hutil.h File Reference

#include "polys/monomials/ring.h"
#include "kernel/polys.h"
#include "misc/intvec.h"

Go to the source code of this file.

Data Structures
struct	monh
struct	indlist

Macros
#define	LEN_MON   (sizeof(scfmon) + sizeof(int))

Typedefs
typedef int *	scmon
typedef scmon *	scfmon
typedef int *	varset
typedef monh *	monp
typedef monp *	monf
typedef indlist *	indset

Functions
void	hDelete (scfmon ev, int ev_length)
void	hComp (scfmon exist, int Nexist, int ak, scfmon stc, int *Nstc)
void	hSupp (scfmon stc, int Nstc, varset var, int *Nvar)
void	hOrdSupp (scfmon stc, int Nstc, varset var, int Nvar)
void	hStaircase (scfmon stc, int *Nstc, varset var, int Nvar)
void	hRadical (scfmon rad, int *Nrad, int Nvar)
void	hLexS (scfmon stc, int Nstc, varset var, int Nvar)
void	hLexR (scfmon rad, int Nrad, varset var, int Nvar)
void	hPure (scfmon stc, int a, int *Nstc, varset var, int Nvar, scmon pure, int *Npure)
void	hElimS (scfmon stc, int *e1, int a2, int e2, varset var, int Nvar)
void	hElimR (scfmon rad, int *e1, int a2, int e2, varset var, int Nvar)
void	hLex2S (scfmon stc, int e1, int a2, int e2, varset var, int Nvar, scfmon w)
void	hLex2R (scfmon rad, int e1, int a2, int e2, varset var, int Nvar, scfmon w)
void	hStepS (scfmon stc, int Nstc, varset var, int Nvar, int *a, int *x)
void	hStepR (scfmon rad, int Nrad, varset var, int Nvar, int *a)
monf	hCreate (int Nvar)
void	hKill (monf xmem, int Nvar)
scfmon	hGetmem (int lm, scfmon old, monp monmem)
scmon	hGetpure (scmon p)
void	hDimSolve (scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
void	hIndMult (scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
void	hIndAllMult (scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
void	hDegreeSeries (intvec *s1, intvec *s2, int *co, int *mu)
scfmon	hInit (ideal S, ideal Q, int *Nexist)
void	slicehilb (ideal I)
void	HilbertSeries_OrbitData (ideal S, int lV, bool ig, bool mgrad, bool odp, int trunDegHs)
ideal	RightColonOperation (ideal i, poly w, int lV)

Variables
EXTERN_VAR omBin	indlist_bin
EXTERN_VAR scfmon	hexist
EXTERN_VAR scfmon	hstc
EXTERN_VAR scfmon	hrad
EXTERN_VAR scfmon	hwork
EXTERN_VAR scmon	hpure
EXTERN_VAR scmon	hpur0
EXTERN_VAR varset	hvar
EXTERN_VAR varset	hsel
EXTERN_VAR int	hNexist
EXTERN_VAR int	hNstc
EXTERN_VAR int	hNrad
EXTERN_VAR int	hNvar
EXTERN_VAR int	hNpure
EXTERN_VAR monf	stcmem
EXTERN_VAR monf	radmem
EXTERN_VAR int	hisModule
EXTERN_VAR indset	ISet
EXTERN_VAR indset	JSet
EXTERN_VAR int	hCo
EXTERN_VAR int	hMu2
EXTERN_VAR long	hMu

---

Data Structure Documentation

monrec

struct monrec

Definition at line 21 of file hutil.h.

Data Fields
int	a
scfmon	mo

sindlist

struct sindlist

Definition at line 29 of file hutil.h.

Data Fields
indset	nx
intvec *	set

Macro Definition Documentation

LEN_MON

#define LEN_MON   (sizeof(scfmon) + sizeof(int))

Definition at line 35 of file hutil.h.

Typedef Documentation

indset

typedef indlist* indset

Definition at line 28 of file hutil.h.

monf

typedef monp* monf

Definition at line 20 of file hutil.h.

monp

typedef monh* monp

Definition at line 19 of file hutil.h.

scfmon

typedef scmon* scfmon

Definition at line 15 of file hutil.h.

scmon

typedef int* scmon

Definition at line 14 of file hutil.h.

varset

typedef int* varset

Definition at line 16 of file hutil.h.

Function Documentation

hComp()

void hComp	(	scfmon	exist,
		int	Nexist,
		int	ak,
		scfmon	stc,
		int *	Nstc
	)

Definition at line 154 of file hutil.cc.

{
  int k = 0;
  scfmon ex = exist, co = stc;
  int i;
 
  for (i = Nexist; i>0; i--)
  {
    if (((**ex) == 0) || ((**ex) == ak))
    {
      *co = *ex;
      co++;
      k++;
    }
    ex++;
  }
  *Nstc = k;
}

hCreate()

monf hCreate

(

int

Nvar

)

Definition at line 996 of file hutil.cc.

{
  monf xmem;
  int  i;
  xmem = (monf)omAlloc((Nvar + 1) * sizeof(monp));
  for (i = Nvar; i>0; i--)
  {
    xmem[i] = (monp)omAlloc(LEN_MON);
    xmem[i]->mo = NULL;
  }
  return xmem;
}

hDegreeSeries()

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

Definition at line 732 of file hilb.cc.

{
  int i, j, k;
  int m;
  *co = *mu = 0;
  if ((s1 == NULL) || (s2 == NULL))
    return;
  i = s1->length();
  j = s2->length();
  if (j > i)
    return;
  m = 0;
  for(k=j-2; k>=0; k--)
    m += (*s2)[k];
  *mu = m;
  *co = i - j;
}

hDelete()

void hDelete	(	scfmon	ev,
		int	ev_length
	)

Definition at line 140 of file hutil.cc.

{
  int i;
 
  if (ev_length>0)
  {
    for (i=ev_length-1;i>=0;i--)
      omFreeSize(hsecure[i],((currRing->N)+1)*sizeof(int));
    omFreeSize(hsecure, ev_length*sizeof(scmon));
    omFreeSize(ev,  ev_length*sizeof(scmon));
  }
}

hDimSolve()

void hDimSolve	(	scmon	pure,
		int	Npure,
		scfmon	rad,
		int	Nrad,
		varset	var,
		int	Nvar
	)

Definition at line 35 of file hdegree.cc.

{
  int  dn, iv, rad0, b, c, x;
  scmon pn;
  scfmon rn;
  if (Nrad < 2)
  {
    dn = Npure + Nrad;
    if (dn < hCo)
      hCo = dn;
    return;
  }
  if (Npure+1 >= hCo)
    return;
  iv = Nvar;
  while(pure[var[iv]]) iv--;
  hStepR(rad, Nrad, var, iv, &rad0);
  if (rad0!=0)
  {
    iv--;
    if (rad0 < Nrad)
    {
      pn = hGetpure(pure);
      rn = hGetmem(Nrad, rad, radmem[iv]);
      hDimSolve(pn, Npure + 1, rn, rad0, var, iv);
      b = rad0;
      c = Nrad;
      hElimR(rn, &rad0, b, c, var, iv);
      hPure(rn, b, &c, var, iv, pn, &x);
      hLex2R(rn, rad0, b, c, var, iv, hwork);
      rad0 += (c - b);
      hDimSolve(pn, Npure + x, rn, rad0, var, iv);
    }
    else
    {
      hDimSolve(pure, Npure, rad, Nrad, var, iv);
    }
  }
  else
    hCo = Npure + 1;
}

hElimR()

void hElimR	(	scfmon	rad,
		int *	e1,
		int	a2,
		int	e2,
		varset	var,
		int	Nvar
	)

Definition at line 742 of file hutil.cc.

{
  int  nc = *e1, z = 0, i, j, k, k1;
  scmon n, o;
  if (!nc || (a2 == e2))
    return;
  j = 0;
  i = a2;
  o = rad[i];
  n = rad[0];
  k = Nvar;
  loop
  {
    k1 = var[k];
    if (o[k1] && !n[k1])
    {
      k = Nvar;
      i++;
      if (i < e2)
        o = rad[i];
      else
      {
        j++;
        if (j < nc)
        {
          i = a2;
          o = rad[i];
          n = rad[j];
        }
        else
        {
          if (z!=0)
          {
            *e1 -= z;
            hShrink(rad, 0, nc);
          }
          return;
        }
      }
    }
    else
    {
      k--;
      if (!k)
      {
        rad[j] = NULL;
        z++;
        j++;
        if (j < nc)
        {
          i = a2;
          o = rad[i];
          n = rad[j];
          k = Nvar;
        }
        else
        {
          if (z!=0)
          {
            *e1 -= z;
            hShrink(rad, 0, nc);
          }
          return;
        }
      }
    }
  }
}

hElimS()

void hElimS	(	scfmon	stc,
		int *	e1,
		int	a2,
		int	e2,
		varset	var,
		int	Nvar
	)

Definition at line 672 of file hutil.cc.

{
  int  nc = *e1, z = 0, i, j, k, k1;
  scmon n, o;
  if (!nc || (a2 == e2))
    return;
  j = 0;
  i = a2;
  o = stc[i];
  n = stc[0];
  k = Nvar;
  loop
  {
    k1 = var[k];
    if (o[k1] > n[k1])
    {
      k = Nvar;
      i++;
      if (i < e2)
        o = stc[i];
      else
      {
        j++;
        if (j < nc)
        {
          i = a2;
          o = stc[i];
          n = stc[j];
        }
        else
        {
          if (z!=0)
          {
            *e1 -= z;
            hShrink(stc, 0, nc);
          }
          return;
        }
      }
    }
    else
    {
      k--;
      if (k==0)
      {
        stc[j] = NULL;
        z++;
        j++;
        if (j < nc)
        {
          i = a2;
          o = stc[i];
          n = stc[j];
          k = Nvar;
        }
        else
        {
          if (z!=0)
          {
            *e1 -= z;
            hShrink(stc, 0, nc);
          }
          return;
        }
      }
    }
  }
}

hGetmem()

scfmon hGetmem	(	int	lm,
		scfmon	old,
		monp	monmem
	)

Definition at line 1023 of file hutil.cc.

{
  scfmon x = monmem->mo;
  int  lx = monmem->a;
  if ((x==NULL) || (lm > lx))
  {
    /* according to http://www.singular.uni-kl.de:8002/trac/ticket/463#comment:4
     * we need to work around a compiler bug:
    * if ((x!=NULL)&&(lx>0)) omFreeSize((ADDRESS)x, lx * sizeof(scmon));
    */
    if (x!=NULL) if (lx>0) omFreeSize((ADDRESS)x, lx * sizeof(scmon));
    monmem->mo = x = (scfmon)omAlloc(lm * sizeof(scmon));
    monmem->a = lm;
  }
  memcpy(x, old, lm * sizeof(scmon));
  return x;
}

hGetpure()

scmon hGetpure

(

scmon

p

)

Definition at line 1052 of file hutil.cc.

{
  scmon p1 = p;
  scmon pn;
  p1++;
  pn = p1;
  pn += (currRing->N);
  memcpy(pn, p1, (currRing->N) * sizeof(int));
  return pn - 1;
}

HilbertSeries_OrbitData()

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

Definition at line 1326 of file hilb.cc.

{
 
        /* new story:
        no lV is needed, i.e.  it is to be determined
        the rest is extracted from the interface input list in extra.cc and makes the input of this proc
        called from extra.cc
        */
 
  /*
   * This is based on iterative right colon operations on a
   * two-sided monomial ideal of the free associative algebra.
   * The algorithm terminates for those monomial ideals
   * whose monomials define  "regular formal languages",
   * that is, all monomials of the input ideal can be obtained
   * from finite languages by applying finite number of
   * rational operations.
   */
 
  int trInd;
  S = minimalMonomialGenSet(S);
  if( !idIs0(S) && p_Totaldegree(S->m[0], currRing)==0)
  {
    PrintS("Hilbert Series:\n 0\n");
    return;
  }
  int (*POS)(ideal, poly, std::vector<ideal>, std::vector<poly>, int, int);
  if(trunDegHs != 0)
  {
    Print("\nTruncation degree = %d\n",trunDegHs);
    POS=&positionInOrbitTruncationCase;
  }
  else
  {
    if(IG_CASE)
    {
      if(idIs0(S))
      {
        WerrorS("wrong input: it is not an infinitely gen. case");
        return;
      }
      trInd = p_Totaldegree(S->m[IDELEMS(S)-1], currRing);
      POS = &positionInOrbit_IG_Case;
    }
    else
    POS = &positionInOrbit_FG_Case;
  }
  std::vector<ideal > idorb;
  std::vector< poly > polist;
 
  ideal orb_init = idInit(1, 1);
  idorb.push_back(orb_init);
 
  polist.push_back( p_One(currRing));
 
  std::vector< std::vector<int> > posMat;
  std::vector<int> posRow(lV,0);
  std::vector<int> C;
 
  int ds, is, ps;
  unsigned long lpcnt = 0;
 
  poly w, wi;
  ideal Jwi;
 
  while(lpcnt < idorb.size())
  {
    w = NULL;
    w = polist[lpcnt];
    if(lpcnt >= 1 && idIs0(idorb[lpcnt]) == FALSE)
    {
      if(p_Totaldegree(idorb[lpcnt]->m[0], currRing) != 0)
      {
        C.push_back(1);
      }
      else
        C.push_back(0);
    }
    else
    {
      C.push_back(1);
    }
 
    ds = p_Totaldegree(w, currRing);
    lpcnt++;
 
    for(is = 1; is <= lV; is++)
    {
      wi = NULL;
      //make new copy 'wi' of word w=polist[lpcnt]
      //and update it (for the colon operation).
      //if corresponding to wi, right colon operation gives
      //a new (right colon) ideal of S,
      //keep 'wi' in the polist else delete it
 
      wi = pCopy(w);
      p_SetExp(wi, (ds*lV)+is, 1, currRing);
      p_Setm(wi, currRing);
      Jwi = NULL;
      //Jwi stores (right) colon ideal of S w.r.t. word
      //wi if colon operation gives a new ideal place it
      //in the vector of ideals  'idorb'
      //otherwise delete it
 
      Jwi = idInit(1,1);
 
      Jwi = colonIdeal(S, wi, lV, Jwi, trunDegHs);
      ps = (*POS)(Jwi, wi, idorb, polist, trInd, trunDegHs);
 
      if(ps == 0)  // finds a new ideal
      {
        posRow[is-1] = idorb.size();
 
        idorb.push_back(Jwi);
        polist.push_back(wi);
      }
      else // ideal is already there  in the set
      {
        posRow[is-1]=ps-1;
        idDelete(&Jwi);
        pDelete(&wi);
      }
    }
    posMat.push_back(posRow);
    posRow.resize(lV,0);
  }
  int lO = C.size();//size of the orbit
  PrintLn();
  Print("maximal length of words = %ld\n", p_Totaldegree(polist[lO-1], currRing));
  Print("\nlength of the Orbit = %d", lO);
  PrintLn();
 
  if(odp)
  {
    Print("words description of the Orbit: \n");
    for(is = 0; is < lO; is++)
    {
      pWrite0(polist[is]);
      PrintS("    ");
    }
    PrintLn();
    PrintS("\nmaximal degree,  #(sum_j R(w,w_j))");
    PrintLn();
    for(is = 0; is < lO; is++)
    {
      if(idIs0(idorb[is]))
      {
        PrintS("NULL\n");
      }
      else
      {
        Print("%ld,  %d \n",p_Totaldegree(idorb[is]->m[IDELEMS(idorb[is])-1], currRing),IDELEMS(idorb[is]));
      }
    }
  }
 
  for(is = idorb.size()-1; is >= 0; is--)
  {
    idDelete(&idorb[is]);
  }
  for(is = polist.size()-1; is >= 0; is--)
  {
    pDelete(&polist[is]);
  }
 
  idorb.resize(0);
  polist.resize(0);
 
  int adjMatrix[lO][lO];
  memset(adjMatrix, 0, lO*lO*sizeof(int));
  int rowCount, colCount;
  int tm = 0;
  if(!mgrad)
  {
    for(rowCount = 0; rowCount < lO; rowCount++)
    {
      for(colCount = 0; colCount < lV; colCount++)
      {
        tm = posMat[rowCount][colCount];
        adjMatrix[rowCount][tm] = adjMatrix[rowCount][tm] + 1;
      }
    }
  }
 
  ring r = currRing;
  int npar;
  char** tt;
  TransExtInfo p;
  if(!mgrad)
  {
    tt=(char**)omAlloc(sizeof(char*));
    tt[0] = omStrDup("t");
    npar = 1;
  }
  else
  {
    tt=(char**)omalloc(lV*sizeof(char*));
    for(is = 0; is < lV; is++)
    {
      tt[is] = (char*)omAlloc(7*sizeof(char)); //if required enlarge it later
      sprintf (tt[is], "t%d", is+1);
    }
    npar = lV;
  }
 
  p.r = rDefault(0, npar, tt);
  coeffs cf = nInitChar(n_transExt, &p);
  char** xx = (char**)omAlloc(sizeof(char*));
  xx[0] = omStrDup("x");
  ring R = rDefault(cf, 1, xx);
  rChangeCurrRing(R);//rWrite(R);
  /*
   * matrix corresponding to the orbit of the ideal
   */
  matrix mR = mpNew(lO, lO);
  matrix cMat = mpNew(lO,1);
  poly rc;
 
  if(!mgrad)
  {
    for(rowCount = 0; rowCount < lO; rowCount++)
    {
      for(colCount = 0; colCount < lO; colCount++)
      {
        if(adjMatrix[rowCount][colCount] != 0)
        {
          MATELEM(mR, rowCount + 1, colCount + 1) = p_ISet(adjMatrix[rowCount][colCount], R);
          p_SetCoeff(MATELEM(mR, rowCount + 1, colCount + 1), n_Mult(pGetCoeff(mR->m[lO*rowCount+colCount]),n_Param(1, R->cf), R->cf), R);
        }
      }
    }
  }
  else
  {
     for(rowCount = 0; rowCount < lO; rowCount++)
     {
       for(colCount = 0; colCount < lV; colCount++)
       {
          rc=NULL;
          rc=p_One(R);
          p_SetCoeff(rc, n_Mult(pGetCoeff(rc), n_Param(colCount+1, R->cf),R->cf), R);
          MATELEM(mR, rowCount +1, posMat[rowCount][colCount]+1)=p_Add_q(rc,MATELEM(mR, rowCount +1, posMat[rowCount][colCount]+1), R);
       }
     }
  }
 
  for(rowCount = 0; rowCount < lO; rowCount++)
  {
    if(C[rowCount] != 0)
    {
      MATELEM(cMat, rowCount + 1, 1) = p_ISet(C[rowCount], R);
    }
  }
 
  matrix u;
  unitMatrix(lO, u); //unit matrix
  matrix gMat = mp_Sub(u, mR, R);
 
  char* s;
 
  if(odp)
  {
    PrintS("\nlinear system:\n");
    if(!mgrad)
    {
      for(rowCount = 0; rowCount < lO; rowCount++)
      {
        Print("H(%d) = ", rowCount+1);
        for(colCount = 0; colCount < lV; colCount++)
        {
          StringSetS(""); nWrite(n_Param(1, R->cf));
          s = StringEndS(); PrintS(s);
          Print("*"); omFree(s);
          Print("H(%d) + ", posMat[rowCount][colCount] + 1);
        }
        Print(" %d\n", C[rowCount] );
      }
      PrintS("where H(1) represents the series corresp. to input ideal\n");
      PrintS("and i^th summand in the rhs of an eqn. is according\n");
      PrintS("to the right colon map corresp. to the i^th variable\n");
    }
    else
    {
      for(rowCount = 0; rowCount < lO; rowCount++)
      {
        Print("H(%d) = ", rowCount+1);
        for(colCount = 0; colCount < lV; colCount++)
        {
           StringSetS(""); nWrite(n_Param(colCount+1, R->cf));
           s = StringEndS(); PrintS(s);
           Print("*");omFree(s);
           Print("H(%d) + ", posMat[rowCount][colCount] + 1);
        }
        Print(" %d\n", C[rowCount] );
      }
      PrintS("where H(1) represents the series corresp. to input ideal\n");
    }
  }
  PrintLn();
  posMat.resize(0);
  C.resize(0);
  matrix pMat;
  matrix lMat;
  matrix uMat;
  matrix H_serVec = mpNew(lO, 1);
  matrix Hnot;
 
  //std::clock_t start;
  //start = std::clock();
 
  luDecomp(gMat, pMat, lMat, uMat, R);
  luSolveViaLUDecomp(pMat, lMat, uMat, cMat, H_serVec, Hnot);
 
  //to print system solving time
  //if(odp){
  //std::cout<<"solving time of the system = "<<(std::clock()-start)/(double)(CLOCKS_PER_SEC / 1000)<<" ms"<<std::endl;}
 
  mp_Delete(&mR, R);
  mp_Delete(&u, R);
  mp_Delete(&pMat, R);
  mp_Delete(&lMat, R);
  mp_Delete(&uMat, R);
  mp_Delete(&cMat, R);
  mp_Delete(&gMat, R);
  mp_Delete(&Hnot, R);
  //print the Hilbert series and length of the Orbit
  PrintLn();
  Print("Hilbert series:");
  PrintLn();
  pWrite(H_serVec->m[0]);
  if(!mgrad)
  {
    omFree(tt[0]);
  }
  else
  {
    for(is = lV-1; is >= 0; is--)
 
      omFree( tt[is]);
  }
  omFree(tt);
  omFree(xx[0]);
  omFree(xx);
  rChangeCurrRing(r);
  rKill(R);
}

hIndAllMult()

void hIndAllMult	(	scmon	pure,
		int	Npure,
		scfmon	rad,
		int	Nrad,
		varset	var,
		int	Nvar
	)

Definition at line 564 of file hdegree.cc.

{
  int  dn, iv, rad0, b, c, x;
  scmon pn;
  scfmon rn;
  if (Nrad < 2)
  {
    dn = Npure + Nrad;
    if (dn > hCo)
    {
      if (!Nrad)
        hCheckIndep(pure);
      else
      {
        pn = *rad;
        for (iv = Nvar; iv; iv--)
        {
          x = var[iv];
          if (pn[x])
          {
            pure[x] = 1;
            hCheckIndep(pure);
            pure[x] = 0;
          }
        }
      }
    }
    return;
  }
  iv = Nvar;
  while(pure[var[iv]]) iv--;
  hStepR(rad, Nrad, var, iv, &rad0);
  iv--;
  if (rad0 < Nrad)
  {
    pn = hGetpure(pure);
    rn = hGetmem(Nrad, rad, radmem[iv]);
    pn[var[iv + 1]] = 1;
    hIndAllMult(pn, Npure + 1, rn, rad0, var, iv);
    pn[var[iv + 1]] = 0;
    b = rad0;
    c = Nrad;
    hElimR(rn, &rad0, b, c, var, iv);
    hPure(rn, b, &c, var, iv, pn, &x);
    hLex2R(rn, rad0, b, c, var, iv, hwork);
    rad0 += (c - b);
    hIndAllMult(pn, Npure + x, rn, rad0, var, iv);
  }
  else
  {
    hIndAllMult(pure, Npure, rad, Nrad, var, iv);
  }
}

hIndMult()

void hIndMult	(	scmon	pure,
		int	Npure,
		scfmon	rad,
		int	Nrad,
		varset	var,
		int	Nvar
	)

Definition at line 384 of file hdegree.cc.

{
  int  dn, iv, rad0, b, c, x;
  scmon pn;
  scfmon rn;
  if (Nrad < 2)
  {
    dn = Npure + Nrad;
    if (dn == hCo)
    {
      if (Nrad==0)
        hIndep(pure);
      else
      {
        pn = *rad;
        for (iv = Nvar; iv!=0; iv--)
        {
          x = var[iv];
          if (pn[x])
          {
            pure[x] = 1;
            hIndep(pure);
            pure[x] = 0;
          }
        }
      }
    }
    return;
  }
  iv = Nvar;
  dn = Npure+1;
  if (dn >= hCo)
  {
    if (dn > hCo)
      return;
    loop
    {
      if(!pure[var[iv]])
      {
        if(hNotZero(rad, Nrad, var, iv))
        {
          pure[var[iv]] = 1;
          hIndep(pure);
          pure[var[iv]] = 0;
        }
      }
      iv--;
      if (!iv)
        return;
    }
  }
  while(pure[var[iv]]) iv--;
  hStepR(rad, Nrad, var, iv, &rad0);
  iv--;
  if (rad0 < Nrad)
  {
    pn = hGetpure(pure);
    rn = hGetmem(Nrad, rad, radmem[iv]);
    pn[var[iv + 1]] = 1;
    hIndMult(pn, Npure + 1, rn, rad0, var, iv);
    pn[var[iv + 1]] = 0;
    b = rad0;
    c = Nrad;
    hElimR(rn, &rad0, b, c, var, iv);
    hPure(rn, b, &c, var, iv, pn, &x);
    hLex2R(rn, rad0, b, c, var, iv, hwork);
    rad0 += (c - b);
    hIndMult(pn, Npure + x, rn, rad0, var, iv);
  }
  else
  {
    hIndMult(pure, Npure, rad, Nrad, var, iv);
  }
}

hInit()

scfmon hInit	(	ideal	S,
		ideal	Q,
		int *	Nexist
	)

Definition at line 31 of file hutil.cc.

{
  id_LmTest(S, currRing);
  if (Q!=NULL) id_LmTest(Q, currRing);
 
  hisModule = id_RankFreeModule(S, currRing);
 
  if (hisModule < 0)
    hisModule = 0;
 
  int  sl, ql, i, k = 0;
  polyset si, qi, ss;
  scfmon ex, ek;
 
  if (S!=NULL)
  {
    si = S->m;
    sl = IDELEMS(S);
  }
  else
  {
    si = NULL;
    sl = 0;
  }
  if (Q!=NULL)
  {
    qi = Q->m;
    ql = IDELEMS(Q);
  }
  else
  {
    qi = NULL;
    ql = 0;
  }
  if ((sl + ql) == 0)
  {
    *Nexist = 0;
    return NULL;
  }
  ss = si;
  for (i = sl; i>0; i--)
  {
    if (*ss!=0)
      k++;
    ss++;
  }
  ss = qi;
  for (i = ql; i>0; i--)
  {
    if (*ss!=0)
      k++;
    ss++;
  }
  *Nexist = k;
  if (k==0)
    return NULL;
  ek = ex = (scfmon)omAlloc0(k * sizeof(scmon));
  hsecure = (scfmon) omAlloc0(k * sizeof(scmon));
  for (i = sl; i>0; i--)
  {
    if (*si!=NULL)
    {
      *ek = (scmon) omAlloc(((currRing->N)+1)*sizeof(int));
      p_GetExpV(*si, *ek, currRing);
      ek++;
    }
    si++;
  }
  for (i = ql; i>0; i--)
  {
    if (*qi!=NULL)
    {
      *ek = (scmon) omAlloc(((currRing->N)+1)*sizeof(int));
      p_GetExpV(*qi, *ek, currRing);
      ek++;
    }
    qi++;
  }
  memcpy(hsecure, ex, k * sizeof(scmon));
  return ex;
}

hKill()

void hKill	(	monf	xmem,
		int	Nvar
	)

Definition at line 1010 of file hutil.cc.

{
  int  i;
  for (i = Nvar; i!=0; i--)
  {
    if (xmem[i]->mo!=NULL)
      omFreeSize((ADDRESS)xmem[i]->mo, xmem[i]->a * sizeof(scmon));
    omFreeSize((ADDRESS)xmem[i], LEN_MON);
  }
  omFreeSize((ADDRESS)xmem, (Nvar + 1) * sizeof(monp));
}

hLex2R()

void hLex2R	(	scfmon	rad,
		int	e1,
		int	a2,
		int	e2,
		varset	var,
		int	Nvar,
		scfmon	w
	)

Definition at line 880 of file hutil.cc.

{
  int  j0 = 0, j = 0, i = a2, k, k1;
  scmon n, o;
  if (!e1)
  {
    for (; i < e2; i++)
      rad[i - a2] = rad[i];
    return;
  }
  else if (i == e2)
    return;
  n = rad[j];
  o = rad[i];
  loop
  {
    k = Nvar;
    loop
    {
      k1 = var[k];
      if (!o[k1] && n[k1])
      {
        w[j0] = o;
        j0++;
        i++;
        if (i < e2)
        {
          o = rad[i];
          break;
        }
        else
        {
          for (; j < e1; j++)
          {
            w[j0] = rad[j];
            j0++;
          }
          memcpy(rad, w, (e1 + e2 - a2) * sizeof(scmon));
          return;
        }
      }
      else if (o[k1] && !n[k1])
      {
        w[j0] = n;
        j0++;
        j++;
        if (j < e1)
        {
          n = rad[j];
          break;
        }
        else
        {
          for (; i < e2; i++)
          {
            w[j0] = rad[i];
            j0++;
          }
          memcpy(rad, w, (e1 + e2 - a2) * sizeof(scmon));
          return;
        }
      }
      k--;
    }
  }
}

hLex2S()

void hLex2S	(	scfmon	stc,
		int	e1,
		int	a2,
		int	e2,
		varset	var,
		int	Nvar,
		scfmon	w
	)

Definition at line 812 of file hutil.cc.

{
  int  j0 = 0, j = 0, i = a2, k, k1;
  scmon n, o;
  if (!e1)
  {
    for (; i < e2; i++)
      rad[i - a2] = rad[i];
    return;
  }  else if (i == e2)
    return;
  n = rad[j];
  o = rad[i];
  loop
  {
    k = Nvar;
    loop
    {
      k1 = var[k];
      if (o[k1] < n[k1])
      {
        w[j0] = o;
        j0++;
        i++;
        if (i < e2)
        {
          o = rad[i];
          break;
        }
        else
        {
          for (; j < e1; j++)
          {
            w[j0] = rad[j];
            j0++;
          }
          memcpy(rad, w, (e1 + e2 - a2) * sizeof(scmon));
          return;
        }
      }
      else if (o[k1] > n[k1])
      {
        w[j0] = n;
        j0++;
        j++;
        if (j < e1)
        {
          n = rad[j];
          break;
        }
        else
        {
          for (; i < e2; i++)
          {
            w[j0] = rad[i];
            j0++;
          }
          memcpy(rad, w, (e1 + e2 - a2) * sizeof(scmon));
          return;
        }
      }
      k--;
    }
  }
}

hLexR()

void hLexR	(	scfmon	rad,
		int	Nrad,
		varset	var,
		int	Nvar
	)

Definition at line 565 of file hutil.cc.

{
  int  j = 1, i = 0, k, k1;
  scmon n, o;
  if (Nrad < 2)
    return;
  n = rad[j];
  o = rad[0];
  k = Nvar;
  loop
  {
    k1 = var[k];
    if (!o[k1] && n[k1])
    {
      i++;
      if (i < j)
      {
        o = rad[i];
        k = Nvar;
      }
      else
      {
        j++;
        if (j < Nrad)
        {
          i = 0;
          o = rad[0];
          n = rad[j];
          k = Nvar;
        }
        else
          return;
      }
    }
    else if (o[k1] && !n[k1])
    {
      for (k = j; k > i; k--)
        rad[k] = rad[k - 1];
      rad[i] = n;
      j++;
      if (j < Nrad)
      {
        i = 0;
        o = rad[0];
        n = rad[j];
        k = Nvar;
      }
      else
        return;
    }
    else
      k--;
  }
}

hLexS()

void hLexS	(	scfmon	stc,
		int	Nstc,
		varset	var,
		int	Nvar
	)

Definition at line 506 of file hutil.cc.

{
  if (Nstc < 2)
    return;
  int  j = 1, i = 0;
  scmon n = stc[j];
  scmon o = stc[0];
  int k = Nvar;
  loop
  {
    int k1 = var[k];
    if (o[k1] < n[k1])
    {
      i++;
      if (i < j)
      {
        o = stc[i];
        k = Nvar;
      }
      else
      {
        j++;
        if (j < Nstc)
        {
          i = 0;
          o = stc[0];
          n = stc[j];
          k = Nvar;
        }
        else
          return;
      }
    }
    else if (o[k1] > n[k1])
    {
      int tmp_k;
      for (tmp_k = j; tmp_k > i; tmp_k--)
        stc[tmp_k] = stc[tmp_k - 1];
      stc[i] = n;
      j++;
      if (j < Nstc)
      {
        i = 0;
        o = stc[0];
        n = stc[j];
        k = Nvar;
      }
      else
        return;
    }
    else
    {
      k--;
      if (k<=0) return;
    }
  }
}

hOrdSupp()

void hOrdSupp	(	scfmon	stc,
		int	Nstc,
		varset	var,
		int	Nvar
	)

Definition at line 202 of file hutil.cc.

{
  int  i, i1, j, jj, k, l;
  int  x;
  scmon temp, count;
  float o, h, g, *v1;
 
  v1 = (float *)omAlloc(Nvar * sizeof(float));
  temp = (int *)omAlloc(Nstc * sizeof(int));
  count = (int *)omAlloc(Nstc * sizeof(int));
  for (i = 1; i <= Nvar; i++)
  {
    i1 = var[i];
    *temp = stc[0][i1];
    *count = 1;
    jj = 1;
    for (j = 1; j < Nstc; j++)
    {
      x = stc[j][i1];
      k = 0;
      loop
      {
        if (x > temp[k])
        {
          k++;
          if (k == jj)
          {
            temp[k] = x;
            count[k] = 1;
            jj++;
            break;
          }
        }
        else if (x < temp[k])
        {
          for (l = jj; l > k; l--)
          {
            temp[l] = temp[l-1];
            count[l] = count[l-1];
          }
          temp[k] = x;
          count[k] = 1;
          jj++;
          break;
        }
        else
        {
          count[k]++;
          break;
        }
      }
    }
    h = 0.0;
    o = (float)Nstc/(float)jj;
    for(j = 0; j < jj; j++)
    {
       g = (float)count[j];
       if (g > o)
         g -= o;
       else
         g = o - g;
       if (g > h)
         h = g;
    }
    v1[i-1] = h * (float)jj;
  }
  omFreeSize((ADDRESS)count, Nstc * sizeof(int));
  omFreeSize((ADDRESS)temp, Nstc * sizeof(int));
  for (i = 1; i < Nvar; i++)
  {
    i1 = var[i+1];
    h = v1[i];
    j = 0;
    loop
    {
      if (h > v1[j])
      {
        for (l = i; l > j; l--)
        {
          v1[l] = v1[l-1];
          var[l+1] = var[l];
        }
        v1[j] = h;
        var[j+1] = i1;
        break;
      }
      j++;
      if (j == i)
        break;
    }
  }
  omFreeSize((ADDRESS)v1, Nvar * sizeof(float));
}

hPure()

void hPure	(	scfmon	stc,
		int	a,
		int *	Nstc,
		varset	var,
		int	Nvar,
		scmon	pure,
		int *	Npure
	)

Definition at line 621 of file hutil.cc.

{
  int  nc = *Nstc, np = 0, nq = 0, j, i, i1, c, l;
  scmon x;
  for (j = a; j < nc; j++)
  {
    x = stc[j];
    i = Nvar;
    c = 2;
    l = 0;
    loop
    {
      i1 = var[i];
      if (x[i1])
      {
        c--;
        if (!c)
        {
          l = 0;
          break;
        }
        else if (c == 1)
          l = i1;
      }
      i--;
      if (!i)
        break;
    }
    if (l)
    {
      if (!pure[l])
      {
        np++;
        pure[l] = x[l];
      }
      else if (x[l] < pure[l])
        pure[l] = x[l];
      stc[j] = NULL;
      nq++;
    }
  }
  *Npure = np;
  if (nq!=0)
  {
    *Nstc -= nq;
    hShrink(stc, a, nc);
  }
}

hRadical()

void hRadical	(	scfmon	rad,
		int *	Nrad,
		int	Nvar
	)

Definition at line 411 of file hutil.cc.

{
  int  nc = *Nrad, z = 0, i, j, k;
  scmon n, o;
  if (nc < 2)
    return;
  i = 0;
  j = 1;
  n = rad[j];
  o = rad[0];
  k = Nvar;
  loop
  {
    if ((o[k]!=0) && (n[k]==0))
    {
      loop
      {
        k--;
        if (k==0)
        {
          rad[i] = NULL;
          z++;
          break;
        }
        else
        {
          if ((o[k]==0) && (n[k]!=0))
            break;
        }
      }
      k = Nvar;
    }
    else if (!o[k] && n[k])
    {
      loop
      {
        k--;
        if (!k)
        {
          rad[j] = NULL;
          z++;
          break;
        }
        else
        {
          if (o[k] && !n[k])
            break;
        }
      }
      k = Nvar;
    }
    else
    {
      k--;
      if (!k)
      {
        rad[j] = NULL;
        z++;
        k = Nvar;
      }
    }
    if (k == Nvar)
    {
      if (!rad[j])
        i = j - 1;
      loop
      {
        i++;
        if (i == j)
        {
          i = -1;
          j++;
          if (j < nc)
            n = rad[j];
          else
          {
            if (z)
            {
              *Nrad -= z;
              hShrink(rad, 0, nc);
            }
            return;
          }
        }
        else if (rad[i])
        {
          o = rad[i];
          break;
        }
      }
    }
  }
}

hStaircase()

void hStaircase	(	scfmon	stc,
		int *	Nstc,
		varset	var,
		int	Nvar
	)

Definition at line 313 of file hutil.cc.

{
  int  nc = *Nstc;
  if (nc < 2)
    return;
  int z = 0;
  int i = 0;
  int j = 1;
  scmon n = stc[1 /*j*/];
  scmon o = stc[0];
  int k = Nvar;
  loop
  {
    int k1 = var[k];
    if (o[k1] > n[k1])
    {
      loop
      {
        k--;
        if (k==0)
        {
          stc[i] = NULL;
          z++;
          break;
        }
        else
        {
          k1 = var[k];
          if (o[k1] < n[k1])
            break;
        }
      }
      k = Nvar;
    }
    else if (o[k1] < n[k1])
    {
      loop
      {
        k--;
        if (k==0)
        {
          stc[j] = NULL;
          z++;
          break;
        }
        else
        {
          k1 = var[k];
          if (o[k1] > n[k1])
            break;
        }
      }
      k = Nvar;
    }
    else
    {
      k--;
      if (k==0)
      {
        stc[j] = NULL;
        z++;
        k = Nvar;
      }
    }
    if (k == Nvar)
    {
      if (stc[j]==NULL)
        i = j - 1;
      loop
      {
        i++;
        if (i == j)
        {
          i = -1;
          j++;
          if (j < nc)
            n = stc[j];
          else
          {
            if (z!=0)
            {
              *Nstc -= z;
              hShrink(stc, 0, nc);
            }
            return;
          }
        }
        else if (stc[i]!=NULL)
        {
          o = stc[i];
          break;
        }
      }
    }
  }
}

hStepR()

void hStepR	(	scfmon	rad,
		int	Nrad,
		varset	var,
		int	Nvar,
		int *	a
	)

Definition at line 974 of file hutil.cc.

{
  int  k1, i;
  k1 = var[Nvar];
  i = 0;
  loop
  {
    if (rad[i][k1])
    {
      *a = i;
      return;
    }
    i++;
    if (i == Nrad)
    {
      *a = i;
      return;
    }
  }
}

hStepS()

void hStepS	(	scfmon	stc,
		int	Nstc,
		varset	var,
		int	Nvar,
		int *	a,
		int *	x
	)

Definition at line 949 of file hutil.cc.

{
  int  k1, i;
  int  y;
  k1 = var[Nvar];
  y = *x;
  i = *a;
  loop
  {
    if (y < stc[i][k1])
    {
      *a = i;
      *x = stc[i][k1];
      return;
    }
    i++;
    if (i == Nstc)
    {
      *a = i;
      return;
    }
  }
}

hSupp()

void hSupp	(	scfmon	stc,
		int	Nstc,
		varset	var,
		int *	Nvar
	)

Definition at line 174 of file hutil.cc.

{
  int  nv, i0, i1, i, j;
  nv = i0 = *Nvar;
  i1 = 0;
  for (i = 1; i <= nv; i++)
  {
    j = 0;
    loop
    {
      if (stc[j][i]>0)
      {
        i1++;
        var[i1] = i;
        break;
      }
      j++;
      if (j == Nstc)
      {
        var[i0] = i;
        i0--;
        break;
      }
    }
  }
  *Nvar = i1;
}

RightColonOperation()

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

Definition at line 1673 of file hilb.cc.

{
  /*
   * This returns right colon ideal of a monomial two-sided ideal of
   * the free associative algebra with respect to a monomial 'w'
   * (S:_R w).
   */
  S = minimalMonomialGenSet(S);
  ideal Iw = idInit(1,1);
  Iw = colonIdeal(S, w, lV, Iw, 0);
  return (Iw);
}

slicehilb()

void slicehilb

(

ideal

I

)

Definition at line 656 of file hilb.cc.

{
    //printf("Adi changes are here: \n");
    int i, NNN = 0;
    int steps = 0, prune = 0, moreprune = 0;
    mpz_ptr hilbertcoef;
    int *hilbpower;
    ideal S = idInit(1,1);
    poly q = p_One(currRing);
    ideal X = idInit(1,1);
    X->m[0]=p_One(currRing);
    for(i=1;i<=currRing->N;i++)
    {
      p_SetExp(X->m[0],i,1,currRing);
    }
    p_Setm(X->m[0],currRing);
    I = id_Mult(I,X,currRing);
    ideal Itmp = SortByDeg(I);
    id_Delete(&I,currRing);
    I = Itmp;
    //printf("\n-------------RouneSlice--------------\n");
    rouneslice(I,S,q,X->m[0],prune, moreprune, steps, NNN, hilbertcoef, hilbpower);
    id_Delete(&X,currRing);
    p_Delete(&q,currRing);
    //printf("\nIn total Prune got rid of %i elements\n",prune);
    //printf("\nIn total More Prune got rid of %i elements\n",moreprune);
    //printf("\nSteps of rouneslice: %i\n\n", steps);
    printf("\n//  %8d t^0",1);
    for(i = 0; i<NNN; i++)
    {
      if(mpz_sgn(&hilbertcoef[i])!=0)
      {
        gmp_printf("\n//  %8Zd t^%d",&hilbertcoef[i],hilbpower[i]);
      }
    }
    PrintLn();
    omFreeSize(hilbertcoef, (NNN)*sizeof(mpz_t));
    omFreeSize(hilbpower, (NNN)*sizeof(int));
    //printf("\n-------------------------------------\n");
}

Variable Documentation

hCo

EXTERN_VAR int hCo

Definition at line 47 of file hutil.h.

hexist

EXTERN_VAR scfmon hexist

Definition at line 39 of file hutil.h.

hisModule

EXTERN_VAR int hisModule

Definition at line 44 of file hutil.h.

hMu

EXTERN_VAR long hMu

Definition at line 48 of file hutil.h.

hMu2

EXTERN_VAR int hMu2

Definition at line 47 of file hutil.h.

hNexist

EXTERN_VAR int hNexist

Definition at line 42 of file hutil.h.

hNpure

EXTERN_VAR int hNpure

Definition at line 42 of file hutil.h.

hNrad

EXTERN_VAR int hNrad

Definition at line 42 of file hutil.h.

hNstc

EXTERN_VAR int hNstc

Definition at line 42 of file hutil.h.

hNvar

EXTERN_VAR int hNvar

Definition at line 42 of file hutil.h.

hpur0

EXTERN_VAR scmon hpur0

Definition at line 40 of file hutil.h.

hpure

EXTERN_VAR scmon hpure

Definition at line 40 of file hutil.h.

hrad

EXTERN_VAR scfmon hrad

Definition at line 39 of file hutil.h.

hsel

EXTERN_VAR varset hsel

Definition at line 41 of file hutil.h.

hstc

EXTERN_VAR scfmon hstc

Definition at line 39 of file hutil.h.

hvar

EXTERN_VAR varset hvar

Definition at line 41 of file hutil.h.

hwork

EXTERN_VAR scfmon hwork

Definition at line 39 of file hutil.h.

indlist_bin

EXTERN_VAR omBin indlist_bin

Definition at line 37 of file hutil.h.

ISet

EXTERN_VAR indset ISet

Definition at line 46 of file hutil.h.

JSet

EXTERN_VAR indset JSet

Definition at line 46 of file hutil.h.

radmem

EXTERN_VAR monf radmem

Definition at line 43 of file hutil.h.

stcmem

EXTERN_VAR monf stcmem

Definition at line 43 of file hutil.h.