_Size;
unsigned long *ep = p1->exp;
unsigned long *eq = p2->exp;
do
{
i--;
if (ep[i] != eq[i]) return FALSE;
}
while (i!=0);
return TRUE;
}
static inline long p_Totaldegree(poly p, const ring r)
{
p_LmCheckPolyRing1(p, r);
unsigned long s = p_GetTotalDegree(p->exp[r->VarL_Offset[0]],
r,
r->ExpPerLong);
for (unsigned i=r->VarL_Size-1; i!=0; i--)
{
s += p_GetTotalDegree(p->exp[r->VarL_Offset[i]], r,r->ExpPerLong);
}
return (long)s;
}
static inline void p_GetExpV(poly p, int *ev, const ring r)
{
p_LmCheckPolyRing1(p, r);
for (unsigned j = r->N; j!=0; j--)
ev[j] = p_GetExp(p, j, r);
ev[0] = p_GetComp(p, r);
}
static inline void p_SetExpV(poly p, int *ev, const ring r)
{
p_LmCheckPolyRing1(p, r);
for (unsigned j = r->N; j!=0; j--)
p_SetExp(p, j, ev[j], r);
p_SetComp(p, ev[0],r);
p_Setm(p, r);
}
/***************************************************************
*
* Comparison w.r.t. monomial ordering
*
***************************************************************/
static inline int p_LmCmp(poly p, poly q, const ring r)
{
p_LmCheckPolyRing1(p, r);
p_LmCheckPolyRing1(q, r);
const unsigned long* _s1 = ((unsigned long*) p->exp);
const unsigned long* _s2 = ((unsigned long*) q->exp);
register unsigned long _v1;
register unsigned long _v2;
const unsigned long _l = r->CmpL_Size;
register unsigned long _i=0;
LengthGeneral_OrdGeneral_LoopTop:
_v1 = _s1[_i];
_v2 = _s2[_i];
if (_v1 == _v2)
{
_i++;
if (_i == _l) return 0;
goto LengthGeneral_OrdGeneral_LoopTop;
}
const long* _ordsgn = (long*) r->ordsgn;
if (_v1 > _v2)
{
if (_ordsgn[_i] == 1) return 1;
return -1;
}
if (_ordsgn[_i] == 1) return -1;
return 1;
}
// The coefficient will be compared in absolute value
static inline int p_LtCmp(poly p, poly q, const ring r)
{
int res = p_LmCmp(p,q,r);
if(res == 0)
{
if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
return res;
number pc = n_Copy(p_GetCoeff(p,r),r->cf);
number qc = n_Copy(p_GetCoeff(q,r),r->cf);
if(!n_GreaterZero(pc,r->cf))
pc = n_InpNeg(pc,r->cf);
if(!n_GreaterZero(qc,r->cf))
qc = n_InpNeg(qc,r->cf);
if(n_Greater(pc,qc,r->cf))
res = 1;
else if(n_Greater(qc,pc,r->cf))
res = -1;
else if(n_Equal(pc,qc,r->cf))
res = 0;
n_Delete(&pc,r->cf);
n_Delete(&qc,r->cf);
}
return res;
}
// The coefficient will be compared in absolute value
static inline int p_LtCmpNoAbs(poly p, poly q, const ring r)
{
int res = p_LmCmp(p,q,r);
if(res == 0)
{
if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
return res;
number pc = p_GetCoeff(p,r);
number qc = p_GetCoeff(q,r);
if(n_Greater(pc,qc,r->cf))
res = 1;
if(n_Greater(qc,pc,r->cf))
res = -1;
if(n_Equal(pc,qc,r->cf))
res = 0;
}
return res;
}
#ifdef HAVE_RINGS
// This is the equivalent of pLmCmp(p,q) != -currRing->OrdSgn for rings
// It is used in posInLRing and posInTRing
static inline int p_LtCmpOrdSgnDiffM(poly p, poly q, const ring r)
{
if(r->OrdSgn == 1)
{
return(p_LtCmp(p,q,r) == 1);
}
else
{
return(p_LmCmp(p,q,r) == -1);
}
}
#endif
#ifdef HAVE_RINGS
// This is the equivalent of pLmCmp(p,q) != currRing->OrdSgn for rings
// It is used in posInLRing and posInTRing
static inline int p_LtCmpOrdSgnDiffP(poly p, poly q, const ring r)
{
if(r->OrdSgn == 1)
{
return(p_LmCmp(p,q,r) == -1);
}
else
{
return(p_LtCmp(p,q,r) != -1);
}
}
#endif
#ifdef HAVE_RINGS
// This is the equivalent of pLmCmp(p,q) == -currRing->OrdSgn for rings
// It is used in posInLRing and posInTRing
static inline int p_LtCmpOrdSgnEqM(poly p, poly q, const ring r)
{
return(p_LtCmp(p,q,r) == -r->OrdSgn);
}
#endif
#ifdef HAVE_RINGS
// This is the equivalent of pLmCmp(p,q) == currRing->OrdSgn for rings
// It is used in posInLRing and posInTRing
static inline int p_LtCmpOrdSgnEqP(poly p, poly q, const ring r)
{
return(p_LtCmp(p,q,r) == r->OrdSgn);
}
#endif
/// returns TRUE if p1 is a skalar multiple of p2
/// assume p1 != NULL and p2 != NULL
BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r);
/***************************************************************
*
* Comparisons: they are all done without regarding coeffs
*
***************************************************************/
#define p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
_p_LmCmpAction(p, q, r, actionE, actionG, actionS)
// returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !!
#define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r)
// pCmp: args may be NULL
// returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))
static inline int p_Cmp(poly p1, poly p2, ring r)
{
if (p2==NULL)
return 1;
if (p1==NULL)
return -1;
return p_LmCmp(p1,p2,r);
}
/***************************************************************
*
* divisibility
*
***************************************************************/
/// return: FALSE, if there exists i, such that a->exp[i] > b->exp[i]
/// TRUE, otherwise
/// (1) Consider long vars, instead of single exponents
/// (2) Clearly, if la > lb, then FALSE
/// (3) Suppose la <= lb, and consider first bits of single exponents in l:
/// if TRUE, then value of these bits is la ^ lb
/// if FALSE, then la-lb causes an "overflow" into one of those bits, i.e.,
/// la ^ lb != la - lb
static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, poly b, const ring r)
{
int i=r->VarL_Size - 1;
unsigned long divmask = r->divmask;
unsigned long la, lb;
if (r->VarL_LowIndex >= 0)
{
i += r->VarL_LowIndex;
do
{
la = a->exp[i];
lb = b->exp[i];
if ((la > lb) ||
(((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask)))
{
pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == FALSE);
return FALSE;
}
i--;
}
while (i>=r->VarL_LowIndex);
}
else
{
do
{
la = a->exp[r->VarL_Offset[i]];
lb = b->exp[r->VarL_Offset[i]];
if ((la > lb) ||
(((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask)))
{
pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == FALSE);
return FALSE;
}
i--;
}
while (i>=0);
}
/*#ifdef HAVE_RINGS
pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf));
return (!rField_is_Ring(r)) || n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf);
#else
*/
pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == TRUE);
return TRUE;
//#endif
}
static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, const ring r_a, poly b, const ring r_b)
{
int i=r_a->N;
pAssume1(r_a->N == r_b->N);
do
{
if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b))
return FALSE;
i--;
}
while (i);
/*#ifdef HAVE_RINGS
return n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf);
#else
*/
return TRUE;
//#endif
}
#ifdef HAVE_RATGRING
static inline BOOLEAN _p_LmDivisibleByNoCompPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end)
{
int i=end;
pAssume1(r_a->N == r_b->N);
do
{
if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b))
return FALSE;
i--;
}
while (i>=start);
/*#ifdef HAVE_RINGS
return n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf);
#else
*/
return TRUE;
//#endif
}
static inline BOOLEAN _p_LmDivisibleByPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end)
{
if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b))
return _p_LmDivisibleByNoCompPart(a, r_a, b, r_b,start,end);
return FALSE;
}
static inline BOOLEAN p_LmDivisibleByPart(poly a, poly b, const ring r,const int start, const int end)
{
p_LmCheckPolyRing1(b, r);
pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r));
if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
return _p_LmDivisibleByNoCompPart(a, r, b, r,start, end);
return FALSE;
}
#endif
static inline BOOLEAN _p_LmDivisibleBy(poly a, poly b, const ring r)
{
if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
return _p_LmDivisibleByNoComp(a, b, r);
return FALSE;
}
static inline BOOLEAN _p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
{
if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b))
return _p_LmDivisibleByNoComp(a, r_a, b, r_b);
return FALSE;
}
static inline BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, const ring r)
{
p_LmCheckPolyRing1(a, r);
p_LmCheckPolyRing1(b, r);
return _p_LmDivisibleByNoComp(a, b, r);
}
static inline BOOLEAN p_LmDivisibleByNoComp(poly a, const ring ra, poly b, const ring rb)
{
p_LmCheckPolyRing1(a, ra);
p_LmCheckPolyRing1(b, rb);
return _p_LmDivisibleByNoComp(a, ra, b, rb);
}
static inline BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
{
p_LmCheckPolyRing1(b, r);
pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r));
if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
return _p_LmDivisibleByNoComp(a, b, r);
return FALSE;
}
static inline BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
{
pIfThen1(b!=NULL, p_LmCheckPolyRing1(b, r));
pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r));
if (a != NULL && (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r)))
return _p_LmDivisibleByNoComp(a,b,r);
return FALSE;
}
static inline BOOLEAN p_DivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
{
pIfThen1(b!=NULL, p_LmCheckPolyRing1(b, r_b));
pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r_a));
if (a != NULL) {
return _p_LmDivisibleBy(a, r_a, b, r_b);
}
return FALSE;
}
static inline BOOLEAN p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
{
p_LmCheckPolyRing(a, r_a);
p_LmCheckPolyRing(b, r_b);
return _p_LmDivisibleBy(a, r_a, b, r_b);
}
static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a,
poly b, unsigned long not_sev_b, const ring r)
{
p_LmCheckPolyRing1(a, r);
p_LmCheckPolyRing1(b, r);
#ifndef PDIV_DEBUG
_pPolyAssume2(p_GetShortExpVector(a, r) == sev_a, a, r);
_pPolyAssume2(p_GetShortExpVector(b, r) == ~ not_sev_b, b, r);
if (sev_a & not_sev_b)
{
pAssume1(p_LmDivisibleByNoComp(a, b, r) == FALSE);
return FALSE;
}
return p_LmDivisibleBy(a, b, r);
#else
return pDebugLmShortDivisibleBy(a, sev_a, r, b, not_sev_b, r);
#endif
}
static inline BOOLEAN p_LmShortDivisibleByNoComp(poly a, unsigned long sev_a,
poly b, unsigned long not_sev_b, const ring r)
{
p_LmCheckPolyRing1(a, r);
p_LmCheckPolyRing1(b, r);
#ifndef PDIV_DEBUG
_pPolyAssume2(p_GetShortExpVector(a, r) == sev_a, a, r);
_pPolyAssume2(p_GetShortExpVector(b, r) == ~ not_sev_b, b, r);
if (sev_a & not_sev_b)
{
pAssume1(p_LmDivisibleByNoComp(a, b, r) == FALSE);
return FALSE;
}
return p_LmDivisibleByNoComp(a, b, r);
#else
return pDebugLmShortDivisibleByNoComp(a, sev_a, r, b, not_sev_b, r);
#endif
}
static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, const ring r_a,
poly b, unsigned long not_sev_b, const ring r_b)
{
p_LmCheckPolyRing1(a, r_a);
p_LmCheckPolyRing1(b, r_b);
#ifndef PDIV_DEBUG
_pPolyAssume2(p_GetShortExpVector(a, r_a) == sev_a, a, r_a);
_pPolyAssume2(p_GetShortExpVector(b, r_b) == ~ not_sev_b, b, r_b);
if (sev_a & not_sev_b)
{
pAssume1(_p_LmDivisibleByNoComp(a, r_a, b, r_b) == FALSE);
return FALSE;
}
return _p_LmDivisibleBy(a, r_a, b, r_b);
#else
return pDebugLmShortDivisibleBy(a, sev_a, r_a, b, not_sev_b, r_b);
#endif
}
/***************************************************************
*
* Misc things on Lm
*
***************************************************************/
// like the respective p_LmIs* routines, except that p might be empty
static inline BOOLEAN p_IsConstantComp(const poly p, const ring r)
{
if (p == NULL) return TRUE;
return (pNext(p)==NULL) && p_LmIsConstantComp(p, r);
}
static inline BOOLEAN p_IsConstant(const poly p, const ring r)
{
if (p == NULL) return TRUE;
p_Test(p, r);
return (pNext(p)==NULL) && p_LmIsConstant(p, r);
}
/// either poly(1) or gen(k)?!
static inline BOOLEAN p_IsOne(const poly p, const ring R)
{
p_Test(p, R);
return (p_IsConstant(p, R) && n_IsOne(p_GetCoeff(p, R), R->cf));
}
static inline BOOLEAN p_IsConstantPoly(const poly p, const ring r)
{
p_Test(p, r);
poly pp=p;
while(pp!=NULL)
{
if (! p_LmIsConstantComp(pp, r))
return FALSE;
pIter(pp);
}
return TRUE;
}
static inline BOOLEAN p_IsUnit(const poly p, const ring r)
{
if (p == NULL) return FALSE;
if (rField_is_Ring(r))
return (p_LmIsConstant(p, r) && n_IsUnit(pGetCoeff(p),r->cf));
return p_LmIsConstant(p, r);
}
static inline BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2,
const ring r)
{
p_LmCheckPolyRing(p1, r);
p_LmCheckPolyRing(p2, r);
unsigned long l1, l2, divmask = r->divmask;
int i;
for (i=0; i<r->VarL_Size; i++)
{
l1 = p1->exp[r->VarL_Offset[i]];
l2 = p2->exp[r->VarL_Offset[i]];
// do the divisiblity trick
if ( (l1 > ULONG_MAX - l2) ||
(((l1 & divmask) ^ (l2 & divmask)) != ((l1 + l2) & divmask)))
return FALSE;
}
return TRUE;
}
void p_Split(poly p, poly * r); /*p => IN(p), r => REST(p) */
BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r);
poly p_mInit(const char *s, BOOLEAN &ok, const ring r); /* monom s -> poly, interpreter */
const char * p_Read(const char *s, poly &p,const ring r); /* monom -> poly */
poly p_Divide(poly a, poly b, const ring r);
poly p_DivideM(poly a, poly b, const ring r);
poly p_Div_nn(poly p, const number n, const ring r);
// returns the LCM of the head terms of a and b in *m, does not p_Setm
void p_Lcm(const poly a, const poly b, poly m, const ring r);
// returns the LCM of the head terms of a and b, does p_Setm
poly p_Lcm(const poly a, const poly b, const ring r);
#ifdef HAVE_RATGRING
poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r);
poly p_GetCoeffRat(poly p, int ishift, ring r);
void p_LmDeleteAndNextRat(poly *p, int ishift, ring r);
void p_ContentRat(poly &ph, const ring r);
#endif /* ifdef HAVE_RATGRING */
poly p_Diff(poly a, int k, const ring r);
poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r);
int p_Weight(int c, const ring r);
/// assumes that p and divisor are univariate polynomials in r,
/// mentioning the same variable;
/// assumes divisor != NULL;
/// p may be NULL;
/// assumes a global monomial ordering in r;
/// performs polynomial division of p by divisor:
/// - afterwards p contains the remainder of the division, i.e.,
/// p_before = result * divisor + p_afterwards;
/// - if needResult == TRUE, then the method computes and returns 'result',
/// otherwise NULL is returned (This parametrization can be used when
/// one is only interested in the remainder of the division. In this
/// case, the method will be slightly faster.)
/// leaves divisor unmodified
poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r);
/* syszygy stuff */
BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r);
void p_VectorHasUnit(poly p, int * k, int * len, const ring r);
poly p_TakeOutComp1(poly * p, int k, const ring r);
// Splits *p into two polys: *q which consists of all monoms with
// component == comp and *p of all other monoms *lq == pLength(*q)
// On return all components pf *q == 0
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r);
// This is something weird -- Don't use it, unless you know what you are doing
poly p_TakeOutComp(poly * p, int k, const ring r);
void p_DeleteComp(poly * p,int k, const ring r);
/*-------------ring management:----------------------*/
// resets the pFDeg and pLDeg: if pLDeg is not given, it is
// set to currRing->pLDegOrig, i.e. to the respective LDegProc which
// only uses pFDeg (and not pDeg, or pTotalDegree, etc).
// If you use this, make sure your procs does not make any assumptions
// on ordering and/or OrdIndex -- otherwise they might return wrong results
// on strat->tailRing
void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg = NULL);
// restores pFDeg and pLDeg:
void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg);
/*-------------pComp for syzygies:-------------------*/
void p_SetModDeg(intvec *w, ring r);
/*------------ Jet ----------------------------------*/
poly pp_Jet(poly p, int m, const ring R);
poly p_Jet(poly p, int m,const ring R);
poly pp_JetW(poly p, int m, short *w, const ring R);
poly p_JetW(poly p, int m, short *w, const ring R);
poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst);
poly p_PermPoly (poly p, const int * perm,const ring OldRing, const ring dst,
nMapFunc nMap, const int *par_perm=NULL, int OldPar=0,
BOOLEAN use_mult=FALSE);
/*----------------------------------------------------*/
poly p_Series(int n,poly p,poly u, intvec *w, const ring R);
/*----------------------------------------------------*/
int p_Var(poly mi, const ring r);
/// the minimal index of used variables - 1
int p_LowVar (poly p, const ring r);
/*----------------------------------------------------*/
/// shifts components of the vector p by i
void p_Shift (poly * p,int i, const ring r);
/*----------------------------------------------------*/
int p_Compare(const poly a, const poly b, const ring R);
/// polynomial gcd for f=mon
poly p_GcdMon(poly f, poly g, const ring r);
/// divide polynomial by monomial
poly p_Div_mm(poly p, const poly m, const ring r);
#endif // P_POLYS_H
|