1424{
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1445 {
1446 PrintS(
"Hilbert Series:\n 0\n");
1447 return;
1448 }
1451 {
1454 }
1455 else
1456 {
1458 {
1460 {
1461 WerrorS(
"wrong input: it is not an infinitely gen. case");
1462 return;
1463 }
1466 }
1467 else
1469 }
1470 std::vector<ideal >
idorb;
1471 std::vector< poly >
polist;
1472
1475
1477
1478 std::vector< std::vector<int> >
posMat;
1480 std::vector<int> C;
1481
1483 unsigned long lpcnt = 0;
1484
1487
1489 {
1493 {
1495 {
1496 C.push_back(1);
1497 }
1498 else
1499 C.push_back(0);
1500 }
1501 else
1502 {
1503 C.push_back(1);
1504 }
1505
1508
1509 for(is = 1; is <=
lV; is++)
1510 {
1512
1513
1514
1515
1516
1517
1522
1523
1524
1525
1526
1528
1531
1533 {
1535
1538 }
1539 else
1540 {
1544 }
1545 }
1548 }
1552 Print(
"\nlength of the Orbit = %d",
lO);
1554
1556 {
1557 Print(
"words description of the Orbit: \n");
1558 for(is = 0; is <
lO; is++)
1559 {
1562 }
1564 PrintS(
"\nmaximal degree, #(sum_j R(w,w_j))");
1566 for(is = 0; is <
lO; is++)
1567 {
1569 {
1571 }
1572 else
1573 {
1575 }
1576 }
1577 }
1578
1579 for(is =
idorb.size()-1; is >= 0; is--)
1580 {
1582 }
1583 for(is =
polist.size()-1; is >= 0; is--)
1584 {
1586 }
1587
1590
1596 {
1598 {
1600 {
1603 }
1604 }
1605 }
1606
1612 {
1616 }
1617 else
1618 {
1620 for(is = 0; is <
lV; is++)
1621 {
1622 tt[is] = (
char*)
omAlloc(7*
sizeof(
char));
1624 }
1626 }
1627
1630 char**
xx = (
char**)
omAlloc(
sizeof(
char*));
1634
1635
1636
1639 poly rc;
1640
1642 {
1644 {
1646 {
1648 {
1651 }
1652 }
1653 }
1654 }
1655 else
1656 {
1658 {
1660 {
1665 }
1666 }
1667 }
1668
1670 {
1672 {
1674 }
1675 }
1676
1680
1682
1684 {
1685 PrintS(
"\nlinear system:\n");
1687 {
1689 {
1692 {
1697 }
1699 }
1700 PrintS(
"where H(1) represents the series corresp. to input ideal\n");
1701 PrintS(
"and i^th summand in the rhs of an eqn. is according\n");
1702 PrintS(
"to the right colon map corresp. to the i^th variable\n");
1703 }
1704 else
1705 {
1707 {
1710 {
1715 }
1717 }
1718 PrintS(
"where H(1) represents the series corresp. to input ideal\n");
1719 }
1720 }
1723 C.resize(0);
1729
1730
1731
1732
1735
1736
1737
1738
1739
1748
1750 Print(
"Hilbert series:");
1754 {
1756 }
1757 else
1758 {
1759 for(is =
lV-1; is >= 0; is--)
1760
1762 }
1768}
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
static FORCE_INLINE number n_Param(const int iParameter, const coeffs r)
return the (iParameter^th) parameter as a NEW number NOTE: parameter numbering: 1....
@ n_transExt
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
const CanonicalForm int s
void WerrorS(const char *s)
static int positionInOrbitTruncationCase(ideal I, poly w, std::vector< ideal > idorb, std::vector< poly > polist, int, int trunDegHs)
static ideal colonIdeal(ideal S, poly w, int lV, ideal Jwi, int trunDegHs)
static int positionInOrbit_FG_Case(ideal I, poly, std::vector< ideal > idorb, std::vector< poly >, int, int)
static int positionInOrbit_IG_Case(ideal I, poly w, std::vector< ideal > idorb, std::vector< poly > polist, int trInd, int)
static ideal minimalMonomialGenSet(ideal I)
#define idDelete(H)
delete an ideal
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
bool unitMatrix(const int n, matrix &unitMat, const ring R)
Creates a new matrix which is the (nxn) unit matrix, and returns true in case of success.
void luDecomp(const matrix aMat, matrix &pMat, matrix &lMat, matrix &uMat, const ring R)
LU-decomposition of a given (m x n)-matrix.
bool luSolveViaLUDecomp(const matrix pMat, const matrix lMat, const matrix uMat, const matrix bVec, matrix &xVec, matrix &H)
Solves the linear system A * x = b, where A is an (m x n)-matrix which is given by its LU-decompositi...
void mp_Delete(matrix *a, const ring r)
matrix mp_Sub(matrix a, matrix b, const ring R)
matrix mpNew(int r, int c)
create a r x c zero-matrix
#define MATELEM(mat, i, j)
1-based access to matrix
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
The main handler for Singular numbers which are suitable for Singular polynomials.
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
static poly p_Add_q(poly p, poly q, const ring r)
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent @Note: VarOffset encodes the position in p->exp
static void p_Setm(poly p, const ring r)
static number p_SetCoeff(poly p, number n, ring r)
static long p_Totaldegree(poly p, const ring r)
void rChangeCurrRing(ring r)
#define pCopy(p)
return a copy of the poly
void StringSetS(const char *st)
void PrintS(const char *s)
ring rDefault(const coeffs cf, int N, char **n, int ord_size, rRingOrder_t *ord, int *block0, int *block1, int **wvhdl, unsigned long bitmask)
ideal idInit(int idsize, int rank)
initialise an ideal / module
struct for passing initialization parameters to naInitChar