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hilb.cc File Reference
#include "kernel/mod2.h"
#include "misc/mylimits.h"
#include "misc/intvec.h"
#include "kernel/combinatorics/hilb.h"
#include "kernel/combinatorics/stairc.h"
#include "kernel/combinatorics/hutil.h"
#include "polys/monomials/ring.h"
#include "polys/monomials/p_polys.h"
#include "polys/simpleideals.h"
#include "kernel/ideals.h"
#include "polys/ext_fields/transext.h"
#include "coeffs/coeffs.h"
#include "kernel/linear_algebra/linearAlgebra.h"
#include "coeffs/numbers.h"
#include <vector>
#include "Singular/ipshell.h"
#include <ctime>
#include <iostream>

Go to the source code of this file.

Macros

#define omsai   1
 

Functions

static int hMinModulweight (intvec *modulweight)
 
static void hHilbEst (scfmon stc, int Nstc, varset var, int Nvar)
 
static int * hAddHilb (int Nv, int x, int *pol, int *lp)
 
static void hLastHilb (scmon pure, int Nv, varset var, int *pol, int lp)
 
static void hHilbStep (scmon pure, scfmon stc, int Nstc, varset var, int Nvar, int *pol, int Lpol)
 
static void hWDegree (intvec *wdegree)
 
static void SortByDeg_p (ideal I, poly p)
 !!!!!!!!!!!!!!!!!!!! Just for Monomial Ideals !!!!!!!!!!!!!!!!!!!!!!!!!!!! More...
 
static ideal SortByDeg (ideal I)
 
ideal idQuotMon (ideal Iorig, ideal p)
 
static void idAddMon (ideal I, ideal p)
 
static poly ChoosePVar (ideal I)
 
static poly ChoosePJL (ideal I)
 
static poly ChooseP (ideal I)
 
static poly SearchP (ideal I)
 searches for a monomial of degree d>=2 and divides it by a variable (result monomial of deg d-1) More...
 
static bool JustVar (ideal I)
 
static void eulerchar (ideal I, int variables, mpz_ptr ec)
 
static poly SqFree (ideal I)
 
static bool IsIn (poly p, ideal I)
 
static poly LCMmon (ideal I)
 
void rouneslice (ideal I, ideal S, poly q, poly x, int &prune, int &moreprune, int &steps, int &NNN, mpz_ptr &hilbertcoef, int *&hilbpower)
 
void slicehilb (ideal I)
 
static intvechSeries (ideal S, intvec *modulweight, int, intvec *wdegree, ideal Q, ring tailRing)
 
intvechHstdSeries (ideal S, intvec *modulweight, intvec *wdegree, ideal Q, ring tailRing)
 
intvechFirstSeries (ideal S, intvec *modulweight, ideal Q, intvec *wdegree, ring tailRing)
 
intvechSecondSeries (intvec *hseries1)
 
void hDegreeSeries (intvec *s1, intvec *s2, int *co, int *mu)
 
static void hPrintHilb (intvec *hseries, intvec *modul_weight)
 
void hLookSeries (ideal S, intvec *modulweight, ideal Q, intvec *wdegree, ring tailRing)
 
static void idInsertMonomial (ideal I, poly p)
 
static int comapreMonoIdBases (ideal J, ideal Ob)
 
static int CountOnIdUptoTruncationIndex (ideal I, int tr)
 
static int comapreMonoIdBases_IG_Case (ideal J, int JCount, ideal Ob, int ObCount)
 
static int positionInOrbit_IG_Case (ideal I, poly w, std::vector< ideal > idorb, std::vector< poly > polist, int trInd, int trunDegHs)
 
static int positionInOrbit_FG_Case (ideal I, poly, std::vector< ideal > idorb, std::vector< poly >, int, int)
 
static int positionInOrbitTruncationCase (ideal I, poly w, std::vector< ideal > idorb, std::vector< poly > polist, int, int trunDegHs)
 
static int monCompare (const void *m, const void *n)
 
void sortMonoIdeal_pCompare (ideal I)
 
static ideal minimalMonomialGenSet (ideal I)
 
static poly shiftInMon (poly p, int i, int lV, const ring r)
 
static poly deleteInMon (poly w, int i, int lV, const ring r)
 
static void TwordMap (poly p, poly w, int lV, int d, ideal Jwi, bool &flag)
 
static ideal colonIdeal (ideal S, poly w, int lV, ideal Jwi, int trunDegHs)
 
void HilbertSeries_OrbitData (ideal S, int lV, bool IG_CASE, bool mgrad, bool odp, int trunDegHs)
 
ideal RightColonOperation (ideal S, poly w, int lV)
 

Variables

STATIC_VAR int ** Qpol
 
STATIC_VAR int * Q0
 
STATIC_VAR int * Ql
 
STATIC_VAR int hLength
 

Macro Definition Documentation

◆ omsai

#define omsai   1

Definition at line 28 of file hilb.cc.

Function Documentation

◆ ChooseP()

static poly ChooseP ( ideal  I)
static

Definition at line 764 of file hilb.cc.

765 {
766  poly m;
767  // TEST TO SEE WHICH ONE IS BETTER
768  //m = ChoosePXL(I);
769  //m = ChoosePXF(I);
770  //m = ChoosePOL(I);
771  //m = ChoosePOF(I);
772  //m = ChoosePVL(I);
773  //m = ChoosePVF(I);
774  m = ChoosePJL(I);
775  //m = ChoosePJF(I);
776  return(m);
777 }
int m
Definition: cfEzgcd.cc:128
static poly ChoosePJL(ideal I)
Definition: hilb.cc:705

◆ ChoosePJL()

static poly ChoosePJL ( ideal  I)
static

Definition at line 705 of file hilb.cc.

706 {
707  int i,j,dummy;
708  bool flag = TRUE;
709  poly m = p_ISet(1,currRing);
710  for(i = IDELEMS(I)-1;(i>=0) && (flag);i--)
711  {
712  flag = TRUE;
713  for(j=1;(j<=currRing->N) && (flag);j++)
714  {
715  dummy = p_GetExp(I->m[i],j,currRing);
716  if(dummy >= 2)
717  {
718  p_SetExp(m,j,dummy-1,currRing);
719  p_Setm(m,currRing);
720  flag = FALSE;
721  }
722  }
723  if(!p_IsOne(m, currRing))
724  {
725  return(m);
726  }
727  }
728  p_Delete(&m,currRing);
729  m = ChoosePVar(I);
730  return(m);
731 }
#define TRUE
Definition: auxiliary.h:100
#define FALSE
Definition: auxiliary.h:96
int i
Definition: cfEzgcd.cc:132
int j
Definition: facHensel.cc:110
static poly ChoosePVar(ideal I)
Definition: hilb.cc:479
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
Definition: p_polys.cc:1292
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
Definition: p_polys.h:488
static void p_Setm(poly p, const ring r)
Definition: p_polys.h:233
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
Definition: p_polys.h:469
static BOOLEAN p_IsOne(const poly p, const ring R)
either poly(1) or gen(k)?!
Definition: p_polys.h:1979
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:861
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13
#define IDELEMS(i)
Definition: simpleideals.h:23

◆ ChoosePVar()

static poly ChoosePVar ( ideal  I)
static

Definition at line 479 of file hilb.cc.

480 {
481  bool flag=TRUE;
482  int i,j;
483  poly res;
484  for(i=1;i<=currRing->N;i++)
485  {
486  flag=TRUE;
487  for(j=IDELEMS(I)-1;(j>=0)&&(flag);j--)
488  {
489  if(p_GetExp(I->m[j], i, currRing)>0)
490  {
491  flag=FALSE;
492  }
493  }
494 
495  if(flag == TRUE)
496  {
497  res = p_ISet(1, currRing);
498  p_SetExp(res, i, 1, currRing);
500  return(res);
501  }
502  else
503  {
504  p_Delete(&res, currRing);
505  }
506  }
507  return(NULL); //i.e. it is the maximal ideal
508 }
CanonicalForm res
Definition: facAbsFact.cc:60
#define NULL
Definition: omList.c:12

◆ colonIdeal()

static ideal colonIdeal ( ideal  S,
poly  w,
int  lV,
ideal  Jwi,
int  trunDegHs 
)
static

Definition at line 1939 of file hilb.cc.

1940 {
1941  /*
1942  * It computes the right colon ideal of a two-sided ideal S
1943  * w.r.t. word w and save it in a new object Jwi.
1944  * It keeps S and w unchanged.
1945  */
1946 
1947  if(idIs0(S))
1948  {
1949  return(S);
1950  }
1951 
1952  int i, d;
1953  d = p_Totaldegree(w, currRing);
1954  if(trunDegHs !=0 && d >= trunDegHs)
1955  {
1957  return(Jwi);
1958  }
1959  bool flag = FALSE;
1960  int SCount = IDELEMS(S);
1961  for(i = 0; i < SCount; i++)
1962  {
1963  TwordMap(S->m[i], w, lV, d, Jwi, flag);
1964  if(flag)
1965  {
1966  break;
1967  }
1968  }
1969 
1970  Jwi = minimalMonomialGenSet(Jwi);
1971  return(Jwi);
1972 }
const CanonicalForm & w
Definition: facAbsFact.cc:51
static void idInsertMonomial(ideal I, poly p)
Definition: hilb.cc:1456
static void TwordMap(poly p, poly w, int lV, int d, ideal Jwi, bool &flag)
Definition: hilb.cc:1878
static ideal minimalMonomialGenSet(ideal I)
Definition: hilb.cc:1779
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
poly p_One(const ring r)
Definition: p_polys.cc:1308
static long p_Totaldegree(poly p, const ring r)
Definition: p_polys.h:1467

◆ comapreMonoIdBases()

static int comapreMonoIdBases ( ideal  J,
ideal  Ob 
)
static

Definition at line 1483 of file hilb.cc.

1484 {
1485  /*
1486  * Monomials of J and Ob are assumed to
1487  * be already sorted. J and Ob are
1488  * represented by the minimal generating set.
1489  */
1490  int i, s;
1491  s = 1;
1492  int JCount = IDELEMS(J);
1493  int ObCount = IDELEMS(Ob);
1494 
1495  if(idIs0(J))
1496  {
1497  return(1);
1498  }
1499  if(JCount != ObCount)
1500  {
1501  return(0);
1502  }
1503 
1504  for(i = 0; i < JCount; i++)
1505  {
1506  if(!(p_LmEqual(J->m[i], Ob->m[i], currRing)))
1507  {
1508  return(0);
1509  }
1510  }
1511  return(s);
1512 }
const CanonicalForm int s
Definition: facAbsFact.cc:51
#define p_LmEqual(p1, p2, r)
Definition: p_polys.h:1691

◆ comapreMonoIdBases_IG_Case()

static int comapreMonoIdBases_IG_Case ( ideal  J,
int  JCount,
ideal  Ob,
int  ObCount 
)
static

Definition at line 1541 of file hilb.cc.

1542 {
1543  /*
1544  * Monomials of J and Ob are assumed to
1545  * be already sorted in increasing degrees.
1546  * J and Ob are represented by the minimal
1547  * generating set. It checks if J and Ob have
1548  * same monomials up to deg <=tr.
1549  */
1550 
1551  int i, s;
1552  s = 1;
1553  //when J is null
1554  //
1555  if(JCount != ObCount)
1556  {
1557  return(0);
1558  }
1559 
1560  if(JCount == 0)
1561  {
1562  return(1);
1563  }
1564 
1565  for(i = 0; i< JCount; i++)
1566  {
1567  if(!(p_LmEqual(J->m[i], Ob->m[i], currRing)))
1568  {
1569  return(0);
1570  }
1571  }
1572 
1573  return(s);
1574 }

◆ CountOnIdUptoTruncationIndex()

static int CountOnIdUptoTruncationIndex ( ideal  I,
int  tr 
)
static

Definition at line 1514 of file hilb.cc.

1515 {
1516  /*
1517  * The ideal I must be sorted in increasing total degree.
1518  * It counts the number of monomials in I up to
1519  * degree less than or equal to tr.
1520  */
1521 
1522  //case when I=1;
1523  if(p_Totaldegree(I->m[0], currRing) == 0)
1524  {
1525  return(1);
1526  }
1527 
1528  int count = 0;
1529  for(int i = 0; i < IDELEMS(I); i++)
1530  {
1531  if(p_Totaldegree(I->m[i], currRing) > tr)
1532  {
1533  return (count);
1534  }
1535  count = count + 1;
1536  }
1537 
1538  return(count);
1539 }
int status int void size_t count
Definition: si_signals.h:59

◆ deleteInMon()

static poly deleteInMon ( poly  w,
int  i,
int  lV,
const ring  r 
)
static

Definition at line 1844 of file hilb.cc.

1845 {
1846  /*
1847  * deletes the variables upto i^th layer of monomial w
1848  * w remains unchanged
1849  * creates new poly and returns it for the colon ideal
1850  */
1851 
1852  poly dw = p_One(currRing);
1853  int *e = (int *)omAlloc((r->N+1)*sizeof(int));
1854  int *s=(int *)omAlloc0((r->N+1)*sizeof(int));
1855  p_GetExpV(w, e, r);
1856  int j, cnt;
1857  cnt = i*lV;
1858  /*
1859  for(j=1;j<=cnt;j++)
1860  {
1861  e[j]=0;
1862  }*/
1863  for(j = (cnt+1); j < (r->N+1); j++)
1864  {
1865  s[j] = e[j];
1866  }
1867 
1868  p_SetExpV(dw, s, currRing);//new exponents
1869  omFree(e);
1870  omFree(s);
1871 
1873  p_Setm(dw, currRing);
1874 
1875  return(dw);
1876 }
#define p_GetComp(p, r)
Definition: monomials.h:64
#define omAlloc(size)
Definition: omAllocDecl.h:210
#define omFree(addr)
Definition: omAllocDecl.h:261
#define omAlloc0(size)
Definition: omAllocDecl.h:211
static void p_SetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1504
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
Definition: p_polys.h:247
static void p_GetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1480

◆ eulerchar()

static void eulerchar ( ideal  I,
int  variables,
mpz_ptr  ec 
)
static

Definition at line 837 of file hilb.cc.

838 {
839  loop
840  {
841  mpz_t dummy;
842  if(JustVar(I) == TRUE)
843  {
844  if(IDELEMS(I) == variables)
845  {
846  mpz_init(dummy);
847  if((variables % 2) == 0)
848  mpz_set_ui(dummy, 1);
849  else
850  mpz_set_si(dummy, -1);
851  mpz_add(ec, ec, dummy);
852  mpz_clear(dummy);
853  }
854  return;
855  }
856  ideal p = idInit(1,1);
857  p->m[0] = SearchP(I);
858  //idPrint(I);
859  //idPrint(p);
860  //printf("\nNow get in idQuotMon\n");
861  ideal Ip = idQuotMon(I,p);
862  //idPrint(Ip);
863  //Ip = SortByDeg(Ip);
864  int i,howmanyvarinp = 0;
865  for(i = 1;i<=currRing->N;i++)
866  {
867  if(p_GetExp(p->m[0],i,currRing)>0)
868  {
869  howmanyvarinp++;
870  }
871  }
872  eulerchar(Ip, variables-howmanyvarinp, ec);
873  id_Delete(&Ip, currRing);
874  idAddMon(I,p);
875  id_Delete(&p, currRing);
876  }
877 }
int p
Definition: cfModGcd.cc:4080
static void idAddMon(ideal I, ideal p)
Definition: hilb.cc:471
static void eulerchar(ideal I, int variables, mpz_ptr ec)
Definition: hilb.cc:837
static poly SearchP(ideal I)
searches for a monomial of degree d>=2 and divides it by a variable (result monomial of deg d-1)
Definition: hilb.cc:780
ideal idQuotMon(ideal Iorig, ideal p)
Definition: hilb.cc:409
static bool JustVar(ideal I)
Definition: hilb.cc:806
STATIC_VAR int variables
ideal idInit(int idsize, int rank)
initialise an ideal / module
Definition: simpleideals.cc:35
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
#define loop
Definition: structs.h:80

◆ hAddHilb()

static int* hAddHilb ( int  Nv,
int  x,
int *  pol,
int *  lp 
)
static

Definition at line 104 of file hilb.cc.

105 {
106  int l = *lp, ln, i;
107  int *pon;
108  *lp = ln = l + x;
109  pon = Qpol[Nv];
110  memcpy(pon, pol, l * sizeof(int));
111  if (l > x)
112  {/*pon[i] -= pol[i - x];*/
113  for (i = x; i < l; i++)
114  { int64 t=pon[i];
115  int64 t2=pol[i - x];
116  t-=t2;
117  if ((t>=INT_MIN)&&(t<=INT_MAX)) pon[i]=t;
118  else if (!errorreported) WerrorS("int overflow in hilb 1");
119  }
120  for (i = l; i < ln; i++)
121  { /*pon[i] = -pol[i - x];*/
122  int64 t= -pol[i - x];
123  if ((t>=INT_MIN)&&(t<=INT_MAX)) pon[i]=t;
124  else if (!errorreported) WerrorS("int overflow in hilb 2");
125  }
126  }
127  else
128  {
129  for (i = l; i < x; i++)
130  pon[i] = 0;
131  for (i = x; i < ln; i++)
132  pon[i] = -pol[i - x];
133  }
134  return pon;
135 }
long int64
Definition: auxiliary.h:68
int l
Definition: cfEzgcd.cc:100
Variable x
Definition: cfModGcd.cc:4084
VAR short errorreported
Definition: feFopen.cc:23
void WerrorS(const char *s)
Definition: feFopen.cc:24
STATIC_VAR int ** Qpol
Definition: hilb.cc:44

◆ hDegreeSeries()

void hDegreeSeries ( intvec s1,
intvec s2,
int *  co,
int *  mu 
)

Definition at line 1380 of file hilb.cc.

1381 {
1382  int i, j, k;
1383  int m;
1384  *co = *mu = 0;
1385  if ((s1 == NULL) || (s2 == NULL))
1386  return;
1387  i = s1->length();
1388  j = s2->length();
1389  if (j > i)
1390  return;
1391  m = 0;
1392  for(k=j-2; k>=0; k--)
1393  m += (*s2)[k];
1394  *mu = m;
1395  *co = i - j;
1396 }
int k
Definition: cfEzgcd.cc:99
void mu(int **points, int sizePoints)
int length() const
Definition: intvec.h:94

◆ hFirstSeries()

intvec* hFirstSeries ( ideal  S,
intvec modulweight,
ideal  Q,
intvec wdegree,
ring  tailRing 
)

Definition at line 1335 of file hilb.cc.

1336 {
1337  id_TestTail(S, currRing, tailRing);
1338  if (Q!= NULL) id_TestTail(Q, currRing, tailRing);
1339 
1340  intvec *hseries1= hSeries(S, modulweight, 1, wdegree, Q, tailRing);
1341  if (errorreported) { delete hseries1; hseries1=NULL; }
1342  return hseries1;
1343 }
Definition: intvec.h:23
static intvec * hSeries(ideal S, intvec *modulweight, int, intvec *wdegree, ideal Q, ring tailRing)
Definition: hilb.cc:1172
STATIC_VAR jList * Q
Definition: janet.cc:30
#define id_TestTail(A, lR, tR)
Definition: simpleideals.h:77

◆ hHilbEst()

static void hHilbEst ( scfmon  stc,
int  Nstc,
varset  var,
int  Nvar 
)
static

Definition at line 63 of file hilb.cc.

64 {
65  int i, j;
66  int x, y, z = 1;
67  int *p;
68  for (i = Nvar; i>0; i--)
69  {
70  x = 0;
71  for (j = 0; j < Nstc; j++)
72  {
73  y = stc[j][var[i]];
74  if (y > x)
75  x = y;
76  }
77  z += x;
78  j = i - 1;
79  if (z > Ql[j])
80  {
81  if (z>(MAX_INT_VAL)/2)
82  {
83  WerrorS("internal arrays too big");
84  return;
85  }
86  p = (int *)omAlloc((unsigned long)z * sizeof(int));
87  if (Ql[j]!=0)
88  {
89  if (j==0)
90  memcpy(p, Qpol[j], Ql[j] * sizeof(int));
91  omFreeSize((ADDRESS)Qpol[j], Ql[j] * sizeof(int));
92  }
93  if (j==0)
94  {
95  for (x = Ql[j]; x < z; x++)
96  p[x] = 0;
97  }
98  Ql[j] = z;
99  Qpol[j] = p;
100  }
101  }
102 }
void * ADDRESS
Definition: auxiliary.h:119
const CanonicalForm int const CFList const Variable & y
Definition: facAbsFact.cc:53
STATIC_VAR int * Ql
Definition: hilb.cc:45
const int MAX_INT_VAL
Definition: mylimits.h:12
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260

◆ hHilbStep()

static void hHilbStep ( scmon  pure,
scfmon  stc,
int  Nstc,
varset  var,
int  Nvar,
int *  pol,
int  Lpol 
)
static

Definition at line 177 of file hilb.cc.

179 {
180  int iv = Nvar -1, ln, a, a0, a1, b, i;
181  int x, x0;
182  scmon pn;
183  scfmon sn;
184  int *pon;
185  if (Nstc==0)
186  {
187  hLastHilb(pure, iv, var, pol, Lpol);
188  return;
189  }
190  x = a = 0;
191  pn = hGetpure(pure);
192  sn = hGetmem(Nstc, stc, stcmem[iv]);
193  hStepS(sn, Nstc, var, Nvar, &a, &x);
194  Q0[iv] = Q0[Nvar];
195  ln = Lpol;
196  pon = pol;
197  if (a == Nstc)
198  {
199  x = pure[var[Nvar]];
200  if (x!=0)
201  pon = hAddHilb(iv, x, pon, &ln);
202  hHilbStep(pn, sn, a, var, iv, pon, ln);
203  return;
204  }
205  else
206  {
207  pon = hAddHilb(iv, x, pon, &ln);
208  hHilbStep(pn, sn, a, var, iv, pon, ln);
209  }
210  b = a;
211  x0 = 0;
212  loop
213  {
214  Q0[iv] += (x - x0);
215  a0 = a;
216  x0 = x;
217  hStepS(sn, Nstc, var, Nvar, &a, &x);
218  hElimS(sn, &b, a0, a, var, iv);
219  a1 = a;
220  hPure(sn, a0, &a1, var, iv, pn, &i);
221  hLex2S(sn, b, a0, a1, var, iv, hwork);
222  b += (a1 - a0);
223  ln = Lpol;
224  if (a < Nstc)
225  {
226  pon = hAddHilb(iv, x - x0, pol, &ln);
227  hHilbStep(pn, sn, b, var, iv, pon, ln);
228  }
229  else
230  {
231  x = pure[var[Nvar]];
232  if (x!=0)
233  pon = hAddHilb(iv, x - x0, pol, &ln);
234  else
235  pon = pol;
236  hHilbStep(pn, sn, b, var, iv, pon, ln);
237  return;
238  }
239  }
240 }
CanonicalForm b
Definition: cfModGcd.cc:4105
STATIC_VAR int * Q0
Definition: hilb.cc:45
static void hLastHilb(scmon pure, int Nv, varset var, int *pol, int lp)
Definition: hilb.cc:137
static int * hAddHilb(int Nv, int x, int *pol, int *lp)
Definition: hilb.cc:104
static void hHilbStep(scmon pure, scfmon stc, int Nstc, varset var, int Nvar, int *pol, int Lpol)
Definition: hilb.cc:177
void hLex2S(scfmon rad, int e1, int a2, int e2, varset var, int Nvar, scfmon w)
Definition: hutil.cc:815
void hElimS(scfmon stc, int *e1, int a2, int e2, varset var, int Nvar)
Definition: hutil.cc:675
VAR monf stcmem
Definition: hutil.cc:21
scfmon hGetmem(int lm, scfmon old, monp monmem)
Definition: hutil.cc:1026
void hPure(scfmon stc, int a, int *Nstc, varset var, int Nvar, scmon pure, int *Npure)
Definition: hutil.cc:624
VAR scfmon hwork
Definition: hutil.cc:16
void hStepS(scfmon stc, int Nstc, varset var, int Nvar, int *a, int *x)
Definition: hutil.cc:952
scmon hGetpure(scmon p)
Definition: hutil.cc:1055
scmon * scfmon
Definition: hutil.h:15
int * scmon
Definition: hutil.h:14

◆ hHstdSeries()

intvec* hHstdSeries ( ideal  S,
intvec modulweight,
intvec wdegree,
ideal  Q,
ring  tailRing 
)

Definition at line 1328 of file hilb.cc.

1329 {
1330  id_TestTail(S, currRing, tailRing);
1331  if (Q!=NULL) id_TestTail(Q, currRing, tailRing);
1332  return hSeries(S, modulweight, 0, wdegree, Q, tailRing);
1333 }

◆ HilbertSeries_OrbitData()

void HilbertSeries_OrbitData ( ideal  S,
int  lV,
bool  IG_CASE,
bool  mgrad,
bool  odp,
int  trunDegHs 
)

Definition at line 1974 of file hilb.cc.

1975 {
1976 
1977  /* new story:
1978  no lV is needed, i.e. it is to be determined
1979  the rest is extracted from the interface input list in extra.cc and makes the input of this proc
1980  called from extra.cc
1981  */
1982 
1983  /*
1984  * This is based on iterative right colon operations on a
1985  * two-sided monomial ideal of the free associative algebra.
1986  * The algorithm terminates for those monomial ideals
1987  * whose monomials define "regular formal languages",
1988  * that is, all monomials of the input ideal can be obtained
1989  * from finite languages by applying finite number of
1990  * rational operations.
1991  */
1992 
1993  int trInd;
1994  S = minimalMonomialGenSet(S);
1995  if( !idIs0(S) && p_Totaldegree(S->m[0], currRing)==0)
1996  {
1997  PrintS("Hilbert Series:\n 0\n");
1998  return;
1999  }
2000  int (*POS)(ideal, poly, std::vector<ideal>, std::vector<poly>, int, int);
2001  if(trunDegHs != 0)
2002  {
2003  Print("\nTruncation degree = %d\n",trunDegHs);
2005  }
2006  else
2007  {
2008  if(IG_CASE)
2009  {
2010  if(idIs0(S))
2011  {
2012  WerrorS("wrong input: it is not an infinitely gen. case");
2013  return;
2014  }
2015  trInd = p_Totaldegree(S->m[IDELEMS(S)-1], currRing);
2016  POS = &positionInOrbit_IG_Case;
2017  }
2018  else
2019  POS = &positionInOrbit_FG_Case;
2020  }
2021  std::vector<ideal > idorb;
2022  std::vector< poly > polist;
2023 
2024  ideal orb_init = idInit(1, 1);
2025  idorb.push_back(orb_init);
2026 
2027  polist.push_back( p_One(currRing));
2028 
2029  std::vector< std::vector<int> > posMat;
2030  std::vector<int> posRow(lV,0);
2031  std::vector<int> C;
2032 
2033  int ds, is, ps;
2034  unsigned long lpcnt = 0;
2035 
2036  poly w, wi;
2037  ideal Jwi;
2038 
2039  while(lpcnt < idorb.size())
2040  {
2041  w = NULL;
2042  w = polist[lpcnt];
2043  if(lpcnt >= 1 && idIs0(idorb[lpcnt]) == FALSE)
2044  {
2045  if(p_Totaldegree(idorb[lpcnt]->m[0], currRing) != 0)
2046  {
2047  C.push_back(1);
2048  }
2049  else
2050  C.push_back(0);
2051  }
2052  else
2053  {
2054  C.push_back(1);
2055  }
2056 
2057  ds = p_Totaldegree(w, currRing);
2058  lpcnt++;
2059 
2060  for(is = 1; is <= lV; is++)
2061  {
2062  wi = NULL;
2063  //make new copy 'wi' of word w=polist[lpcnt]
2064  //and update it (for the colon operation).
2065  //if corresponding to wi, right colon operation gives
2066  //a new (right colon) ideal of S,
2067  //keep 'wi' in the polist else delete it
2068 
2069  wi = pCopy(w);
2070  p_SetExp(wi, (ds*lV)+is, 1, currRing);
2071  p_Setm(wi, currRing);
2072  Jwi = NULL;
2073  //Jwi stores (right) colon ideal of S w.r.t. word
2074  //wi if colon operation gives a new ideal place it
2075  //in the vector of ideals 'idorb'
2076  //otherwise delete it
2077 
2078  Jwi = idInit(1,1);
2079 
2080  Jwi = colonIdeal(S, wi, lV, Jwi, trunDegHs);
2081  ps = (*POS)(Jwi, wi, idorb, polist, trInd, trunDegHs);
2082 
2083  if(ps == 0) // finds a new ideal
2084  {
2085  posRow[is-1] = idorb.size();
2086 
2087  idorb.push_back(Jwi);
2088  polist.push_back(wi);
2089  }
2090  else // ideal is already there in the set
2091  {
2092  posRow[is-1]=ps-1;
2093  idDelete(&Jwi);
2094  pDelete(&wi);
2095  }
2096  }
2097  posMat.push_back(posRow);
2098  posRow.resize(lV,0);
2099  }
2100  int lO = C.size();//size of the orbit
2101  PrintLn();
2102  Print("maximal length of words = %ld\n", p_Totaldegree(polist[lO-1], currRing));
2103  Print("\nlength of the Orbit = %d", lO);
2104  PrintLn();
2105 
2106  if(odp)
2107  {
2108  Print("words description of the Orbit: \n");
2109  for(is = 0; is < lO; is++)
2110  {
2111  pWrite0(polist[is]);
2112  PrintS(" ");
2113  }
2114  PrintLn();
2115  PrintS("\nmaximal degree, #(sum_j R(w,w_j))");
2116  PrintLn();
2117  for(is = 0; is < lO; is++)
2118  {
2119  if(idIs0(idorb[is]))
2120  {
2121  PrintS("NULL\n");
2122  }
2123  else
2124  {
2125  Print("%ld, %d \n",p_Totaldegree(idorb[is]->m[IDELEMS(idorb[is])-1], currRing),IDELEMS(idorb[is]));
2126  }
2127  }
2128  }
2129 
2130  for(is = idorb.size()-1; is >= 0; is--)
2131  {
2132  idDelete(&idorb[is]);
2133  }
2134  for(is = polist.size()-1; is >= 0; is--)
2135  {
2136  pDelete(&polist[is]);
2137  }
2138 
2139  idorb.resize(0);
2140  polist.resize(0);
2141 
2142  int adjMatrix[lO][lO];
2143  memset(adjMatrix, 0, lO*lO*sizeof(int));
2144  int rowCount, colCount;
2145  int tm = 0;
2146  if(!mgrad)
2147  {
2148  for(rowCount = 0; rowCount < lO; rowCount++)
2149  {
2150  for(colCount = 0; colCount < lV; colCount++)
2151  {
2152  tm = posMat[rowCount][colCount];
2153  adjMatrix[rowCount][tm] = adjMatrix[rowCount][tm] + 1;
2154  }
2155  }
2156  }
2157 
2158  ring r = currRing;
2159  int npar;
2160  char** tt;
2161  TransExtInfo p;
2162  if(!mgrad)
2163  {
2164  tt=(char**)omAlloc(sizeof(char*));
2165  tt[0] = omStrDup("t");
2166  npar = 1;
2167  }
2168  else
2169  {
2170  tt=(char**)omalloc(lV*sizeof(char*));
2171  for(is = 0; is < lV; is++)
2172  {
2173  tt[is] = (char*)omAlloc(7*sizeof(char)); //if required enlarge it later
2174  sprintf (tt[is], "t%d", is+1);
2175  }
2176  npar = lV;
2177  }
2178 
2179  p.r = rDefault(0, npar, tt);
2181  char** xx = (char**)omAlloc(sizeof(char*));
2182  xx[0] = omStrDup("x");
2183  ring R = rDefault(cf, 1, xx);
2184  rChangeCurrRing(R);//rWrite(R);
2185  /*
2186  * matrix corresponding to the orbit of the ideal
2187  */
2188  matrix mR = mpNew(lO, lO);
2189  matrix cMat = mpNew(lO,1);
2190  poly rc;
2191 
2192  if(!mgrad)
2193  {
2194  for(rowCount = 0; rowCount < lO; rowCount++)
2195  {
2196  for(colCount = 0; colCount < lO; colCount++)
2197  {
2198  if(adjMatrix[rowCount][colCount] != 0)
2199  {
2200  MATELEM(mR, rowCount + 1, colCount + 1) = p_ISet(adjMatrix[rowCount][colCount], R);
2201  p_SetCoeff(MATELEM(mR, rowCount + 1, colCount + 1), n_Mult(pGetCoeff(mR->m[lO*rowCount+colCount]),n_Param(1, R->cf), R->cf), R);
2202  }
2203  }
2204  }
2205  }
2206  else
2207  {
2208  for(rowCount = 0; rowCount < lO; rowCount++)
2209  {
2210  for(colCount = 0; colCount < lV; colCount++)
2211  {
2212  rc=NULL;
2213  rc=p_One(R);
2214  p_SetCoeff(rc, n_Mult(pGetCoeff(rc), n_Param(colCount+1, R->cf),R->cf), R);
2215  MATELEM(mR, rowCount +1, posMat[rowCount][colCount]+1)=p_Add_q(rc,MATELEM(mR, rowCount +1, posMat[rowCount][colCount]+1), R);
2216  }
2217  }
2218  }
2219 
2220  for(rowCount = 0; rowCount < lO; rowCount++)
2221  {
2222  if(C[rowCount] != 0)
2223  {
2224  MATELEM(cMat, rowCount + 1, 1) = p_ISet(C[rowCount], R);
2225  }
2226  }
2227 
2228  matrix u;
2229  unitMatrix(lO, u); //unit matrix
2230  matrix gMat = mp_Sub(u, mR, R);
2231 
2232  char* s;
2233 
2234  if(odp)
2235  {
2236  PrintS("\nlinear system:\n");
2237  if(!mgrad)
2238  {
2239  for(rowCount = 0; rowCount < lO; rowCount++)
2240  {
2241  Print("H(%d) = ", rowCount+1);
2242  for(colCount = 0; colCount < lV; colCount++)
2243  {
2244  StringSetS(""); nWrite(n_Param(1, R->cf));
2245  s = StringEndS(); PrintS(s);
2246  Print("*"); omFree(s);
2247  Print("H(%d) + ", posMat[rowCount][colCount] + 1);
2248  }
2249  Print(" %d\n", C[rowCount] );
2250  }
2251  PrintS("where H(1) represents the series corresp. to input ideal\n");
2252  PrintS("and i^th summand in the rhs of an eqn. is according\n");
2253  PrintS("to the right colon map corresp. to the i^th variable\n");
2254  }
2255  else
2256  {
2257  for(rowCount = 0; rowCount < lO; rowCount++)
2258  {
2259  Print("H(%d) = ", rowCount+1);
2260  for(colCount = 0; colCount < lV; colCount++)
2261  {
2262  StringSetS(""); nWrite(n_Param(colCount+1, R->cf));
2263  s = StringEndS(); PrintS(s);
2264  Print("*");omFree(s);
2265  Print("H(%d) + ", posMat[rowCount][colCount] + 1);
2266  }
2267  Print(" %d\n", C[rowCount] );
2268  }
2269  PrintS("where H(1) represents the series corresp. to input ideal\n");
2270  }
2271  }
2272  PrintLn();
2273  posMat.resize(0);
2274  C.resize(0);
2275  matrix pMat;
2276  matrix lMat;
2277  matrix uMat;
2278  matrix H_serVec = mpNew(lO, 1);
2279  matrix Hnot;
2280 
2281  //std::clock_t start;
2282  //start = std::clock();
2283 
2284  luDecomp(gMat, pMat, lMat, uMat, R);
2285  luSolveViaLUDecomp(pMat, lMat, uMat, cMat, H_serVec, Hnot);
2286 
2287  //to print system solving time
2288  //if(odp){
2289  //std::cout<<"solving time of the system = "<<(std::clock()-start)/(double)(CLOCKS_PER_SEC / 1000)<<" ms"<<std::endl;}
2290 
2291  mp_Delete(&mR, R);
2292  mp_Delete(&u, R);
2293  mp_Delete(&pMat, R);
2294  mp_Delete(&lMat, R);
2295  mp_Delete(&uMat, R);
2296  mp_Delete(&cMat, R);
2297  mp_Delete(&gMat, R);
2298  mp_Delete(&Hnot, R);
2299  //print the Hilbert series and length of the Orbit
2300  PrintLn();
2301  Print("Hilbert series:");
2302  PrintLn();
2303  pWrite(H_serVec->m[0]);
2304  if(!mgrad)
2305  {
2306  omFree(tt[0]);
2307  }
2308  else
2309  {
2310  for(is = lV-1; is >= 0; is--)
2311 
2312  omFree( tt[is]);
2313  }
2314  omFree(tt);
2315  omFree(xx[0]);
2316  omFree(xx);
2317  rChangeCurrRing(r);
2318  rKill(R);
2319 }
CanonicalForm cf
Definition: cfModGcd.cc:4085
poly * m
Definition: matpol.h:18
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
Definition: coeffs.h:637
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....
Definition: coeffs.h:807
@ n_transExt
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
Definition: coeffs.h:39
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
Definition: numbers.cc:353
#define Print
Definition: emacs.cc:80
static int positionInOrbitTruncationCase(ideal I, poly w, std::vector< ideal > idorb, std::vector< poly > polist, int, int trunDegHs)
Definition: hilb.cc:1685
static ideal colonIdeal(ideal S, poly w, int lV, ideal Jwi, int trunDegHs)
Definition: hilb.cc:1939
static int positionInOrbit_FG_Case(ideal I, poly, std::vector< ideal > idorb, std::vector< poly >, int, int)
Definition: hilb.cc:1654
static int positionInOrbit_IG_Case(ideal I, poly w, std::vector< ideal > idorb, std::vector< poly > polist, int trInd, int trunDegHs)
Definition: hilb.cc:1576
#define idDelete(H)
delete an ideal
Definition: ideals.h:29
void rKill(ring r)
Definition: ipshell.cc:6179
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)
Definition: matpol.cc:880
matrix mp_Sub(matrix a, matrix b, const ring R)
Definition: matpol.cc:196
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition: matpol.cc:37
#define MATELEM(mat, i, j)
1-based access to matrix
Definition: matpol.h:29
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition: monomials.h:44
The main handler for Singular numbers which are suitable for Singular polynomials.
#define nWrite(n)
Definition: numbers.h:29
#define omStrDup(s)
Definition: omAllocDecl.h:263
#define omalloc(size)
Definition: omAllocDecl.h:228
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:896
static number p_SetCoeff(poly p, number n, ring r)
Definition: p_polys.h:412
void rChangeCurrRing(ring r)
Definition: polys.cc:15
#define pDelete(p_ptr)
Definition: polys.h:186
void pWrite0(poly p)
Definition: polys.h:309
void pWrite(poly p)
Definition: polys.h:308
#define pCopy(p)
return a copy of the poly
Definition: polys.h:185
void StringSetS(const char *st)
Definition: reporter.cc:128
void PrintS(const char *s)
Definition: reporter.cc:284
char * StringEndS()
Definition: reporter.cc:151
void PrintLn()
Definition: reporter.cc:310
ring rDefault(const coeffs cf, int N, char **n, int ord_size, rRingOrder_t *ord, int *block0, int *block1, int **wvhdl, unsigned long bitmask)
Definition: ring.cc:102
#define R
Definition: sirandom.c:27
struct for passing initialization parameters to naInitChar
Definition: transext.h:88

◆ hLastHilb()

static void hLastHilb ( scmon  pure,
int  Nv,
varset  var,
int *  pol,
int  lp 
)
static

Definition at line 137 of file hilb.cc.

138 {
139  int l = lp, x, i, j;
140  int *pl;
141  int *p;
142  p = pol;
143  for (i = Nv; i>0; i--)
144  {
145  x = pure[var[i + 1]];
146  if (x!=0)
147  p = hAddHilb(i, x, p, &l);
148  }
149  pl = *Qpol;
150  j = Q0[Nv + 1];
151  for (i = 0; i < l; i++)
152  { /* pl[i + j] += p[i];*/
153  int64 t=pl[i+j];
154  int64 t2=p[i];
155  t+=t2;
156  if ((t>=INT_MIN)&&(t<=INT_MAX)) pl[i+j]=t;
157  else if (!errorreported) WerrorS("int overflow in hilb 3");
158  }
159  x = pure[var[1]];
160  if (x!=0)
161  {
162  j += x;
163  for (i = 0; i < l; i++)
164  { /* pl[i + j] -= p[i];*/
165  int64 t=pl[i+j];
166  int64 t2=p[i];
167  t-=t2;
168  if ((t>=INT_MIN)&&(t<=INT_MAX)) pl[i+j]=t;
169  else if (!errorreported) WerrorS("int overflow in hilb 4");
170  }
171  }
172  j += l;
173  if (j > hLength)
174  hLength = j;
175 }
STATIC_VAR int hLength
Definition: hilb.cc:46

◆ hLookSeries()

void hLookSeries ( ideal  S,
intvec modulweight,
ideal  Q,
intvec wdegree,
ring  tailRing 
)

Definition at line 1424 of file hilb.cc.

1425 {
1426  id_TestTail(S, currRing, tailRing);
1427 
1428  intvec *hseries1 = hFirstSeries(S, modulweight, Q, wdegree, tailRing);
1429  if (errorreported) return;
1430 
1431  hPrintHilb(hseries1,modulweight);
1432 
1433  const int l = hseries1->length()-1;
1434 
1435  intvec *hseries2 = (l > 1) ? hSecondSeries(hseries1) : hseries1;
1436 
1437  int co, mu;
1438  hDegreeSeries(hseries1, hseries2, &co, &mu);
1439 
1440  PrintLn();
1441  hPrintHilb(hseries2,modulweight);
1442  if ((l == 1) &&(mu == 0))
1443  scPrintDegree(rVar(currRing)+1, 0);
1444  else
1445  scPrintDegree(co, mu);
1446  if (l>1)
1447  delete hseries1;
1448  delete hseries2;
1449 }
void scPrintDegree(int co, int mu)
Definition: hdegree.cc:881
static void hPrintHilb(intvec *hseries, intvec *modul_weight)
Definition: hilb.cc:1398
void hDegreeSeries(intvec *s1, intvec *s2, int *co, int *mu)
Definition: hilb.cc:1380
intvec * hSecondSeries(intvec *hseries1)
Definition: hilb.cc:1345
intvec * hFirstSeries(ideal S, intvec *modulweight, ideal Q, intvec *wdegree, ring tailRing)
Definition: hilb.cc:1335
static short rVar(const ring r)
#define rVar(r) (r->N)
Definition: ring.h:597

◆ hMinModulweight()

static int hMinModulweight ( intvec modulweight)
static

Definition at line 49 of file hilb.cc.

50 {
51  int i,j,k;
52 
53  if(modulweight==NULL) return 0;
54  j=(*modulweight)[0];
55  for(i=modulweight->rows()-1;i!=0;i--)
56  {
57  k=(*modulweight)[i];
58  if(k<j) j=k;
59  }
60  return j;
61 }
int rows() const
Definition: intvec.h:96

◆ hPrintHilb()

static void hPrintHilb ( intvec hseries,
intvec modul_weight 
)
static

Definition at line 1398 of file hilb.cc.

1399 {
1400  int i, j, l, k;
1401  if (hseries == NULL)
1402  return;
1403  l = hseries->length()-1;
1404  k = (*hseries)[l];
1405  if ((modul_weight!=NULL)&&(modul_weight->compare(0)!=0))
1406  {
1407  char *s=modul_weight->ivString(1,0,1);
1408  Print("module weights:%s\n",s);
1409  omFree(s);
1410  }
1411  for (i = 0; i < l; i++)
1412  {
1413  j = (*hseries)[i];
1414  if (j != 0)
1415  {
1416  Print("// %8d t^%d\n", j, i+k);
1417  }
1418  }
1419 }
int compare(const intvec *o) const
Definition: intvec.cc:206
char * ivString(int not_mat=1, int spaces=0, int dim=2) const
Definition: intvec.cc:58

◆ hSecondSeries()

intvec* hSecondSeries ( intvec hseries1)

Definition at line 1345 of file hilb.cc.

1346 {
1347  intvec *work, *hseries2;
1348  int i, j, k, t, l;
1349  int s;
1350  if (hseries1 == NULL)
1351  return NULL;
1352  work = new intvec(hseries1);
1353  k = l = work->length()-1;
1354  s = 0;
1355  for (i = k-1; i >= 0; i--)
1356  s += (*work)[i];
1357  loop
1358  {
1359  if ((s != 0) || (k == 1))
1360  break;
1361  s = 0;
1362  t = (*work)[k-1];
1363  k--;
1364  for (i = k-1; i >= 0; i--)
1365  {
1366  j = (*work)[i];
1367  (*work)[i] = -t;
1368  s += t;
1369  t += j;
1370  }
1371  }
1372  hseries2 = new intvec(k+1);
1373  for (i = k-1; i >= 0; i--)
1374  (*hseries2)[i] = (*work)[i];
1375  (*hseries2)[k] = (*work)[l];
1376  delete work;
1377  return hseries2;
1378 }

◆ hSeries()

static intvec* hSeries ( ideal  S,
intvec modulweight,
int  ,
intvec wdegree,
ideal  Q,
ring  tailRing 
)
static

Definition at line 1172 of file hilb.cc.

1174 {
1175 // id_TestTail(S, currRing, tailRing);
1176 
1177  intvec *work, *hseries1=NULL;
1178  int mc;
1179  int p0;
1180  int i, j, k, l, ii, mw;
1181  hexist = hInit(S, Q, &hNexist, tailRing);
1182  if (hNexist==0)
1183  {
1184  hseries1=new intvec(2);
1185  (*hseries1)[0]=1;
1186  (*hseries1)[1]=0;
1187  return hseries1;
1188  }
1189 
1190  #if 0
1191  if (wdegree == NULL)
1192  hWeight();
1193  else
1194  hWDegree(wdegree);
1195  #else
1196  if (wdegree != NULL) hWDegree(wdegree);
1197  #endif
1198 
1199  p0 = 1;
1200  hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
1201  hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int));
1202  hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int));
1203  stcmem = hCreate((currRing->N) - 1);
1204  Qpol = (int **)omAlloc(((currRing->N) + 1) * sizeof(int *));
1205  Ql = (int *)omAlloc0(((currRing->N) + 1) * sizeof(int));
1206  Q0 = (int *)omAlloc(((currRing->N) + 1) * sizeof(int));
1207  *Qpol = NULL;
1208  hLength = k = j = 0;
1209  mc = hisModule;
1210  if (mc!=0)
1211  {
1212  mw = hMinModulweight(modulweight);
1213  hstc = (scfmon)omAlloc(hNexist * sizeof(scmon));
1214  }
1215  else
1216  {
1217  mw = 0;
1218  hstc = hexist;
1219  hNstc = hNexist;
1220  }
1221  loop
1222  {
1223  if (mc!=0)
1224  {
1225  hComp(hexist, hNexist, mc, hstc, &hNstc);
1226  if (modulweight != NULL)
1227  j = (*modulweight)[mc-1]-mw;
1228  }
1229  if (hNstc!=0)
1230  {
1231  hNvar = (currRing->N);
1232  for (i = hNvar; i>=0; i--)
1233  hvar[i] = i;
1234  //if (notstc) // TODO: no mon divides another
1236  hSupp(hstc, hNstc, hvar, &hNvar);
1237  if (hNvar!=0)
1238  {
1239  if ((hNvar > 2) && (hNstc > 10))
1242  memset(hpure, 0, ((currRing->N) + 1) * sizeof(int));
1243  hPure(hstc, 0, &hNstc, hvar, hNvar, hpure, &hNpure);
1244  hLexS(hstc, hNstc, hvar, hNvar);
1245  Q0[hNvar] = 0;
1246  hHilbStep(hpure, hstc, hNstc, hvar, hNvar, &p0, 1);
1247  }
1248  }
1249  else
1250  {
1251  if(*Qpol!=NULL)
1252  (**Qpol)++;
1253  else
1254  {
1255  *Qpol = (int *)omAlloc(sizeof(int));
1256  hLength = *Ql = **Qpol = 1;
1257  }
1258  }
1259  if (*Qpol!=NULL)
1260  {
1261  i = hLength;
1262  while ((i > 0) && ((*Qpol)[i - 1] == 0))
1263  i--;
1264  if (i > 0)
1265  {
1266  l = i + j;
1267  if (l > k)
1268  {
1269  work = new intvec(l);
1270  for (ii=0; ii<k; ii++)
1271  (*work)[ii] = (*hseries1)[ii];
1272  if (hseries1 != NULL)
1273  delete hseries1;
1274  hseries1 = work;
1275  k = l;
1276  }
1277  while (i > 0)
1278  {
1279  (*hseries1)[i + j - 1] += (*Qpol)[i - 1];
1280  (*Qpol)[i - 1] = 0;
1281  i--;
1282  }
1283  }
1284  }
1285  mc--;
1286  if (mc <= 0)
1287  break;
1288  }
1289  if (k==0)
1290  {
1291  hseries1=new intvec(2);
1292  (*hseries1)[0]=0;
1293  (*hseries1)[1]=0;
1294  }
1295  else
1296  {
1297  l = k+1;
1298  while ((*hseries1)[l-2]==0) l--;
1299  if (l!=k)
1300  {
1301  work = new intvec(l);
1302  for (ii=l-2; ii>=0; ii--)
1303  (*work)[ii] = (*hseries1)[ii];
1304  delete hseries1;
1305  hseries1 = work;
1306  }
1307  (*hseries1)[l-1] = mw;
1308  }
1309  for (i = 0; i <= (currRing->N); i++)
1310  {
1311  if (Ql[i]!=0)
1312  omFreeSize((ADDRESS)Qpol[i], Ql[i] * sizeof(int));
1313  }
1314  omFreeSize((ADDRESS)Q0, ((currRing->N) + 1) * sizeof(int));
1315  omFreeSize((ADDRESS)Ql, ((currRing->N) + 1) * sizeof(int));
1316  omFreeSize((ADDRESS)Qpol, ((currRing->N) + 1) * sizeof(int *));
1317  hKill(stcmem, (currRing->N) - 1);
1318  omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int));
1319  omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int));
1320  omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
1322  if (hisModule!=0)
1323  omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon));
1324  return hseries1;
1325 }
static void hHilbEst(scfmon stc, int Nstc, varset var, int Nvar)
Definition: hilb.cc:63
static int hMinModulweight(intvec *modulweight)
Definition: hilb.cc:49
static void hWDegree(intvec *wdegree)
Definition: hilb.cc:245
monf hCreate(int Nvar)
Definition: hutil.cc:999
void hComp(scfmon exist, int Nexist, int ak, scfmon stc, int *Nstc)
Definition: hutil.cc:157
scfmon hInit(ideal S, ideal Q, int *Nexist, ring tailRing)
Definition: hutil.cc:31
VAR scfmon hstc
Definition: hutil.cc:16
VAR varset hvar
Definition: hutil.cc:18
void hKill(monf xmem, int Nvar)
Definition: hutil.cc:1013
VAR int hNexist
Definition: hutil.cc:19
void hLexS(scfmon stc, int Nstc, varset var, int Nvar)
Definition: hutil.cc:509
void hDelete(scfmon ev, int ev_length)
Definition: hutil.cc:143
void hSupp(scfmon stc, int Nstc, varset var, int *Nvar)
Definition: hutil.cc:177
VAR scmon hpure
Definition: hutil.cc:17
VAR int hisModule
Definition: hutil.cc:20
void hStaircase(scfmon stc, int *Nstc, varset var, int Nvar)
Definition: hutil.cc:316
void hOrdSupp(scfmon stc, int Nstc, varset var, int Nvar)
Definition: hutil.cc:205
VAR int hNpure
Definition: hutil.cc:19
VAR scfmon hexist
Definition: hutil.cc:16
VAR int hNstc
Definition: hutil.cc:19
VAR int hNvar
Definition: hutil.cc:19
int * varset
Definition: hutil.h:16

◆ hWDegree()

static void hWDegree ( intvec wdegree)
static

Definition at line 245 of file hilb.cc.

246 {
247  int i, k;
248  int x;
249 
250  for (i=(currRing->N); i; i--)
251  {
252  x = (*wdegree)[i-1];
253  if (x != 1)
254  {
255  for (k=hNexist-1; k>=0; k--)
256  {
257  hexist[k][i] *= x;
258  }
259  }
260  }
261 }

◆ idAddMon()

static void idAddMon ( ideal  I,
ideal  p 
)
static

Definition at line 471 of file hilb.cc.

472 {
473  SortByDeg_p(I,p->m[0]);
474  p->m[0]=NULL; // is now in I
475  //idSkipZeroes(I);
476 }
static void SortByDeg_p(ideal I, poly p)
!!!!!!!!!!!!!!!!!!!! Just for Monomial Ideals !!!!!!!!!!!!!!!!!!!!!!!!!!!!
Definition: hilb.cc:288

◆ idInsertMonomial()

static void idInsertMonomial ( ideal  I,
poly  p 
)
static

Definition at line 1456 of file hilb.cc.

1457 {
1458  /*
1459  * It adds monomial in I and if required,
1460  * enlarge the size of poly-set by 16.
1461  * It does not make copy of p.
1462  */
1463 
1464  if(I == NULL)
1465  {
1466  return;
1467  }
1468 
1469  int j = IDELEMS(I) - 1;
1470  while ((j >= 0) && (I->m[j] == NULL))
1471  {
1472  j--;
1473  }
1474  j++;
1475  if (j == IDELEMS(I))
1476  {
1477  pEnlargeSet(&(I->m), IDELEMS(I), 16);
1478  IDELEMS(I) +=16;
1479  }
1480  I->m[j] = p;
1481 }
void pEnlargeSet(poly **p, int l, int increment)
Definition: p_polys.cc:3766

◆ idQuotMon()

ideal idQuotMon ( ideal  Iorig,
ideal  p 
)

Definition at line 409 of file hilb.cc.

410 {
411  if(idIs0(Iorig))
412  {
413  ideal res = idInit(1,1);
414  res->m[0] = poly(0);
415  return(res);
416  }
417  if(idIs0(p))
418  {
419  ideal res = idInit(1,1);
420  res->m[0] = pOne();
421  return(res);
422  }
423  ideal I = id_Head(Iorig,currRing);
424  ideal res = idInit(IDELEMS(I),1);
425  int i,j;
426  int dummy;
427  for(i = 0; i<IDELEMS(I); i++)
428  {
429  res->m[i] = p_Head(I->m[i], currRing);
430  for(j = 1; (j<=currRing->N) ; j++)
431  {
432  dummy = p_GetExp(p->m[0], j, currRing);
433  if(dummy > 0)
434  {
435  if(p_GetExp(I->m[i], j, currRing) < dummy)
436  {
437  p_SetExp(res->m[i], j, 0, currRing);
438  }
439  else
440  {
441  p_SetExp(res->m[i], j, p_GetExp(I->m[i], j, currRing) - dummy, currRing);
442  }
443  }
444  }
445  p_Setm(res->m[i], currRing);
446  if(p_Totaldegree(res->m[i],currRing) == p_Totaldegree(I->m[i],currRing))
447  {
448  p_Delete(&res->m[i],currRing);
449  }
450  else
451  {
452  p_Delete(&I->m[i],currRing);
453  }
454  }
455  idSkipZeroes(res);
456  idSkipZeroes(I);
457  if(!idIs0(res))
458  {
459  for(i = 0; i<=IDELEMS(res)-1; i++)
460  {
461  SortByDeg_p(I,res->m[i]);
462  res->m[i]=NULL; // is now in I
463  }
464  }
466  //idDegSortTest(I);
467  return(I);
468 }
static poly p_Head(poly p, const ring r)
copy the i(leading) term of p
Definition: p_polys.h:826
#define pOne()
Definition: polys.h:315
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size

◆ IsIn()

static bool IsIn ( poly  p,
ideal  I 
)
static

Definition at line 909 of file hilb.cc.

910 {
911  //assumes that I is ordered by degree
912  if(idIs0(I))
913  {
914  if(p==poly(0))
915  {
916  return(TRUE);
917  }
918  else
919  {
920  return(FALSE);
921  }
922  }
923  if(p==poly(0))
924  {
925  return(FALSE);
926  }
927  int i,j;
928  bool flag;
929  for(i = 0;i<IDELEMS(I);i++)
930  {
931  flag = TRUE;
932  for(j = 1;(j<=currRing->N) &&(flag);j++)
933  {
934  if(p_GetExp(p, j, currRing)<p_GetExp(I->m[i], j, currRing))
935  {
936  flag = FALSE;
937  }
938  }
939  if(flag)
940  {
941  return(TRUE);
942  }
943  }
944  return(FALSE);
945 }

◆ JustVar()

static bool JustVar ( ideal  I)
static

Definition at line 806 of file hilb.cc.

807 {
808  #if 0
809  int i,j;
810  bool foundone;
811  for(i=0;i<=IDELEMS(I)-1;i++)
812  {
813  foundone = FALSE;
814  for(j = 1;j<=currRing->N;j++)
815  {
816  if(p_GetExp(I->m[i], j, currRing)>0)
817  {
818  if(foundone == TRUE)
819  {
820  return(FALSE);
821  }
822  foundone = TRUE;
823  }
824  }
825  }
826  return(TRUE);
827  #else
828  if(p_Totaldegree(I->m[IDELEMS(I)-1],currRing)>1)
829  {
830  return(FALSE);
831  }
832  return(TRUE);
833  #endif
834 }

◆ LCMmon()

static poly LCMmon ( ideal  I)
static

Definition at line 948 of file hilb.cc.

949 {
950  if(idIs0(I))
951  {
952  return(NULL);
953  }
954  poly m;
955  int dummy,i,j;
956  m = p_ISet(1,currRing);
957  for(i=1;i<=currRing->N;i++)
958  {
959  dummy=0;
960  for(j=IDELEMS(I)-1;j>=0;j--)
961  {
962  if(p_GetExp(I->m[j],i,currRing) > dummy)
963  {
964  dummy = p_GetExp(I->m[j],i,currRing);
965  }
966  }
967  p_SetExp(m,i,dummy,currRing);
968  }
969  p_Setm(m,currRing);
970  return(m);
971 }

◆ minimalMonomialGenSet()

static ideal minimalMonomialGenSet ( ideal  I)
static

Definition at line 1779 of file hilb.cc.

1780 {
1781  /*
1782  * eliminates monomials which
1783  * can be generated by others in I
1784  */
1785  //first sort monomials of the ideal
1786 
1787  idSkipZeroes(I);
1788 
1790 
1791  int i, k;
1792  int ICount = IDELEMS(I);
1793 
1794  for(k = ICount - 1; k >=1; k--)
1795  {
1796  for(i = 0; i < k; i++)
1797  {
1798 
1799  if(p_LmDivisibleBy(I->m[i], I->m[k], currRing))
1800  {
1801  pDelete(&(I->m[k]));
1802  break;
1803  }
1804  }
1805  }
1806 
1807  idSkipZeroes(I);
1808  return(I);
1809 }
void sortMonoIdeal_pCompare(ideal I)
Definition: hilb.cc:1766
static BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1863

◆ monCompare()

static int monCompare ( const void *  m,
const void *  n 
)
static

Definition at line 1759 of file hilb.cc.

1760 {
1761  /* compares monomials */
1762 
1763  return(p_Compare(*(poly*) m, *(poly*)n, currRing));
1764 }
int p_Compare(const poly a, const poly b, const ring R)
Definition: p_polys.cc:4932

◆ positionInOrbit_FG_Case()

static int positionInOrbit_FG_Case ( ideal  I,
poly  ,
std::vector< ideal >  idorb,
std::vector< poly >  ,
int  ,
int   
)
static

Definition at line 1654 of file hilb.cc.

1655 {
1656  /*
1657  * It compares the ideal I with ideals in the set 'idorb'.
1658  * I and ideals of 'idorb' are sorted.
1659  *
1660  * It returns 0 if I is not equal to any ideal of 'idorb'
1661  * else returns position of the matched ideal.
1662  */
1663  int ps = 0;
1664  int i, s = 0;
1665  int OrbCount = idorb.size();
1666 
1667  if(idIs0(I))
1668  {
1669  return(1);
1670  }
1671 
1672  for(i = 1; i < OrbCount; i++)
1673  {
1674  s = comapreMonoIdBases(I, idorb[i]);
1675  if(s)
1676  {
1677  ps = i + 1;
1678  break;
1679  }
1680  }
1681 
1682  return(ps);
1683 }
static int comapreMonoIdBases(ideal J, ideal Ob)
Definition: hilb.cc:1483

◆ positionInOrbit_IG_Case()

static int positionInOrbit_IG_Case ( ideal  I,
poly  w,
std::vector< ideal >  idorb,
std::vector< poly >  polist,
int  trInd,
int  trunDegHs 
)
static

Definition at line 1576 of file hilb.cc.

1577 {
1578  /*
1579  * It compares the ideal I with ideals in the set 'idorb'
1580  * up to total degree =
1581  * trInd - max(deg of w, deg of word in polist) polynomials.
1582  *
1583  * It returns 0 if I is not equal to any ideal in the
1584  * 'idorb' else returns position of the matched ideal.
1585  */
1586 
1587  int ps = 0;
1588  int i, s = 0;
1589  int orbCount = idorb.size();
1590 
1591  if(idIs0(I))
1592  {
1593  return(1);
1594  }
1595 
1596  int degw = p_Totaldegree(w, currRing);
1597  int degp;
1598  int dtr;
1599  int dtrp;
1600 
1601  dtr = trInd - degw;
1602  int IwCount;
1603 
1604  IwCount = CountOnIdUptoTruncationIndex(I, dtr);
1605 
1606  if(IwCount == 0)
1607  {
1608  return(1);
1609  }
1610 
1611  int ObCount;
1612 
1613  bool flag2 = FALSE;
1614 
1615  for(i = 1;i < orbCount; i++)
1616  {
1617  degp = p_Totaldegree(polist[i], currRing);
1618  if(degw > degp)
1619  {
1620  dtr = trInd - degw;
1621 
1622  ObCount = 0;
1623  ObCount = CountOnIdUptoTruncationIndex(idorb[i], dtr);
1624  if(ObCount == 0)
1625  {continue;}
1626  if(flag2)
1627  {
1628  IwCount = 0;
1629  IwCount = CountOnIdUptoTruncationIndex(I, dtr);
1630  flag2 = FALSE;
1631  }
1632  }
1633  else
1634  {
1635  flag2 = TRUE;
1636  dtrp = trInd - degp;
1637  ObCount = 0;
1638  ObCount = CountOnIdUptoTruncationIndex(idorb[i], dtrp);
1639  IwCount = 0;
1640  IwCount = CountOnIdUptoTruncationIndex(I, dtrp);
1641  }
1642 
1643  s = comapreMonoIdBases_IG_Case(I, IwCount, idorb[i], ObCount);
1644 
1645  if(s)
1646  {
1647  ps = i + 1;
1648  break;
1649  }
1650  }
1651  return(ps);
1652 }
static int comapreMonoIdBases_IG_Case(ideal J, int JCount, ideal Ob, int ObCount)
Definition: hilb.cc:1541
static int CountOnIdUptoTruncationIndex(ideal I, int tr)
Definition: hilb.cc:1514

◆ positionInOrbitTruncationCase()

static int positionInOrbitTruncationCase ( ideal  I,
poly  w,
std::vector< ideal >  idorb,
std::vector< poly >  polist,
int  ,
int  trunDegHs 
)
static

Definition at line 1685 of file hilb.cc.

1686 {
1687  /*
1688  * It compares the ideal I with ideals in the set 'idorb'.
1689  * I and ideals in 'idorb' are sorted.
1690 
1691  * returns 0 if I is not equal to any ideal of 'idorb'
1692  * else returns position of the matched ideal.
1693  */
1694 
1695  int ps = 0;
1696  int i, s = 0;
1697  int OrbCount = idorb.size();
1698  int dtr=0; int IwCount, ObCount;
1699  dtr = trunDegHs - 1 - p_Totaldegree(w, currRing);
1700 
1701  if(idIs0(I))
1702  {
1703  for(i = 1; i < OrbCount; i++)
1704  {
1705  if(p_Totaldegree(w, currRing) == p_Totaldegree(polist[i], currRing))
1706  {
1707  if(idIs0(idorb[i]))
1708  return(i+1);
1709  ObCount=0;
1710  ObCount = CountOnIdUptoTruncationIndex(idorb[i], dtr);
1711  if(ObCount==0)
1712  {
1713  ps = i + 1;
1714  break;
1715  }
1716  }
1717  }
1718 
1719  return(ps);
1720  }
1721 
1722  IwCount = CountOnIdUptoTruncationIndex(I, dtr);
1723 
1724  if(p_Totaldegree(I->m[0], currRing)==0)
1725  {
1726  for(i = 1; i < OrbCount; i++)
1727  {
1728  if(idIs0(idorb[i]))
1729  continue;
1730  if(p_Totaldegree(idorb[i]->m[0], currRing)==0)
1731  {
1732  ps = i + 1;
1733  break;
1734  }
1735  }
1736  return(ps);
1737  }
1738 
1739  for(i = 1; i < OrbCount; i++)
1740  {
1741  if(p_Totaldegree(w, currRing) == p_Totaldegree(polist[i], currRing))
1742  {
1743  if(idIs0(idorb[i]))
1744  continue;
1745  ObCount=0;
1746  ObCount = CountOnIdUptoTruncationIndex(idorb[i], dtr);
1747  s = comapreMonoIdBases_IG_Case(I, IwCount, idorb[i], ObCount);
1748  if(s)
1749  {
1750  ps = i + 1;
1751  break;
1752  }
1753  }
1754  }
1755 
1756  return(ps);
1757 }

◆ RightColonOperation()

ideal RightColonOperation ( ideal  S,
poly  w,
int  lV 
)

Definition at line 2321 of file hilb.cc.

2322 {
2323  /*
2324  * This returns right colon ideal of a monomial two-sided ideal of
2325  * the free associative algebra with respect to a monomial 'w'
2326  * (S:_R w).
2327  */
2328  S = minimalMonomialGenSet(S);
2329  ideal Iw = idInit(1,1);
2330  Iw = colonIdeal(S, w, lV, Iw, 0);
2331  return (Iw);
2332 }

◆ rouneslice()

void rouneslice ( ideal  I,
ideal  S,
poly  q,
poly  x,
int &  prune,
int &  moreprune,
int &  steps,
int &  NNN,
mpz_ptr &  hilbertcoef,
int *&  hilbpower 
)

Definition at line 974 of file hilb.cc.

975 {
976  loop
977  {
978  (steps)++;
979  int i,j;
980  int dummy;
981  poly m;
982  ideal p;
983  //----------- PRUNING OF S ---------------
984  //S SHOULD IN THIS POINT BE ORDERED BY DEGREE
985  for(i=IDELEMS(S)-1;i>=0;i--)
986  {
987  if(IsIn(S->m[i],I))
988  {
989  p_Delete(&S->m[i],currRing);
990  prune++;
991  }
992  }
993  idSkipZeroes(S);
994  //----------------------------------------
995  for(i=IDELEMS(I)-1;i>=0;i--)
996  {
997  m = p_Head(I->m[i],currRing);
998  for(j=1;j<=currRing->N;j++)
999  {
1000  dummy = p_GetExp(m,j,currRing);
1001  if(dummy > 0)
1002  {
1003  p_SetExp(m,j,dummy-1,currRing);
1004  }
1005  }
1006  p_Setm(m, currRing);
1007  if(IsIn(m,S))
1008  {
1009  p_Delete(&I->m[i],currRing);
1010  //printf("\n Deleted, since pi(m) is in S\n");pWrite(m);
1011  }
1012  p_Delete(&m,currRing);
1013  }
1014  idSkipZeroes(I);
1015  //----------- MORE PRUNING OF S ------------
1016  m = LCMmon(I);
1017  if(m != NULL)
1018  {
1019  for(i=0;i<IDELEMS(S);i++)
1020  {
1021  if(!(p_DivisibleBy(S->m[i], m, currRing)))
1022  {
1023  S->m[i] = NULL;
1024  j++;
1025  moreprune++;
1026  }
1027  else
1028  {
1029  if(pLmEqual(S->m[i],m))
1030  {
1031  S->m[i] = NULL;
1032  moreprune++;
1033  }
1034  }
1035  }
1036  idSkipZeroes(S);
1037  }
1038  p_Delete(&m,currRing);
1039  /*printf("\n---------------------------\n");
1040  printf("\n I\n");idPrint(I);
1041  printf("\n S\n");idPrint(S);
1042  printf("\n q\n");pWrite(q);
1043  getchar();*/
1044 
1045  if(idIs0(I))
1046  {
1047  id_Delete(&I, currRing);
1048  id_Delete(&S, currRing);
1049  break;
1050  }
1051  m = LCMmon(I);
1052  if(!p_DivisibleBy(x,m, currRing))
1053  {
1054  //printf("\nx does not divide lcm(I)");
1055  //printf("\nEmpty set");pWrite(q);
1056  id_Delete(&I, currRing);
1057  id_Delete(&S, currRing);
1058  p_Delete(&m, currRing);
1059  break;
1060  }
1061  p_Delete(&m, currRing);
1062  m = SqFree(I);
1063  if(m==NULL)
1064  {
1065  //printf("\n Corner: ");
1066  //pWrite(q);
1067  //printf("\n With the facets of the dual simplex:\n");
1068  //idPrint(I);
1069  mpz_t ec;
1070  mpz_init(ec);
1071  mpz_ptr ec_ptr = ec;
1072  eulerchar(I, currRing->N, ec_ptr);
1073  bool flag = FALSE;
1074  if(NNN==0)
1075  {
1076  hilbertcoef = (mpz_ptr)omAlloc((NNN+1)*sizeof(mpz_t));
1077  hilbpower = (int*)omAlloc((NNN+1)*sizeof(int));
1078  mpz_init_set( &hilbertcoef[NNN], ec);
1079  hilbpower[NNN] = p_Totaldegree(q,currRing);
1080  NNN++;
1081  }
1082  else
1083  {
1084  //I look if the power appears already
1085  for(i = 0;(i<NNN)&&(flag == FALSE)&&(p_Totaldegree(q,currRing)>=hilbpower[i]);i++)
1086  {
1087  if((hilbpower[i]) == (p_Totaldegree(q,currRing)))
1088  {
1089  flag = TRUE;
1090  mpz_add(&hilbertcoef[i],&hilbertcoef[i],ec_ptr);
1091  }
1092  }
1093  if(flag == FALSE)
1094  {
1095  hilbertcoef = (mpz_ptr)omRealloc(hilbertcoef, (NNN+1)*sizeof(mpz_t));
1096  hilbpower = (int*)omRealloc(hilbpower, (NNN+1)*sizeof(int));
1097  mpz_init(&hilbertcoef[NNN]);
1098  for(j = NNN; j>i; j--)
1099  {
1100  mpz_set(&hilbertcoef[j],&hilbertcoef[j-1]);
1101  hilbpower[j] = hilbpower[j-1];
1102  }
1103  mpz_set( &hilbertcoef[i], ec);
1104  hilbpower[i] = p_Totaldegree(q,currRing);
1105  NNN++;
1106  }
1107  }
1108  mpz_clear(ec);
1109  id_Delete(&I, currRing);
1110  id_Delete(&S, currRing);
1111  break;
1112  }
1113  else
1114  p_Delete(&m, currRing);
1115  m = ChooseP(I);
1116  p = idInit(1,1);
1117  p->m[0] = m;
1118  ideal Ip = idQuotMon(I,p);
1119  ideal Sp = idQuotMon(S,p);
1120  poly pq = pp_Mult_mm(q,m,currRing);
1121  rouneslice(Ip, Sp, pq, x, prune, moreprune, steps, NNN, hilbertcoef,hilbpower);
1122  idAddMon(S,p);
1123  p->m[0]=NULL;
1124  id_Delete(&p, currRing); // p->m[0] was also in S
1125  p_Delete(&pq,currRing);
1126  }
1127 }
void FACTORY_PUBLIC prune(Variable &alpha)
Definition: variable.cc:261
static poly SqFree(ideal I)
Definition: hilb.cc:880
static poly ChooseP(ideal I)
Definition: hilb.cc:764
static poly LCMmon(ideal I)
Definition: hilb.cc:948
static bool IsIn(poly p, ideal I)
Definition: hilb.cc:909
void rouneslice(ideal I, ideal S, poly q, poly x, int &prune, int &moreprune, int &steps, int &NNN, mpz_ptr &hilbertcoef, int *&hilbpower)
Definition: hilb.cc:974
#define omRealloc(addr, size)
Definition: omAllocDecl.h:225
static poly pp_Mult_mm(poly p, poly m, const ring r)
Definition: p_polys.h:991
static BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1872
#define pLmEqual(p1, p2)
Definition: polys.h:111

◆ SearchP()

static poly SearchP ( ideal  I)
static

searches for a monomial of degree d>=2 and divides it by a variable (result monomial of deg d-1)

Definition at line 780 of file hilb.cc.

781 {
782  int i,j,exp;
783  poly res;
784  if(p_Totaldegree(I->m[IDELEMS(I)-1],currRing)<=1)
785  {
786  res = ChoosePVar(I);
787  return(res);
788  }
789  i = IDELEMS(I)-1;
790  res = p_Copy(I->m[i], currRing);
791  for(j=1;j<=currRing->N;j++)
792  {
793  exp = p_GetExp(I->m[i], j, currRing);
794  if(exp > 0)
795  {
796  p_SetExp(res, j, exp - 1, currRing);
798  break;
799  }
800  }
801  assume( j <= currRing->N );
802  return(res);
803 }
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:56
#define assume(x)
Definition: mod2.h:387
gmp_float exp(const gmp_float &a)
Definition: mpr_complex.cc:357
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:812

◆ shiftInMon()

static poly shiftInMon ( poly  p,
int  i,
int  lV,
const ring  r 
)
static

Definition at line 1811 of file hilb.cc.

1812 {
1813  /*
1814  * shifts the varibles of monomial p in the i^th layer,
1815  * p remains unchanged,
1816  * creates new poly and returns it for the colon ideal
1817  */
1818  poly smon = p_One(r);
1819  int j, sh, cnt;
1820  cnt = r->N;
1821  sh = i*lV;
1822  int *e=(int *)omAlloc((r->N+1)*sizeof(int));
1823  int *s=(int *)omAlloc0((r->N+1)*sizeof(int));
1824  p_GetExpV(p, e, r);
1825 
1826  for(j = 1; j <= cnt; j++)
1827  {
1828  if(e[j] == 1)
1829  {
1830  s[j+sh] = e[j];
1831  }
1832  }
1833 
1834  p_SetExpV(smon, s, currRing);
1835  omFree(e);
1836  omFree(s);
1837 
1839  p_Setm(smon, currRing);
1840 
1841  return(smon);
1842 }

◆ slicehilb()

void slicehilb ( ideal  I)

Definition at line 1130 of file hilb.cc.

1131 {
1132  //printf("Adi changes are here: \n");
1133  int i, NNN = 0;
1134  int steps = 0, prune = 0, moreprune = 0;
1135  mpz_ptr hilbertcoef;
1136  int *hilbpower;
1137  ideal S = idInit(1,1);
1138  poly q = p_One(currRing);
1139  ideal X = idInit(1,1);
1140  X->m[0]=p_One(currRing);
1141  for(i=1;i<=currRing->N;i++)
1142  {
1143  p_SetExp(X->m[0],i,1,currRing);
1144  }
1145  p_Setm(X->m[0],currRing);
1146  I = id_Mult(I,X,currRing);
1147  ideal Itmp = SortByDeg(I);
1148  id_Delete(&I,currRing);
1149  I = Itmp;
1150  //printf("\n-------------RouneSlice--------------\n");
1151  rouneslice(I,S,q,X->m[0],prune, moreprune, steps, NNN, hilbertcoef, hilbpower);
1152  id_Delete(&X,currRing);
1153  p_Delete(&q,currRing);
1154  //printf("\nIn total Prune got rid of %i elements\n",prune);
1155  //printf("\nIn total More Prune got rid of %i elements\n",moreprune);
1156  //printf("\nSteps of rouneslice: %i\n\n", steps);
1157  printf("\n// %8d t^0",1);
1158  for(i = 0; i<NNN; i++)
1159  {
1160  if(mpz_sgn(&hilbertcoef[i])!=0)
1161  {
1162  gmp_printf("\n// %8Zd t^%d",&hilbertcoef[i],hilbpower[i]);
1163  }
1164  }
1165  PrintLn();
1166  omFreeSize(hilbertcoef, (NNN)*sizeof(mpz_t));
1167  omFreeSize(hilbpower, (NNN)*sizeof(int));
1168  //printf("\n-------------------------------------\n");
1169 }
static ideal SortByDeg(ideal I)
Definition: hilb.cc:388
ideal id_Mult(ideal h1, ideal h2, const ring R)
h1 * h2 one h_i must be an ideal (with at least one column) the other h_i may be a module (with no co...

◆ SortByDeg()

static ideal SortByDeg ( ideal  I)
static

Definition at line 388 of file hilb.cc.

389 {
390  if(idIs0(I))
391  {
392  return id_Copy(I,currRing);
393  }
394  int i;
395  ideal res;
396  idSkipZeroes(I);
397  res = idInit(1,1);
398  for(i = 0; i<=IDELEMS(I)-1;i++)
399  {
400  SortByDeg_p(res, I->m[i]);
401  I->m[i]=NULL; // I->m[i] is now in res
402  }
403  idSkipZeroes(res);
404  //idDegSortTest(res);
405  return(res);
406 }
ideal id_Copy(ideal h1, const ring r)
copy an ideal

◆ SortByDeg_p()

static void SortByDeg_p ( ideal  I,
poly  p 
)
static

!!!!!!!!!!!!!!!!!!!! Just for Monomial Ideals !!!!!!!!!!!!!!!!!!!!!!!!!!!!

Definition at line 288 of file hilb.cc.

289 {
290  int i,j;
291  if(idIs0(I))
292  {
293  I->m[0] = p;
294  return;
295  }
296  idSkipZeroes(I);
297  #if 1
298  for(i = 0; (i<IDELEMS(I)) && (p_Totaldegree(I->m[i],currRing)<=p_Totaldegree(p,currRing)); i++)
299  {
300  if(p_DivisibleBy( I->m[i],p, currRing))
301  {
302  p_Delete(&p,currRing);
303  return;
304  }
305  }
306  for(i = IDELEMS(I)-1; (i>=0) && (p_Totaldegree(I->m[i],currRing)>=p_Totaldegree(p,currRing)); i--)
307  {
308  if(p_DivisibleBy(p,I->m[i], currRing))
309  {
310  p_Delete(&I->m[i],currRing);
311  }
312  }
313  if(idIs0(I))
314  {
315  idSkipZeroes(I);
316  I->m[0] = p;
317  return;
318  }
319  #endif
320  idSkipZeroes(I);
321  //First I take the case when all generators have the same degree
322  if(p_Totaldegree(I->m[0],currRing) == p_Totaldegree(I->m[IDELEMS(I)-1],currRing))
323  {
325  {
326  idInsertPoly(I,p);
327  idSkipZeroes(I);
328  for(i=IDELEMS(I)-1;i>=1; i--)
329  {
330  I->m[i] = I->m[i-1];
331  }
332  I->m[0] = p;
333  return;
334  }
336  {
337  idInsertPoly(I,p);
338  idSkipZeroes(I);
339  return;
340  }
341  }
343  {
344  idInsertPoly(I,p);
345  idSkipZeroes(I);
346  for(i=IDELEMS(I)-1;i>=1; i--)
347  {
348  I->m[i] = I->m[i-1];
349  }
350  I->m[0] = p;
351  return;
352  }
354  {
355  idInsertPoly(I,p);
356  idSkipZeroes(I);
357  return;
358  }
359  for(i = IDELEMS(I)-2; ;)
360  {
362  {
363  idInsertPoly(I,p);
364  idSkipZeroes(I);
365  for(j = IDELEMS(I)-1; j>=i+1;j--)
366  {
367  I->m[j] = I->m[j-1];
368  }
369  I->m[i] = p;
370  return;
371  }
373  {
374  idInsertPoly(I,p);
375  idSkipZeroes(I);
376  for(j = IDELEMS(I)-1; j>=i+2;j--)
377  {
378  I->m[j] = I->m[j-1];
379  }
380  I->m[i+1] = p;
381  return;
382  }
383  i--;
384  }
385 }
BOOLEAN idInsertPoly(ideal h1, poly h2)
insert h2 into h1 (if h2 is not the zero polynomial) return TRUE iff h2 was indeed inserted

◆ sortMonoIdeal_pCompare()

void sortMonoIdeal_pCompare ( ideal  I)

Definition at line 1766 of file hilb.cc.

1767 {
1768  /*
1769  * sorts monomial ideal in ascending order
1770  * order must be a total degree
1771  */
1772 
1773  qsort(I->m, IDELEMS(I), sizeof(poly), monCompare);
1774 
1775 }
static int monCompare(const void *m, const void *n)
Definition: hilb.cc:1759

◆ SqFree()

static poly SqFree ( ideal  I)
static

Definition at line 880 of file hilb.cc.

881 {
882  int i,j;
883  bool flag=TRUE;
884  poly notsqrfree = NULL;
885  if(p_Totaldegree(I->m[IDELEMS(I)-1],currRing)<=1)
886  {
887  return(notsqrfree);
888  }
889  for(i=IDELEMS(I)-1;(i>=0)&&(flag);i--)
890  {
891  for(j=1;(j<=currRing->N)&&(flag);j++)
892  {
893  if(p_GetExp(I->m[i],j,currRing)>1)
894  {
895  flag=FALSE;
896  notsqrfree = p_ISet(1,currRing);
897  p_SetExp(notsqrfree,j,1,currRing);
898  }
899  }
900  }
901  if(notsqrfree != NULL)
902  {
903  p_Setm(notsqrfree,currRing);
904  }
905  return(notsqrfree);
906 }

◆ TwordMap()

static void TwordMap ( poly  p,
poly  w,
int  lV,
int  d,
ideal  Jwi,
bool &  flag 
)
static

Definition at line 1878 of file hilb.cc.

1879 {
1880  /*
1881  * computes T_w(p) in a new poly object and places it
1882  * in Jwi which stores elements of colon ideal of I,
1883  * p and w remain unchanged,
1884  * the new polys for Jwi are constructed by sub-routines
1885  * deleteInMon, shiftInMon, p_MDivide,
1886  * places the result in Jwi and deletes the new polys
1887  * coming in dw, smon, qmon
1888  */
1889  int i;
1890  poly smon, dw;
1891  poly qmonp = NULL;
1892  bool del;
1893 
1894  for(i = 0;i <= d - 1; i++)
1895  {
1896  dw = deleteInMon(w, i, lV, currRing);
1897  smon = shiftInMon(p, i, lV, currRing);
1898  del = TRUE;
1899 
1900  if(pLmDivisibleBy(smon, w))
1901  {
1902  flag = TRUE;
1903  del = FALSE;
1904 
1905  pDelete(&dw);
1906  pDelete(&smon);
1907 
1908  //delete all monomials of Jwi
1909  //and make Jwi =1
1910 
1911  for(int j = 0;j < IDELEMS(Jwi); j++)
1912  {
1913  pDelete(&Jwi->m[j]);
1914  }
1915 
1917  break;
1918  }
1919 
1920  if(pLmDivisibleBy(dw, smon))
1921  {
1922  del = FALSE;
1923  qmonp = p_MDivide(smon, dw, currRing);
1924  idInsertMonomial(Jwi, shiftInMon(qmonp, -d, lV, currRing));
1925  pLmFree(&qmonp);
1926  pDelete(&dw);
1927  pDelete(&smon);
1928  }
1929  //in case both if are false, delete dw and smon
1930  if(del)
1931  {
1932  pDelete(&dw);
1933  pDelete(&smon);
1934  }
1935  }
1936 
1937 }
static poly deleteInMon(poly w, int i, int lV, const ring r)
Definition: hilb.cc:1844
static poly shiftInMon(poly p, int i, int lV, const ring r)
Definition: hilb.cc:1811
poly p_MDivide(poly a, poly b, const ring r)
Definition: p_polys.cc:1479
#define pLmDivisibleBy(a, b)
like pDivisibleBy, except that it is assumed that a!=NULL, b!=NULL
Definition: polys.h:140
static void pLmFree(poly p)
frees the space of the monomial m, assumes m != NULL coef is not freed, m is not advanced
Definition: polys.h:70

Variable Documentation

◆ hLength

STATIC_VAR int hLength

Definition at line 46 of file hilb.cc.

◆ Q0

STATIC_VAR int* Q0

Definition at line 45 of file hilb.cc.

◆ Ql

STATIC_VAR int * Ql

Definition at line 45 of file hilb.cc.

◆ Qpol

STATIC_VAR int** Qpol

Definition at line 44 of file hilb.cc.