walk.cc File Reference

#include "kernel/mod2.h"
#include "misc/intvec.h"
#include "Singular/cntrlc.h"
#include "misc/options.h"
#include "omalloc/omalloc.h"
#include "Singular/ipshell.h"
#include "Singular/ipconv.h"
#include "coeffs/ffields.h"
#include "coeffs/coeffs.h"
#include "Singular/subexpr.h"
#include "polys/templates/p_Procs.h"
#include "polys/monomials/maps.h"
#include "kernel/combinatorics/stairc.h"
#include "kernel/GBEngine/kutil.h"
#include "kernel/GBEngine/khstd.h"
#include "Singular/walk.h"
#include "kernel/polys.h"
#include "kernel/ideals.h"
#include "Singular/ipid.h"
#include "Singular/tok.h"
#include "coeffs/numbers.h"
#include "polys/monomials/ring.h"
#include "kernel/GBEngine/kstd1.h"
#include "polys/matpol.h"
#include "polys/weight.h"
#include "kernel/GBEngine/syz.h"
#include "Singular/lists.h"
#include "polys/prCopy.h"
#include "polys/clapsing.h"
#include "coeffs/mpr_complex.h"
#include <cmath>
#include "misc/mylimits.h"

Go to the source code of this file.

Macros
#define	BUCHBERGER_ALG
#define	CHECK_IDEAL_MWALK
#define	INVEPS_SMALL_IN_FRACTAL
#define	INVEPS_SMALL_IN_MPERTVECTOR
#define	INVEPS_SMALL_IN_TRAN
#define	FIRST_STEP_FRACTAL
#define	MSTDCC_FRACTAL

Functions
BOOLEAN	ErrorCheck ()
void	Set_Error (BOOLEAN f)
static intset	initec (int maxnr)
static unsigned long *	initsevS (int maxnr)
static int *	initS_2_R (int maxnr)
static ideal	kInterRedCC (ideal F, ideal Q)
static void	idString (ideal L, const char *st)
static void	ivString (intvec *iv, const char *ch)
static long	gcd (const long a, const long b)
static void	cancel (mpz_t zaehler, mpz_t nenner)
static int	MLmWeightedDegree (const poly p, intvec *weight)
static int	MwalkWeightDegree (poly p, intvec *weight_vector)
static void	MLmWeightedDegree_gmp (mpz_t result, const poly p, intvec *weight)
static poly	MpolyInitialForm (poly g, intvec *curr_weight)
ideal	MwalkInitialForm (ideal G, intvec *ivw)
static int	test_w_in_ConeCC (ideal G, intvec *iv)
static long	Mlcm (long &i1, long &i2)
static long	MivDotProduct (intvec *a, intvec *b)
static intvec *	MivSub (intvec *a, intvec *b)
static intvec *	MExpPol (poly f)
int	MivSame (intvec *u, intvec *v)
int	M3ivSame (intvec *temp, intvec *u, intvec *v)
static ideal	MstdCC (ideal G)
static ideal	MstdhomCC (ideal G)
intvec *	MivMatrixOrder (intvec *iv)
intvec *	MivMatrixOrderRefine (intvec *iv, intvec *iw)
intvec *	Mivdp (int nR)
intvec *	Mivlp (int nR)
intvec *	MPertVectors (ideal G, intvec *ivtarget, int pdeg)
intvec *	MPertVectorslp (ideal G, intvec *ivtarget, int pdeg)
intvec *	MivMatrixOrderlp (int nV)
intvec *	MivMatrixOrderdp (int nV)
intvec *	MivWeightOrderlp (intvec *ivstart)
intvec *	MivWeightOrderdp (intvec *ivstart)
intvec *	MivUnit (int nV)
intvec *	Mfpertvector (ideal G, intvec *ivtarget)
static ideal	MidMult (ideal A, ideal B)
static ideal	MLifttwoIdeal (ideal Gw, ideal M, ideal G)
static int	MivComp (intvec *iva, intvec *ivb)
static int	MivAbsMax (intvec *vec)
static int	MivAbsMaxArg (intvec *vec)
static intvec *	MwalkNextWeightCC (intvec *curr_weight, intvec *target_weight, ideal G)
intvec *	MkInterRedNextWeight (intvec *iva, intvec *ivb, ideal G)
static ring	VMrDefault (intvec *va)
static ring	VMrRefine (intvec *va, intvec *vb)
static ring	VMatrDefault (intvec *va)
static ring	VMatrRefine (intvec *va, intvec *vb)
static void	VMrDefaultlp (void)
static void	DefRingPar (intvec *va)
static void	DefRingParlp (void)
static int	isNegNolVector (intvec *hilb)
static ideal	middleOfCone (ideal G, ideal Gomega)
static ideal	LastGB (ideal G, intvec *curr_weight, int tp_deg)
static int	lengthpoly (ideal G)
static int	maxlengthpoly (ideal G)
static int	islengthpoly2 (ideal G)
static ideal	idHeadCC (ideal h)
static int	test_G_GB_walk (ideal H0, ideal H1)
static ideal	Rec_LastGB (ideal G, intvec *curr_weight, intvec *orig_target_weight, int tp_deg, int npwinc)
ideal	MAltwalk2 (ideal Go, intvec *curr_weight, intvec *target_weight)
static intvec *	NewVectorlp (ideal I)
static intvec *	MWalkRandomNextWeight (ideal G, intvec *orig_M, intvec *target_weight, int weight_rad, int pert_deg)
static ideal	REC_GB_Mwalk (ideal G, intvec *curr_weight, intvec *orig_target_weight, int tp_deg, int npwinc)
ideal	MwalkAlt (ideal Go, intvec *curr_weight, intvec *target_weight)
ideal	Mwalk (ideal Go, intvec *orig_M, intvec *target_M, ring baseRing, int reduction, int printout)
ideal	Mrwalk (ideal Go, intvec *orig_M, intvec *target_M, int weight_rad, int pert_deg, int reduction, int printout)
ideal	Mpwalk (ideal Go, int op_deg, int tp_deg, intvec *curr_weight, intvec *target_weight, int nP, int reduction, int printout)
ideal	Mprwalk (ideal Go, intvec *orig_M, intvec *target_M, int weight_rad, int op_deg, int tp_deg, int nP, int reduction, int printout)
intvec *	MMatrixone (int nV)
static ideal	rec_fractal_call (ideal G, int nlev, intvec *ivtarget, int reduction, int printout)
static ideal	rec_r_fractal_call (ideal G, int nlev, intvec *ivtarget, int weight_rad, int reduction, int printout)
ideal	Mfwalk (ideal G, intvec *ivstart, intvec *ivtarget, int reduction, int printout)
ideal	Mfrwalk (ideal G, intvec *ivstart, intvec *ivtarget, int weight_rad, int reduction, int printout)
ideal	TranMImprovwalk (ideal G, intvec *curr_weight, intvec *target_tmp, int nP)
static ideal	Mpwalk_MAltwalk1 (ideal Go, intvec *curr_weight, int tp_deg)
ideal	MAltwalk1 (ideal Go, int op_deg, int tp_deg, intvec *curr_weight, intvec *target_weight)

Variables
VAR int	nstep
	kstd2.cc More...
EXTERN_VAR BOOLEAN	pSetm_error
VAR BOOLEAN	Overflow_Error = FALSE
VAR int	Xnlev
VAR int	ngleich
VAR intvec *	Xsigma
VAR intvec *	Xtau
VAR int	xn
VAR intvec *	Xivinput
VAR intvec *	Xivlp
VAR intvec *	XivNull
VAR int	nnflow
VAR int	Xcall
VAR int	Xngleich

Macro Definition Documentation

BUCHBERGER_ALG

#define BUCHBERGER_ALG

Definition at line 11 of file walk.cc.

CHECK_IDEAL_MWALK

#define CHECK_IDEAL_MWALK

Definition at line 18 of file walk.cc.

FIRST_STEP_FRACTAL

#define FIRST_STEP_FRACTAL

Definition at line 27 of file walk.cc.

INVEPS_SMALL_IN_FRACTAL

#define INVEPS_SMALL_IN_FRACTAL

Definition at line 23 of file walk.cc.

INVEPS_SMALL_IN_MPERTVECTOR

#define INVEPS_SMALL_IN_MPERTVECTOR

Definition at line 24 of file walk.cc.

INVEPS_SMALL_IN_TRAN

#define INVEPS_SMALL_IN_TRAN

Definition at line 25 of file walk.cc.

MSTDCC_FRACTAL

#define MSTDCC_FRACTAL

Definition at line 28 of file walk.cc.

Function Documentation

cancel()

static void cancel ( mpz_t  zaehler, mpz_t  nenner  )

static

Definition at line 588 of file walk.cc.

{
//  assume(zaehler >= 0 && nenner > 0);
  mpz_t g;
  mpz_init(g);
  mpz_gcd(g, zaehler, nenner);
 
  mpz_div(zaehler , zaehler, g);
  mpz_div(nenner ,  nenner, g);
 
  mpz_clear(g);
}

DefRingPar()

static void DefRingPar ( intvec *  va )

static

Definition at line 2939 of file walk.cc.

{
  int nv = currRing->N;
  int nb = rBlocks(currRing) + 1;
 
  ring res=rCopy0(currRing,FALSE,FALSE);
 
  /*weights: entries for 3 blocks: NULL Made:???*/
  res->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr));
  res->wvhdl[0] = (int*) omAlloc(nv*sizeof(int));
  for(int i=0; i<nv; i++)
    res->wvhdl[0][i] = (*va)[i];
 
  /* order: a,lp,C,0 */
 
  res->order = (rRingOrder_t *) omAlloc(nb * sizeof(rRingOrder_t *));
  res->block0 = (int *)omAlloc0(nb * sizeof(int *));
  res->block1 = (int *)omAlloc0(nb * sizeof(int *));
 
  // ringorder a for the first block: var 1..nv
  res->order[0]  = ringorder_a;
  res->block0[0] = 1;
  res->block1[0] = nv;
 
  // ringorder lp for the second block: var 1..nv
  res->order[1]  = ringorder_lp;
  res->block0[1] = 1;
  res->block1[1] = nv;
 
  // ringorder C for the third block
  // it is very important within "idLift",
  // especially, by ring syz_ring=rCurrRingAssure_SyzComp();
  // therefore, nb  must be (nBlocks(currRing)  + 1)
  res->order[2]  = ringorder_C;
 
  // the last block: everything is 0
  res->order[3]  = (rRingOrder_t)0;
 
  // polynomial ring
  res->OrdSgn    = 1;
 
 
  // complete ring intializations
  rComplete(res);
 
  // execute the created ring
  rChangeCurrRing(res);
}

DefRingParlp()

static void DefRingParlp ( void  )

static

Definition at line 2988 of file walk.cc.

{
  int nv = currRing->N;
 
  ring r=rCopy0(currRing,FALSE,FALSE);
 
  int nb = rBlocks(currRing) + 1;
 
  /*weights: entries for 3 blocks: NULL Made:???*/
 
  r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr));
 
  /* order: lp,C,0 */
  r->order = (rRingOrder_t *) omAlloc(nb * sizeof(rRingOrder_t *));
  r->block0 = (int *)omAlloc0(nb * sizeof(int *));
  r->block1 = (int *)omAlloc0(nb * sizeof(int *));
 
  /* ringorder lp for the first block: var 1..nv */
  r->order[0]  = ringorder_lp;
  r->block0[0] = 1;
  r->block1[0] = nv;
 
  /* ringorder C for the second block */
  r->order[1]  = ringorder_C;
 
  /* the last block: everything is 0 */
  r->order[2]  = (rRingOrder_t)0;
 
  /*polynomial ring*/
  r->OrdSgn    = 1;
 
 
//   if (rParameter(currRing)!=NULL)
//   {
//     r->cf->extRing->qideal->m[0]=p_Copy(currRing->cf->extRing->qideal->m[0], currRing->cf->extRing);
//     int l=rPar(currRing);
//     r->cf->extRing->names=(char **)omAlloc(l*sizeof(char_ptr));
//
//     for(int i=l-1;i>=0;i--)
//     {
//       rParameter(r)[i]=omStrDup(rParameter(currRing)[i]);
//     }
//   }
 
  // complete ring intializations
 
  rComplete(r);
 
  // execute the created ring
  rChangeCurrRing(r);
}

ErrorCheck()

BOOLEAN ErrorCheck

(

)

gcd()

static long gcd ( const long  a, const long  b  )

inlinestatic

Definition at line 532 of file walk.cc.

{
  long r, p0 = a, p1 = b;
  //assume(p0 >= 0 && p1 >= 0);
  if(p0 < 0)
  {
    p0 = -p0;
  }
  if(p1 < 0)
  {
    p1 = -p1;
  }
  while(p1 != 0)
  {
    r = p0 % p1;
    p0 = p1;
    p1 = r;
  }
  return p0;
}

idHeadCC()

static ideal idHeadCC ( ideal  h )

static

Definition at line 3513 of file walk.cc.

{
  int i, nH =IDELEMS(h);
 
  ideal m = idInit(nH,h->rank);
 
  for (i=nH-1;i>=0; i--)
  {
    if (h->m[i]!=NULL)
    {
      m->m[i]=pHead(h->m[i]);
    }
  }
  return m;
}

idString()

static void idString ( ideal  L, const char *  st  )

static

Definition at line 424 of file walk.cc.

{
  int i, nL = IDELEMS(L);
 
  Print("\n//  ideal %s =  ", st);
  for(i=0; i<nL-1; i++)
  {
    Print(" %s, ", pString(L->m[i]));
  }
  Print(" %s;", pString(L->m[nL-1]));
}

initec()

static intset initec ( int  maxnr )

inlinestatic

Definition at line 98 of file walk.cc.

{
  return (intset)omAlloc(maxnr*sizeof(int));
}

initS_2_R()

static int * initS_2_R ( int  maxnr )

inlinestatic

Definition at line 107 of file walk.cc.

{
  return (int*)omAlloc0(maxnr*sizeof(int));
}

initsevS()

static unsigned long * initsevS ( int  maxnr )

inlinestatic

Definition at line 103 of file walk.cc.

{
  return (unsigned long*)omAlloc0(maxnr*sizeof(unsigned long));
}

islengthpoly2()

static int islengthpoly2 ( ideal  G )

static

Definition at line 3477 of file walk.cc.

{
  int i;
  for(i=IDELEMS(G)-1; i>=0; i--)
  {
    if((G->m[i]!=NULL) /* len >=0 */
       && (G->m[i]->next!=NULL) /* len >=1 */
       && (G->m[i]->next->next!=NULL)) /* len >=2 */
    {
      return 1;
    }
  }
  return 0;
}

isNegNolVector()

static int isNegNolVector ( intvec *  hilb )

static

Definition at line 3061 of file walk.cc.

{
  int i;
  for(i=hilb->length()-1; i>=0; i--)
  {
    if((* hilb)[i]<=0)
    {
      return 1;
    }
  }
  return 0;
}

ivString()

static void ivString ( intvec *  iv, const char *  ch  )

static

Definition at line 492 of file walk.cc.

{
  int nV = iv->length()-1;
  Print("\n// intvec %s =  ", ch);
 
  for(int i=0; i<nV; i++)
  {
    Print("%d, ", (*iv)[i]);
  }
  Print("%d;", (*iv)[nV]);
}

kInterRedCC()

static ideal kInterRedCC ( ideal  F, ideal  Q  )

static

Definition at line 268 of file walk.cc.

{
  int j;
  kStrategy strat = new skStrategy;
/*
  if (TEST_OPT_PROT)
  {
    writeTime("start InterRed:");
    mflush();
  }
  strat->syzComp     = 0;
*/
  strat->kAllAxis = (currRing->ppNoether) != NULL;
  strat->kNoether=pCopy((currRing->ppNoether));
  strat->ak = id_RankFreeModule(F, currRing);
  initBuchMoraCrit(strat);
  strat->NotUsedAxis = (BOOLEAN *)omAlloc((currRing->N+1)*sizeof(BOOLEAN));
  for(j=currRing->N; j>0; j--)
  {
    strat->NotUsedAxis[j] = TRUE;
  }
  strat->enterS      = enterSBba;
  strat->posInT      = posInT0;
  strat->initEcart   = initEcartNormal;
  strat->sl   = -1;
  strat->tl          = -1;
  strat->tmax        = setmaxT;
  strat->T           = initT();
  strat->R           = initR();
  strat->sevT        = initsevT();
  if(rHasLocalOrMixedOrdering(currRing))
  {
    strat->honey = TRUE;
  }
 
  //initSCC(F,Q,strat);
  initS(F,Q,strat);
 
  /*
  timetmp=clock();//22.01.02
  initSSpecialCC(F,Q,NULL,strat);
  tininitS=tininitS+clock()-timetmp;//22.01.02
  */
  if(TEST_OPT_REDSB)
  {
    strat->noTailReduction=FALSE;
  }
  updateS(TRUE,strat);
 
  if(TEST_OPT_REDSB && TEST_OPT_INTSTRATEGY)
  {
    completeReduce(strat);
  }
  if(strat->kNoether!=NULL) pLmFree(&strat->kNoether);
  omFreeSize((ADDRESS)strat->T,strat->tmax*sizeof(TObject));
  omFreeSize((ADDRESS)strat->ecartS,IDELEMS(strat->Shdl)*sizeof(int));
  omFreeSize((ADDRESS)strat->sevS,IDELEMS(strat->Shdl)*sizeof(unsigned long));
  omFreeSize((ADDRESS)strat->NotUsedAxis,(currRing->N+1)*sizeof(BOOLEAN));
  omfree(strat->sevT);
  omfree(strat->S_2_R);
  omfree(strat->R);
 
  if(strat->fromQ)
  {
    for(j=0; j<IDELEMS(strat->Shdl); j++)
    {
      if(strat->fromQ[j])
      {
        pDelete(&strat->Shdl->m[j]);
      }
    }
    omFreeSize((ADDRESS)strat->fromQ,IDELEMS(strat->Shdl)*sizeof(int));
    strat->fromQ = NULL;
  }
/*
  if (TEST_OPT_PROT)
  {
    writeTime("end Interred:");
    mflush();
  }
*/
  ideal shdl=strat->Shdl;
  idSkipZeroes(shdl);
  delete(strat);
 
  return shdl;
}

LastGB()

static ideal LastGB ( ideal  G, intvec *  curr_weight, int  tp_deg  )

static

Definition at line 3145 of file walk.cc.

{
  BOOLEAN nError = Overflow_Error;
  Overflow_Error = FALSE;
 
  int i, nV = currRing->N;
  int nwalk=0, endwalks=0, nnwinC=1;
  int nlast = 0;
  ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG;
  ring newRing, oldRing, TargetRing;
  intvec* iv_M_lp;
  intvec* target_weight;
  intvec* iv_lp = Mivlp(nV); //define (1,0,...,0)
  intvec* pert_target_vector;
  intvec* ivNull = new intvec(nV);
  intvec* extra_curr_weight = new intvec(nV);
  intvec* next_weight;
 
#ifndef  BUCHBERGER_ALG
  intvec* hilb_func;
#endif
 
  // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
  {
    (*last_omega)[i] = 1;
  }
  (*last_omega)[0] = 10000;
 
  ring EXXRing = currRing;
 
  // compute a pertubed weight vector of the target weight vector
  if(tp_deg > 1 && tp_deg <= nV)
  {
    //..25.03.03 VMrDefaultlp();//    VMrDefault(target_weight);
    if (rParameter (currRing) != NULL)
    {
      DefRingParlp();
    }
    else
    {
      VMrDefaultlp();
    }
    TargetRing = currRing;
    ssG = idrMoveR(G,EXXRing,currRing);
    iv_M_lp = MivMatrixOrderlp(nV);
    //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg);
    target_weight = MPertVectors(ssG, iv_M_lp, tp_deg);
    delete iv_M_lp;
    pert_target_vector = target_weight;
 
    rChangeCurrRing(EXXRing);
    G = idrMoveR(ssG, TargetRing,currRing);
  }
  else
  {
    target_weight = Mivlp(nV);
  }
  //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing));
 
  while(1)
  {
    nwalk++;
    nstep++;
#ifdef TIME_TEST
    to=clock();
#endif
   // compute a next weight vector
    next_weight = MkInterRedNextWeight(curr_weight,target_weight, G);
#ifdef TIME_TEST
    xtnw=xtnw+clock()-to;
#endif
 
#ifdef PRINT_VECTORS
    MivString(curr_weight, target_weight, next_weight);
#endif
 
    if(Overflow_Error == TRUE)
    {
      newRing = currRing;
      nnwinC = 0;
      if(tp_deg == 1)
      {
        nlast = 1;
      }
      delete next_weight;
 
      //idElements(G, "G");
      //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing));
 
      break;
    }
 
    if(MivComp(next_weight, ivNull) == 1)
    {
      //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing));
      newRing = currRing;
      delete next_weight;
      break;
    }
 
    if(MivComp(next_weight, target_weight) == 1)
      endwalks = 1;
 
    for(i=nV-1; i>=0; i--)
    {
      (*extra_curr_weight)[i] = (*curr_weight)[i];
    }
    /* 06.11.01 NOT Changed */
    for(i=nV-1; i>=0; i--)
    {
      (*curr_weight)[i] = (*next_weight)[i];
    }
    oldRing = currRing;
#ifdef TIME_TEST
    to=clock();
#endif
    // compute an initial form ideal of <G> w.r.t. "curr_vector"
    Gomega = MwalkInitialForm(G, curr_weight);
#ifdef TIME_TEST
    xtif=xtif+clock()-to;
#endif
 
#ifdef ENDWALKS
    if(endwalks == 1)
    {
      Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing));
/*
      idElements(Gomega, "Gw");
      headidString(Gomega, "Gw");
*/
    }
#endif
 
#ifndef  BUCHBERGER_ALG
    if(isNolVector(curr_weight) == 0)
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    }
    else
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
    }
#endif // BUCHBERGER_ALG
 
    /* define a new ring that its ordering is "(a(curr_weight),lp) */
    //..25.03.03 VMrDefault(curr_weight);
    if (rParameter (currRing) != NULL)
    {
      DefRingPar(curr_weight);
    }
    else
    {
      rChangeCurrRing(VMrDefault(curr_weight));
    }
    newRing = currRing;
    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
 
#ifdef TIME_TEST
    to=clock();
#endif
    /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */
#ifdef  BUCHBERGER_ALG
    M = MstdhomCC(Gomega1);
#else
    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    delete hilb_func;
#endif // BUCHBERGER_ALG
#ifdef TIME_TEST
    xtstd=xtstd+clock()-to;
#endif
    /* change the ring to oldRing */
    rChangeCurrRing(oldRing);
    M1 =  idrMoveR(M, newRing,currRing);
    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
 
#ifdef TIME_TEST
    to=clock();
#endif
    /* compute a reduced Groebner basis of <G> w.r.t. "newRing" */
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    xtlift=xtlift+clock()-to;
#endif
 
    idDelete(&M1);
    idDelete(&G);
 
    /* change the ring to newRing */
    rChangeCurrRing(newRing);
    F1 = idrMoveR(F, oldRing,currRing);
 
#ifdef TIME_TEST
    to=clock();
#endif
    /* reduce the Groebner basis <G> w.r.t. new ring */
    G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
    xtred=xtred+clock()-to;
#endif
    idDelete(&F1);
 
    if(endwalks == 1)
    {
      //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing));
      break;
    }
 
    delete next_weight;
  }//while
 
  delete ivNull;
 
  if(tp_deg != 1)
  {
    //..25.03.03 VMrDefaultlp();//define and execute the ring "lp"
    if (rParameter (currRing) != NULL)
    {
      DefRingParlp();
    }
    else
    {
      VMrDefaultlp();
    }
    F1 = idrMoveR(G, newRing,currRing);
 
    if(nnwinC == 0 || test_w_in_ConeCC(F1, pert_target_vector) != 1)
    {
      oldRing = currRing;
      rChangeCurrRing(newRing);
      G = idrMoveR(F1, oldRing,currRing);
      Print("\n// takes %d steps and calls the recursion of level %d:",
             nwalk, tp_deg-1);
 
      F1 = LastGB(G,curr_weight, tp_deg-1);
    }
 
    TargetRing = currRing;
    rChangeCurrRing(EXXRing);
    result = idrMoveR(F1, TargetRing,currRing);
  }
  else
  {
    if(nlast == 1)
    {
      //OMEGA_OVERFLOW_LASTGB:
      /*
      if(MivSame(curr_weight, iv_lp) == 1)
        if (rParameter(currRing) != NULL)
          DefRingParlp();
        else
          VMrDefaultlp();
      else
        if (rParameter(currRing) != NULL)
          DefRingPar(curr_weight);
        else
          VMrDefault(curr_weight);
      */
 
        //..25.03.03 VMrDefaultlp();//define and execute the ring "lp"
        if (rParameter (currRing) != NULL)
        {
          DefRingParlp();
        }
        else
        {
          VMrDefaultlp();
        }
 
      F1 = idrMoveR(G, newRing,currRing);
      //Print("\n// Apply \"std\" in ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing));
 
      G = MstdCC(F1);
      idDelete(&F1);
      newRing = currRing;
    }
 
    rChangeCurrRing(EXXRing);
    result = idrMoveR(G, newRing,currRing);
  }
  delete target_weight;
  delete last_omega;
  delete iv_lp;
 
  if(Overflow_Error == FALSE)
  {
    Overflow_Error = nError;
  }
  return(result);
}

lengthpoly()

static int lengthpoly ( ideal  G )

static

Definition at line 3440 of file walk.cc.

{
  int i;
  for(i=IDELEMS(G)-1; i>=0; i--)
  {
    if((G->m[i]!=NULL) /* len >=0 */
       && (G->m[i]->next!=NULL) /* len >=1 */
       && (G->m[i]->next->next!=NULL) /* len >=2 */
       && (G->m[i]->next->next->next!=NULL) /* len >=3 */
       && (G->m[i]->next->next->next->next!=NULL) /* len >=4*/ )
    {
      return 1;
    }
  }
  return 0;
}

M3ivSame()

int M3ivSame	(	intvec *	temp,
		intvec *	u,
		intvec *	v
	)

Definition at line 914 of file walk.cc.

{
  assume(temp->length() == u->length() && u->length() == v->length());
 
  if((MivSame(temp, u)) == 1)
  {
    return 0;
  }
  if((MivSame(temp, v)) == 1)
  {
    return 1;
  }
  return 2;
}

MAltwalk1()

ideal MAltwalk1	(	ideal	Go,
		int	op_deg,
		int	tp_deg,
		intvec *	curr_weight,
		intvec *	target_weight
	)

Definition at line 9671 of file walk.cc.

{
  Set_Error(FALSE  );
  Overflow_Error = FALSE;
#ifdef TIME_TEST
  BOOLEAN nOverflow_Error = FALSE;
#endif
  // Print("// pSetm_Error = (%d)", ErrorCheck());
 
#ifdef TIME_TEST
  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0;
  xftinput = clock();
  clock_t tostd, tproc;
#endif
 
  nstep = 0;
  int i, nV = currRing->N;
  int nwalk=0, endwalks=0;
  int op_tmp = op_deg;
  ideal Gomega, M, F, G, Gomega1, Gomega2, M1, F1;
  ring newRing, oldRing;
  intvec* next_weight;
  intvec* iv_M_dp;
  intvec* ivNull = new intvec(nV);
  intvec* iv_dp = MivUnit(nV);// define (1,1,...,1)
  intvec* exivlp = Mivlp(nV);
  //intvec* extra_curr_weight = new intvec(nV);
#ifndef  BUCHBERGER_ALG
  intvec* hilb_func;
#endif
  intvec* cw_tmp = curr_weight;
 
  // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
  {
    (*last_omega)[i] = 1;
  }
  (*last_omega)[0] = 10000;
 
  ring XXRing = currRing;
 
#ifdef TIME_TEST
  to=clock();
#endif
  /* compute a pertubed weight vector of the original weight vector.
     The perturbation degree is recursive decrease until that vector
     stays inn the correct cone. */
  while(1)
  {
    if(Overflow_Error == FALSE)
    {
      if(MivComp(curr_weight, iv_dp) == 1)
      {
      //rOrdStr(currRing) = "dp"
        if(op_tmp == op_deg)
        {
          G = MstdCC(Go);
          if(op_deg != 1)
          {
            iv_M_dp = MivMatrixOrderdp(nV);
          }
        }
      }
    }
    else
    {
      if(op_tmp == op_deg)
      {
        //rOrdStr(currRing) = (a(...),lp,C)
        if (rParameter(currRing) != NULL)
        {
          DefRingPar(cw_tmp);
        }
        else
        {
          rChangeCurrRing(VMrDefault(cw_tmp));
        }
        G = idrMoveR(Go, XXRing,currRing);
        G = MstdCC(G);
        if(op_deg != 1)
          iv_M_dp = MivMatrixOrder(cw_tmp);
      }
    }
    Overflow_Error = FALSE;
    if(op_deg != 1)
    {
      curr_weight = MPertVectors(G, iv_M_dp, op_deg);
    }
    else
    {
      curr_weight =  cw_tmp;
      break;
    }
    if(Overflow_Error == FALSE)
    {
      break;
    }
    Overflow_Error = TRUE;
    op_deg --;
  }
#ifdef TIME_TEST
  tostd=clock()-to;
#endif
 
  if(op_tmp != 1 )
    delete iv_M_dp;
  delete iv_dp;
 
  if(currRing->order[0] == ringorder_a)
    goto NEXT_VECTOR;
 
  while(1)
  {
    nwalk ++;
    nstep ++;
 
#ifdef TIME_TEST
    to = clock();
#endif
    // compute an initial form ideal of <G> w.r.t. "curr_vector"
    Gomega = MwalkInitialForm(G, curr_weight);
#ifdef TIME_TEST
    xtif=xtif+clock()-to;
#endif
#if 0
    if(Overflow_Error == TRUE)
    {
      for(i=nV-1; i>=0; i--)
        (*curr_weight)[i] = (*extra_curr_weight)[i];
      delete extra_curr_weight;
 
      newRing = currRing;
      goto MSTD_ALT1;
    }
#endif
#ifndef  BUCHBERGER_ALG
    if(isNolVector(curr_weight) == 0)
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    }
    else
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
    }
#endif // BUCHBERGER_ALG
 
    oldRing = currRing;
 
    // define a new ring which ordering is "(a(curr_weight),lp)
    if (rParameter(currRing) != NULL)
    {
      DefRingPar(curr_weight);
    }
    else
    {
      rChangeCurrRing(VMrDefault(curr_weight));
    }
    newRing = currRing;
    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
 
#ifdef TIME_TEST
    to=clock();
#endif
    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
#ifdef  BUCHBERGER_ALG
    M = MstdhomCC(Gomega1);
#else
    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    delete hilb_func;
#endif // BUCHBERGER_ALG
#ifdef TIME_TEST
    xtstd=xtstd+clock()-to;
#endif
 
    // change the ring to oldRing
    rChangeCurrRing(oldRing);
    M1 =  idrMoveR(M, newRing,currRing);
    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
 
#ifdef TIME_TEST
    to=clock();
#endif
    // compute a reduced Groebner basis of <G> w.r.t. "newRing" by the lifting process
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    xtlift=xtlift+clock()-to;
#endif
 
    idDelete(&M1);
    idDelete(&Gomega2);
    idDelete(&G);
 
    // change the ring to newRing
    rChangeCurrRing(newRing);
    F1 = idrMoveR(F, oldRing,currRing);
    if (oldRing!=IDRING(currRingHdl)) rDelete(oldRing); // do not delete the global currRing
    oldRing=NULL;
 
#ifdef TIME_TEST
    to=clock();
#endif
    // reduce the Groebner basis <G> w.r.t. new ring
    G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
    xtred=xtred+clock()-to;
#endif
    idDelete(&F1);
 
    if(endwalks == 1)
    {
      break;
    }
  NEXT_VECTOR:
#ifdef TIME_TEST
    to=clock();
#endif
    // compute a next weight vector
    next_weight = MkInterRedNextWeight(curr_weight,target_weight, G);
#ifdef TIME_TEST
    xtnw=xtnw+clock()-to;
#endif
#ifdef PRINT_VECTORS
    MivString(curr_weight, target_weight, next_weight);
#endif
    if(Overflow_Error == TRUE)
    {
      newRing = currRing;
 
      if (rParameter(currRing) != NULL)
      {
        DefRingPar(target_weight);
      }
      else
      {
        rChangeCurrRing(VMrDefault(target_weight));
      }
      F1 = idrMoveR(G, newRing,currRing);
      G = MstdCC(F1);
      idDelete(&F1);
      newRing = currRing;
      break; //for while
    }
 
 
    /* G is the wanted Groebner basis if next_weight == curr_weight */
    if(MivComp(next_weight, ivNull) == 1)
    {
      newRing = currRing;
      delete next_weight;
      break; //for while
    }
 
    if(MivComp(next_weight, target_weight) == 1)
    {
      if(tp_deg == 1 || MivSame(target_weight, exivlp) == 0)
        endwalks = 1;
      else
      {
       // MSTD_ALT1:
#ifdef TIME_TEST
        nOverflow_Error = Overflow_Error;
        tproc = clock()-xftinput;
#endif
 
        //Print("\n//  main routine takes %d steps and calls \"Mpwalk\" (1,%d):", nwalk,  tp_deg);
 
        // compute the red. GB of <G> w.r.t. the lex order by the "recursive-modified" perturbation walk alg (1,tp_deg)
        G = Mpwalk_MAltwalk1(G, curr_weight, tp_deg);
        delete next_weight;
        break; // for while
      }
    }
 
    //NOT Changed, to free memory
    for(i=nV-1; i>=0; i--)
    {
      //(*extra_curr_weight)[i] = (*curr_weight)[i];
      (*curr_weight)[i] = (*next_weight)[i];
    }
    delete next_weight;
  }//while
 
  rChangeCurrRing(XXRing);
  ideal result = idrMoveR(G, newRing,currRing);
  id_Delete(&G, newRing);
 
  delete ivNull;
  if(op_deg != 1 )
  {
    delete curr_weight;
  }
  delete exivlp;
#ifdef TIME_TEST
/*
  Print("\n// \"Main procedure\"  took %d steps, %.2f sec. and Overflow_Error(%d)",
        nwalk, ((double) tproc)/1000000, nOverflow_Error);
 
  TimeStringFractal(xftinput, tostd, xtif, xtstd,xtextra, xtlift, xtred, xtnw);
*/
 // Print("\n// pSetm_Error = (%d)", ErrorCheck());
 // Print("\n// Overflow_Error? (%d)", Overflow_Error);
 // Print("\n// Awalk1 took %d steps.\n", nstep);
#endif
  return(result);
}

MAltwalk2()

ideal MAltwalk2	(	ideal	Go,
		intvec *	curr_weight,
		intvec *	target_weight
	)

Definition at line 4280 of file walk.cc.

{
  Set_Error(FALSE);
  Overflow_Error = FALSE;
  //BOOLEAN nOverflow_Error = FALSE;
  //Print("// pSetm_Error = (%d)", ErrorCheck());
#ifdef TIME_TEST
  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0;
  xftinput = clock();
  clock_t tostd, tproc;
#endif
  nstep = 0;
  int i, nV = currRing->N;
  int nwalk=0, endwalks=0;
  // int nhilb = 1;
  ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G;
  //ideal  G1;
  //ring endRing;
  ring newRing, oldRing;
  intvec* ivNull = new intvec(nV);
  intvec* next_weight;
  //intvec* extra_curr_weight = new intvec(nV);
  //intvec* hilb_func;
  intvec* exivlp = Mivlp(nV);
  ring XXRing = currRing;
 
  //Print("\n// ring r_input = %s;", rString(currRing));
#ifdef TIME_TEST
  to = clock();
#endif
  /* compute the reduced Groebner basis of the given ideal w.r.t.
     a "fast" monomial order, e.g. degree reverse lex. order (dp) */
  G = MstdCC(Go);
#ifdef TIME_TEST
  tostd=clock()-to;
 
  Print("\n// Computation of the first std took = %.2f sec",
        ((double) tostd)/1000000);
#endif
  if(currRing->order[0] == ringorder_a)
  {
    goto NEXT_VECTOR;
  }
  while(1)
  {
    nwalk ++;
    nstep ++;
#ifdef TIME_TEST
    to = clock();
#endif
    /* compute an initial form ideal of <G> w.r.t. "curr_vector" */
    Gomega = MwalkInitialForm(G, curr_weight);
#ifdef TIME_TEST
    xtif=xtif+clock()-to;
#endif
/*
    if(Overflow_Error == TRUE)
    {
      for(i=nV-1; i>=0; i--)
        (*curr_weight)[i] = (*extra_curr_weight)[i];
      delete extra_curr_weight;
      goto LAST_GB_ALT2;
    }
*/
    oldRing = currRing;
 
    /* define a new ring that its ordering is "(a(curr_weight),lp) */
    if (rParameter(currRing) != NULL)
    {
      DefRingPar(curr_weight);
    }
    else
    {
      rChangeCurrRing(VMrDefault(curr_weight));
    }
    newRing = currRing;
    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
#ifdef TIME_TEST
    to = clock();
#endif
    /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */
    M = MstdhomCC(Gomega1);
#ifdef TIME_TEST
    xtstd=xtstd+clock()-to;
#endif
    /* change the ring to oldRing */
    rChangeCurrRing(oldRing);
    M1 =  idrMoveR(M, newRing,currRing);
    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
#ifdef TIME_TEST
    to = clock();
#endif
    /* compute the reduced Groebner basis of <G> w.r.t. "newRing"
       by the liftig process */
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    xtlift=xtlift+clock()-to;
#endif
    idDelete(&M1);
    idDelete(&Gomega2);
    idDelete(&G);
 
    /* change the ring to newRing */
    rChangeCurrRing(newRing);
    F1 = idrMoveR(F, oldRing,currRing);
#ifdef TIME_TEST
    to = clock();
#endif
    /* reduce the Groebner basis <G> w.r.t. newRing */
    G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
    xtred=xtred+clock()-to;
#endif
    idDelete(&F1);
 
    if(endwalks == 1)
      break;
 
  NEXT_VECTOR:
#ifdef TIME_TEST
    to = clock();
#endif
    /* compute a next weight vector */
    next_weight = MkInterRedNextWeight(curr_weight,target_weight, G);
#ifdef TIME_TEST
    xtnw=xtnw+clock()-to;
#endif
#ifdef PRINT_VECTORS
    MivString(curr_weight, target_weight, next_weight);
#endif
 
    if(Overflow_Error == TRUE)
    {
      /*
        ivString(next_weight, "omega");
        PrintS("\n// ** The weight vector does NOT stay in Cone!!\n");
      */
#ifdef TEST_OVERFLOW
      goto  TEST_OVERFLOW_OI;
#endif
 
      newRing = currRing;
      if (rParameter(currRing) != NULL)
      {
        DefRingPar(target_weight);
      }
      else
      {
        rChangeCurrRing(VMrDefault(target_weight)); // Aenderung
      }
      F1 = idrMoveR(G, newRing,currRing);
      G = MstdCC(F1);
      idDelete(&F1);
      newRing = currRing;
      break;
    }
 
    if(MivComp(next_weight, ivNull) == 1)
    {
      newRing = currRing;
      delete next_weight;
      break;
    }
 
    if(MivComp(next_weight, target_weight) == 1)
    {
      if(MivSame(target_weight, exivlp)==1)
      {
     // LAST_GB_ALT2:
        //nOverflow_Error = Overflow_Error;
#ifdef TIME_TEST
        tproc = clock()-xftinput;
#endif
        //Print("\n// takes %d steps and calls the recursion of level 2:",  nwalk);
        /* call the changed perturbation walk algorithm with degree 2 */
        G = Rec_LastGB(G, curr_weight, target_weight, 2,1);
        newRing = currRing;
        delete next_weight;
        break;
      }
      endwalks = 1;
    }
 
    for(i=nV-1; i>=0; i--)
    {
      //(*extra_curr_weight)[i] = (*curr_weight)[i];
      (*curr_weight)[i] = (*next_weight)[i];
    }
    delete next_weight;
  }
#ifdef TEST_OVERFLOW
 TEST_OVERFLOW_OI:
#endif
  rChangeCurrRing(XXRing);
  G = idrMoveR(G, newRing,currRing);
  delete ivNull;
  delete exivlp;
 
#ifdef TIME_TEST
  /*Print("\n// \"Main procedure\"  took %d steps dnd %.2f sec. Overflow_Error (%d)",
        nwalk, ((double) tproc)/1000000, nOverflow_Error);
*/
  TimeStringFractal(xftinput, tostd, xtif, xtstd, xtextra,xtlift, xtred,xtnw);
 
  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
  //Print("\n// Overflow_Error? (%d)", nOverflow_Error);
  //Print("\n// Awalk2 took %d steps!!", nstep);
#endif
 
  return(G);
}

maxlengthpoly()

static int maxlengthpoly ( ideal  G )

static

Definition at line 3460 of file walk.cc.

{
  int i,k,length=0;
  for(i=IDELEMS(G)-1; i>=0; i--)
  {
    k = pLength(G->m[i]);
    if(k>length)
    {
      length = k;
    }
  }
  return length;
}

MExpPol()

static intvec * MExpPol ( poly  f )

static

Definition at line 877 of file walk.cc.

{
  int i, nR = currRing->N;
  intvec* result = new intvec(nR);
 
  for(i=nR-1; i>=0; i--)
  {
    (*result)[i] = pGetExp(f,i+1);
  }
  return result;
}

Mfpertvector()

intvec * Mfpertvector	(	ideal	G,
		intvec *	ivtarget
	)

Definition at line 1512 of file walk.cc.

{
  int i, j, nG = IDELEMS(G);
  int nV = currRing->N;
  int niv = nV*nV;
 
 
  // Calculate maxA = Max(A2) + Max(A3) + ... + Max(AnV),
  // where the Ai are the i-te rows of the matrix 'targer_ord'.
  int ntemp, maxAi, maxA=0;
  for(i=1; i<nV; i++)
  {
    maxAi = (*ivtarget)[i*nV];
    if(maxAi<0)
    {
      maxAi = -maxAi;
    }
    for(j=i*nV+1; j<(i+1)*nV; j++)
    {
      ntemp = (*ivtarget)[j];
      if(ntemp < 0)
      {
        ntemp = -ntemp;
      }
      if(ntemp > maxAi)
      {
        maxAi = ntemp;
      }
    }
    maxA = maxA + maxAi;
  }
  intvec* ivUnit = Mivdp(nV);
 
  // Calculate inveps = 1/eps, where 1/eps > deg(p)*maxA for all p in G.
  mpz_t tot_deg; mpz_init(tot_deg);
  mpz_t maxdeg; mpz_init(maxdeg);
  mpz_t inveps; mpz_init(inveps);
 
 
  for(i=nG-1; i>=0; i--)
  {
    mpz_set_ui(maxdeg, MwalkWeightDegree(G->m[i], ivUnit));
    if (mpz_cmp(maxdeg,  tot_deg) > 0 )
    {
      mpz_set(tot_deg, maxdeg);
    }
  }
 
  delete ivUnit;
  //inveps = (tot_deg * maxA) + 1;
  mpz_mul_ui(inveps, tot_deg, maxA);
  mpz_add_ui(inveps, inveps, 1);
 
  // takes  "small" inveps
#ifdef INVEPS_SMALL_IN_FRACTAL
  if(mpz_cmp_ui(inveps, nV)>0 && nV > 3)
  {
    mpz_cdiv_q_ui(inveps, inveps, nV);
  }
  // choose the small inverse epsilon
#endif
 
  // PrintLn();  mpz_out_str(stdout, 10, inveps);
 
  // Calculate the perturbed target orders:
  mpz_t *ivtemp=(mpz_t *)omAlloc(nV*sizeof(mpz_t));
  mpz_t *pert_vector=(mpz_t *)omAlloc(niv*sizeof(mpz_t));
 
  for(i=0; i < nV; i++)
  {
    mpz_init_set_si(ivtemp[i], (*ivtarget)[i]);
    mpz_init_set_si(pert_vector[i], (*ivtarget)[i]);
  }
 
  mpz_t ztmp; mpz_init(ztmp);
  // BOOLEAN isneg = FALSE;
 
  for(i=1; i<nV; i++)
  {
    for(j=0; j<nV; j++)
    {
      mpz_mul(ztmp, inveps, ivtemp[j]);
      if((*ivtarget)[i*nV+j]<0)
      {
        mpz_sub_ui(ivtemp[j], ztmp, -(*ivtarget)[i*nV+j]);
      }
      else
      {
        mpz_add_ui(ivtemp[j], ztmp,(*ivtarget)[i*nV+j]);
      }
    }
 
    for(j=0; j<nV; j++)
    {
      mpz_init_set(pert_vector[i*nV+j],ivtemp[j]);
    }
  }
 
  // 2147483647 is max. integer representation in SINGULAR
  mpz_t sing_int;
  mpz_init_set_ui(sing_int,  2147483647);
 
  intvec* result = new intvec(niv);
  BOOLEAN nflow = FALSE;
 
  // computes gcd
  mpz_set(ztmp, pert_vector[0]);
  for(i=0; i<niv; i++)
  {
    mpz_gcd(ztmp, ztmp, pert_vector[i]);
    if(mpz_cmp_si(ztmp, 1)==0)
    {
      break;
    }
  }
 
  for(i=0; i<niv; i++)
  {
    mpz_divexact(pert_vector[i], pert_vector[i], ztmp);
    (* result)[i] = mpz_get_si(pert_vector[i]);
  }
 
  //CHECK_OVERFLOW:
 
  for(i=0; i<niv; i++)
  {
    if(mpz_cmp(pert_vector[i], sing_int)>0)
    {
      if(nflow == FALSE)
      {
        Xnlev = i / nV;
        nflow = TRUE;
        Overflow_Error = TRUE;
        Print("\n// Xlev = %d and the %d-th element is", Xnlev,  i+1);
        PrintS("\n// ** OVERFLOW in \"Mfpertvector\": ");
        mpz_out_str( stdout, 10, pert_vector[i]);
        PrintS(" is greater than 2147483647 (max. integer representation)");
        Print("\n//  So vector[%d] := %d is wrong!!", i+1, (*result)[i]);
      }
    }
  }
  if(Overflow_Error == TRUE)
  {
    ivString(result, "new_vector");
  }
  omFree(pert_vector);
  omFree(ivtemp);
  mpz_clear(ztmp);
  mpz_clear(tot_deg);
  mpz_clear(maxdeg);
  mpz_clear(inveps);
  mpz_clear(sing_int);
 
  rComplete(currRing);
  for(j=0; j<IDELEMS(G); j++)
  {
    poly p=G->m[j];
    while(p!=NULL)
    {
      p_Setm(p,currRing);
      pIter(p);
    }
  }
  return result;
}

Mfrwalk()

ideal Mfrwalk	(	ideal	G,
		intvec *	ivstart,
		intvec *	ivtarget,
		int	weight_rad,
		int	reduction,
		int	printout
	)

Definition at line 8212 of file walk.cc.

{
  BITSET save1 = si_opt_1; // save current options
  //check that weight radius is valid
  if(weight_rad < 0)
  {
    WerrorS("Invalid radius.\n");
    return NULL;
  }
  if(reduction == 0)
  {
    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
    si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
  }
  Set_Error(FALSE);
  Overflow_Error = FALSE;
  //Print("// pSetm_Error = (%d)", ErrorCheck());
  //Print("\n// ring ro = %s;", rString(currRing));
 
  nnflow = 0;
  Xngleich = 0;
  Xcall = 0;
#ifdef TIME_TEST
  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0;
  xftinput = clock();
#endif
  ring  oldRing = currRing;
  int i, nV = currRing->N;
  XivNull = new intvec(nV);
  Xivinput = ivtarget;
  ngleich = 0;
#ifdef TIME_TEST
  to=clock();
#endif
  ideal I = MstdCC(G);
  G = NULL;
#ifdef TIME_TEST
  xftostd=clock()-to;
#endif
  Xsigma = ivstart;
 
  Xnlev=nV;
 
#ifdef FIRST_STEP_FRACTAL
  ideal Gw = MwalkInitialForm(I, ivstart);
  for(i=IDELEMS(Gw)-1; i>=0; i--)
  {
    if((Gw->m[i]!=NULL) // len >=0
    && (Gw->m[i]->next!=NULL) // len >=1
    && (Gw->m[i]->next->next!=NULL)) // len >=2
    {
      intvec* iv_dp = MivUnit(nV); // define (1,1,...,1)
      intvec* Mdp;
      if(ivstart->length() == nV)
      {
        if(MivSame(ivstart, iv_dp) != 1)
          Mdp = MivWeightOrderdp(ivstart);
        else
          Mdp = MivMatrixOrderdp(nV);
      }
      else
      {
        Mdp = ivstart;
      }
 
      Xsigma = Mfpertvector(I, Mdp);
      Overflow_Error = FALSE;
 
      delete Mdp;
      delete iv_dp;
      break;
    }
  }
  idDelete(&Gw);
#endif
 
  ideal I1;
  intvec* Mlp;
  Xivlp = Mivlp(nV);
 
  if(ivtarget->length() == nV)
  {
    if(MivComp(ivtarget, Xivlp)  != 1)
    {
      if (rParameter(currRing) != NULL)
        DefRingPar(ivtarget);
      else
        rChangeCurrRing(VMrDefault(ivtarget));
 
      I1 = idrMoveR(I, oldRing,currRing);
      Mlp = MivWeightOrderlp(ivtarget);
      Xtau = Mfpertvector(I1, Mlp);
    }
    else
    {
      if (rParameter(currRing) != NULL)
        DefRingParlp();
      else
        VMrDefaultlp();
 
      I1 = idrMoveR(I, oldRing,currRing);
      Mlp =  MivMatrixOrderlp(nV);
      Xtau = Mfpertvector(I1, Mlp);
    }
  }
  else
  {
    rChangeCurrRing(VMatrDefault(ivtarget));
    I1 = idrMoveR(I,oldRing,currRing);
    Mlp =  ivtarget;
    Xtau = Mfpertvector(I1, Mlp);
  }
  delete Mlp;
  Overflow_Error = FALSE;
 
  //ivString(Xsigma, "Xsigma");
  //ivString(Xtau, "Xtau");
 
  id_Delete(&I, oldRing);
  ring tRing = currRing;
  if(ivtarget->length() == nV)
  {
/*
    if (rParameter(currRing) != NULL)
      DefRingPar(ivstart);
    else
      rChangeCurrRing(VMrDefault(ivstart));
*/
    rChangeCurrRing(VMrRefine(ivtarget,ivstart));
  }
  else
  {
    //rChangeCurrRing(VMatrDefault(ivstart));
    rChangeCurrRing(VMatrRefine(ivtarget,ivstart));
  }
 
  I = idrMoveR(I1,tRing,currRing);
#ifdef TIME_TEST
  to=clock();
#endif
  ideal J = MstdCC(I);
  idDelete(&I);
#ifdef TIME_TEST
  xftostd=xftostd+clock()-to;
#endif
  ideal resF;
  ring helpRing = currRing;
 
  J = rec_r_fractal_call(J,1,ivtarget,weight_rad,reduction,printout);
  //idString(J,"//*** Mfrwalk: J");
  //Print("\n//** Mfrwalk hier (1)\n");
  rChangeCurrRing(oldRing);
  //Print("\n//** Mfrwalk hier (2)\n");
  resF = idrMoveR(J, helpRing,currRing);
  //Print("\n//** Mfrwalk hier (3)\n");
  //idSkipZeroes(resF);
  //Print("\n//** Mfrwalk hier (4)\n");
  si_opt_1 = save1; //set original options, e. g. option(RedSB)
  delete Xivlp;
  //delete Xsigma;
  delete Xtau;
  delete XivNull;
  //Print("\n//** Mfrwalk hier (5)\n");
#ifdef TIME_TEST
  TimeStringFractal(xftinput, xftostd, xtif, xtstd, xtextra,
                    xtlift, xtred, xtnw);
 
 
 // Print("\n// pSetm_Error = (%d)", ErrorCheck());
  Print("\n// Overflow_Error? (%d)\n", Overflow_Error);
  Print("\n// the numbers of Overflow_Error (%d)", nnflow);
#endif
  //Print("\n//** Mfrwalk hier (6)\n");
  //idString(resF,"resF");
  //Print("\n//** Mfrwalk hier (7)\n");
  return(resF);
}

Mfwalk()

ideal Mfwalk	(	ideal	G,
		intvec *	ivstart,
		intvec *	ivtarget,
		int	reduction,
		int	printout
	)

Definition at line 8031 of file walk.cc.

{
  BITSET save1 = si_opt_1; // save current options
  if(reduction == 0)
  {
    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
    //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
  }
  Set_Error(FALSE);
  Overflow_Error = FALSE;
  //Print("// pSetm_Error = (%d)", ErrorCheck());
  //Print("\n// ring ro = %s;", rString(currRing));
 
  nnflow = 0;
  Xngleich = 0;
  Xcall = 0;
#ifdef TIME_TEST
  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0;
  xftinput = clock();
#endif
  ring  oldRing = currRing;
  int i, nV = currRing->N;
  XivNull = new intvec(nV);
  Xivinput = ivtarget;
  ngleich = 0;
#ifdef TIME_TEST
  to=clock();
#endif
  ideal I = MstdCC(G);
  G = NULL;
#ifdef TIME_TEST
  xftostd=clock()-to;
#endif
  Xsigma = ivstart;
 
  Xnlev=nV;
 
#ifdef FIRST_STEP_FRACTAL
  ideal Gw = MwalkInitialForm(I, ivstart);
  for(i=IDELEMS(Gw)-1; i>=0; i--)
  {
    if((Gw->m[i]!=NULL) // len >=0
    && (Gw->m[i]->next!=NULL) // len >=1
    && (Gw->m[i]->next->next!=NULL)) // len >=2
    {
      intvec* iv_dp = MivUnit(nV); // define (1,1,...,1)
      intvec* Mdp;
      if(ivstart->length() == nV)
      {
        if(MivSame(ivstart, iv_dp) != 1)
          Mdp = MivWeightOrderdp(ivstart);
        else
          Mdp = MivMatrixOrderdp(nV);
      }
      else
      {
        Mdp = ivstart;
      }
 
      Xsigma = Mfpertvector(I, Mdp);
      Overflow_Error = FALSE;
 
      delete Mdp;
      delete iv_dp;
      break;
    }
  }
  idDelete(&Gw);
#endif
 
  ideal I1;
  intvec* Mlp;
  Xivlp = Mivlp(nV);
 
  if(ivtarget->length() == nV)
  {
    if(MivComp(ivtarget, Xivlp)  != 1)
    {
      if (rParameter(currRing) != NULL)
        DefRingPar(ivtarget);
      else
        rChangeCurrRing(VMrDefault(ivtarget));
 
      I1 = idrMoveR(I, oldRing,currRing);
      Mlp = MivWeightOrderlp(ivtarget);
      Xtau = Mfpertvector(I1, Mlp);
    }
    else
    {
      if (rParameter(currRing) != NULL)
        DefRingParlp();
      else
        VMrDefaultlp();
 
      I1 = idrMoveR(I, oldRing,currRing);
      Mlp =  MivMatrixOrderlp(nV);
      Xtau = Mfpertvector(I1, Mlp);
    }
  }
  else
  {
    rChangeCurrRing(VMatrDefault(ivtarget));
    I1 = idrMoveR(I,oldRing,currRing);
    Mlp =  ivtarget;
    Xtau = Mfpertvector(I1, Mlp);
  }
  delete Mlp;
  Overflow_Error = FALSE;
 
  //ivString(Xsigma, "Xsigma");
  //ivString(Xtau, "Xtau");
 
  id_Delete(&I, oldRing);
  ring tRing = currRing;
  if(ivtarget->length() == nV)
  {
/*
    if (rParameter(currRing) != NULL)
      DefRingPar(ivstart);
    else
      rChangeCurrRing(VMrDefault(ivstart));
*/
    rChangeCurrRing(VMrRefine(ivtarget,ivstart));
  }
  else
  {
    //rChangeCurrRing(VMatrDefault(ivstart));
    rChangeCurrRing(VMatrRefine(ivtarget,ivstart));
  }
 
  I = idrMoveR(I1,tRing,currRing);
#ifdef TIME_TEST
  to=clock();
#endif
  ideal J = MstdCC(I);
  idDelete(&I);
#ifdef TIME_TEST
  xftostd=xftostd+clock()-to;
#endif
  ideal resF;
  ring helpRing = currRing;
 
  J = rec_fractal_call(J,1,ivtarget,reduction,printout);
  //idString(J,"//** Mfwalk: J");
  rChangeCurrRing(oldRing);
  //Print("\n//Mfwalk: (2)\n");
  resF = idrMoveR(J, helpRing,currRing);
  //Print("\n//Mfwalk: (3)\n");
  idSkipZeroes(resF);
  //Print("\n//Mfwalk: (4)\n");
 
  si_opt_1 = save1; //set original options, e. g. option(RedSB)
  delete Xivlp;
  //delete Xsigma;
  delete Xtau;
  delete XivNull;
  //Print("\n//Mfwalk: (5)\n");
#ifdef TIME_TEST
  TimeStringFractal(xftinput, xftostd, xtif, xtstd, xtextra,
                    xtlift, xtred, xtnw);
 
 
  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
  Print("\n// Overflow_Error? (%d)\n", Overflow_Error);
  Print("\n// the numbers of Overflow_Error (%d)", nnflow);
#endif
  //Print("\n//Mfwalk: (6)\n");
  //idString(resF,"//** Mfwalk: resF");
  return(idCopy(resF));
}

middleOfCone()

static ideal middleOfCone ( ideal  G, ideal  Gomega  )

static

Definition at line 3079 of file walk.cc.

{
  BOOLEAN middle = FALSE;
  int i,j,N = IDELEMS(Gomega);
  poly p,lm,factor1,factor2;
 
  ideal Go = idCopy(G);
 
  // check whether leading monomials of G and Gomega coincide
  // and return NULL if not
  for(i=0; i<N; i++)
  {
    if(!pIsConstant(pSub(pCopy(Gomega->m[i]),pCopy(pHead(G->m[i])))))
    {
      idDelete(&Go);
      return NULL;
    }
  }
  for(i=0; i<N; i++)
  {
    for(j=0; j<N; j++)
    {
      if(i!=j)
      {
        p = pCopy(Gomega->m[i]);
        lm = pCopy(Gomega->m[j]);
        pIter(p);
        while(p!=NULL)
        {
          if(pDivisibleBy(lm,p))
          {
            if(middle == FALSE)
            {
              middle = TRUE;
            }
            factor1 = singclap_pdivide(pHead(p),lm,currRing);
            factor2 = pMult(pCopy(factor1),pCopy(Go->m[j]));
            pDelete(&factor1);
            Go->m[i] = pAdd((Go->m[i]),pNeg(pCopy(factor2)));
            pDelete(&factor2);
          }
          pIter(p);
        }
        pDelete(&lm);
        pDelete(&p);
      }
    }
  }
 
  if(middle == TRUE)
  {
    return Go;
  }
  idDelete(&Go);
  return NULL;
}

MidMult()

static ideal MidMult ( ideal  A, ideal  B  )

static

Definition at line 1683 of file walk.cc.

{
  int mA = IDELEMS(A), mB = IDELEMS(B);
 
  if(A==NULL || B==NULL)
  {
    return NULL;
  }
  if(mB < mA)
  {
    mA = mB;
  }
  ideal result = idInit(mA, 1);
 
  int i, k=0;
  for(i=0; i<mA; i++)
    {
      result->m[k] = pMult(A->m[i], pCopy(B->m[i]));
      A->m[i]=NULL;
      if (result->m[k]!=NULL)
      {
        k++;
      }
    }
 
  idDelete(&A);
  idSkipZeroes(result);
  return result;
}

MivAbsMax()

static int MivAbsMax ( intvec *  vec )

static

Definition at line 1815 of file walk.cc.

{
  int i,k;
  if((*vec)[0] < 0)
  {
    k = -(*vec)[0];
  }
  else
  {
    k = (*vec)[0];
  }
  for(i=1; i < (vec->length()); i++)
  {
    if((*vec)[i] < 0)
    {
      if(-(*vec)[i] > k)
      {
        k = -(*vec)[i];
      }
    }
    else
    {
      if((*vec)[i] > k)
      {
        k = (*vec)[i];
      }
    }
  }
  return k;
}

MivAbsMaxArg()

static int MivAbsMaxArg ( intvec *  vec )

static

Definition at line 1850 of file walk.cc.

{
  int k = MivAbsMax(vec);
  int i=0;
  while(1)
  {
    if((*vec)[i] == k || (*vec)[i] == -k)
    {
      break;
    }
    i++;
  }
  return i;
}

MivComp()

static int MivComp ( intvec *  iva, intvec *  ivb  )

inlinestatic

Definition at line 1798 of file walk.cc.

{
  assume(iva->length() == ivb->length());
  int i;
  for(i=iva->length()-1; i>=0; i--)
  {
    if((*iva)[i] - (*ivb)[i] != 0)
    {
      return 0;
    }
  }
  return 1;
}

MivDotProduct()

static long MivDotProduct ( intvec *  a, intvec *  b  )

inlinestatic

Definition at line 845 of file walk.cc.

{
  assume( a->length() ==  b->length());
  int i, n = a->length();
  long result = 0;
 
  for(i=n-1; i>=0; i--)
    {
    result += (*a)[i] * (*b)[i];
    }
  return result;
}

Mivdp()

intvec * Mivdp

(

int

nR

)

Definition at line 1007 of file walk.cc.

{
  int i;
  intvec* ivm = new intvec(nR);
 
  for(i=nR-1; i>=0; i--)
  {
    (*ivm)[i] = 1;
  }
  return ivm;
}

Mivlp()

intvec * Mivlp

(

int

nR

)

Definition at line 1022 of file walk.cc.

{
  intvec* ivm = new intvec(nR);
  (*ivm)[0] = 1;
 
  return ivm;
}

MivMatrixOrder()

intvec * MivMatrixOrder

(

intvec *

iv

)

Definition at line 963 of file walk.cc.

{
  int i, nR = iv->length();
 
  intvec* ivm = new intvec(nR*nR);
 
  for(i=0; i<nR; i++)
  {
    (*ivm)[i] = (*iv)[i];
  }
  for(i=1; i<nR; i++)
  {
    (*ivm)[i*nR+i-1] = 1;
  }
  return ivm;
}

MivMatrixOrderdp()

intvec * MivMatrixOrderdp

(

int

nV

)

Definition at line 1417 of file walk.cc.

{
  int i;
  intvec* ivM = new intvec(nV*nV);
 
  for(i=0; i<nV; i++)
  {
    (*ivM)[i] = 1;
  }
  for(i=1; i<nV; i++)
  {
    (*ivM)[(i+1)*nV - i] = -1;
  }
  return(ivM);
}

MivMatrixOrderlp()

intvec * MivMatrixOrderlp

(

int

nV

)

Definition at line 1401 of file walk.cc.

{
  int i;
  intvec* ivM = new intvec(nV*nV);
 
  for(i=0; i<nV; i++)
  {
    (*ivM)[i*nV + i] = 1;
  }
  return(ivM);
}

MivMatrixOrderRefine()

intvec * MivMatrixOrderRefine	(	intvec *	iv,
		intvec *	iw
	)

Definition at line 983 of file walk.cc.

{
  assume((iv->length())*(iv->length()) == iw->length());
  int i,j, nR = iv->length();
 
  intvec* ivm = new intvec(nR*nR);
 
  for(i=0; i<nR; i++)
  {
    (*ivm)[i] = (*iv)[i];
  }
  for(i=1; i<nR; i++)
  {
    for(j=0; j<nR; j++)
    {
      (*ivm)[j+i*nR] = (*iw)[j+i*nR];
    }
  }
  return ivm;
}

MivSame()

int MivSame	(	intvec *	u,
		intvec *	v
	)

Definition at line 893 of file walk.cc.

{
  assume(u->length() == v->length());
 
  int i, niv = u->length();
 
  for (i=0; i<niv; i++)
  {
    if ((*u)[i] != (*v)[i])
    {
      return 0;
    }
  }
  return 1;
}

MivSub()

static intvec * MivSub ( intvec *  a, intvec *  b  )

static

Definition at line 861 of file walk.cc.

{
  assume( a->length() ==  b->length());
  int i, n = a->length();
  intvec* result = new intvec(n);
 
  for(i=n-1; i>=0; i--)
  {
    (*result)[i] = (*a)[i] - (*b)[i];
  }
  return result;
}

MivUnit()

intvec * MivUnit

(

int

nV

)

Definition at line 1496 of file walk.cc.

{
  int i;
  intvec* ivM = new intvec(nV);
  for(i=nV-1; i>=0; i--)
  {
    (*ivM)[i] = 1;
  }
  return(ivM);
}

MivWeightOrderdp()

intvec * MivWeightOrderdp

(

intvec *

ivstart

)

Definition at line 1456 of file walk.cc.

{
  int i;
  int nV = ivstart->length();
  intvec* ivM = new intvec(nV*nV);
 
  for(i=0; i<nV; i++)
  {
    (*ivM)[i] = (*ivstart)[i];
  }
  for(i=0; i<nV; i++)
  {
    (*ivM)[nV+i] = 1;
  }
  for(i=2; i<nV; i++)
  {
    (*ivM)[(i+1)*nV - i] = -1;
  }
  return(ivM);
}

MivWeightOrderlp()

intvec * MivWeightOrderlp

(

intvec *

ivstart

)

Definition at line 1436 of file walk.cc.

{
  int i;
  int nV = ivstart->length();
  intvec* ivM = new intvec(nV*nV);
 
  for(i=0; i<nV; i++)
  {
    (*ivM)[i] = (*ivstart)[i];
  }
  for(i=1; i<nV; i++)
  {
    (*ivM)[i*nV + i-1] = 1;
  }
  return(ivM);
}

MkInterRedNextWeight()

intvec * MkInterRedNextWeight	(	intvec *	iva,
		intvec *	ivb,
		ideal	G
	)

Definition at line 2570 of file walk.cc.

{
  intvec* tmp = new intvec(iva->length());
  intvec* result;
 
  if(G == NULL)
  {
    return tmp;
  }
  if(MivComp(iva, ivb) == 1)
  {
    return tmp;
  }
  result = MwalkNextWeightCC(iva, ivb, G);
 
  if(MivComp(result, iva) == 1)
  {
    delete result;
    return tmp;
  }
 
  delete tmp;
  return result;
}

Mlcm()

static long Mlcm ( long &  i1, long &  i2  )

inlinestatic

Definition at line 835 of file walk.cc.

{
  long temp = gcd(i1, i2);
  return ((i1 / temp)* i2);
}

MLifttwoIdeal()

static ideal MLifttwoIdeal ( ideal  Gw, ideal  M, ideal  G  )

static

Definition at line 1721 of file walk.cc.

{
  ideal Mtmp = idLift(Gw, M, NULL, FALSE, TRUE, TRUE, NULL);
 
  // If Gw is a GB, then isSB = TRUE, otherwise FALSE
  // So, it is better, if one tests whether Gw is a GB
  // in ideals.cc:
  // idLift (ideal mod, ideal submod,ideal * rest, BOOLEAN goodShape,
  //           BOOLEAN isSB,BOOLEAN divide,matrix * unit)
 
  // Let be Mtmp = {m1,...,ms}, where mi=sum hij.in_gj, for all i=1,...,s
  // We compute F = {f1,...,fs}, where fi=sum hij.gj
  int i, j, nM = IDELEMS(Mtmp);
  ideal idpol, idLG;
  ideal F = idInit(nM, 1);
 
  for(i=0; i<nM; i++)
  {
     idpol = idVec2Ideal(Mtmp->m[i]);
     idLG = MidMult(idpol, G);
     idpol = NULL;
     F->m[i] = NULL;
     for(j=IDELEMS(idLG)-1; j>=0; j--)
     {
       F->m[i] = pAdd(F->m[i], idLG->m[j]);
       idLG->m[j]=NULL;
     }
     idDelete(&idLG);
  }
  idDelete(&Mtmp);
  return F;
}

MLmWeightedDegree()

static int MLmWeightedDegree ( const poly  p, intvec *  weight  )

inlinestatic

Definition at line 621 of file walk.cc.

{
  /* 2147483647 is max. integer representation in SINGULAR */
  mpz_t sing_int;
  mpz_init_set_ui(sing_int,  2147483647);
 
  int i, wgrad;
 
  mpz_t zmul;
  mpz_init(zmul);
  mpz_t zvec;
  mpz_init(zvec);
  mpz_t zsum;
  mpz_init(zsum);
 
  for (i=currRing->N; i>0; i--)
  {
    mpz_set_si(zvec, (*weight)[i-1]);
    mpz_mul_ui(zmul, zvec, pGetExp(p, i));
    mpz_add(zsum, zsum, zmul);
  }
 
  wgrad = mpz_get_ui(zsum);
 
  if(mpz_cmp(zsum, sing_int)>0)
  {
    if(Overflow_Error ==  FALSE)
    {
      PrintLn();
      PrintS("\n// ** OVERFLOW in \"MwalkInitialForm\": ");
      mpz_out_str( stdout, 10, zsum);
      PrintS(" is greater than 2147483647 (max. integer representation)");
      Overflow_Error = TRUE;
    }
  }
 
  mpz_clear(zmul);
  mpz_clear(zvec);
  mpz_clear(zsum);
  mpz_clear(sing_int);
 
  return wgrad;
}

MLmWeightedDegree_gmp()

static void MLmWeightedDegree_gmp ( mpz_t  result, const poly  p, intvec *  weight  )

static

Definition at line 690 of file walk.cc.

{
  /* 2147483647 is max. integer representation in SINGULAR */
  mpz_t sing_int;
  mpz_init_set_ui(sing_int,  2147483647);
 
  int i;
 
  mpz_t zmul;
  mpz_init(zmul);
  mpz_t zvec;
  mpz_init(zvec);
  mpz_t ztmp;
  mpz_init(ztmp);
 
  for (i=currRing->N; i>0; i--)
  {
    mpz_set_si(zvec, (*weight)[i-1]);
    mpz_mul_ui(zmul, zvec, pGetExp(p, i));
    mpz_add(ztmp, ztmp, zmul);
  }
  mpz_init_set(result, ztmp);
  mpz_clear(ztmp);
  mpz_clear(sing_int);
  mpz_clear(zvec);
  mpz_clear(zmul);
}

MMatrixone()

intvec * MMatrixone

(

int

nV

)

Definition at line 6932 of file walk.cc.

{
  int i,j;
  intvec* ivM = new intvec(nV*nV);
 
  for(i=0; i<nV; i++)
    for(j=0; j<nV; j++)
    (*ivM)[i*nV + j] = 1;
 
  return(ivM);
}

MPertVectors()

intvec * MPertVectors	(	ideal	G,
		intvec *	ivtarget,
		int	pdeg
	)

Definition at line 1088 of file walk.cc.

{
  // ivtarget is a matrix order of a degree reverse lex. order
  int nV = currRing->N;
  //assume(pdeg <= nV && pdeg >= 0);
 
  int i, j, nG = IDELEMS(G);
  intvec* v_null =  new intvec(nV);
 
  // Check that the perturbed degree is valid
  if(pdeg > nV || pdeg <= 0)
  {
    WerrorS("//** The perturbed degree is wrong!!");
    return v_null;
  }
  delete v_null;
 
  if(pdeg == 1)
  {
    return ivtarget;
  }
  mpz_t *pert_vector = (mpz_t*)omAlloc(nV*sizeof(mpz_t));
  mpz_t *pert_vector1 = (mpz_t*)omAlloc(nV*sizeof(mpz_t));
 
  for(i=0; i<nV; i++)
  {
    mpz_init_set_si(pert_vector[i], (*ivtarget)[i]);
    mpz_init_set_si(pert_vector1[i], (*ivtarget)[i]);
  }
  // Calculate max1 = Max(A2)+Max(A3)+...+Max(Apdeg),
  // where the Ai are the i-te rows of the matrix target_ord.
  int ntemp, maxAi, maxA=0;
  for(i=1; i<pdeg; i++)
  {
    maxAi = (*ivtarget)[i*nV];
    if(maxAi<0)
    {
      maxAi = -maxAi;
    }
    for(j=i*nV+1; j<(i+1)*nV; j++)
    {
      ntemp = (*ivtarget)[j];
      if(ntemp < 0)
      {
        ntemp = -ntemp;
      }
      if(ntemp > maxAi)
      {
        maxAi = ntemp;
      }
    }
    maxA += maxAi;
  }
 
  // Calculate inveps = 1/eps, where 1/eps > totaldeg(p)*max1 for all p in G.
 
  intvec* ivUnit = Mivdp(nV);
 
  mpz_t tot_deg; mpz_init(tot_deg);
  mpz_t maxdeg; mpz_init(maxdeg);
  mpz_t inveps; mpz_init(inveps);
 
 
  for(i=nG-1; i>=0; i--)
  {
     mpz_set_ui(maxdeg, MwalkWeightDegree(G->m[i], ivUnit));
     if (mpz_cmp(maxdeg,  tot_deg) > 0 )
     {
       mpz_set(tot_deg, maxdeg);
     }
  }
 
  delete ivUnit;
  mpz_mul_ui(inveps, tot_deg, maxA);
  mpz_add_ui(inveps, inveps, 1);
 
 
  // takes  "small" inveps
#ifdef INVEPS_SMALL_IN_MPERTVECTOR
  if(mpz_cmp_ui(inveps, pdeg)>0 && pdeg > 3)
  {
    //  Print("\n// choose the\"small\" inverse epsilon := %d / %d = ", mpz_get_si(inveps), pdeg);
    mpz_fdiv_q_ui(inveps, inveps, pdeg);
    // mpz_out_str(stdout, 10, inveps);
  }
#else
  // PrintS("\n// the \"big\" inverse epsilon: ");
  mpz_out_str(stdout, 10, inveps);
#endif
 
  // pert(A1) = inveps^(pdeg-1)*A1 + inveps^(pdeg-2)*A2+...+A_pdeg,
  // pert_vector := A1
  for( i=1; i < pdeg; i++ )
  {
    for(j=0; j<nV; j++)
    {
      mpz_mul(pert_vector[j], pert_vector[j], inveps);
      if((*ivtarget)[i*nV+j]<0)
      {
        mpz_sub_ui(pert_vector[j], pert_vector[j],-(*ivtarget)[i*nV+j]);
      }
      else
      {
        mpz_add_ui(pert_vector[j], pert_vector[j],(*ivtarget)[i*nV+j]);
      }
    }
  }
 
  // 2147483647 is max. integer representation in SINGULAR
  mpz_t sing_int;
  mpz_init_set_ui(sing_int,  2147483647);
 
  mpz_t check_int;
  mpz_init_set_ui(check_int,  100000);
 
  mpz_t ztemp;
  mpz_init(ztemp);
  mpz_set(ztemp, pert_vector[0]);
  for(i=1; i<nV; i++)
  {
    mpz_gcd(ztemp, ztemp, pert_vector[i]);
    if(mpz_cmp_si(ztemp, 1)  == 0)
    {
      break;
    }
  }
  if(mpz_cmp_si(ztemp, 1) != 0)
  {
    for(i=0; i<nV; i++)
    {
      mpz_divexact(pert_vector[i], pert_vector[i], ztemp);
    }
  }
 
  for(i=0; i<nV; i++)
  {
    if(mpz_cmp(pert_vector[i], check_int)>=0)
    {
      for(j=0; j<nV; j++)
      {
        mpz_fdiv_q_ui(pert_vector1[j], pert_vector[j], 100);
      }
    }
  }
 
  intvec* result = new intvec(nV);
 
  int ntrue=0;
 
  for(i=0; i<nV; i++)
  {
    (*result)[i] = mpz_get_si(pert_vector1[i]);
    if(mpz_cmp(pert_vector1[i], sing_int)>=0)
    {
      ntrue++;
    }
  }
  if(ntrue > 0 || test_w_in_ConeCC(G,result)==0)
  {
    ntrue=0;
    for(i=0; i<nV; i++)
    {
      (*result)[i] = mpz_get_si(pert_vector[i]);
      if(mpz_cmp(pert_vector[i], sing_int)>=0)
      {
        ntrue++;
        if(Overflow_Error == FALSE)
        {
          Overflow_Error = TRUE;
          PrintS("\n// ** OVERFLOW in \"MPertvectors\": ");
          mpz_out_str( stdout, 10, pert_vector[i]);
          PrintS(" is greater than 2147483647 (max. integer representation)");
          Print("\n//  So vector[%d] := %d is wrong!!", i+1, (*result)[i]);
        }
      }
    }
 
    if(Overflow_Error == TRUE)
    {
      ivString(result, "pert_vector");
      Print("\n// %d element(s) of it is overflow!!", ntrue);
    }
  }
 
  mpz_clear(ztemp);
  mpz_clear(sing_int);
  mpz_clear(check_int);
  omFree(pert_vector);
  omFree(pert_vector1);
  mpz_clear(tot_deg);
  mpz_clear(maxdeg);
  mpz_clear(inveps);
 
  rComplete(currRing);
  for(j=0; j<IDELEMS(G); j++)
  {
    poly p=G->m[j];
    while(p!=NULL)
    {
      p_Setm(p,currRing); pIter(p);
    }
  }
  return result;
}

MPertVectorslp()

intvec * MPertVectorslp	(	ideal	G,
		intvec *	ivtarget,
		int	pdeg
	)

Definition at line 1299 of file walk.cc.

{
  // ivtarget is a matrix order of the lex. order
  int nV = currRing->N;
  //assume(pdeg <= nV && pdeg >= 0);
 
  int i, j, nG = IDELEMS(G);
  intvec* pert_vector =  new intvec(nV);
 
  //Checking that the perturbated degree is valid
  if(pdeg > nV || pdeg <= 0)
  {
    WerrorS("//** The perturbed degree is wrong!!");
    return pert_vector;
  }
  for(i=0; i<nV; i++)
  {
    (*pert_vector)[i]=(*ivtarget)[i];
  }
  if(pdeg == 1)
  {
    return pert_vector;
  }
  // Calculate max1 = Max(A2)+Max(A3)+...+Max(Apdeg),
  // where the Ai are the i-te rows of the matrix target_ord.
  int ntemp, maxAi, maxA=0;
  for(i=1; i<pdeg; i++)
  {
    maxAi = (*ivtarget)[i*nV];
    for(j=i*nV+1; j<(i+1)*nV; j++)
    {
      ntemp = (*ivtarget)[j];
      if(ntemp > maxAi)
      {
        maxAi = ntemp;
      }
    }
    maxA += maxAi;
  }
 
  // Calculate inveps := 1/eps, where 1/eps > deg(p)*max1 for all p in G.
  int inveps, tot_deg = 0, maxdeg;
 
  intvec* ivUnit = Mivdp(nV);//19.02
  for(i=nG-1; i>=0; i--)
  {
    // maxdeg = pTotaldegree(G->m[i], currRing); //it's wrong for ex1,2,rose
    maxdeg = MwalkWeightDegree(G->m[i], ivUnit);
    if (maxdeg > tot_deg )
    {
      tot_deg = maxdeg;
    }
  }
  delete ivUnit;
 
  inveps = (tot_deg * maxA) + 1;
 
#ifdef INVEPS_SMALL_IN_FRACTAL
  //  Print("\n// choose the\"small\" inverse epsilon := %d / %d = ", inveps, pdeg);
  if(inveps > pdeg && pdeg > 3)
  {
    inveps = inveps / pdeg;
  }
  // Print(" %d", inveps);
#else
  PrintS("\n// the \"big\" inverse epsilon %d", inveps);
#endif
 
  // Pert(A1) = inveps^(pdeg-1)*A1 + inveps^(pdeg-2)*A2+...+A_pdeg
  for ( i=1; i < pdeg; i++ )
  {
    for(j=0; j<nV; j++)
    {
      (*pert_vector)[j] = inveps*((*pert_vector)[j]) + (*ivtarget)[i*nV+j];
    }
  }
 
  int temp = (*pert_vector)[0];
  for(i=1; i<nV; i++)
  {
    temp = gcd(temp, (*pert_vector)[i]);
    if(temp == 1)
    {
      break;
    }
  }
  if(temp != 1)
  {
    for(i=0; i<nV; i++)
    {
      (*pert_vector)[i] = (*pert_vector)[i] / temp;
    }
  }
 
  intvec* result = pert_vector;
  delete pert_vector;
  return result;
}

MpolyInitialForm()

static poly MpolyInitialForm ( poly  g, intvec *  curr_weight  )

static

Definition at line 722 of file walk.cc.

{
  if(g == NULL)
  {
    return NULL;
  }
  mpz_t max; mpz_init(max);
  mpz_t maxtmp; mpz_init(maxtmp);
 
  poly hg, in_w_g = NULL;
 
  while(g != NULL)
  {
    hg = g;
    pIter(g);
    MLmWeightedDegree_gmp(maxtmp, hg, curr_weight);
 
    if(mpz_cmp(maxtmp, max)>0)
    {
      mpz_set(max, maxtmp);
      if (in_w_g!=NULL) pDelete(&in_w_g);
      in_w_g = pHead(hg);
    }
    else
    {
      if(mpz_cmp(maxtmp, max)==0)
      {
        in_w_g = pAdd(in_w_g, pHead(hg));
      }
    }
  }
  mpz_clear(maxtmp);
  mpz_clear(max);
  return in_w_g;
}

Mprwalk()

ideal Mprwalk	(	ideal	Go,
		intvec *	orig_M,
		intvec *	target_M,
		int	weight_rad,
		int	op_deg,
		int	tp_deg,
		int	nP,
		int	reduction,
		int	printout
	)

Definition at line 6388 of file walk.cc.

{
  BITSET save1 = si_opt_1; // save current options
  if(reduction == 0)
  {
    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
    si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
  }
  Set_Error(FALSE);
  Overflow_Error = FALSE;
  //Print("// pSetm_Error = (%d)", ErrorCheck());
#ifdef TIME_TEST
  clock_t  tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0;
  xtextra=0;
  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0;
  tinput = clock();
 
  clock_t tim;
#endif
  nstep = 0;
  int i, ntwC=1, ntestw=1, nV = currRing->N; //polylength
 
  //check that weight radius is valid
  if(weight_rad < 0)
  {
    WerrorS("Invalid radius.\n");
    return NULL;
  }
 
  //check that perturbation degree is valid
  if(op_deg < 1 || tp_deg < 1 || op_deg > nV || tp_deg > nV)
  {
    WerrorS("Invalid perturbation degree.\n");
    return NULL;
  }
 
  BOOLEAN endwalks = FALSE;
 
  ideal Gomega, M, F, FF, G, Gomega1, Gomega2, M1,F1,Eresult,ssG;
  ring newRing, oldRing, TargetRing;
  intvec* iv_M;
  intvec* iv_M_dp;
  intvec* iv_M_lp;
  intvec* exivlp = Mivlp(nV);
  intvec* curr_weight = new intvec(nV);
  intvec* target_weight = new intvec(nV);
  for(i=0; i<nV; i++)
  {
    (*curr_weight)[i] = (*orig_M)[i];
    (*target_weight)[i] = (*target_M)[i];
  }
  intvec* orig_target = target_weight;
  intvec* pert_target_vector = target_weight;
  intvec* ivNull = new intvec(nV);
  intvec* iv_dp = MivUnit(nV);// define (1,1,...,1)
#ifndef BUCHBERGER_ALG
  intvec* hilb_func;
#endif
  intvec* next_weight;
 
  // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
    (*last_omega)[i] = 1;
  (*last_omega)[0] = 10000;
 
  ring XXRing = currRing;
 
  // perturbs the original vector
  if(orig_M->length() == nV)
  {
    if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) := "dp"
    {
#ifdef TIME_TEST
  to = clock();
#endif
      G = MstdCC(Go);
#ifdef TIME_TEST
      tostd = clock()-to;
#endif
      if(op_deg != 1)
      {
        iv_M_dp = MivMatrixOrderdp(nV);
        curr_weight = MPertVectors(G, iv_M_dp, op_deg);
      }
    }
    else
    {
      //define ring order := (a(curr_weight),lp);
      if (rParameter(currRing) != NULL)
        DefRingPar(curr_weight);
      else
        rChangeCurrRing(VMrDefault(curr_weight));
 
      G = idrMoveR(Go, XXRing,currRing);
#ifdef TIME_TEST
  to = clock();
#endif
      G = MstdCC(G);
#ifdef TIME_TEST
      tostd = clock()-to;
#endif
      if(op_deg != 1)
      {
        iv_M_dp = MivMatrixOrder(curr_weight);
        curr_weight = MPertVectors(G, iv_M_dp, op_deg);
      }
    }
  }
  else
  {
    rChangeCurrRing(VMatrDefault(orig_M));
    G = idrMoveR(Go, XXRing,currRing);
#ifdef TIME_TEST
    to = clock();
#endif
    G = MstdCC(G);
#ifdef TIME_TEST
    tostd = clock()-to;
#endif
    if(op_deg != 1)
    {
      curr_weight = MPertVectors(G, orig_M, op_deg);
    }
  }
 
  delete iv_dp;
  if(op_deg != 1) delete iv_M_dp;
 
  ring HelpRing = currRing;
 
  // perturbs the target weight vector
  if(target_M->length() == nV)
  {
    if(tp_deg > 1 && tp_deg <= nV)
    {
      if (rParameter(currRing) != NULL)
        DefRingPar(target_weight);
      else
        rChangeCurrRing(VMrDefault(target_weight));
 
      TargetRing = currRing;
      ssG = idrMoveR(G,HelpRing,currRing);
      if(MivSame(target_weight, exivlp) == 1)
      {
        iv_M_lp = MivMatrixOrderlp(nV);
        target_weight = MPertVectors(ssG, iv_M_lp, tp_deg);
      }
      else
      {
        iv_M_lp = MivMatrixOrder(target_weight);
        target_weight = MPertVectors(ssG, iv_M_lp, tp_deg);
      }
      delete iv_M_lp;
      pert_target_vector = target_weight;
      rChangeCurrRing(HelpRing);
      G = idrMoveR(ssG, TargetRing,currRing);
    }
  }
  else
  {
    if(tp_deg > 1 && tp_deg <= nV)
    {
      rChangeCurrRing(VMatrDefault(target_M));
      TargetRing = currRing;
      ssG = idrMoveR(G,HelpRing,currRing);
      target_weight = MPertVectors(ssG, target_M, tp_deg);
    }
  }
  if(printout > 0)
  {
    Print("\n//** Mprwalk: Random Perturbation Walk of degree (%d,%d):",op_deg,tp_deg);
    ivString(curr_weight, "//** Mprwalk: new current weight");
    ivString(target_weight, "//** Mprwalk: new target weight");
  }
 
#ifdef TIME_TEST
  to = clock();
#endif
  Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
#ifdef TIME_TEST
  tif = tif + clock()-to; //time for computing initial form ideal
#endif
 
  while(1)
  {
    nstep ++;
#ifdef CHECK_IDEAL_MWALK
    if(printout > 1)
    {
      idString(Gomega,"//** Mprwalk: Gomega");
    }
#endif
 
    if(reduction == 0 && nstep > 1)
    {
      FF = middleOfCone(G,Gomega);
      if(FF != NULL)
      {
        idDelete(&G);
        G = idCopy(FF);
        idDelete(&FF);
        goto NEXT_VECTOR;
      }
    }
 
#ifdef ENDWALKS
    if(endwalks == TRUE)
    {
      if(printout > 0)
      {
        Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
        //idElements(G, "G");
        //headidString(G, "G");
      }
    }
#endif
 
#ifndef  BUCHBERGER_ALG
    if(isNolVector(curr_weight) == 0)
      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    else
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
#endif // BUCHBERGER_ALG
 
    oldRing = currRing;
 
    if(target_M->length() == nV)
    {/*
      // define a new ring with ordering "(a(curr_weight),lp)
      if (rParameter(currRing) != NULL)
        DefRingPar(curr_weight);
      else
        rChangeCurrRing(VMrDefault(curr_weight));
*/
      rChangeCurrRing(VMrRefine(target_M,curr_weight));
    }
    else
    {
      rChangeCurrRing(VMatrRefine(target_M,curr_weight));
    }
    newRing = currRing;
    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
#ifdef ENDWALKS
    if(endwalks == TRUE)
    {
      if(printout > 0)
      {
        Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
 
        //idElements(Gomega1, "Gw");
        //headidString(Gomega1, "headGw");
 
        PrintS("\n// compute a rGB of Gw:\n");
      }
#ifndef  BUCHBERGER_ALG
      ivString(hilb_func, "w");
#endif
    }
#endif
#ifdef TIME_TEST
    tim = clock();
    to = clock();
#endif
    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
#ifdef  BUCHBERGER_ALG
    M = MstdhomCC(Gomega1);
#else
    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    delete hilb_func;
#endif
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(M,"//** Mprwalk: M");
    }
#endif
#ifdef TIME_TEST
    if(endwalks == TRUE)
    {
      xtstd = xtstd+clock()-to;
#ifdef ENDWALKS
      Print("\n// time for the last std(Gw)  = %.2f sec\n",
            ((double) clock())/1000000 -((double)tim) /1000000);
#endif
    }
    else
      tstd=tstd+clock()-to;
#endif
    /* change the ring to oldRing */
    rChangeCurrRing(oldRing);
    M1 =  idrMoveR(M, newRing,currRing);
    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
#ifdef TIME_TEST
    to=clock();
#endif
    /* compute a representation of the generators of submod (M)
       with respect to those of mod (Gomega).
       Gomega is a reduced Groebner basis w.r.t. the current ring */
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    if(endwalks == FALSE)
      tlift = tlift+clock()-to;
    else
      xtlift=clock()-to;
#endif
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(F,"//** Mprwalk: F");
    }
#endif
 
    idDelete(&M1);
    idDelete(&Gomega2);
    idDelete(&G);
 
    // change the ring to newRing
    rChangeCurrRing(newRing);
    if(reduction == 0)
    {
      G = idrMoveR(F,oldRing,currRing);
    }
    else
    {
      F1 = idrMoveR(F, oldRing,currRing);
      if(printout > 2)
      {
        PrintS("\n //** Mprwalk: reduce the Groebner basis.\n");
      }
#ifdef TIME_TEST
      to=clock();
#endif
      G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
      if(endwalks == FALSE)
        tred = tred+clock()-to;
      else
        xtred=clock()-to;
#endif
      idDelete(&F1);
    }
 
    if(endwalks == TRUE)
      break;
 
    NEXT_VECTOR:
#ifdef TIME_TEST
    to = clock();
#endif
    next_weight = MkInterRedNextWeight(curr_weight,target_weight, G);
#ifdef TIME_TEST
    tnw = tnw + clock() - to;
#endif
 
#ifdef TIME_TEST
    to = clock();
#endif
    // compute an initial form ideal of <G> w.r.t. "next_vector"
    Gomega = MwalkInitialForm(G, next_weight);
#ifdef TIME_TEST
    tif = tif + clock()-to; //time for computing initial form ideal
#endif
 
    //lengthpoly(Gomega) = 1 if there is a polynomial in Gomega with at least 3 monomials and 0 otherwise
    if(lengthpoly(Gomega) > 0)
    {
      if(printout > 1)
      {
        PrintS("\n Mpwalk: there is a polynomial in Gomega with at least 3 monomials.\n");
      }
      // low-dimensional facet of the cone
      delete next_weight;
      if(target_M->length() == nV)
      {
        iv_M = MivMatrixOrder(curr_weight);
      }
      else
      {
        iv_M = MivMatrixOrderRefine(curr_weight,target_M);
      }
#ifdef TIME_TEST
      to = clock();
#endif
      next_weight = MWalkRandomNextWeight(G, iv_M, target_weight, weight_rad, op_deg);
#ifdef TIME_TEST
      tnw = tnw + clock() - to;
#endif
      idDelete(&Gomega);
#ifdef TIME_TEST
      to = clock();
#endif
      Gomega = MwalkInitialForm(G, next_weight);
#ifdef TIME_TEST
      tif = tif + clock()-to; //time for computing initial form ideal
#endif
      delete iv_M;
    }
 
#ifdef PRINT_VECTORS
    if(printout > 0)
    {
      MivString(curr_weight, target_weight, next_weight);
    }
#endif
 
    if(Overflow_Error == TRUE)
    {
      ntwC = 0;
      //Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
      //idElements(G, "G");
      delete next_weight;
      goto FINISH_160302;
    }
    if(MivComp(next_weight, ivNull) == 1){
      newRing = currRing;
      delete next_weight;
      //Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
      break;
    }
    if(MivComp(next_weight, target_weight) == 1)
      endwalks = TRUE;
 
    for(i=nV-1; i>=0; i--)
      (*curr_weight)[i] = (*next_weight)[i];
 
    delete next_weight;
  }// end of while-loop
 
  if(tp_deg != 1)
  {
    FINISH_160302:
    if(target_M->length() == nV)
    {
      if(MivSame(orig_target, exivlp) == 1)
        if (rParameter(currRing) != NULL)
          DefRingParlp();
        else
          VMrDefaultlp();
      else
        if (rParameter(currRing) != NULL)
          DefRingPar(orig_target);
        else
          rChangeCurrRing(VMrDefault(orig_target));
    }
    else
    {
      rChangeCurrRing(VMatrDefault(target_M));
    }
    TargetRing=currRing;
    F1 = idrMoveR(G, newRing,currRing);
 
    // check whether the pertubed target vector stays in the correct cone
    if(ntwC != 0)
    {
      ntestw = test_w_in_ConeCC(F1, pert_target_vector);
    }
    if(ntestw != 1 || ntwC == 0)
    {
      if(ntestw != 1 && printout > 2)
      {
#ifdef PRINT_VECTORS
        ivString(pert_target_vector, "tau");
#endif
        PrintS("\n// **Mprwalk: perturbed target vector doesn't stay in cone.");
        Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
        //idElements(F1, "G");
      }
      // LastGB is "better" than the kStd subroutine
#ifdef TIME_TEST
      to=clock();
#endif
      ideal eF1;
      if(nP == 0 || tp_deg == 1 || MivSame(orig_target, exivlp) != 1 || target_M->length() != nV)
      {
        if(printout > 2)
        {
          PrintS("\n// ** Mprwalk: Call \"std\" to compute a Groebner basis.\n");
        }
        eF1 = MstdCC(F1);
        idDelete(&F1);
      }
      else
      {
        if(printout > 2)
        {
          PrintS("\n// **Mprwalk: Call \"LastGB\" to compute a Groebner basis.\n");
        }
        rChangeCurrRing(newRing);
        ideal F2 = idrMoveR(F1, TargetRing,currRing);
        eF1 = LastGB(F2, curr_weight, tp_deg-1);
        F2=NULL;
      }
#ifdef TIME_TEST
      xtextra=clock()-to;
#endif
      ring exTargetRing = currRing;
 
      rChangeCurrRing(XXRing);
      Eresult = idrMoveR(eF1, exTargetRing,currRing);
    }
    else
    {
      rChangeCurrRing(XXRing);
      Eresult = idrMoveR(F1, TargetRing,currRing);
    }
  }
  else
  {
    rChangeCurrRing(XXRing);
    Eresult = idrMoveR(G, newRing,currRing);
  }
  si_opt_1 = save1; //set original options, e. g. option(RedSB)
  delete ivNull;
  if(tp_deg != 1)
    delete target_weight;
 
  if(op_deg != 1 )
    delete curr_weight;
 
  delete exivlp;
  delete last_omega;
 
#ifdef TIME_TEST
  TimeStringFractal(tinput, tostd, tif+xtif, tstd+xtstd,0, tlift+xtlift, tred+xtred,
             tnw+xtnw);
 
  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
  //Print("\n// It took %d steps and Overflow_Error? (%d)\n", nstep,  Overflow_Error);
#endif
 
  if(printout > 0)
  {
    Print("\n//** Mprwalk: Perturbation Walk took %d steps.\n", nstep);
  }
  return(Eresult);
}

Mpwalk()

ideal Mpwalk	(	ideal	Go,
		int	op_deg,
		int	tp_deg,
		intvec *	curr_weight,
		intvec *	target_weight,
		int	nP,
		int	reduction,
		int	printout
	)

Definition at line 5947 of file walk.cc.

{
  BITSET save1 = si_opt_1; // save current options
  if(reduction == 0)
  {
    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
    si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
  }
  Set_Error(FALSE  );
  Overflow_Error = FALSE;
  //Print("// pSetm_Error = (%d)", ErrorCheck());
#ifdef TIME_TEST
  clock_t  tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0;
  xtextra=0;
  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0;
  tinput = clock();
 
  clock_t tim;
#endif
  nstep = 0;
  int i, ntwC=1, ntestw=1,  nV = currRing->N;
 
  //check that perturbation degree is valid
  if(op_deg < 1 || tp_deg < 1 || op_deg > nV || tp_deg > nV)
  {
    WerrorS("Invalid perturbation degree.\n");
    return NULL;
  }
 
  BOOLEAN endwalks = FALSE;
  ideal Gomega, M, F, FF, G, Gomega1, Gomega2, M1,F1,Eresult,ssG;
  ring newRing, oldRing, TargetRing;
  intvec* iv_M_dp;
  intvec* iv_M_lp;
  intvec* exivlp = Mivlp(nV);
  intvec* orig_target = target_weight;
  intvec* pert_target_vector = target_weight;
  intvec* ivNull = new intvec(nV);
  intvec* iv_dp = MivUnit(nV);// define (1,1,...,1)
#ifndef BUCHBERGER_ALG
  intvec* hilb_func;
#endif
  intvec* next_weight;
 
  // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
    (*last_omega)[i] = 1;
  (*last_omega)[0] = 10000;
 
  ring XXRing = currRing;
#ifdef TIME_TEST
  to = clock();
#endif
  // perturbs the original vector
  if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) := "dp"
  {
    G = MstdCC(Go);
#ifdef TIME_TEST
    tostd = clock()-to;
#endif
    if(op_deg != 1){
      iv_M_dp = MivMatrixOrderdp(nV);
      //ivString(iv_M_dp, "iv_M_dp");
      curr_weight = MPertVectors(G, iv_M_dp, op_deg);
    }
  }
  else
  {
    //define ring order := (a(curr_weight),lp);
/*
    if (rParameter(currRing) != NULL)
      DefRingPar(curr_weight);
    else
      rChangeCurrRing(VMrDefault(curr_weight));
*/
    rChangeCurrRing(VMrRefine(target_weight,curr_weight));
 
    G = idrMoveR(Go, XXRing,currRing);
    G = MstdCC(G);
#ifdef TIME_TEST
    tostd = clock()-to;
#endif
    if(op_deg != 1){
      iv_M_dp = MivMatrixOrder(curr_weight);
      curr_weight = MPertVectors(G, iv_M_dp, op_deg);
    }
  }
  delete iv_dp;
  if(op_deg != 1) delete iv_M_dp;
 
  ring HelpRing = currRing;
 
  // perturbs the target weight vector
  if(tp_deg > 1 && tp_deg <= nV)
  {
/*
    if (rParameter(currRing) != NULL)
      DefRingPar(target_weight);
    else
      rChangeCurrRing(VMrDefault(target_weight));
*/
    rChangeCurrRing(VMrRefine(target_weight,curr_weight));
 
    TargetRing = currRing;
    ssG = idrMoveR(G,HelpRing,currRing);
    if(MivSame(target_weight, exivlp) == 1)
    {
      iv_M_lp = MivMatrixOrderlp(nV);
      target_weight = MPertVectors(ssG, iv_M_lp, tp_deg);
    }
    else
    {
      iv_M_lp = MivMatrixOrder(target_weight);
      target_weight = MPertVectors(ssG, iv_M_lp, tp_deg);
    }
    delete iv_M_lp;
    pert_target_vector = target_weight;
    rChangeCurrRing(HelpRing);
    G = idrMoveR(ssG, TargetRing,currRing);
  }
  if(printout > 0)
  {
    Print("\n//** Mpwalk: Perturbation Walk of degree (%d,%d):",op_deg,tp_deg);
#ifdef PRINT_VECTORS
    ivString(curr_weight, "//** Mpwalk: new current weight");
    ivString(target_weight, "//** Mpwalk: new target weight");
#endif
  }
  while(1)
  {
    nstep ++;
#ifdef TIME_TEST
    to = clock();
#endif
    // compute an initial form ideal of <G> w.r.t. the weight vector
    // "curr_weight"
    Gomega = MwalkInitialForm(G, curr_weight);
#ifdef TIME_TEST
    tif = tif + clock()-to;
#endif
#ifdef CHECK_IDEAL_MWALK
    if(printout > 1)
    {
      idString(Gomega,"//** Mpwalk: Gomega");
    }
#endif
    if(reduction == 0 && nstep > 1)
    {
      FF = middleOfCone(G,Gomega);
      if(FF != NULL)
      {
        idDelete(&G);
        G = idCopy(FF);
        idDelete(&FF);
        goto NEXT_VECTOR;
      }
    }
 
#ifdef ENDWALKS
    if(endwalks == TRUE)
    {
      if(printout > 0)
      {
        Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
      }
      //idElements(G, "G");
      //headidString(G, "G");
    }
#endif
 
#ifndef  BUCHBERGER_ALG
    if(isNolVector(curr_weight) == 0)
      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    else
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
#endif // BUCHBERGER_ALG
 
    oldRing = currRing;
 
    // define a new ring with ordering "(a(curr_weight),lp)
/*
    if (rParameter(currRing) != NULL)
      DefRingPar(curr_weight);
    else
      rChangeCurrRing(VMrDefault(curr_weight));
*/
    rChangeCurrRing(VMrRefine(target_weight,curr_weight));
 
    newRing = currRing;
    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
 
#ifdef ENDWALKS
    if(endwalks==TRUE)
    {
      if(printout > 0)
      {
        Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
        //idElements(Gomega1, "Gw");
        //headidString(Gomega1, "headGw");
        PrintS("\n// compute a rGB of Gw:\n");
      }
#ifndef  BUCHBERGER_ALG
      ivString(hilb_func, "w");
#endif
    }
#endif
#ifdef TIME_TEST
    tim = clock();
    to = clock();
#endif
    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
#ifdef  BUCHBERGER_ALG
    M = MstdhomCC(Gomega1);
#else
    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    delete hilb_func;
#endif
 
    if(endwalks == TRUE)
    {
#ifdef TIME_TEST
      xtstd = xtstd+clock()-to;
#endif
#ifdef ENDWALKS
#ifdef TIME_TEST
      if(printout > 1)
      {
        Print("\n// time for the last std(Gw)  = %.2f sec\n",
            ((double) clock())/1000000 -((double)tim) /1000000);
      }
#endif
#endif
    }
    else
    {
#ifdef TIME_TEST
      tstd=tstd+clock()-to;
#endif
    }
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(M,"//** Mpwalk: M");
    }
#endif
    // change the ring to oldRing
    rChangeCurrRing(oldRing);
    M1 =  idrMoveR(M, newRing,currRing);
    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
#ifdef TIME_TEST
    to=clock();
#endif
    /* compute a representation of the generators of submod (M)
       with respect to those of mod (Gomega).
       Gomega is a reduced Groebner basis w.r.t. the current ring */
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    if(endwalks == FALSE)
      tlift = tlift+clock()-to;
    else
      xtlift=clock()-to;
#endif
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(F,"//** Mpwalk: F");
    }
#endif
 
    idDelete(&M1);
    idDelete(&Gomega2);
    idDelete(&G);
 
    // change the ring to newRing
    rChangeCurrRing(newRing);
    if(reduction == 0)
    {
      G = idrMoveR(F,oldRing,currRing);
    }
    else
    {
      F1 = idrMoveR(F, oldRing,currRing);
      if(printout > 2)
      {
        PrintS("\n //** Mpwalk: reduce the Groebner basis.\n");
      }
#ifdef TIME_TEST
      to=clock();
#endif
      G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
      if(endwalks == FALSE)
        tred = tred+clock()-to;
      else
        xtred=clock()-to;
#endif
      idDelete(&F1);
    }
    if(endwalks == TRUE)
      break;
 
    NEXT_VECTOR:
#ifdef TIME_TEST
    to=clock();
#endif
    // compute a next weight vector
    next_weight = MkInterRedNextWeight(curr_weight,target_weight, G);
#ifdef TIME_TEST
    tnw=tnw+clock()-to;
#endif
#ifdef PRINT_VECTORS
    if(printout > 0)
    {
      MivString(curr_weight, target_weight, next_weight);
    }
#endif
 
    if(Overflow_Error == TRUE)
    {
      ntwC = 0;
      //ntestomega = 1;
      //Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
      //idElements(G, "G");
      delete next_weight;
      goto FINISH_160302;
    }
    if(MivComp(next_weight, ivNull) == 1){
      newRing = currRing;
      delete next_weight;
      //Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
      break;
    }
    if(MivComp(next_weight, target_weight) == 1)
      endwalks = TRUE;
 
    for(i=nV-1; i>=0; i--)
      (*curr_weight)[i] = (*next_weight)[i];
 
    delete next_weight;
  }//end of while-loop
 
  if(tp_deg != 1)
  {
  FINISH_160302:
    if(MivSame(orig_target, exivlp) == 1) {
    /*  if (rParameter(currRing) != NULL)
        DefRingParlp();
      else
        VMrDefaultlp();
    else
      if (rParameter(currRing) != NULL)
        DefRingPar(orig_target);
      else*/
        rChangeCurrRing(VMrDefault(orig_target));
    }
    TargetRing=currRing;
    F1 = idrMoveR(G, newRing,currRing);
/*
#ifdef CHECK_IDEAL_MWALK
      headidString(G, "G");
#endif
*/
 
    // check whether the pertubed target vector stays in the correct cone
    if(ntwC != 0){
      ntestw = test_w_in_ConeCC(F1, pert_target_vector);
    }
 
    if( ntestw != 1 || ntwC == 0)
    {
      if(ntestw != 1 && printout >2)
      {
        ivString(pert_target_vector, "tau");
        PrintS("\n// ** perturbed target vector doesn't stay in cone!!");
        Print("\n// ring r%d = %s;\n", nstep, rString(currRing));
        //idElements(F1, "G");
      }
      // LastGB is "better" than the kStd subroutine
#ifdef TIME_TEST
      to=clock();
#endif
      ideal eF1;
      if(nP == 0 || tp_deg == 1 || MivSame(orig_target, exivlp) != 1){
        // PrintS("\n// ** calls \"std\" to compute a GB");
        eF1 = MstdCC(F1);
        idDelete(&F1);
      }
      else {
        // PrintS("\n// ** calls \"LastGB\" to compute a GB");
        rChangeCurrRing(newRing);
        ideal F2 = idrMoveR(F1, TargetRing,currRing);
        eF1 = LastGB(F2, curr_weight, tp_deg-1);
        F2=NULL;
      }
#ifdef TIME_TEST
      xtextra=clock()-to;
#endif
      ring exTargetRing = currRing;
 
      rChangeCurrRing(XXRing);
      Eresult = idrMoveR(eF1, exTargetRing,currRing);
    }
    else{
      rChangeCurrRing(XXRing);
      Eresult = idrMoveR(F1, TargetRing,currRing);
    }
  }
  else {
    rChangeCurrRing(XXRing);
    Eresult = idrMoveR(G, newRing,currRing);
  }
  si_opt_1 = save1; //set original options, e. g. option(RedSB)
  delete ivNull;
  if(tp_deg != 1)
    delete target_weight;
 
  if(op_deg != 1 )
    delete curr_weight;
 
  delete exivlp;
  delete last_omega;
 
#ifdef TIME_TEST
  TimeStringFractal(tinput, tostd, tif+xtif, tstd+xtstd,0, tlift+xtlift, tred+xtred,
             tnw+xtnw);
 
  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
  //Print("\n// It took %d steps and Overflow_Error? (%d)\n", nstep,  Overflow_Error);
#endif
  if(printout > 0)
  {
    Print("\n//** Mpwalk: Perturbation Walk took %d steps.\n", nstep);
  }
  return(Eresult);
}

Mpwalk_MAltwalk1()

static ideal Mpwalk_MAltwalk1 ( ideal  Go, intvec *  curr_weight, int  tp_deg  )

static

Definition at line 9377 of file walk.cc.

{
  Overflow_Error = FALSE;
 // BOOLEAN nOverflow_Error = FALSE;
#ifdef TIME_TEST
  clock_t tproc=0;
  clock_t tinput=clock();
#endif
  int i, nV = currRing->N;
 
  //check that perturbation degree is valid
  if(tp_deg < 1 || tp_deg > nV)
  {
    WerrorS("Invalid perturbation degree.\n");
    return NULL;
  }
 
  int nwalk=0, endwalks=0, ntestwinC=1;
  int tp_deg_tmp = tp_deg;
  ideal Gomega, M, F, G, M1, F1, Gomega1, Gomega2, G1;
  ring newRing, oldRing, TargetRing;
  intvec* next_weight;
  intvec* ivNull = new intvec(nV);
 
  ring YXXRing = currRing;
 
  intvec* iv_M_dpp = MivMatrixOrderlp(nV);
  intvec* target_weight;// = Mivlp(nV);
  ideal ssG;
 
  // perturb the target vector
  while(1)
  {
    if(Overflow_Error == FALSE)
    {
      if (rParameter(currRing) != NULL)
      {
        DefRingParlp();
      }
      else
      {
        VMrDefaultlp();
      }
      TargetRing = currRing;
      ssG = idrMoveR(Go,YXXRing,currRing);
    }
    Overflow_Error = FALSE;
    if(tp_deg != 1)
    {
      target_weight = MPertVectors(ssG, iv_M_dpp, tp_deg);
    }
    else
    {
      target_weight = Mivlp(nV);
      break;
    }
    if(Overflow_Error == FALSE)
    {
      break;
    }
    Overflow_Error = TRUE;
    tp_deg --;
  }
  if(tp_deg != tp_deg_tmp)
  {
    Overflow_Error = TRUE;
    //nOverflow_Error = TRUE;
  }
 
  //  Print("\n// tp_deg = %d", tp_deg);
  // ivString(target_weight, "pert target");
 
  delete iv_M_dpp;
#ifndef  BUCHBERGER_ALG
  intvec* hilb_func;
#endif
  // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
  {
    (*last_omega)[i] = 1;
  }
  (*last_omega)[0] = 10000;
 
  rChangeCurrRing(YXXRing);
  G = idrMoveR(ssG, TargetRing,currRing);
 
  while(1)
  {
    nwalk ++;
    nstep ++;
 
    if(nwalk==1)
    {
      goto FIRST_STEP;
    }
#ifdef TIME_TEST
    to=clock();
#endif
    // compute an initial form ideal of <G> w.r.t. "curr_vector"
    Gomega = MwalkInitialForm(G, curr_weight);
#ifdef TIME_TEST
    xtif=xtif+clock()-to;
#endif
 
#ifndef  BUCHBERGER_ALG
    if(isNolVector(curr_weight) == 0)
      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    else
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
#endif
 
    oldRing = currRing;
 
    // define a new ring that its ordering is "(a(curr_weight),lp)
    if (rParameter(currRing) != NULL)
    {
      DefRingPar(curr_weight);
    }
    else
    {
      rChangeCurrRing(VMrDefault(curr_weight));
    }
    newRing = currRing;
    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
/*
#ifdef ENDWALKS
    if(endwalks == 1)
    {
      Print("\n//  it is  %d-th step!!", nwalk);
      idString(Gomega1, "Gw");
      PrintS("\n//  compute a rGB of Gw:");
    }
#endif
*/
#ifdef TIME_TEST
    to=clock();
#endif
    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
#ifdef  BUCHBERGER_ALG
    M = MstdhomCC(Gomega1);
#else
    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    delete hilb_func;
#endif // BUCHBERGER_ALG
#ifdef TIME_TEST
    xtstd=xtstd+clock()-to;
#endif
 
    // change the ring to oldRing
    rChangeCurrRing(oldRing);
    M1 =  idrMoveR(M, newRing,currRing);
    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
#ifdef TIME_TEST
    to=clock();
#endif
 
    // if(endwalks == 1){PrintS("\n//  Lifting is still working:");}
 
    // compute a reduced Groebner basis of <G> w.r.t. "newRing" by the lifting process
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    xtlift=xtlift+clock()-to;
#endif
 
    idDelete(&M1);
    idDelete(&Gomega2);
    idDelete(&G);
 
    // change the ring to newRing
    rChangeCurrRing(newRing);
    F1 = idrMoveR(F, oldRing,currRing);
#ifdef TIME_TEST
    to=clock();
#endif
    //if(endwalks == 1){ PrintS("\n//  InterRed is still working:");}
    // reduce the Groebner basis <G> w.r.t. the new ring
    G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
    xtred=xtred+clock()-to;
#endif
    idDelete(&F1);
 
    if(endwalks == 1)
      break;
 
  FIRST_STEP:
    Overflow_Error=FALSE;
#ifdef TIME_TEST
    to=clock();
#endif
    // compute a next weight vector
    next_weight = MkInterRedNextWeight(curr_weight,target_weight, G);
#ifdef TIME_TEST
    xtnw=xtnw+clock()-to;
#endif
#ifdef PRINT_VECTORS
    MivString(curr_weight, target_weight, next_weight);
#endif
 
    if(Overflow_Error == TRUE)
    {
      delete next_weight;
      if(tp_deg > 1){
        //nOverflow_Error = Overflow_Error;
#ifdef TIME_TEST
        tproc = tproc+clock()-tinput;
#endif
        //Print("\n// A subroutine takes %d steps and calls \"Mpwalk\" (1,%d):", nwalk, tp_deg-1);
        G1 = Mpwalk_MAltwalk1(G, curr_weight, tp_deg-1);
        goto MPW_Finish;
      }
      else {
        newRing = currRing;
        ntestwinC = 0;
        break;
      }
    }
 
    if(MivComp(next_weight, ivNull) == 1)
    {
      newRing = currRing;
      delete next_weight;
      break;
    }
    if(MivComp(next_weight, target_weight) == 1)
    {
      endwalks = 1;
    }
    for(i=nV-1; i>=0; i--)
    {
      //(*extra_curr_weight)[i] = (*curr_weight)[i];
      (*curr_weight)[i] = (*next_weight)[i];
    }
    delete next_weight;
  }//while
 
  // check whether the pertubed target vector is correct
 
  //define and execute ring with lex. order
  if (rParameter(currRing) != NULL)
  {
    DefRingParlp();
  }
  else
  {
    VMrDefaultlp();
  }
  G1 = idrMoveR(G, newRing,currRing);
 
  if( test_w_in_ConeCC(G1, target_weight) != 1 || ntestwinC == 0)
  {
    //PrintS("\n// The perturbed target vector doesn't STAY in the correct cone!!");
    if(tp_deg == 1)
    {
      //Print("\n// subroutine takes %d steps and applys \"std\"", nwalk);
#ifdef TIME_TEST
      to=clock();
#endif
      ideal G2 = MstdCC(G1);
#ifdef TIME_TEST
      xtextra=xtextra+clock()-to;
#endif
      idDelete(&G1);
      G1 = G2;
      G2 = NULL;
    }
    else
    {
      //nOverflow_Error = Overflow_Error;
#ifdef TIME_TEST
      tproc = tproc+clock()-tinput;
#endif
      // Print("\n// B subroutine takes %d steps and calls \"Mpwalk\" (1,%d) :", nwalk,  tp_deg-1);
      G1 = Mpwalk_MAltwalk1(G1, curr_weight, tp_deg-1);
    }
  }
 
 MPW_Finish:
  newRing = currRing;
  rChangeCurrRing(YXXRing);
  ideal result = idrMoveR(G1, newRing,currRing);
 
  delete ivNull;
  delete target_weight;
 
  //Print("\n// \"Mpwalk\" (1,%d) took %d steps and %.2f sec. Overflow_Error (%d)", tp_deg, nwalk, ((double) clock()-tinput)/1000000, nOverflow_Error);
  //Print("\n// Mprwalk took %d steps. Ring= %s;\n", nwalk, rString(currRing));
  return(result);
}

Mrwalk()

ideal Mrwalk	(	ideal	Go,
		intvec *	orig_M,
		intvec *	target_M,
		int	weight_rad,
		int	pert_deg,
		int	reduction,
		int	printout
	)

Definition at line 5603 of file walk.cc.

{
  BITSET save1 = si_opt_1; // save current options
  if(reduction == 0)
  {
    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
    si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
  }
 
  Set_Error(FALSE);
  Overflow_Error = FALSE;
#ifdef TIME_TEST
  clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0;
  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0;
  tinput = clock();
  clock_t tim;
#endif
  nstep=0;
  int i,nwalk;//polylength;
  int nV = currRing->N;
 
  //check that weight radius is valid
  if(weight_rad < 0)
  {
    WerrorS("Invalid radius.\n");
    return NULL;
  }
 
  //check that perturbation degree is valid
  if(pert_deg > nV || pert_deg < 1)
  {
    WerrorS("Invalid perturbation degree.\n");
    return NULL;
  }
 
  ideal Gomega, M, F,FF, Gomega1, Gomega2, M1;
  ring newRing;
  ring targetRing;
  ring baseRing = currRing;
  ring XXRing = currRing;
  intvec* iv_M;
  intvec* ivNull = new intvec(nV);
  intvec* curr_weight = new intvec(nV);
  intvec* target_weight = new intvec(nV);
  intvec* next_weight= new intvec(nV);
 
  for(i=0; i<nV; i++)
  {
    (*curr_weight)[i] = (*orig_M)[i];
    (*target_weight)[i] = (*target_M)[i];
  }
 
#ifndef BUCHBERGER_ALG
  intvec* hilb_func;
   // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
  {
    (*last_omega)[i] = 1;
  }
  (*last_omega)[0] = 10000;
#endif
  rComplete(currRing);
 
  if(target_M->length() == nV)
  {
    targetRing = VMrDefault(target_weight); // define the target ring
  }
  else
  {
    targetRing = VMatrDefault(target_M);
  }
  if(orig_M->length() == nV)
  {
    //newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)
    newRing=VMrRefine(target_weight, curr_weight);
  }
  else
  {
    newRing = VMatrRefine(target_M,curr_weight);//newRing = VMatrDefault(orig_M);
  }
  rChangeCurrRing(newRing);
#ifdef TIME_TEST
  to = clock();
#endif
  ideal G = MstdCC(idrMoveR(Go,baseRing,currRing));
#ifdef TIME_TEST
  tostd = clock()-to;
#endif
  baseRing = currRing;
  nwalk = 0;
 
#ifdef TIME_TEST
  to = clock();
#endif
  Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
#ifdef TIME_TEST
  tif = tif + clock()-to; //time for computing initial form ideal
#endif
 
  while(1)
  {
    nwalk ++;
    nstep ++;
#ifdef CHECK_IDEAL_MWALK
    if(printout > 1)
    {
      idString(Gomega,"//** Mrwalk: Gomega");
    }
#endif
    if(reduction == 0)
    {
      FF = middleOfCone(G,Gomega);
      if(FF != NULL)
      {
        idDelete(&G);
        G = idCopy(FF);
        idDelete(&FF);
        goto NEXT_VECTOR;
      }
    }
#ifndef  BUCHBERGER_ALG
    if(isNolVector(curr_weight) == 0)
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    }
    else
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
    }
#endif
    if(nwalk == 1)
    {
      if(orig_M->length() == nV)
      {
        /*newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)*/
        newRing=VMrRefine(target_weight, curr_weight);
      }
      else
      {
        newRing = VMatrRefine(target_M,curr_weight);//newRing = VMatrDefault(orig_M);
      }
    }
    else
    {
     if(target_M->length() == nV)
     {
       /*newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)*/
       newRing=VMrRefine(target_weight, curr_weight);
     }
     else
     {
       newRing = VMatrRefine(target_M,curr_weight);
     }
    }
    rChangeCurrRing(newRing);
    Gomega1 = idrMoveR(Gomega, baseRing,currRing);
    idDelete(&Gomega);
    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
#ifdef TIME_TEST
    to = clock();
#endif
#ifndef BUCHBERGER_ALG
    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    delete hilb_func;
#else
    M = kStd(Gomega1,NULL,testHomog,NULL,NULL,0,0,NULL);
#endif
#ifdef TIME_TEST
    tstd = tstd + clock() - to;
#endif
    idSkipZeroes(M);
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(M, "//** Mrwalk: M");
    }
#endif
    //change the ring to baseRing
    rChangeCurrRing(baseRing);
    M1 =  idrMoveR(M, newRing,currRing);
    idDelete(&M);
    Gomega2 = idrMoveR(Gomega1, newRing,currRing);
    idDelete(&Gomega1);
#ifdef TIME_TEST
    to = clock();
#endif
    // compute a representation of the generators of submod (M) with respect to those of mod (Gomega),
    // where Gomega is a reduced Groebner basis w.r.t. the current ring
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    tlift = tlift + clock() - to;
#endif
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(F,"//** Mrwalk: F");
    }
#endif
    idDelete(&Gomega2);
    idDelete(&M1);
    rChangeCurrRing(newRing); // change the ring to newRing
    G = idrMoveR(F,baseRing,currRing);
    idDelete(&F);
    baseRing = currRing;
#ifdef TIME_TEST
    to = clock();
    tstd = tstd + clock() - to;
#endif
    idSkipZeroes(G);
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(G,"//** Mrwalk: G");
    }
#endif
 
    rChangeCurrRing(targetRing);
    G = idrMoveR(G,newRing,currRing);
 
    // test whether target cone is reached
    if(reduction !=0 && test_w_in_ConeCC(G,curr_weight) == 1)
    {
      baseRing = currRing;
      break;
    }
 
    rChangeCurrRing(newRing);
    G = idrMoveR(G,targetRing,currRing);
    baseRing = currRing;
 
    NEXT_VECTOR:
#ifdef TIME_TEST
    to = clock();
#endif
    next_weight = MwalkNextWeightCC(curr_weight,target_weight,G);
#ifdef TIME_TEST
    tnw = tnw + clock() - to;
#endif
 
#ifdef TIME_TEST
    to = clock();
#endif
    Gomega = MwalkInitialForm(G, next_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector"
#ifdef TIME_TEST
    tif = tif + clock()-to; //time for computing initial form ideal
#endif
 
    //lengthpoly(Gomega) = 1 if there is a polynomial in Gomega with at least 3 monomials and 0 otherwise
    //polylength = lengthpoly(Gomega);
    if(lengthpoly(Gomega) > 0)
    {
      //there is a polynomial in Gomega with at least 3 monomials,
      //low-dimensional facet of the cone
      delete next_weight;
      if(target_M->length() == nV)
      {
        //iv_M = MivMatrixOrder(curr_weight);
        iv_M = MivMatrixOrderRefine(curr_weight,target_M);
      }
      else
      {
        iv_M = MivMatrixOrderRefine(curr_weight,target_M);
      }
#ifdef TIME_TEST
      to = clock();
#endif
      next_weight = MWalkRandomNextWeight(G, iv_M, target_weight, weight_rad, pert_deg);
#ifdef TIME_TEST
      tnw = tnw + clock() - to;
#endif
      idDelete(&Gomega);
#ifdef TIME_TEST
      to = clock();
#endif
      Gomega = MwalkInitialForm(G, next_weight);
#ifdef TIME_TEST
      tif = tif + clock()-to; //time for computing initial form ideal
#endif
      delete iv_M;
    }
 
    // test whether target weight vector is reached
    if(MivComp(next_weight, ivNull) == 1 || MivComp(target_weight,curr_weight) == 1)
    {
      baseRing = currRing;
      delete next_weight;
      break;
    }
    if(reduction ==0)
    {
      if(MivComp(curr_weight,next_weight)==1)
      {
        break;
      }
    }
#ifdef PRINT_VECTORS
    if(printout > 0)
    {
      MivString(curr_weight, target_weight, next_weight);
    }
#endif
 
    for(i=nV-1; i>=0; i--)
    {
      (*curr_weight)[i] = (*next_weight)[i];
    }
    delete next_weight;
  }
  baseRing = currRing;
  rChangeCurrRing(XXRing);
  ideal result = idrMoveR(G,baseRing,currRing);
  idDelete(&G);
  delete ivNull;
#ifndef BUCHBERGER_ALG
  delete last_omega;
#endif
  if(printout > 0)
  {
    Print("\n//** Mrwalk: Groebner Walk took %d steps.\n", nstep);
  }
#ifdef TIME_TEST
  TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep);
  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
  //Print("\n// Overflow_Error? (%d)\n", Overflow_Error);
#endif
  si_opt_1 = save1; //set original options
  return(result);
}

MstdCC()

static ideal MstdCC ( ideal  G )

static

Definition at line 932 of file walk.cc.

{
  BITSET save1,save2;
  SI_SAVE_OPT(save1,save2);
  si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
  ideal G1 = kStd(G, NULL, testHomog, NULL);
  SI_RESTORE_OPT(save1,save2);
 
  idSkipZeroes(G1);
  return G1;
}

MstdhomCC()

static ideal MstdhomCC ( ideal  G )

static

Definition at line 947 of file walk.cc.

{
  BITSET save1,save2;
  SI_SAVE_OPT(save1,save2);
  si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB));
  ideal G1 = kStd(G, NULL, isHomog, NULL);
  SI_RESTORE_OPT(save1,save2);
 
  idSkipZeroes(G1);
  return G1;
}

Mwalk()

ideal Mwalk	(	ideal	Go,
		intvec *	orig_M,
		intvec *	target_M,
		ring	baseRing,
		int	reduction,
		int	printout
	)

Definition at line 5302 of file walk.cc.

{
  // save current options
  BITSET save1 = si_opt_1;
  if(reduction == 0)
  {
    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
    si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
  }
  Set_Error(FALSE);
  Overflow_Error = FALSE;
  //BOOLEAN endwalks = FALSE;
#ifdef TIME_TEST
  clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0;
  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0;
  tinput = clock();
  clock_t tim;
#endif
  nstep=0;
  int i,nwalk;
  int nV = baseRing->N;
 
  ideal Gomega, M, F, FF, Gomega1, Gomega2, M1;
  ring newRing;
  ring XXRing = baseRing;
  ring targetRing;
  intvec* ivNull = new intvec(nV);
  intvec* curr_weight = new intvec(nV);
  intvec* target_weight = new intvec(nV);
  intvec* exivlp = Mivlp(nV);
/*
  intvec* tmp_weight = new intvec(nV);
  for(i=0; i<nV; i++)
  {
    (*tmp_weight)[i] = (*orig_M)[i];
  }
*/
  for(i=0; i<nV; i++)
  {
    (*curr_weight)[i] = (*orig_M)[i];
    (*target_weight)[i] = (*target_M)[i];
  }
#ifndef BUCHBERGER_ALG
  intvec* hilb_func;
   // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
  {
    (*last_omega)[i] = 1;
  }
  (*last_omega)[0] = 10000;
#endif
  rComplete(currRing);
#ifdef CHECK_IDEAL_MWALK
  if(printout > 2)
  {
    idString(Go,"//** Mwalk: Go");
  }
#endif
 
  if(target_M->length() == nV)
  {
   // define the target ring
    targetRing = VMrDefault(target_weight);
  }
  else
  {
    targetRing = VMatrDefault(target_M);
  }
  if(orig_M->length() == nV)
  {
    // define a new ring with ordering "(a(curr_weight),lp)
    //newRing = VMrDefault(curr_weight);
    newRing=VMrRefine(target_weight, curr_weight);
  }
  else
  {
    newRing = VMatrRefine(target_M,curr_weight); //newRing = VMatrDefault(orig_M);
  }
  rChangeCurrRing(newRing);
  if(printout > 2)
  {
    Print("\n//** Mrwalk: Current ring r = %s;\n", rString(currRing));
  }
#ifdef TIME_TEST
  to = clock();
#endif
  ideal G = MstdCC(idrMoveR(Go,baseRing,currRing));
#ifdef TIME_TEST
  tostd = clock()-to;
#endif
 
  baseRing = currRing;
  nwalk = 0;
 
  while(1)
  {
    nwalk ++;
    nstep ++;
    //compute an initial form ideal of <G> w.r.t. "curr_vector"
#ifdef TIME_TEST
    to = clock();
#endif
    Gomega = MwalkInitialForm(G, curr_weight);
#ifdef TIME_TEST
    tif = tif + clock()-to;
#endif
 
#ifdef CHECK_IDEAL_MWALK
    if(printout > 1)
    {
      idString(Gomega,"//** Mwalk: Gomega");
    }
#endif
 
    if(reduction == 0)
    {
      FF = middleOfCone(G,Gomega);
      if(FF != NULL)
      {
      PrintS("middle of Cone");
        idDelete(&G);
        G = idCopy(FF);
        idDelete(&FF);
        goto NEXT_VECTOR;
      }
    }
 
#ifndef  BUCHBERGER_ALG
    if(isNolVector(curr_weight) == 0)
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    }
    else
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
    }
#endif
 
    if(nwalk == 1)
    {
      if(orig_M->length() == nV)
      {
        // define a new ring with ordering "(a(curr_weight),lp)
        //newRing = VMrDefault(curr_weight);
        newRing=VMrRefine(target_weight, curr_weight);
      }
      else
      {
        newRing = VMatrRefine(target_M,curr_weight);//newRing = VMatrDefault(orig_M);
      }
    }
    else
    {
     if(target_M->length() == nV)
     {
       //define a new ring with ordering "(a(curr_weight),lp)"
       //newRing = VMrDefault(curr_weight);
       newRing=VMrRefine(target_weight, curr_weight);
     }
     else
     {
       //define a new ring with matrix ordering
       newRing = VMatrRefine(target_M,curr_weight);
     }
    }
    rChangeCurrRing(newRing);
    if(printout > 2)
    {
      Print("\n// Current ring r = %s;\n", rString(currRing));
    }
    Gomega1 = idrMoveR(Gomega, baseRing,currRing);
    idDelete(&Gomega);
    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
#ifdef TIME_TEST
    to = clock();
#endif
#ifndef  BUCHBERGER_ALG
    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    delete hilb_func;
#else
    M = kStd(Gomega1,NULL,testHomog,NULL,NULL,0,0,NULL);
#endif
#ifdef TIME_TEST
    tstd = tstd + clock() - to;
#endif
    idSkipZeroes(M);
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(M, "//** Mwalk: M");
    }
#endif
    //change the ring to baseRing
    rChangeCurrRing(baseRing);
    M1 =  idrMoveR(M, newRing,currRing);
    idDelete(&M);
    Gomega2 = idrMoveR(Gomega1, newRing,currRing);
    idDelete(&Gomega1);
#ifdef TIME_TEST
    to = clock();
#endif
    // compute a representation of the generators of submod (M) with respect to those of mod (Gomega),
    // where Gomega is a reduced Groebner basis w.r.t. the current ring
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    tlift = tlift + clock() - to;
#endif
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(F, "//** Mwalk: F");
    }
#endif
    idDelete(&Gomega2);
    idDelete(&M1);
 
    rChangeCurrRing(newRing); // change the ring to newRing
    G = idrMoveR(F,baseRing,currRing);
    idDelete(&F);
    idSkipZeroes(G);
 
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(G, "//** Mwalk: G");
    }
#endif
 
    rChangeCurrRing(targetRing);
    G = idrMoveR(G,newRing,currRing);
    // test whether target cone is reached
    if(reduction !=0 && test_w_in_ConeCC(G,curr_weight) == 1)
    {
      baseRing = currRing;
      break;
      //endwalks = TRUE;
    }
 
    rChangeCurrRing(newRing);
    G = idrMoveR(G,targetRing,currRing);
    baseRing = currRing;
 
    NEXT_VECTOR:
#ifdef TIME_TEST
    to = clock();
#endif
    intvec* next_weight = MwalkNextWeightCC(curr_weight,target_weight,G);
#ifdef TIME_TEST
    tnw = tnw + clock() - to;
#endif
#ifdef PRINT_VECTORS
    if(printout > 0)
    {
      MivString(curr_weight, target_weight, next_weight);
    }
#endif
    if(reduction ==0)
    {
      if(MivComp(curr_weight,next_weight)==1)
      {
        break;
      }
    }
    if(MivComp(target_weight,curr_weight) == 1)
    {
      break;
    }
 
    for(i=nV-1; i>=0; i--)
    {
      //(*tmp_weight)[i] = (*curr_weight)[i];
      (*curr_weight)[i] = (*next_weight)[i];
    }
    delete next_weight;
  }
  rChangeCurrRing(XXRing);
  ideal result = idrMoveR(G,baseRing,currRing);
  idDelete(&Go);
  idDelete(&G);
  //delete tmp_weight;
  delete ivNull;
  delete exivlp;
#ifndef BUCHBERGER_ALG
  delete last_omega;
#endif
#ifdef TIME_TEST
  TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep);
  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
  //Print("\n// Overflow_Error? (%d)\n", Overflow_Error);
#endif
  if(printout > 0)
  {
    Print("\n//** Mwalk: Groebner Walk took %d steps.\n", nstep);
  }
  si_opt_1 = save1; //set original options
  return(result);
}

MwalkAlt()

ideal MwalkAlt	(	ideal	Go,
		intvec *	curr_weight,
		intvec *	target_weight
	)

Definition at line 5027 of file walk.cc.

{
  Set_Error(FALSE);
  Overflow_Error = FALSE;
  //Print("// pSetm_Error = (%d)", ErrorCheck());
 
#ifdef TIME_TEST
  clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0;
  tinput = clock();
  clock_t tim;
  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0;
#endif
  nstep=0;
  int i;
  int nV = currRing->N;
  int nwalk=0;
  int endwalks=0;
 
  ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G;
 
  ring newRing, oldRing;
  intvec* ivNull = new intvec(nV);
  intvec* exivlp = Mivlp(nV);
#ifndef BUCHBERGER_ALG
  intvec* hilb_func;
#endif
  intvec* tmp_weight = new intvec(nV);
  for(i=nV-1; i>=0; i--)
    (*tmp_weight)[i] = (*curr_weight)[i];
 
   // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
    (*last_omega)[i] = 1;
  (*last_omega)[0] = 10000;
 
  ring XXRing = currRing;
 
#ifdef TIME_TEST
  to = clock();
#endif
  // the monomial ordering of this current ring would be "dp"
  G = MstdCC(Go);
#ifdef TIME_TEST
  tostd = clock()-to;
#endif
 
  if(currRing->order[0] == ringorder_a)
    goto NEXT_VECTOR;
 
  while(1)
  {
    nwalk ++;
    nstep ++;
#ifdef TIME_TEST
    to = clock();
#endif
    // compute an initial form ideal of <G> w.r.t. "curr_vector"
    Gomega = MwalkInitialForm(G, curr_weight);
#ifdef TIME_TEST
    tif = tif + clock()-to;
#endif
    oldRing = currRing;
 
    if(endwalks == 1)
    {
      /* compute a reduced Groebner basis of Gomega w.r.t. >>_cw by
         the recursive changed perturbation walk alg. */
#ifdef TIME_TEST
      tim = clock();
#endif
#ifdef CHECK_IDEAL_MWALK
        Print("\n// **** Groebnerwalk took %d steps and ", nwalk);
        PrintS("\n// **** call the rec. Pert. Walk to compute a red GB of:");
        idString(Gomega, "Gomega");
#endif
 
      if(MivSame(exivlp, target_weight)==1)
        M = REC_GB_Mwalk(idCopy(Gomega), tmp_weight, curr_weight, 2,1);
      else
        goto NORMAL_GW;
#ifdef TIME_TEST
        Print("\n//  time for the last std(Gw)  = %.2f sec",
        ((double) (clock()-tim)/1000000));
#endif
/*
#ifdef CHECK_IDEAL_MWALK
      idElements(Gomega, "G_omega");
      headidString(Gomega, "Gw");
      idElements(M, "M");
      //headidString(M, "M");
#endif
*/
#ifdef TIME_TEST
      to = clock();
#endif
      F = MLifttwoIdeal(Gomega, M, G);
#ifdef TIME_TEST
      xtlift = xtlift + clock() - to;
#endif
 
      idDelete(&Gomega);
      idDelete(&M);
      idDelete(&G);
 
      oldRing = currRing;
 
      // create a new ring newRing
       if (rParameter(currRing) != NULL)
       {
         DefRingPar(curr_weight);
       }
       else
       {
         rChangeCurrRing(VMrDefault(curr_weight));
       }
      newRing = currRing;
      F1 = idrMoveR(F, oldRing,currRing);
    }
    else
    {
    NORMAL_GW:
#ifndef  BUCHBERGER_ALG
      if(isNolVector(curr_weight) == 0)
      {
        hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
      }
      else
      {
        hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
      }
#endif // BUCHBERGER_ALG
 
      // define a new ring that its ordering is "(a(curr_weight),lp)
      if (rParameter(currRing) != NULL)
      {
        DefRingPar(curr_weight);
      }
      else
      {
        rChangeCurrRing(VMrDefault(curr_weight));
      }
      newRing = currRing;
      Gomega1 = idrMoveR(Gomega, oldRing,currRing);
 
#ifdef TIME_TEST
      to = clock();
#endif
      // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
#ifdef  BUCHBERGER_ALG
      M = MstdhomCC(Gomega1);
#else
      M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
      delete hilb_func;
#endif
#ifdef TIME_TEST
      tstd = tstd + clock() - to;
#endif
 
      // change the ring to oldRing
      rChangeCurrRing(oldRing);
      M1 =  idrMoveR(M, newRing,currRing);
      Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
 
#ifdef TIME_TEST
      to = clock();
#endif
      // compute a representation of the generators of submod (M) with respect
      // to those of mod (Gomega).
      // Gomega is a reduced Groebner basis w.r.t. the current ring.
      F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
      tlift = tlift + clock() - to;
#endif
 
      idDelete(&M1);
      idDelete(&Gomega2);
      idDelete(&G);
 
      // change the ring to newRing
      rChangeCurrRing(newRing);
      F1 = idrMoveR(F, oldRing,currRing);
    }
 
#ifdef TIME_TEST
    to = clock();
#endif
    // reduce the Groebner basis <G> w.r.t. new ring
    G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
    if(endwalks != 1)
    {
      tred = tred + clock() - to;
    }
    else
    {
      xtred = xtred + clock() - to;
    }
#endif
    idDelete(&F1);
    if(endwalks == 1)
    {
      break;
    }
  NEXT_VECTOR:
#ifdef TIME_TEST
    to = clock();
#endif
    // compute a next weight vector
    intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight,G);
#ifdef TIME_TEST
    tnw = tnw + clock() - to;
#endif
#ifdef PRINT_VECTORS
    MivString(curr_weight, target_weight, next_weight);
#endif
 
    //if(test_w_in_ConeCC(G, next_weight) != 1)
    if(Overflow_Error == TRUE)
    {
      newRing = currRing;
      PrintS("\n// ** The computed vector does NOT stay in Cone!!\n");
 
      if (rParameter(currRing) != NULL)
      {
        DefRingPar(target_weight);
      }
      else
      {
        rChangeCurrRing(VMrDefault(target_weight));
      }
      F1 = idrMoveR(G, newRing,currRing);
      G = MstdCC(F1);
      idDelete(&F1);
 
      newRing = currRing;
      break;
    }
 
    if(MivComp(next_weight, ivNull) == 1)
    {
      newRing = currRing;
      delete next_weight;
      break;
    }
    if(MivComp(next_weight, target_weight) == 1)
    {
      endwalks = 1;
    }
    for(i=nV-1; i>=0; i--)
    {
      (*tmp_weight)[i] = (*curr_weight)[i];
      (*curr_weight)[i] = (*next_weight)[i];
    }
    delete next_weight;
  }
  rChangeCurrRing(XXRing);
  G = idrMoveR(G, newRing,currRing);
 
  delete tmp_weight;
  delete ivNull;
  delete exivlp;
 
#ifdef TIME_TEST
  TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep);
 
  //Print("\n// pSetm_Error = (%d)", ErrorCheck());
  Print("\n// Overflow_Error? (%d)\n", Overflow_Error);
#endif
  return(G);
}

MwalkInitialForm()

ideal MwalkInitialForm	(	ideal	G,
		intvec *	ivw
	)

Definition at line 761 of file walk.cc.

{
  BOOLEAN nError =  Overflow_Error;
  Overflow_Error = FALSE;
 
  int i, nG = IDELEMS(G);
  ideal Gomega = idInit(nG, 1);
 
  for(i=nG-1; i>=0; i--)
  {
    Gomega->m[i] = MpolyInitialForm(G->m[i], ivw);
  }
  if(Overflow_Error == FALSE)
  {
    Overflow_Error = nError;
  }
  return Gomega;
}

MwalkNextWeightCC()

static intvec * MwalkNextWeightCC ( intvec *  curr_weight, intvec *  target_weight, ideal  G  )

static

Definition at line 2228 of file walk.cc.

{
  BOOLEAN nError = Overflow_Error;
  Overflow_Error = FALSE;
 
  assume(currRing != NULL && curr_weight != NULL &&
         target_weight != NULL && G != NULL);
 
  int nRing = currRing->N;
  int j, nG = IDELEMS(G);
  intvec* ivtemp;
 
  mpz_t t_zaehler, t_nenner;
  mpz_init(t_zaehler);
  mpz_init(t_nenner);
 
  mpz_t s_zaehler, s_nenner, temp, MwWd;
  mpz_init(s_zaehler);
  mpz_init(s_nenner);
  mpz_init(temp);
  mpz_init(MwWd);
 
  mpz_t sing_int;
  mpz_init(sing_int);
  mpz_set_ui(sing_int,  2147483647);
 
  mpz_t sing_int_half;
  mpz_init(sing_int_half);
  mpz_set_ui(sing_int_half,  3*(1073741824/2));
 
  mpz_t deg_w0_p1, deg_d0_p1;
  mpz_init(deg_w0_p1);
  mpz_init(deg_d0_p1);
 
  mpz_t sztn, sntz;
  mpz_init(sztn);
  mpz_init(sntz);
 
  mpz_t t_null;
  mpz_init(t_null);
 
  mpz_t ggt;
  mpz_init(ggt);
 
  mpz_t dcw;
  mpz_init(dcw);
 
  int gcd_tmp;
  //intvec* diff_weight = MivSub(target_weight, curr_weight);
 
  intvec* diff_weight1 = new intvec(nRing); //MivSub(target_weight, curr_weight);
  poly g;
 
  // reduce the size of the entries of the current weight vector
  if(TEST_OPT_REDSB)
  {
    for (j=0; j<nRing; j++)
    {
      (*diff_weight1)[j] = (*curr_weight)[j];
    }
    while(MivAbsMax(diff_weight1)>10000 && test_w_in_ConeCC(G,diff_weight1)==1)
    {
      for(j=0; j<nRing; j++)
      {
        (*curr_weight)[j] = (*diff_weight1)[j];
      }
      for(j=0; j<nRing; j++)
      {
        (*diff_weight1)[j] = ((*diff_weight1)[j] + 5) / 10;
      }
    }
 
    if(MivAbsMax(curr_weight)>100000)
    {
      for(j=0; j<nRing; j++)
      {
        (*diff_weight1)[j] = (*curr_weight)[j];
      }
      j = 0;
      while(test_w_in_ConeCC(G,diff_weight1)==1 && MivAbsMax(diff_weight1)>1000)
      {
        (*curr_weight)[j] = (*diff_weight1)[j];
        j = MivAbsMaxArg(diff_weight1);
        (*diff_weight1)[j] = ((*diff_weight1)[j] + 5) / 10;
      }
    }
 
  }
  intvec* diff_weight = MivSub(target_weight, curr_weight);
 
  // compute a suitable next weight vector
  for (j=0; j<nG; j++)
  {
    g = G->m[j];
    if (g != NULL)
    {
      ivtemp = MExpPol(g);
      mpz_set_si(deg_w0_p1, MivDotProduct(ivtemp, curr_weight));
      mpz_set_si(deg_d0_p1, MivDotProduct(ivtemp, diff_weight));
      delete ivtemp;
 
      pIter(g);
      while (g != NULL)
      {
        ivtemp = MExpPol(g);
        mpz_set_si(MwWd, MivDotProduct(ivtemp, curr_weight));
        mpz_sub(s_zaehler, deg_w0_p1, MwWd);
        if(mpz_cmp(s_zaehler, t_null) != 0)
        {
          mpz_set_si(MwWd, MivDotProduct(ivtemp, diff_weight));
          mpz_sub(s_nenner, MwWd, deg_d0_p1);
          // check for 0 < s <= 1
          if( (mpz_cmp(s_zaehler,t_null) > 0 &&
               mpz_cmp(s_nenner, s_zaehler)>=0) ||
              (mpz_cmp(s_zaehler, t_null) < 0 &&
               mpz_cmp(s_nenner, s_zaehler)<=0))
          {
            // make both positive
            if (mpz_cmp(s_zaehler, t_null) < 0)
            {
              mpz_neg(s_zaehler, s_zaehler);
              mpz_neg(s_nenner, s_nenner);
            }
 
            //compute a simple fraction of s
            cancel(s_zaehler, s_nenner);
 
            if(mpz_cmp(t_nenner, t_null) != 0)
            {
              mpz_mul(sztn, s_zaehler, t_nenner);
              mpz_mul(sntz, s_nenner, t_zaehler);
 
              if(mpz_cmp(sztn,sntz) < 0)
              {
                mpz_add(t_nenner, t_null, s_nenner);
                mpz_add(t_zaehler,t_null, s_zaehler);
              }
            }
            else
            {
              mpz_add(t_nenner, t_null, s_nenner);
              mpz_add(t_zaehler,t_null, s_zaehler);
            }
          }
        }
        pIter(g);
        delete ivtemp;
      }
    }
  }
  //Print("\n// Alloc Size = %d \n", nRing*sizeof(mpz_t));
  mpz_t *vec=(mpz_t*)omAlloc(nRing*sizeof(mpz_t));
 
 
  // there is no 0<t<1 and define the next weight vector that is equal
  // to the current weight vector
  if(mpz_cmp(t_nenner, t_null) == 0)
  {
#ifndef SING_NDEBUG
    PrintS("\n//MwalkNextWeightCC: t_nenner=0\n");
#endif
    delete diff_weight;
    diff_weight = ivCopy(curr_weight);//take memory
    goto FINISH;
  }
 
  // define the target vector as the next weight vector, if t = 1
  if(mpz_cmp_si(t_nenner, 1)==0 && mpz_cmp_si(t_zaehler,1)==0)
  {
    delete diff_weight;
    diff_weight = ivCopy(target_weight); //this takes memory
    goto FINISH;
  }
 
  //SIMPLIFY_GCD:
 
  // simplify the vectors curr_weight and diff_weight (C-int)
  gcd_tmp = (*curr_weight)[0];
 
  for (j=1; j<nRing; j++)
  {
    gcd_tmp = gcd(gcd_tmp, (*curr_weight)[j]);
    if(gcd_tmp == 1)
    {
      break;
    }
  }
  if(gcd_tmp != 1)
  {
    for (j=0; j<nRing; j++)
    {
      gcd_tmp = gcd(gcd_tmp, (*diff_weight)[j]);
      if(gcd_tmp == 1)
      {
        break;
      }
    }
  }
  if(gcd_tmp != 1)
  {
    for (j=0; j<nRing; j++)
    {
      (*curr_weight)[j] =  (*curr_weight)[j]/gcd_tmp;
      (*diff_weight)[j] =  (*diff_weight)[j]/gcd_tmp;
    }
  }
 
#ifdef  NEXT_VECTORS_CC
  Print("\n// gcd of the weight vectors (current and target) = %d", gcd_tmp);
  ivString(curr_weight, "new cw");
  ivString(diff_weight, "new dw");
 
  PrintS("\n// t_zaehler: ");  mpz_out_str( stdout, 10, t_zaehler);
  PrintS(", t_nenner: ");  mpz_out_str( stdout, 10, t_nenner);
#endif
 
// construct a new weight vector and check whether vec[j] is overflow, i.e. vec[j] > 2^31.
// If vec[j] doesn't overflow, define a weight vector. Otherwise, report that overflow
// appears. In the second case, test whether the the correctness of the new vector plays
// an important role
 
  for (j=0; j<nRing; j++)
  {
    mpz_set_si(dcw, (*curr_weight)[j]);
    mpz_mul(s_nenner, t_nenner, dcw);
 
    if( (*diff_weight)[j]>0)
    {
      mpz_mul_ui(s_zaehler, t_zaehler, (*diff_weight)[j]);
    }
    else
    {
      mpz_mul_ui(s_zaehler, t_zaehler, -(*diff_weight)[j]);
      mpz_neg(s_zaehler, s_zaehler);
    }
    mpz_add(sntz, s_nenner, s_zaehler);
    mpz_init_set(vec[j], sntz);
 
#ifdef NEXT_VECTORS_CC
    Print("\n//   j = %d ==> ", j);
    PrintS("(");
    mpz_out_str( stdout, 10, t_nenner);
    Print(" * %d)", (*curr_weight)[j]);
    PrintS(" + ("); mpz_out_str( stdout, 10, t_zaehler);
    Print(" * %d) =  ",  (*diff_weight)[j]);
    mpz_out_str( stdout, 10, s_nenner);
    PrintS(" + ");
    mpz_out_str( stdout, 10, s_zaehler);
    PrintS(" = "); mpz_out_str( stdout, 10, sntz);
    Print(" ==> vector[%d]: ", j); mpz_out_str(stdout, 10, vec[j]);
#endif
 
    if(j==0)
    {
      mpz_set(ggt, sntz);
    }
    else
    {
      if(mpz_cmp_si(ggt,1) != 0)
      {
        mpz_gcd(ggt, ggt, sntz);
      }
    }
  }
  // reduce the vector with the gcd
  if(mpz_cmp_si(ggt,1) != 0)
  {
    for (j=0; j<nRing; j++)
    {
      mpz_divexact(vec[j], vec[j], ggt);
    }
  }
#ifdef  NEXT_VECTORS_CC
  PrintS("\n// gcd of elements of the vector: ");
  mpz_out_str( stdout, 10, ggt);
#endif
 
  for (j=0; j<nRing; j++)
  {
    (*diff_weight)[j] = mpz_get_si(vec[j]);
  }
 
 //TEST_OVERFLOW:
 
  for (j=0; j<nRing; j++)
  {
    if(mpz_cmp(vec[j], sing_int)>=0)
    {
      if(Overflow_Error == FALSE)
      {
        Overflow_Error = TRUE;
        PrintS("\n// ** OVERFLOW in \"MwalkNextWeightCC\": ");
        mpz_out_str( stdout, 10, vec[j]);
        PrintS(" is greater than 2147483647 (max. integer representation)\n");
        //Print("//  So vector[%d] := %d is wrong!!\n",j+1, vec[j]);// vec[j] is mpz_t
      }
    }
  }
 
 FINISH:
   delete diff_weight1;
   mpz_clear(t_zaehler);
   mpz_clear(t_nenner);
   mpz_clear(s_zaehler);
   mpz_clear(s_nenner);
   mpz_clear(sntz);
   mpz_clear(sztn);
   mpz_clear(temp);
   mpz_clear(MwWd);
   mpz_clear(deg_w0_p1);
   mpz_clear(deg_d0_p1);
   mpz_clear(ggt);
   omFree(vec);
   mpz_clear(sing_int_half);
   mpz_clear(sing_int);
   mpz_clear(dcw);
   mpz_clear(t_null);
 
  if(Overflow_Error == FALSE)
  {
    Overflow_Error = nError;
  }
  rComplete(currRing);
  for(j=0; j<IDELEMS(G); j++)
  {
    poly p=G->m[j];
    while(p!=NULL)
    {
      p_Setm(p,currRing);
      pIter(p);
    }
  }
return diff_weight;
}

MWalkRandomNextWeight()

static intvec * MWalkRandomNextWeight ( ideal  G, intvec *  orig_M, intvec *  target_weight, int  weight_rad, int  pert_deg  )

static

Definition at line 4516 of file walk.cc.

{
  assume(currRing != NULL && orig_M != NULL &&
         target_weight != NULL && G->m[0] != NULL);
 
  //BOOLEAN nError = Overflow_Error;
  Overflow_Error = FALSE;
 
  BOOLEAN found_random_weight = FALSE;
  int i,nV = currRing->N;
  intvec* curr_weight = new intvec(nV);
 
  for(i=0; i<nV; i++)
  {
    (*curr_weight)[i] = (*orig_M)[i];
  }
 
  int k=0,weight_norm;
  intvec* next_weight;
  intvec* next_weight1 = MkInterRedNextWeight(curr_weight,target_weight,G);
  intvec* next_weight2 = new intvec(nV);
  intvec* result = new intvec(nV);
  intvec* curr_weight1;
  ideal G_test, G_test1, G_test2;
 
  //try to find a random next weight vector "next_weight2"
  if(weight_rad > 0)
  {
    while(k<10)
    {
      weight_norm = 0;
      while(weight_norm == 0)
      {
        for(i=0; i<nV; i++)
        {
          (*next_weight2)[i] = rand() % 60000 - 30000;
          weight_norm = weight_norm + (*next_weight2)[i]*(*next_weight2)[i];
        }
        weight_norm = 1 + static_cast<int>(sqrt(double(weight_norm)));
      }
      for(i=0; i<nV; i++)
      {
        if((*next_weight2)[i] < 0)
        {
          (*next_weight2)[i] = 1 + (*curr_weight)[i] + weight_rad*(*next_weight2)[i]/weight_norm;
        }
        else
        {
          (*next_weight2)[i] = (*curr_weight)[i] + weight_rad*(*next_weight2)[i]/weight_norm;
        }
      }
      if(test_w_in_ConeCC(G,next_weight2) == 1)
      {
        if(maxlengthpoly(MwalkInitialForm(G,next_weight2))<2)
        {
          next_weight2 = MkInterRedNextWeight(next_weight2,target_weight,G);
        }
        G_test2 = MwalkInitialForm(G, next_weight2);
        found_random_weight = TRUE;
        break;
      }
      k++;
    }
  }
 
  // compute "perturbed" next weight vector
  if(pert_deg > 1)
  {
    curr_weight1 = MPertVectors(G,orig_M,pert_deg);
    next_weight = MkInterRedNextWeight(curr_weight1,target_weight,G);
    delete curr_weight1;
  }
  else
  {
    next_weight = MkInterRedNextWeight(curr_weight,target_weight,G);
  }
  if(MivSame(curr_weight,next_weight)==1 || Overflow_Error == TRUE)
  {
    Overflow_Error = FALSE;
    delete next_weight;
    next_weight = MkInterRedNextWeight(curr_weight,target_weight,G);
  }
  G_test=MwalkInitialForm(G,next_weight);
  G_test1=MwalkInitialForm(G,next_weight1);
 
  // compare next weights
  if(Overflow_Error == FALSE)
  {
    if(found_random_weight == TRUE)
    {
    // random next weight vector found
      if(G_test1->m[0] != NULL && maxlengthpoly(G_test1) < maxlengthpoly(G_test))
      {
        if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test1))
        {
          for(i=0; i<nV; i++)
          {
            (*result)[i] = (*next_weight2)[i];
          }
        }
        else
        {
          for(i=0; i<nV; i++)
          {
            (*result)[i] = (*next_weight1)[i];
          }
        }
      }
      else
      {
        if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test))
        {
          for(i=0; i<nV; i++)
          {
            (*result)[i] = (*next_weight2)[i];
          }
        }
        else
        {
          for(i=0; i<nV; i++)
          {
            (*result)[i] = (*next_weight)[i];
          }
        }
      }
    }
    else
    {
      // no random next weight vector found
      if(G_test1->m[0] != NULL && maxlengthpoly(G_test1) < maxlengthpoly(G_test))
      {
       for(i=0; i<nV; i++)
        {
          (*result)[i] = (*next_weight1)[i];
        }
      }
      else
      {
        for(i=0; i<nV; i++)
        {
          (*result)[i] = (*next_weight)[i];
        }
      }
    }
  }
  else
  {
    Overflow_Error = FALSE;
    if(found_random_weight == TRUE)
    {
      if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test))
      {
        for(i=1; i<nV; i++)
        {
          (*result)[i] = (*next_weight2)[i];
        }
      }
      else
      {
        for(i=0; i<nV; i++)
        {
          (*result)[i] = (*next_weight)[i];
        }
      }
    }
    else
    {
      for(i=0; i<nV; i++)
      {
        (*result)[i] = (*next_weight)[i];
      }
    }
  }
 
  delete next_weight;
  delete next_weight2;
  idDelete(&G_test);
  idDelete(&G_test1);
  if(found_random_weight == TRUE)
  {
    idDelete(&G_test2);
  }
  if(test_w_in_ConeCC(G, result) == 1 && MivSame(curr_weight,result)==0)
  {
    delete curr_weight;
    delete next_weight1;
    return result;
  }
  else
  {
    delete curr_weight;
    delete result;
    return next_weight1;
  }
}

MwalkWeightDegree()

static int MwalkWeightDegree ( poly  p, intvec *  weight_vector  )

inlinestatic

Definition at line 668 of file walk.cc.

{
  assume(weight_vector->length() >= currRing->N);
  int max = 0, maxtemp;
 
  while(p != NULL)
  {
    maxtemp = MLmWeightedDegree(p, weight_vector);
    pIter(p);
 
    if (maxtemp > max)
    {
      max = maxtemp;
    }
  }
  return max;
}

NewVectorlp()

static intvec * NewVectorlp ( ideal  I )

static

Definition at line 4496 of file walk.cc.

{
  int nV = currRing->N;
  intvec* iv_wlp =  MivMatrixOrderlp(nV);
  intvec* result = Mfpertvector(I, iv_wlp);
  delete iv_wlp;
  return result;
}

rec_fractal_call()

static ideal rec_fractal_call ( ideal  G, int  nlev, intvec *  ivtarget, int  reduction, int  printout  )

static

Definition at line 6951 of file walk.cc.

{
  Overflow_Error =  FALSE;
  if(printout >0)
  {
    Print("\n\n// Entering the %d-th recursion:", nlev);
  }
  int i, nV = currRing->N;
  ring new_ring, testring;
  //ring extoRing;
  ideal Gomega, Gomega1, Gomega2, FF, F, Gresult, Gresult1, G1, Gt;
  int nwalks = 0;
  intvec* Mwlp;
#ifndef BUCHBERGER_ALG
  intvec* hilb_func;
#endif
  //intvec* extXtau;
  intvec* next_vect;
  intvec* omega2 = new intvec(nV);
  intvec* omtmp = new intvec(nV);
  //intvec* altomega = new intvec(nV);
 
  for(i = nV -1; i>=0; i--)//Aenderung!!
  {
    (*omtmp)[i] = (*ivtarget)[i];
  }
  //BOOLEAN isnewtarget = FALSE;
 
  // to avoid (1,0,...,0) as the target vector (Hans)
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
    (*last_omega)[i] = 1;
  (*last_omega)[0] = 10000;
 
  intvec* omega = new intvec(nV);
  for(i=0; i<nV; i++) {
    if(Xsigma->length() == nV)
      (*omega)[i] =  (*Xsigma)[i];
    else
      (*omega)[i] = (*Xsigma)[(nV*(nlev-1))+i];
 
    (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i];
  }
 
   if(nlev == 1)  Xcall = 1;
   else Xcall = 0;
 
  ring oRing = currRing;
 
  while(1)
  {
#ifdef FIRST_STEP_FRACTAL
    // perturb the current weight vector only on the top level or
    // after perturbation of the both vectors, nlev = 2 as the top level
    if((nlev == 1 && Xcall == 0) || (nlev == 2 && Xngleich == 1))
      if(islengthpoly2(G) == 1)
      {
        Mwlp = MivWeightOrderlp(omega);
        Xsigma = Mfpertvector(G, Mwlp);
        delete Mwlp;
        Overflow_Error = FALSE;
      }
#endif
    nwalks ++;
    NEXT_VECTOR_FRACTAL:
#ifdef TIME_TEST
    to=clock();
#endif
    // determine the next border
    next_vect = MkInterRedNextWeight(omega,omega2,G);
#ifdef TIME_TEST
    xtnw=xtnw+clock()-to;
#endif
    oRing = currRing;
 
    // We only perturb the current target vector at the recursion level 1
    if(Xngleich == 0 && nlev == 1) //(ngleich == 0) important, e.g. ex2, ex3
      if (MivComp(next_vect, omega2) == 1)
      {
        // to dispense with taking initial (and lifting/interreducing
        // after the call of recursion
        if(printout > 0)
        {
          Print("\n//** rec_fractal_call: Perturb the both vectors with degree %d.",nlev);
          //idElements(G, "G");
        }
 
        Xngleich = 1;
        nlev +=1;
 
        if(ivtarget->length() == nV)
        {
/*
          if (rParameter(currRing) != NULL)
            DefRingPar(omtmp);
          else
            rChangeCurrRing(VMrDefault(omtmp));
*/
          rChangeCurrRing(VMrRefine(ivtarget,omtmp));
        }
        else
        {
          //rChangeCurrRing(VMatrDefault(ivtarget));
          rChangeCurrRing(VMatrRefine(ivtarget,omtmp));
        }
        testring = currRing;
        Gt = idrMoveR(G, oRing,currRing);
 
        // perturb the original target vector w.r.t. the current GB
        if(ivtarget->length() == nV)
        {
          delete Xtau;
          Xtau = NewVectorlp(Gt);
        }
        else
        {
          delete Xtau;
          Xtau = Mfpertvector(Gt,ivtarget);
        }
 
        rChangeCurrRing(oRing);
        G = idrMoveR(Gt, testring,currRing);
 
        // perturb the current vector w.r.t. the current GB
        Mwlp = MivWeightOrderlp(omega);
        Xsigma = Mfpertvector(G, Mwlp);
        delete Mwlp;
 
        for(i=nV-1; i>=0; i--) {
          (*omega2)[i] = (*Xtau)[nV+i];
          (*omega)[i] = (*Xsigma)[nV+i];
        }
 
        delete next_vect;
#ifdef TIME_TEST
        to=clock();
#endif
        // to avoid the value of Overflow_Error that occur in Mfpertvector
        Overflow_Error = FALSE;
        next_vect = MkInterRedNextWeight(omega,omega2,G);
#ifdef TIME_TEST
        xtnw=xtnw+clock()-to;
#endif
      }// end of (if MivComp(next_vect, omega2) == 1)
 
#ifdef PRINT_VECTORS
      if(printout > 0)
      {
        MivString(omega, omega2, next_vect);
      }
#endif
 
    // check whether the the computed vector is in the correct cone.
    // If no, compute the reduced Groebner basis of an omega-homogeneous
    // ideal with Buchberger's algorithm and stop this recursion step
    if(Overflow_Error == TRUE || test_w_in_ConeCC(G, next_vect) != 1)  //e.g. Example s7, cyc6
    {
      delete next_vect;
      if(ivtarget->length() == nV)
      {
/*
        if (rParameter(currRing) != NULL)
          DefRingPar(omtmp);
        else
          rChangeCurrRing(VMrDefault(omtmp));
*/
        rChangeCurrRing(VMrRefine(ivtarget,omtmp));
      }
      else
      {
        //rChangeCurrRing(VMatrDefault(ivtarget));
        rChangeCurrRing(VMatrRefine(ivtarget,omtmp));
      }
#ifdef TEST_OVERFLOW
      Gt = idrMoveR(G, oRing,currRing);
      Gt = NULL; return(Gt);
#endif
      if(printout > 0)
      {
        Print("\n//** rec_fractal_call: Applying Buchberger's algorithm in ring r = %s;",
              rString(currRing));
      }
#ifdef TIME_TEST
      to=clock();
#endif
      Gt = idrMoveR(G, oRing,currRing);
      G1 = MstdCC(Gt);
#ifdef TIME_TEST
      xtextra=xtextra+clock()-to;
#endif
      Gt = NULL;
 
      delete omega2;
      //delete altomega;
      if(printout > 0)
      {
        Print("\n//** rec_fractal_call: Overflow. (4) Leaving the %d-th recursion with %d steps.\n",
              nlev, nwalks);
        //Print(" ** Overflow_Error? (%d)", Overflow_Error);
      }
 
      nnflow ++;
      Overflow_Error = FALSE;
      return (G1);
    }
 
    /* If the perturbed target vector stays in the correct cone,
       return the current GB,
       otherwise, return the computed  GB by the Buchberger-algorithm.
       Then we update the perturbed target vectors w.r.t. this GB. */
 
    /* the computed vector is equal to the origin vector, since
       t is not defined */
 
    if (MivComp(next_vect, XivNull) == 1)
    {
      if(ivtarget->length() == nV)
      {
/*
        if (rParameter(currRing) != NULL)
          DefRingPar(omtmp);
        else
          rChangeCurrRing(VMrDefault(omtmp));
*/
        rChangeCurrRing(VMrRefine(ivtarget,omtmp));
      }
      else
      {
        //rChangeCurrRing(VMatrDefault(ivtarget));
        rChangeCurrRing(VMatrRefine(ivtarget,omtmp));
      }
 
      testring = currRing;
      Gt = idrMoveR(G, oRing,currRing);
      if(test_w_in_ConeCC(Gt, omega2) == 1)
      {
        delete omega2;
        delete next_vect;
        //delete altomega;
        if(printout > 0)
        {
          Print("\n//** rec_fractal_call: Correct cone. (5) Leaving the %d-th recursion with %d steps.\n",
              nlev, nwalks);
        }
        if(printout>2)
        {
          idString(Gt,"//** rec_fractal_call: Gt");
        }
        return (Gt);
      }
      else
      {
        if(printout > 0)
        {
          PrintS("\n//** rec_fractal_call: Wrong cone. Tau doesn't stay in the correct cone.\n");
        }
 
#ifndef  MSTDCC_FRACTAL
        intvec* Xtautmp;
        if(ivtarget->length() == nV)
        {
          Xtautmp = Mfpertvector(Gt, MivMatrixOrder(omtmp));
        }
        else
        {
          Xtautmp = Mfpertvector(Gt, ivtarget);
        }
#ifdef TEST_OVERFLOW
      if(Overflow_Error == TRUE)
      Gt = NULL; return(Gt);
#endif
 
        if(MivSame(Xtau, Xtautmp) == 1)
        {
          if(printout > 0)
          {
            PrintS("\n//** rec_fractal_call: Updated vectors are equal to the old vectors.\n");
          }
          delete Xtautmp;
          goto FRACTAL_MSTDCC;
        }
 
        Xtau = Xtautmp;
        Xtautmp = NULL;
 
        for(i=nV-1; i>=0; i--)
          (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i];
 
        rChangeCurrRing(oRing);
        G = idrMoveR(Gt, testring,currRing);
 
        goto NEXT_VECTOR_FRACTAL;
#endif
 
      //FRACTAL_MSTDCC:
        if(printout > 0)
        {
          Print("\n//** rec_fractal_call: Wrong cone. Applying Buchberger's algorithm in ring = %s.\n",
                rString(currRing));
        }
#ifdef TIME_TEST
        to=clock();
#endif
        G = MstdCC(Gt);
#ifdef TIME_TEST
        xtextra=xtextra+clock()-to;
#endif
        oRing = currRing;
 
        // update the original target vector w.r.t. the current GB
        if(ivtarget->length() == nV)
        {
/*
          if(MivSame(Xivinput, Xivlp) == 1)
            if (rParameter(currRing) != NULL)
              DefRingParlp();
            else
              VMrDefaultlp();
          else
            if (rParameter(currRing) != NULL)
              DefRingPar(Xivinput);
            else
              rChangeCurrRing(VMrDefault(Xivinput));
*/
          rChangeCurrRing(VMrRefine(ivtarget,Xivinput));
        }
        else
        {
          rChangeCurrRing(VMatrRefine(ivtarget,Xivinput));
        }
        testring = currRing;
        Gt = idrMoveR(G, oRing,currRing);
 
        // perturb the original target vector w.r.t. the current GB
        if(ivtarget->length() == nV)
        {
          delete Xtau;
          Xtau = NewVectorlp(Gt);
        }
        else
        {
          delete Xtau;
          Xtau = Mfpertvector(Gt,ivtarget);
        }
 
        rChangeCurrRing(oRing);
        G = idrMoveR(Gt, testring,currRing);
 
        delete omega2;
        delete next_vect;
        //delete altomega;
        if(printout > 0)
        {
          Print("\n//** rec_fractal_call: Vectors updated. (6) Leaving the %d-th recursion with %d steps.\n",
              nlev, nwalks);
          //Print(" ** Overflow_Error? (%d)", Overflow_Error);
        }
        if(Overflow_Error == TRUE)
          nnflow ++;
 
        Overflow_Error = FALSE;
        return(G);
      }
    }// end of (if next_vect==nullvector)
 
    for(i=nV-1; i>=0; i--) {
      //(*altomega)[i] = (*omega)[i];
      (*omega)[i] = (*next_vect)[i];
    }
    delete next_vect;
#ifdef TIME_TEST
    to=clock();
#endif
    // Take the initial form of <G> w.r.t. omega
    Gomega = MwalkInitialForm(G, omega);
#ifdef TIME_TEST
    xtif=xtif+clock()-to;
#endif
#ifdef CHECK_IDEAL_MWALK
    if(printout > 1)
    {
      idString(Gomega,"//** rec_fractal_call: Gomega");
    }
#endif
    if(reduction == 0)
    {
      // Check whether the intermediate weight vector lies in the interior of the cone.
      // If so, only perform reductions. Otherwise apply Buchberger's algorithm.
      FF = middleOfCone(G,Gomega);
      if( FF != NULL)
      {
        idDelete(&G);
        G = idCopy(FF);
        idDelete(&FF);
        // Compue next vector.
        goto NEXT_VECTOR_FRACTAL;
      }
    }
 
#ifndef  BUCHBERGER_ALG
    if(isNolVector(omega) == 0)
      hilb_func = hFirstSeries(Gomega,NULL,NULL,omega,currRing);
    else
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
#endif
 
    if(ivtarget->length() == nV)
    {
/*
      if (rParameter(currRing) != NULL)
        DefRingPar(omega);
      else
        rChangeCurrRing(VMrDefault(omega));
*/
      rChangeCurrRing(VMrRefine(ivtarget,omega));
    }
    else
    {
      rChangeCurrRing(VMatrRefine(ivtarget,omega));
    }
    Gomega1 = idrMoveR(Gomega, oRing,currRing);
 
    // Maximal recursion depth, to compute a red. GB
    // Fractal walk with the alternative recursion
    // alternative recursion
    if(nlev == Xnlev || lengthpoly(Gomega1) == 0)
    {
      if(printout > 1)
      {
        PrintS("\n//** rec_fractal_call: Maximal recursion depth.\n");
      }
#ifdef TIME_TEST
      to=clock();
#endif
#ifdef  BUCHBERGER_ALG
      Gresult = MstdhomCC(Gomega1);
#else
      Gresult =kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,omega);
      delete hilb_func;
#endif
#ifdef TIME_TEST
      xtstd=xtstd+clock()-to;
#endif
    }
    else
    {
      rChangeCurrRing(oRing);
      Gomega1 = idrMoveR(Gomega1, oRing,currRing);
      Gresult = rec_fractal_call(idCopy(Gomega1),nlev+1,omega,reduction,printout);
    }
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(Gresult,"//** rec_fractal_call: M");
    }
#endif
    //convert a Groebner basis from a ring to another ring
    new_ring = currRing;
 
    rChangeCurrRing(oRing);
    Gresult1 = idrMoveR(Gresult, new_ring,currRing);
    Gomega2 = idrMoveR(Gomega1, new_ring,currRing);
#ifdef TIME_TEST
    to=clock();
#endif
    // Lifting process
    F = MLifttwoIdeal(Gomega2, Gresult1, G);
#ifdef TIME_TEST
    xtlift=xtlift+clock()-to;
#endif
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(F,"//** rec_fractal_call: F");
    }
#endif
    id_Normalize(F,currRing);
    idDelete(&Gresult1);
    idDelete(&Gomega2);
    idDelete(&G);
 
    rChangeCurrRing(new_ring);
    G = idrMoveR(F,oRing,currRing);
/*
    ideal F1 = idrMoveR(F, oRing,currRing);
#ifdef TIME_TEST
    to=clock();
#endif
    // Interreduce G
    G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
    xtred=xtred+clock()-to;
#endif
    idDelete(&F1);
*/
  }
}

REC_GB_Mwalk()

static ideal REC_GB_Mwalk ( ideal  G, intvec *  curr_weight, intvec *  orig_target_weight, int  tp_deg, int  npwinc  )

static

Definition at line 4719 of file walk.cc.

{
  BOOLEAN nError = Overflow_Error;
  Overflow_Error = FALSE;
 
  int i,  nV = currRing->N;
  int nwalk=0, endwalks=0, nnwinC=1, nlast = 0;
  ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG;
  ring newRing, oldRing, TargetRing;
  intvec* target_weight;
  intvec* ivNull = new intvec(nV);
#ifndef BUCHBERGER_ALG
  intvec* hilb_func;
  // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
  {
    (*last_omega)[i] = 1;
  }
  (*last_omega)[0] = 10000;
#endif
  BOOLEAN isGB = FALSE;
 
  ring EXXRing = currRing;
 
  // compute a pertubed weight vector of the target weight vector
  if(tp_deg > 1 && tp_deg <= nV)
  {
    ideal H0 = idHeadCC(G);
    if (rParameter(currRing) != NULL)
    {
      DefRingPar(orig_target_weight);
    }
    else
    {
      rChangeCurrRing(VMrDefault(orig_target_weight));
    }
    TargetRing = currRing;
    ssG = idrMoveR(G,EXXRing,currRing);
 
    ideal H0_tmp = idrMoveR(H0,EXXRing,currRing);
    ideal H1 = idHeadCC(ssG);
    id_Delete(&H0,EXXRing);
 
    if(test_G_GB_walk(H0_tmp,H1)==1)
    {
      //Print("\n//REC_GB_Mwalk: input in %d-th recursive is a GB!\n",tp_deg);
      idDelete(&H0_tmp);
      idDelete(&H1);
      G = ssG;
      ssG = NULL;
      newRing = currRing;
      delete ivNull;
      if(npwinc == 0)
      {
        isGB = TRUE;
        goto KSTD_Finish;
      }
      else
      {
        goto LastGB_Finish;
      }
    }
    idDelete(&H0_tmp);
    idDelete(&H1);
 
    target_weight  = MPertVectors(ssG, MivMatrixOrder(orig_target_weight), tp_deg);
 
    rChangeCurrRing(EXXRing);
    G = idrMoveR(ssG, TargetRing,currRing);
  }
 
  while(1)
  {
    nwalk ++;
    nstep++;
    if(nwalk == 1)
    {
      goto NEXT_STEP;
    }
    //Print("\n//REC_GB_Mwalk: Entering the %d-th step in the %d-th recursive:\n",nwalk,tp_deg);
#ifdef TIME_TEST
    to = clock();
#endif
    // compute an initial form ideal of <G> w.r.t. "curr_vector"
    Gomega = MwalkInitialForm(G, curr_weight);
#ifdef TIME_TEST
    xtif = xtif + clock()-to;
#endif
 
#ifndef  BUCHBERGER_ALG
    if(isNolVector(curr_weight) == 0)
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    }
    else
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
    }
#endif
 
    oldRing = currRing;
 
    // define a new ring with ordering "(a(curr_weight),lp)
    if (rParameter(currRing) != NULL)
    {
      DefRingPar(curr_weight);
    }
    else
    {
      rChangeCurrRing(VMrDefault(curr_weight));
    }
    newRing = currRing;
    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
 
#ifdef TIME_TEST
    to = clock();
#endif
    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
#ifdef  BUCHBERGER_ALG
    M = MstdhomCC(Gomega1);
#else
    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    delete hilb_func;
#endif
#ifdef TIME_TEST
    xtstd = xtstd + clock() - to;
#endif
 
    // change the ring to oldRing
    rChangeCurrRing(oldRing);
 
    M1 =  idrMoveR(M, newRing,currRing);
    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
 
#ifdef TIME_TEST
    to = clock();
#endif
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    xtlift = xtlift + clock() -to;
#endif
 
    idDelete(&M1);
    idDelete(&Gomega2);
    idDelete(&G);
 
 
    // change the ring to newRing
    rChangeCurrRing(newRing);
    F1 = idrMoveR(F, oldRing,currRing);
 
#ifdef TIME_TEST
    to = clock();
#endif
    // reduce the Groebner basis <G> w.r.t. new ring
    G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
    xtred = xtred + clock() -to;
#endif
 
    idDelete(&F1);
 
    if(endwalks == 1)
    {
      break;
    }
  NEXT_STEP:
#ifdef TIME_TEST
    to = clock();
#endif
    // compute a next weight vector
    intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight, G);
 
 
#ifdef TIME_TEST
    xtnw = xtnw + clock() - to;
#endif
 
#ifdef PRINT_VECTORS
    MivString(curr_weight, target_weight, next_weight);
#endif
 
    if(Overflow_Error == TRUE)
    {
      //PrintS("\n//REC_GB_Mwalk: The computed vector does NOT stay in the correct cone!!\n");
      nnwinC = 0;
      if(tp_deg == nV)
      {
        nlast = 1;
      }
      delete next_weight;
      break;
    }
    if(MivComp(next_weight, ivNull) == 1)
    {
      newRing = currRing;
      delete next_weight;
      break;
    }
 
    if(MivComp(next_weight, target_weight) == 1)
    {
      if(tp_deg == nV)
      {
        endwalks = 1;
      }
      else
      {
        G = REC_GB_Mwalk(G,curr_weight, orig_target_weight, tp_deg+1,nnwinC);
        newRing = currRing;
        delete next_weight;
        break;
      }
    }
 
    for(i=nV-1; i>=0; i--)
    {
      (*curr_weight)[i] = (*next_weight)[i];
    }
    delete next_weight;
  }
 
  delete ivNull;
 
  if(tp_deg != nV)
  {
    newRing = currRing;
 
    if (rParameter(currRing) != NULL)
    {
      DefRingPar(orig_target_weight);
    }
    else
    {
      rChangeCurrRing(VMrDefault(orig_target_weight));
    }
    F1 = idrMoveR(G, newRing,currRing);
 
    if(nnwinC == 0)
    {
      F1 = REC_GB_Mwalk(F1,curr_weight, orig_target_weight, tp_deg+1,nnwinC);
    }
    else
    {
      if(test_w_in_ConeCC(F1, target_weight) != 1)
      {
        F1 = REC_GB_Mwalk(F1,curr_weight, orig_target_weight,tp_deg+1,nnwinC);
      }
    }
    delete target_weight;
 
    TargetRing = currRing;
    rChangeCurrRing(EXXRing);
    result = idrMoveR(F1, TargetRing,currRing);
  }
  else
  {
    if(nlast == 1)
    {
      if (rParameter(currRing) != NULL)
      {
        DefRingPar(orig_target_weight);
      }
      else
      {
        rChangeCurrRing(VMrDefault(orig_target_weight));
      }
    KSTD_Finish:
      if(isGB == FALSE)
      {
        F1 = idrMoveR(G, newRing,currRing);
      }
      else
      {
        F1 = G;
      }
#ifdef TIME_TEST
      to=clock();
#endif
      // apply Buchberger alg to compute a red. GB of F1
      G = MstdCC(F1);
#ifdef TIME_TEST
      xtextra=clock()-to;
#endif
      idDelete(&F1);
      newRing = currRing;
    }
 
  LastGB_Finish:
    rChangeCurrRing(EXXRing);
    result = idrMoveR(G, newRing,currRing);
  }
 
  if(Overflow_Error == FALSE)
    {
    Overflow_Error = nError;
    }
#ifndef BUCHBERGER_ALG
  delete last_omega;
#endif
  return(result);
}

Rec_LastGB()

static ideal Rec_LastGB ( ideal  G, intvec *  curr_weight, intvec *  orig_target_weight, int  tp_deg, int  npwinc  )

static

Definition at line 3933 of file walk.cc.

{
  BOOLEAN nError = Overflow_Error;
  Overflow_Error = FALSE;
  // BOOLEAN nOverflow_Error = FALSE;
 
#ifdef TIME_TEST
  clock_t tproc=0;
  clock_t tinput = clock();
#endif
 
  int i,  nV = currRing->N;
  int nwalk=0, endwalks=0, nnwinC=1;
  int nlast = 0;
  ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG;
  ring newRing, oldRing, TargetRing;
  intvec* iv_M_lp;
  intvec* target_weight;
  intvec* ivNull = new intvec(nV); //define (0,...,0)
  ring EXXRing = currRing;
  //int NEG=0; //19 juni 03
  intvec* next_weight;
#ifndef  BUCHBERGER_ALG
  //08 Juli 03
  intvec* hilb_func;
#endif
  // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
    (*last_omega)[i] = 1;
  (*last_omega)[0] = 10000;
 
  BOOLEAN isGB = FALSE;
 
  // compute a pertubed weight vector of the target weight vector
  if(tp_deg > 1 && tp_deg <= nV)
  {
    ideal H0 = idHeadCC(G);
 
    if (rParameter (currRing) != NULL)
    {
      DefRingParlp();
    }
    else
    {
      VMrDefaultlp();
    }
    TargetRing = currRing;
    ssG = idrMoveR(G,EXXRing,currRing);
 
    ideal H0_tmp = idrMoveR(H0,EXXRing,currRing);
    ideal H1 = idHeadCC(ssG);
 
    // Apply Lemma 2.2 in Collart et. al (1997) to check whether cone(k-1) is equal to cone(k)
    if(test_G_GB_walk(H0_tmp,H1)==1)
    {
      idDelete(&H0_tmp);
      idDelete(&H1);
      G = ssG;
      ssG = NULL;
      newRing = currRing;
      delete ivNull;
 
      if(npwinc != 0)
      {
        goto LastGB_Finish;
      }
      else
      {
        isGB = TRUE;
        goto KSTD_Finish;
      }
    }
    idDelete(&H0_tmp);
    idDelete(&H1);
 
    iv_M_lp = MivMatrixOrderlp(nV);
    target_weight  = MPertVectors(ssG, iv_M_lp, tp_deg);
    delete iv_M_lp;
    //PrintS("\n// Input is not GB!!");
    rChangeCurrRing(EXXRing);
    G = idrMoveR(ssG, TargetRing,currRing);
 
    if(Overflow_Error == TRUE)
    {
      //nOverflow_Error = Overflow_Error;
      //NEG = 1;
      newRing = currRing;
      goto JUNI_STD;
    }
  }
 
  while(1)
  {
    nwalk ++;
    nstep++;
 
    if(nwalk==1)
    {
      goto FIRST_STEP;
    }
#ifdef TIME_TEST
    to=clock();
#endif
    // compute an initial form ideal of <G> w.r.t. "curr_vector"
    Gomega = MwalkInitialForm(G, curr_weight);
#ifdef TIME_TEST
    xtif=xtif+clock()-to;
#endif
 
#ifndef  BUCHBERGER_ALG
    if(isNolVector(curr_weight) == 0)
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    }
    else
    {
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
    }
#endif // BUCHBERGER_ALG
 
    oldRing = currRing;
 
    // defiNe a new ring that its ordering is "(a(curr_weight),lp)
    if (rParameter(currRing) != NULL)
    {
      DefRingPar(curr_weight);
    }
    else
    {
      rChangeCurrRing(VMrDefault(curr_weight));
    }
    newRing = currRing;
    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
#ifdef TIME_TEST
    to=clock();
#endif
    // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing"
#ifdef  BUCHBERGER_ALG
    M = MstdhomCC(Gomega1);
#else
    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    delete hilb_func;
#endif // BUCHBERGER_ALG
#ifdef TIME_TEST
    xtstd=xtstd+clock()-to;
#endif
    // change the ring to oldRing
    rChangeCurrRing(oldRing);
    M1 =  idrMoveR(M, newRing,currRing);
    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
 
#ifdef TIME_TEST
     to=clock();
#endif
    // compute a reduced Groebner basis of <G> w.r.t. "newRing" by the lifting process
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    xtlift=xtlift+clock()-to;
#endif
    idDelete(&M1);
    idDelete(&Gomega2);
    idDelete(&G);
 
    // change the ring to newRing
    rChangeCurrRing(newRing);
    F1 = idrMoveR(F, oldRing,currRing);
 
#ifdef TIME_TEST
    to=clock();
#endif
    // reduce the Groebner basis <G> w.r.t. new ring
    G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
    xtred=xtred+clock()-to;
#endif
    idDelete(&F1);
 
    if(endwalks == 1)
    {
      break;
    }
  FIRST_STEP:
#ifdef TIME_TEST
    to=clock();
#endif
    Overflow_Error = FALSE;
    // compute a next weight vector
    next_weight = MkInterRedNextWeight(curr_weight,target_weight, G);
#ifdef TIME_TEST
    xtnw=xtnw+clock()-to;
#endif
#ifdef PRINT_VECTORS
    MivString(curr_weight, target_weight, next_weight);
#endif
    if(Overflow_Error == TRUE)
    {
      //PrintS("\n// ** The next vector does NOT stay in Cone!!\n");
#ifdef TEST_OVERFLOW
      goto  LastGB_Finish;
#endif
 
      nnwinC = 0;
      if(tp_deg == nV)
      {
        nlast = 1;
      }
      delete next_weight;
      break;
    }
 
    if(MivComp(next_weight, ivNull) == 1)
    {
      //newRing = currRing;
      delete next_weight;
      break;
    }
 
    if(MivComp(next_weight, target_weight) == 1)
    {
      if(tp_deg == nV)
      {
        endwalks = 1;
      }
      else
      {
        // REC_LAST_GB_ALT2:
        //nOverflow_Error = Overflow_Error;
#ifdef TIME_TEST
        tproc=tproc+clock()-tinput;
#endif
 
        /*Print("\n// takes %d steps and calls \"Rec_LastGB\" (%d):",
        nwalk, tp_deg+1);
        */
        G = Rec_LastGB(G,curr_weight, orig_target_weight, tp_deg+1,nnwinC);
        newRing = currRing;
        delete next_weight;
        break;
      }
    }
 
    for(i=nV-1; i>=0; i--)
    {
      (*curr_weight)[i] = (*next_weight)[i];
    }
    delete next_weight;
  }//while
 
  delete ivNull;
 
  if(tp_deg != nV)
  {
    newRing = currRing;
 
    if (rParameter(currRing) != NULL)
    {
      DefRingParlp();
    }
    else
    {
      VMrDefaultlp();
    }
    F1 = idrMoveR(G, newRing,currRing);
 
    if(nnwinC == 0 || test_w_in_ConeCC(F1, target_weight) != 1 )
    {
      // nOverflow_Error = Overflow_Error;
      //Print("\n//  takes %d steps and calls \"Rec_LastGB (%d):", tp_deg+1);
#ifdef TIME_TEST
      tproc=tproc+clock()-tinput;
#endif
      F1 = Rec_LastGB(F1,curr_weight, orig_target_weight, tp_deg+1,nnwinC);
    }
    delete target_weight;
 
    TargetRing = currRing;
    rChangeCurrRing(EXXRing);
    result = idrMoveR(F1, TargetRing,currRing);
  }
  else
  {
    if(nlast == 1)
    {
      JUNI_STD:
 
      newRing = currRing;
      if (rParameter(currRing) != NULL)
      {
        DefRingParlp();
      }
      else
      {
        VMrDefaultlp();
      }
      KSTD_Finish:
      if(isGB == FALSE)
      {
        F1 = idrMoveR(G, newRing,currRing);
      }
      else
      {
        F1 = G;
      }
#ifdef TIME_TEST
      to=clock();
#endif
      // Print("\n// apply the Buchberger's alg in ring = %s",rString(currRing));
      // idElements(F1, "F1");
      G = MstdCC(F1);
#ifdef TIME_TEST
      xtextra=xtextra+clock()-to;
#endif
 
 
      idDelete(&F1);
      newRing = currRing;
    }
 
    LastGB_Finish:
    rChangeCurrRing(EXXRing);
    result = idrMoveR(G, newRing,currRing);
  }
 
  if(Overflow_Error == FALSE)
    {
    Overflow_Error=nError;
    }
#ifdef TIME_TEST
   //Print("\n// \"Rec_LastGB\" (%d) took %d steps and %.2f sec.Overflow_Error (%d)", tp_deg, nwalk, ((double) tproc)/1000000, nOverflow_Error);
#endif
  return(result);
}

rec_r_fractal_call()

static ideal rec_r_fractal_call ( ideal  G, int  nlev, intvec *  ivtarget, int  weight_rad, int  reduction, int  printout  )

static

Definition at line 7453 of file walk.cc.

{
  Overflow_Error =  FALSE;
  //Print("\n\n// Entering the %d-th recursion:", nlev);
 
  int nwalks = 0,i,nV=currRing->N;//polylength
  ring new_ring, testring;
  //ring extoRing;
  ideal Gomega, Gomega1, Gomega2, F, FF, Gresult, Gresult1, G1, Gt;
#ifdef TIME_TEST
  ideal F1;
#endif
  intvec* Mwlp;
#ifndef BUCHBERGER_ALG
  intvec* hilb_func;
#endif
//  intvec* extXtau;
  intvec* next_vect;
  intvec* iv_M;
  intvec* omega2 = new intvec(nV);
  intvec* omtmp = new intvec(nV);
  intvec* altomega = new intvec(nV);
 
  //BOOLEAN isnewtarget = FALSE;
 
  for(i = nV -1; i>=0; i--)
  {
    (*omtmp)[i] = (*ivtarget)[i];
  }
  // to avoid (1,0,...,0) as the target vector (Hans)
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
    (*last_omega)[i] = 1;
  (*last_omega)[0] = 10000;
 
  intvec* omega = new intvec(nV);
  for(i=0; i<nV; i++) {
    if(Xsigma->length() == nV)
      (*omega)[i] =  (*Xsigma)[i];
    else
      (*omega)[i] = (*Xsigma)[(nV*(nlev-1))+i];
 
    (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i];
  }
 
   if(nlev == 1)  Xcall = 1;
   else Xcall = 0;
 
  ring oRing = currRing;
 
  while(1)
  {
#ifdef FIRST_STEP_FRACTAL
    /*
    perturb the current weight vector only on the top level or
    after perturbation of the both vectors, nlev = 2 as the top level
    */
    if((nlev == 1 && Xcall == 0) || (nlev == 2 && Xngleich == 1))
      if(islengthpoly2(G) == 1)
      {
        Mwlp = MivWeightOrderlp(omega);
        Xsigma = Mfpertvector(G, Mwlp);
        delete Mwlp;
        Overflow_Error = FALSE;
      }
#endif
    nwalks ++;
    NEXT_VECTOR_FRACTAL:
#ifdef TIME_TEST
    to=clock();
#endif
    /* determine the next border */
    next_vect = MkInterRedNextWeight(omega,omega2,G);
#ifdef TIME_TEST
    xtnw=xtnw+clock()-to;
#endif
    if(lengthpoly(MwalkInitialForm(G, next_vect)) > 0 && G->m[0] != NULL)
    {
      if(printout > 0)
      {
        PrintS("\n**// rec_r_fractal_call: there is a polynomial in Gomega with at least 3 monomials.\n");
      }
      delete next_vect;
      iv_M = MivMatrixOrder(omega);
#ifdef TIME_TEST
      to=clock();
#endif
      next_vect = MWalkRandomNextWeight(G,iv_M,omega2,weight_rad,nlev);
#ifdef TIME_TEST
      xtnw=xtnw+clock()-to;
#endif
      if(isNegNolVector(next_vect) == 1)
      {
        delete next_vect;
#ifdef TIME_TEST
        to=clock();
#endif
        next_vect = MkInterRedNextWeight(omega,omega2,G);
#ifdef TIME_TEST
        xtnw=xtnw+clock()-to;
#endif
      }
    }
    oRing = currRing;
 
    // We only perturb the current target vector at the recursion  level 1
    if(Xngleich == 0 && nlev == 1) //(ngleich == 0) important, e.g. ex2, ex3
      if (MivComp(next_vect, omega2) == 1)
      {
        // to dispense with taking initials and lifting/interreducing
        // after the call of recursion.
        if(printout > 0)
        {
          Print("\n//** rec_r_fractal_call: Perturb both vectors with degree %d.",nlev);
          //idElements(G, "G");
        }
        Xngleich = 1;
        nlev +=1;
        if(ivtarget->length() == nV)
        {
/*
          if (rParameter(currRing) != NULL)
            DefRingPar(omtmp);
          else
            rChangeCurrRing(VMrDefault(omtmp));
*/
          rChangeCurrRing(VMrRefine(ivtarget,omtmp));
        }
        else
        {
          //rChangeCurrRing(VMatrDefault(ivtarget));
          rChangeCurrRing(VMatrRefine(ivtarget,omtmp));
        }
        testring = currRing;
        Gt = idrMoveR(G, oRing,currRing);
 
        // perturb the original target vector w.r.t. the current GB
        if(ivtarget->length() == nV)
        {
          delete Xtau;
          Xtau = NewVectorlp(Gt);
        }
        else
        {
          delete Xtau;
          Xtau = Mfpertvector(Gt,ivtarget);
        }
 
        rChangeCurrRing(oRing);
        G = idrMoveR(Gt,testring,currRing);
 
        // perturb the current vector w.r.t. the current GB
        Mwlp = MivWeightOrderlp(omega);
        if(ivtarget->length() > nV)
        {
          delete Mwlp;
          Mwlp = MivMatrixOrderRefine(omega,ivtarget);
        }
        Xsigma = Mfpertvector(G, Mwlp);
        delete Mwlp;
 
        for(i=nV-1; i>=0; i--)
        {
          (*omega2)[i] = (*Xtau)[nV+i];
          (*omega)[i] = (*Xsigma)[nV+i];
        }
 
        delete next_vect;
 
   //to avoid the value of Overflow_Error that occur in Mfpertvector
        Overflow_Error = FALSE;
#ifdef TIME_TEST
        to=clock();
#endif
        next_vect = MkInterRedNextWeight(omega,omega2,G);
#ifdef TIME_TEST
        xtnw=xtnw+clock()-to;
#endif
        if(lengthpoly(MwalkInitialForm(G, next_vect)) > 0 && G->m[0] != NULL)
        {
          // there is a polynomial in Gomega with at least 3 monomials
          iv_M = MivMatrixOrder(omega);
          delete next_vect;
#ifdef TIME_TEST
          to=clock();
#endif
          next_vect = MWalkRandomNextWeight(G,iv_M,omega2,weight_rad,nlev);
#ifdef TIME_TEST
          xtnw=xtnw+clock()-to;
#endif
          delete iv_M;
          if(isNegNolVector(next_vect) == 1)
          {
            delete next_vect;
#ifdef TIME_TEST
            to=clock();
#endif
            next_vect = MkInterRedNextWeight(omega,omega2,G);
#ifdef TIME_TEST
        xtnw=xtnw+clock()-to;
#endif
          }
        }
      }
#ifdef PRINT_VECTORS
      if(printout > 0)
      {
        MivString(omega, omega2, next_vect);
      }
#endif
 
/*     check whether the the computed vector is in the correct cone
       If no, the reduced GB of an omega-homogeneous ideal will be
       computed by Buchberger algorithm and stop this recursion step
*/
    if(Overflow_Error == TRUE || test_w_in_ConeCC(G,next_vect) != 1)//e.g. Example s7, cyc6
    {
      delete next_vect;
      if(ivtarget->length() == nV)
      {
/*
        if (rParameter(currRing) != NULL)
        {
          DefRingPar(omtmp);
        }
        else
        {
          rChangeCurrRing(VMrDefault(omtmp));
        }
*/
        rChangeCurrRing(VMrRefine(ivtarget,omtmp));
      }
      else
      {
        //rChangeCurrRing(VMatrDefault(ivtarget));
        rChangeCurrRing(VMatrRefine(ivtarget,omtmp));
      }
#ifdef TEST_OVERFLOW
      Gt = idrMoveR(G, oRing,currRing);
      Gt = NULL;
      return(Gt);
#endif
      if(printout > 0)
      {
        Print("\n//** rec_r_fractal_call: applying Buchberger's algorithm in ring r = %s;",
              rString(currRing));
      }
      Gt = idrMoveR(G, oRing,currRing);
#ifdef TIME_TEST
      to=clock();
#endif
      G1 = MstdCC(Gt);
#ifdef TIME_TEST
      xtextra=xtextra+clock()-to;
#endif
      Gt = NULL;
 
      delete omega2;
      delete altomega;
      if(printout > 0)
      {
        Print("\n//** rec_r_fractal_call: (1) Leaving the %d-th recursion with %d steps.\n",
              nlev, nwalks);
        //Print(" ** Overflow_Error? (%d)", Overflow_Error);
      }
      nnflow ++;
      Overflow_Error = FALSE;
      return (G1);
    }
    /*
       If the perturbed target vector stays in the correct cone,
       return the current Groebner basis.
       Otherwise, return the Groebner basis computed with Buchberger's
       algorithm.
       Then we update the perturbed target vectors w.r.t. this GB.
    */
    if (MivComp(next_vect, XivNull) == 1)
    {
      // The computed vector is equal to the origin vector,
      // because t is not defined
      if(ivtarget->length() == nV)
      {
/*
        if (rParameter(currRing) != NULL)
          DefRingPar(omtmp);
        else
          rChangeCurrRing(VMrDefault(omtmp));
*/
        rChangeCurrRing(VMrRefine(ivtarget,omtmp));
      }
      else
      {
        //rChangeCurrRing(VMatrDefault(ivtarget));
        rChangeCurrRing(VMatrRefine(ivtarget,omtmp));
      }
      testring = currRing;
      Gt = idrMoveR(G, oRing,currRing);
 
      if(test_w_in_ConeCC(Gt, omega2) == 1)
      {
        delete omega2;
        delete next_vect;
        delete altomega;
        if(printout > 0)
        {
          Print("\n//** rec_r_fractal_call: (2) Leaving the %d-th recursion with %d steps.\n",
                nlev, nwalks);
          //Print(" ** Overflow_Error? (%d)", Overflow_Error);
        }
        return (Gt);
      }
      else
      {
        if(printout > 0)
        {
          Print("\n//** rec_r_fractal_call: target weight doesn't stay in the correct cone.\n");
        }
 
#ifndef  MSTDCC_FRACTAL
#ifdef PRINT_VECTORS
        if(printout > 0)
        {
          ivString(Xtau, "old Xtau");
        }
#endif
        intvec* Xtautmp;
        if(ivtarget->length() == nV)
        {
          Xtautmp = Mfpertvector(Gt, MivMatrixOrder(omtmp));
        }
        else
        {
          Xtautmp = Mfpertvector(Gt, ivtarget);
        }
#ifdef TEST_OVERFLOW
      if(Overflow_Error == TRUE)
      Gt = NULL; return(Gt);
#endif
 
        if(MivSame(Xtau, Xtautmp) == 1)
        {
          //PrintS("\n// Update vectors are equal to the old vectors!!");
          delete Xtautmp;
          goto FRACTAL_MSTDCC;
        }
 
        Xtau = Xtautmp;
        Xtautmp = NULL;
#ifdef PRINT_VECTORS
        if(printout > 0)
        {
          ivString(Xtau, "new  Xtau");
        }
#endif
 
        for(i=nV-1; i>=0; i--)
          (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i];
 
        //Print("\n//  ring tau = %s;", rString(currRing));
        rChangeCurrRing(oRing);
        G = idrMoveR(Gt, testring,currRing);
 
        goto NEXT_VECTOR_FRACTAL;
#endif
 
      //FRACTAL_MSTDCC:
        if(printout > 0)
        {
          Print("\n//** rec_r_fractal_call: apply Buchberger's algorithm in ring = %s.\n",
                rString(currRing));
        }
#ifdef TIME_TEST
        to=clock();
#endif
        G = MstdCC(Gt);
#ifdef TIME_TEST
        xtextra=xtextra+clock()-to;
#endif
        oRing = currRing;
 
        // update the original target vector w.r.t. the current GB
        if(ivtarget->length() == nV)
        {
/*
          if(MivSame(Xivinput, Xivlp) == 1)
            if (rParameter(currRing) != NULL)
              DefRingParlp();
            else
              VMrDefaultlp();
          else
            if (rParameter(currRing) != NULL)
              DefRingPar(Xivinput);
            else
              rChangeCurrRing(VMrDefault(Xivinput));
*/
          rChangeCurrRing(VMrRefine(ivtarget,Xivinput));
        }
        else
        {
          rChangeCurrRing(VMatrRefine(ivtarget,Xivinput));
        }
        testring = currRing;
        Gt = idrMoveR(G, oRing,currRing);
 
        // perturb the original target vector w.r.t. the current GB
        if(ivtarget->length() == nV)
        {
          delete Xtau;
          Xtau = NewVectorlp(Gt);
        }
        else
        {
          delete Xtau;
          Xtau = Mfpertvector(Gt,ivtarget);
        }
 
        rChangeCurrRing(oRing);
        G = idrMoveR(Gt, testring,currRing);
 
        delete omega2;
        delete next_vect;
        delete altomega;
        if(printout > 0)
        {
          Print("\n//** rec_r_fractal_call: (3) Leaving the %d-th recursion with %d steps.\n",
                nlev,nwalks);
          //Print(" ** Overflow_Error? (%d)", Overflow_Error);
        }
        if(Overflow_Error == TRUE)
          nnflow ++;
 
        Overflow_Error = FALSE;
        return(G);
      }
    } //end of if(MivComp(next_vect, XivNull) == 1)
 
    for(i=nV-1; i>=0; i--)
    {
      (*altomega)[i] = (*omega)[i];
      (*omega)[i] = (*next_vect)[i];
    }
    delete next_vect;
#ifdef TIME_TEST
    to=clock();
#endif
    // Take the initial form of <G> w.r.t. omega
    Gomega = MwalkInitialForm(G, omega);
#ifdef TIME_TEST
    xtif=xtif+clock()-to;
#endif
    //polylength = 1 if there is a polynomial in Gomega with at least 3 monomials and 0 otherwise
    //polylength = lengthpoly(Gomega);
#ifdef CHECK_IDEAL_MWALK
    if(printout > 1)
    {
      idString(Gomega,"//** rec_r_fractal_call: Gomega");
    }
#endif
    if(reduction == 0)
    {
      /* Check whether the intermediate weight vector lies in the interior of the cone.
       * If so, only perform reductions. Otherwise apply Buchberger's algorithm. */
      FF = middleOfCone(G,Gomega);
      if( FF != NULL)
      {
        idDelete(&G);
        G = idCopy(FF);
        idDelete(&FF);
        /* Compue next vector. */
        goto NEXT_VECTOR_FRACTAL;
      }
    }
 
#ifndef  BUCHBERGER_ALG
    if(isNolVector(omega) == 0)
      hilb_func = hFirstSeries(Gomega,NULL,NULL,omega,currRing);
    else
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
#endif
    if(ivtarget->length() == nV)
    {
/*
      if (rParameter(currRing) != NULL)
        DefRingPar(omega);
      else
        rChangeCurrRing(VMrDefault(omega));
*/
      rChangeCurrRing(VMrRefine(ivtarget,omega));
    }
    else
    {
      rChangeCurrRing(VMatrRefine(ivtarget,omega));
    }
    Gomega1 = idrMoveR(Gomega, oRing,currRing);
 
    // Maximal recursion depth, to compute a red. GB
    // Fractal walk with the alternative recursion
    // alternative recursion
    if(nlev == Xnlev || lengthpoly(Gomega1) == 0)
    {
#ifdef TIME_TEST
      to=clock();
#endif
#ifdef  BUCHBERGER_ALG
      Gresult = MstdhomCC(Gomega1);
#else
      Gresult =kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,omega);
      delete hilb_func;
#endif
#ifdef TIME_TEST
      xtstd=xtstd+clock()-to;
#endif
    }
    else
    {
      rChangeCurrRing(oRing);
      Gomega1 = idrMoveR(Gomega1, oRing,currRing);
      Gresult = rec_r_fractal_call(idCopy(Gomega1),nlev+1,omega,weight_rad,reduction,printout);
    }
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(Gresult,"//** rec_r_fractal_call: M");
    }
#endif
    //convert a Groebner basis from a ring to another ring
    new_ring = currRing;
 
    rChangeCurrRing(oRing);
    Gresult1 = idrMoveR(Gresult, new_ring,currRing);
    Gomega2 = idrMoveR(Gomega1, new_ring,currRing);
#ifdef TIME_TEST
    to=clock();
#endif
    // Lifting process
    F = MLifttwoIdeal(Gomega2, Gresult1, G);
#ifdef TIME_TEST
    xtlift=xtlift+clock()-to;
#endif
#ifdef CHECK_IDEAL_MWALK
    if(printout > 2)
    {
      idString(F,"//** rec_r_fractal_call: F");
    }
#endif
    id_Normalize(F,currRing);
    idDelete(&Gresult1);
    idDelete(&Gomega2);
    idDelete(&G);
 
    rChangeCurrRing(new_ring);
    //F1 = idrMoveR(F, oRing,currRing);
    G = idrMoveR(F,oRing,currRing);
/*
#ifdef TIME_TEST
    to=clock();
#endif
    // Interreduce G
    G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
    xtred=xtred+clock()-to;
#endif
    idDelete(&F1);
*/
  }
}

Set_Error()

void Set_Error

(

BOOLEAN

f

)

Definition at line 86 of file walk.cc.

{ pSetm_error=f; }

test_G_GB_walk()

static int test_G_GB_walk ( ideal  H0, ideal  H1  )

inlinestatic

Definition at line 3532 of file walk.cc.

{
  int i, nG = IDELEMS(H0);
 
  if(nG != IDELEMS(H1))
  {
    return 0;
  }
  for(i=nG-1; i>=0; i--)
  {
/*
    poly t;
    if((t=pSub(pCopy(H0->m[i]), pCopy(H1->m[i]))) != NULL)
    {
      pDelete(&t);
      return 0;
    }
    pDelete(&t);
*/
    if(!pEqualPolys(H0->m[i],H1->m[i]))
    {
      return 0;
    }
  }
  return 1;
}

test_w_in_ConeCC()

static int test_w_in_ConeCC ( ideal  G, intvec *  iv  )

static

Definition at line 785 of file walk.cc.

{
  if(G->m[0] == NULL)
  {
    PrintS("//** the result may be WRONG, i.e. 0!!\n");
    return 0;
  }
 
  BOOLEAN nError =  Overflow_Error;
  Overflow_Error = FALSE;
 
  int i, nG = IDELEMS(G);
  poly mi, gi;
 
  for(i=nG-1; i>=0; i--)
  {
    mi = MpolyInitialForm(G->m[i], iv);
    //Print("\n **// test_w_in_ConeCC: lm(initial)= %s \n",pString(mi));
    gi = G->m[i];
    //Print("\n **// test_w_in_ConeCC: lm(ideal)= %s \n",pString(gi));
    if(mi == NULL)
    {
      if(Overflow_Error == FALSE)
      {
        Overflow_Error = nError;
      }
      return 0;
    }
    if(!pLmEqual(mi, gi))
    {
      pDelete(&mi);
      if(Overflow_Error == FALSE)
      {
        Overflow_Error = nError;
      }
      return 0;
    }
    pDelete(&mi);
  }
 
  if(Overflow_Error == FALSE)
  {
    Overflow_Error = nError;
  }
  return 1;
}

TranMImprovwalk()

ideal TranMImprovwalk	(	ideal	G,
		intvec *	curr_weight,
		intvec *	target_tmp,
		int	nP
	)

Definition at line 8396 of file walk.cc.

{
#ifdef TIME_TEST
  clock_t mtim = clock();
#endif
  Set_Error(FALSE  );
  Overflow_Error =  FALSE;
  //Print("// pSetm_Error = (%d)", ErrorCheck());
  //Print("\n// ring ro = %s;", rString(currRing));
 
#ifdef TIME_TEST
  clock_t tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0, textra=0;
  clock_t tinput = clock();
#endif
  int nsteppert=0, i, nV = currRing->N, nwalk=0, npert_tmp=0;
  int *npert=(int*)omAlloc(2*nV*sizeof(int));
  ideal Gomega, M,F,  G1, Gomega1, Gomega2, M1, F1;
  //ring endRing;
  ring newRing, oldRing, lpRing;
  intvec* next_weight;
  intvec* ivNull = new intvec(nV); //define (0,...,0)
  intvec* iv_dp = MivUnit(nV);// define (1,1,...,1)
  intvec* iv_lp = Mivlp(nV); //define (1,0,...,0)
  ideal H0;
  //ideal  H1;
  ideal H2, Glp;
  int nGB, endwalks = 0,  nwalkpert=0;
  intvec* Mlp =  MivMatrixOrderlp(nV);
  intvec* vector_tmp = new intvec(nV);
#ifndef BUCHBERGER_ALG
  intvec* hilb_func;
#endif
  // to avoid (1,0,...,0) as the target vector
  intvec* last_omega = new intvec(nV);
  for(i=nV-1; i>0; i--)
    (*last_omega)[i] = 1;
  (*last_omega)[0] = 10000;
 
  //  intvec* extra_curr_weight = new intvec(nV);
  intvec* target_weight = new intvec(nV);
  for(i=nV-1; i>=0; i--)
    (*target_weight)[i] = (*target_tmp)[i];
 
  ring XXRing = currRing;
  newRing = currRing;
 
#ifdef TIME_TEST
  to=clock();
#endif
  // compute a red. GB w.r.t. the help ring
  if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) = "dp"
    G = MstdCC(G);
  else
  {
    //rOrdStr(currRing) = (a(.c_w..),lp,C)
    if (rParameter(currRing) != NULL)
      DefRingPar(curr_weight);
    else
      rChangeCurrRing(VMrDefault(curr_weight));
    G = idrMoveR(G, XXRing,currRing);
    G = MstdCC(G);
  }
#ifdef TIME_TEST
  tostd=clock()-to;
#endif
 
#ifdef REPRESENTATION_OF_SIGMA
  ideal Gw = MwalkInitialForm(G, curr_weight);
 
  if(islengthpoly2(Gw)==1)
  {
    intvec* MDp;
    if(MivComp(curr_weight, iv_dp) == 1)
      MDp = MatrixOrderdp(nV); //MivWeightOrderlp(iv_dp);
    else
      MDp = MivWeightOrderlp(curr_weight);
 
    curr_weight = RepresentationMatrix_Dp(G, MDp);
 
    delete MDp;
 
    ring exring = currRing;
 
    if (rParameter(currRing) != NULL)
      DefRingPar(curr_weight);
    else
      rChangeCurrRing(VMrDefault(curr_weight));
#ifdef TIME_TEST
    to=clock();
#endif
    Gw = idrMoveR(G, exring,currRing);
    G = MstdCC(Gw);
    Gw = NULL;
#ifdef TIME_TEST
    tostd=tostd+clock()-to;
#endif
    //ivString(curr_weight,"rep. sigma");
    goto COMPUTE_NEW_VECTOR;
  }
 
  idDelete(&Gw);
  delete iv_dp;
#endif
 
 
  while(1)
  {
#ifdef TIME_TEST
    to=clock();
#endif
    /* compute an initial form ideal of <G> w.r.t. "curr_vector" */
    Gomega = MwalkInitialForm(G, curr_weight);
#ifdef TIME_TEST
    tif=tif+clock()-to;
#endif
 
#ifndef  BUCHBERGER_ALG
    if(isNolVector(curr_weight) == 0)
      hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing);
    else
      hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing);
#endif // BUCHBERGER_ALG
 
    oldRing = currRing;
 
    /* define a new ring that its ordering is "(a(curr_weight),lp) */
    if (rParameter(currRing) != NULL)
      DefRingPar(curr_weight);
    else
      rChangeCurrRing(VMrDefault(curr_weight));
 
    newRing = currRing;
    Gomega1 = idrMoveR(Gomega, oldRing,currRing);
 
#ifdef TIME_TEST
    to=clock();
#endif
    /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */
#ifdef  BUCHBERGER_ALG
    M = MstdhomCC(Gomega1);
#else
    M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight);
    delete hilb_func;
#endif // BUCHBERGER_ALG
#ifdef TIME_TEST
    tstd=tstd+clock()-to;
#endif
 
    /* change the ring to oldRing */
    rChangeCurrRing(oldRing);
    M1 =  idrMoveR(M, newRing,currRing);
    Gomega2 =  idrMoveR(Gomega1, newRing,currRing);
 
#ifdef TIME_TEST
    to=clock();
#endif
    /* compute a representation of the generators of submod (M)
       with respect to those of mod (Gomega).
       Gomega is a reduced Groebner basis w.r.t. the current ring */
    F = MLifttwoIdeal(Gomega2, M1, G);
#ifdef TIME_TEST
    tlift=tlift+clock()-to;
#endif
 
    idDelete(&M1);
    idDelete(&Gomega2);
    idDelete(&G);
 
    /* change the ring to newRing */
    rChangeCurrRing(newRing);
    F1 = idrMoveR(F, oldRing,currRing);
 
#ifdef TIME_TEST
    to=clock();
#endif
    /* reduce the Groebner basis <G> w.r.t. new ring */
    G = kInterRedCC(F1, NULL);
#ifdef TIME_TEST
    tred=tred+clock()-to;
#endif
    idDelete(&F1);
 
 
  COMPUTE_NEW_VECTOR:
    newRing = currRing;
    nwalk++;
    nwalkpert++;
#ifdef TIME_TEST
    to=clock();
#endif
    // compute a next weight vector
    next_weight = MwalkNextWeightCC(curr_weight,target_weight, G);
#ifdef TIME_TEST
    tnw=tnw+clock()-to;
#endif
#ifdef PRINT_VECTORS
    MivString(curr_weight, target_weight, next_weight);
#endif
 
    /* check whether the computed intermediate weight vector is in
       the correct cone; sometimes it is very big e.g. s7, cyc7.
       If it is NOT in the correct cone, then compute directly
       a reduced Groebner basis with respect to the lexicographic ordering
       for the known Groebner basis that it is computed in the last step.
    */
    //if(test_w_in_ConeCC(G, next_weight) != 1)
    if(Overflow_Error == TRUE)
    {
    OMEGA_OVERFLOW_TRAN_NEW:
      //Print("\n//  takes %d steps!", nwalk-1);
      //Print("\n//ring lastRing = %s;", rString(currRing));
#ifdef TEST_OVERFLOW
      goto  BE_FINISH;
#endif
/*
#ifdef CHECK_IDEAL_MWALK
      idElements(G, "G");
      //headidString(G, "G");
#endif
*/
      if(MivSame(target_tmp, iv_lp) == 1)
        if (rParameter(currRing) != NULL)
          DefRingParlp();
        else
          VMrDefaultlp();
      else
        if (rParameter(currRing) != NULL)
          DefRingPar(target_tmp);
        else
          rChangeCurrRing(VMrDefault(target_tmp));
 
      lpRing = currRing;
      G1 = idrMoveR(G, newRing,currRing);
 
#ifdef TIME_TEST
      to=clock();
#endif
      /*apply kStd or LastGB to compute  a lex. red. Groebner basis of <G>*/
      if(nP == 0 || MivSame(target_tmp, iv_lp) == 0){
        //Print("\n\n// calls \"std in ring r_%d = %s;", nwalk, rString(currRing));
        G = MstdCC(G1);//no result for qnt1
      }
      else {
        rChangeCurrRing(newRing);
        G1 = idrMoveR(G1, lpRing,currRing);
 
        //Print("\n\n// calls \"LastGB\" (%d) to compute a GB", nV-1);
        G = LastGB(G1, curr_weight, nV-1); //no result for kats7
 
        rChangeCurrRing(lpRing);
        G = idrMoveR(G, newRing,currRing);
      }
#ifdef TIME_TEST
      textra=clock()-to;
#endif
      npert[endwalks]=nwalk-npert_tmp;
      npert_tmp = nwalk;
      endwalks ++;
      break;
    }
 
    /* check whether the computed Groebner basis is really a Groebner basis.
       If not, we perturb the target vector with the maximal "perturbation"
       degree.*/
    if(MivComp(next_weight, target_weight) == 1 ||
       MivComp(next_weight, curr_weight) == 1 )
    {
      //Print("\n//ring r_%d = %s;", nwalk, rString(currRing));
 
 
      //compute the number of perturbations and its step
      npert[endwalks]=nwalk-npert_tmp;
      npert_tmp = nwalk;
 
      endwalks ++;
 
      /*it is very important if the walk only uses one step, e.g. Fate, liu*/
      if(endwalks == 1 && MivComp(next_weight, curr_weight) == 1){
        rChangeCurrRing(XXRing);
        G = idrMoveR(G, newRing,currRing);
        goto FINISH;
      }
      H0 = id_Head(G,currRing);
 
      if(MivSame(target_tmp, iv_lp) == 1)
        if (rParameter(currRing) != NULL)
          DefRingParlp();
        else
          VMrDefaultlp();
      else
        if (rParameter(currRing) != NULL)
          DefRingPar(target_tmp);
        else
          rChangeCurrRing(VMrDefault(target_tmp));
 
      lpRing = currRing;
      Glp = idrMoveR(G, newRing,currRing);
      H2 = idrMoveR(H0, newRing,currRing);
 
      /* Apply Lemma 2.2 in Collart et. al (1997) to check whether
         cone(k-1) is equal to cone(k) */
      nGB = 1;
      for(i=IDELEMS(Glp)-1; i>=0; i--)
      {
        poly t;
        if((t=pSub(pHead(Glp->m[i]), pCopy(H2->m[i]))) != NULL)
        {
          pDelete(&t);
          idDelete(&H2);//5.5.02
          nGB = 0; //i.e. Glp is no reduced Groebner basis
          break;
        }
        pDelete(&t);
      }
 
      idDelete(&H2);//5.5.02
 
      if(nGB == 1)
      {
        G = Glp;
        Glp = NULL;
        break;
      }
 
       /* perturb the target weight vector, if the vector target_tmp
          stays in many cones */
      poly p;
      BOOLEAN plength3 = FALSE;
      for(i=IDELEMS(Glp)-1; i>=0; i--)
      {
        p = MpolyInitialForm(Glp->m[i], target_tmp);
        if(p->next != NULL &&
           p->next->next != NULL &&
           p->next->next->next != NULL)
        {
          Overflow_Error = FALSE;
 
          for(i=0; i<nV; i++)
            (*vector_tmp)[i] = (*target_weight)[i];
 
          delete target_weight;
          target_weight = MPertVectors(Glp, Mlp, nV);
 
          if(MivComp(vector_tmp, target_weight)==1)
          {
            //PrintS("\n// The old and new representaion vector are the same!!");
            G = Glp;
            newRing = currRing;
            goto OMEGA_OVERFLOW_TRAN_NEW;
           }
 
          if(Overflow_Error == TRUE)
          {
            rChangeCurrRing(newRing);
            G = idrMoveR(Glp, lpRing,currRing);
            goto OMEGA_OVERFLOW_TRAN_NEW;
          }
 
          plength3 = TRUE;
          pDelete(&p);
          break;
        }
        pDelete(&p);
      }
 
      if(plength3 == FALSE)
      {
        rChangeCurrRing(newRing);
        G = idrMoveR(Glp, lpRing,currRing);
        goto TRAN_LIFTING;
      }
 
 
      nwalkpert = 1;
      nsteppert ++;
 
      /*
      Print("\n// Subroutine needs (%d) steps.", nwalk);
      idElements(Glp, "last G in walk:");
      PrintS("\n// ****************************************");
      Print("\n// Perturb the original target vector (%d): ", nsteppert);
      ivString(target_weight, "new target");
      PrintS("\n// ****************************************\n");
      */
      rChangeCurrRing(newRing);
      G = idrMoveR(Glp, lpRing,currRing);
 
      delete next_weight;
 
      //Print("\n// ring rNEW = %s;", rString(currRing));
      goto COMPUTE_NEW_VECTOR;
    }
 
  TRAN_LIFTING:
    for(i=nV-1; i>=0; i--)
      (*curr_weight)[i] = (*next_weight)[i];
 
    delete next_weight;
  }//while
#ifdef TEST_OVERFLOW
 BE_FINISH:
#endif
  rChangeCurrRing(XXRing);
  G = idrMoveR(G, lpRing,currRing);
 
 FINISH:
  delete ivNull;
  delete next_weight;
  delete iv_lp;
  omFree(npert);
/*
#ifdef TIME_TEST
  Print("\n// Computation took %d steps and %.2f sec",
        nwalk, ((double) (clock()-mtim)/1000000));
 
  TimeStringFractal(tinput, tostd, tif, tstd, textra, tlift, tred, tnw);
 
 // Print("\n// pSetm_Error = (%d)", ErrorCheck());
  Print("\n// Overflow_Error? (%d)\n", Overflow_Error);
#endif
*/
  return(G);
}

VMatrDefault()

static ring VMatrDefault ( intvec *  va )

static

Definition at line 2790 of file walk.cc.

{
 
  ring r = rCopy0(currRing,FALSE,FALSE);
  int i, nv = currRing->N;
 
  int nb = 4;
 
  /*weights: entries for 3 blocks: NULL Made:???*/
  r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr));
  r->wvhdl[0] = (int*) omAlloc(nv*nv*sizeof(int));
  r->wvhdl[1] =NULL; // (int*) omAlloc(nv*sizeof(int));
  r->wvhdl[2]=NULL;
  r->wvhdl[3]=NULL;
  for(i=0; i<nv*nv; i++)
    r->wvhdl[0][i] = (*va)[i];
 
  /* order: a,lp,C,0 */
  r->order = (rRingOrder_t*) omAlloc(nb * sizeof(rRingOrder_t*));
  r->block0 = (int *)omAlloc0(nb * sizeof(int *));
  r->block1 = (int *)omAlloc0(nb * sizeof(int *));
 
  // ringorder a for the first block: var 1..nv
  r->order[0]  = ringorder_M;
  r->block0[0] = 1;
  r->block1[0] = nv;
 
  // ringorder C for the second block
  r->order[1]  = ringorder_C;
  r->block0[1] = 1;
  r->block1[1] = nv;
 
// ringorder C for the third block: var 1..nv
  r->order[2]  = ringorder_C;
  r->block0[2] = 1;
  r->block1[2] = nv;
 
  // the last block: everything is 0
  r->order[3]  = (rRingOrder_t)0;
 
  // complete ring intializations
 
  rComplete(r);
 
  //rChangeCurrRing(r);
  return r;
}

VMatrRefine()

static ring VMatrRefine ( intvec *  va, intvec *  vb  )

static

Definition at line 2841 of file walk.cc.

{
 
  ring r = rCopy0(currRing,FALSE,FALSE);
  int i, nv = currRing->N;
  int nvs = nv*nv;
 
  int nb = 4;
 
  /*weights: entries for 3 blocks: NULL Made:???*/
  r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr));
  r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int));
  r->wvhdl[1] = (int*) omAlloc(nvs*sizeof(int));
  r->wvhdl[2]=NULL;
  r->wvhdl[3]=NULL;
  for(i=0; i<nvs; i++)
  {
    r->wvhdl[1][i] = (*va)[i];
  }
  for(i=0; i<nv; i++)
  {
    r->wvhdl[0][i] = (*vb)[i];
  }
  /* order: a,lp,C,0 */
  r->order = (rRingOrder_t *) omAlloc(nb * sizeof(rRingOrder_t *));
  r->block0 = (int *)omAlloc0(nb * sizeof(int *));
  r->block1 = (int *)omAlloc0(nb * sizeof(int *));
 
  // ringorder a for the first block: var 1..nv
  r->order[0]  = ringorder_a;
  r->block0[0] = 1;
  r->block1[0] = nv;
 
  // ringorder M for the second block: var 1..nv
  r->order[1]  = ringorder_M;
  r->block0[1] = 1;
  r->block1[1] = nv;
 
  // ringorder C for the third block: var 1..nv
  r->order[2]  = ringorder_C;
  r->block0[2] = 1;
  r->block1[2] = nv;
 
  // the last block: everything is 0
  r->order[3]  = (rRingOrder_t)0;
 
  // complete ring intializations
 
  rComplete(r);
 
  //rChangeCurrRing(r);
  return r;
}

VMrDefault()

static ring VMrDefault ( intvec *  va )

static

Definition at line 2680 of file walk.cc.

{
 
  ring r = rCopy0(currRing,FALSE,FALSE);
  int i, nv = currRing->N;
 
  int nb = 4;
 
  /*weights: entries for 3 blocks: NULL Made:???*/
  r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr));
  r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int));
  for(i=0; i<nv; i++)
    r->wvhdl[0][i] = (*va)[i];
 
  /* order: a,lp,C,0 */
  r->order = (rRingOrder_t *) omAlloc(nb * sizeof(rRingOrder_t *));
  r->block0 = (int *)omAlloc0(nb * sizeof(int *));
  r->block1 = (int *)omAlloc0(nb * sizeof(int *));
 
  // ringorder a for the first block: var 1..nv
  r->order[0]  = ringorder_a;
  r->block0[0] = 1;
  r->block1[0] = nv;
 
  // ringorder lp for the second block: var 1..nv
  r->order[1]  = ringorder_lp;
  r->block0[1] = 1;
  r->block1[1] = nv;
 
  // ringorder C for the third block
  // it is very important within "idLift",
  // especially, by ring syz_ring=rCurrRingAssure_SyzComp();
  // therefore, nb  must be (nBlocks(currRing)  + 1)
  r->order[2]  = ringorder_C;
 
  // the last block: everything is 0
  r->order[3]  = (rRingOrder_t)0;
 
  // polynomial ring
  r->OrdSgn    = 1;
 
  // complete ring intializations
 
  rComplete(r);
  return r;
  //rChangeCurrRing(r);
}

VMrDefaultlp()

static void VMrDefaultlp ( void  )

static

Definition at line 2898 of file walk.cc.

{
  ring r = rCopy0(currRing,FALSE,FALSE);
  int nv = currRing->N;
 
  int nb = rBlocks(currRing) + 1;
 
  /*weights: entries for 3 blocks: NULL Made:???*/
 
  r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr));
 
  /* order: lp,C,0 */
  r->order = (rRingOrder_t *) omAlloc(nb * sizeof(rRingOrder_t *));
  r->block0 = (int *)omAlloc0(nb * sizeof(int *));
  r->block1 = (int *)omAlloc0(nb * sizeof(int *));
 
  /* ringorder lp for the first block: var 1..nv */
  r->order[0]  = ringorder_lp;
  r->block0[0] = 1;
  r->block1[0] = nv;
 
  /* ringorder C for the second block */
  r->order[1]  = ringorder_C;
 
  /* the last block: everything is 0 */
  r->order[2]  = (rRingOrder_t)0;
 
  /*polynomial ring*/
  r->OrdSgn    = 1;
 
  /* complete ring intializations */
 
  rComplete(r);
 
  rChangeCurrRing(r);
}

VMrRefine()

static ring VMrRefine ( intvec *  va, intvec *  vb  )

static

Definition at line 2731 of file walk.cc.

{
 
  ring r = rCopy0(currRing,FALSE,FALSE);
  int i, nv = currRing->N;
 
  int nb = 5;
 
  //weights: entries for 3 blocks: NULL Made:???
  r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr));
  r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int));
  r->wvhdl[1] = (int*) omAlloc(nv*sizeof(int));
 
  for(i=0; i<nv; i++)
  {
    r->wvhdl[0][i] = (*vb)[i];
    r->wvhdl[1][i] = (*va)[i];
  }
 
  // order: (1..1),a,lp,C
  r->order = (rRingOrder_t *) omAlloc(nb * sizeof(rRingOrder_t *));
  r->block0 = (int *)omAlloc0(nb * sizeof(int *));
  r->block1 = (int *)omAlloc0(nb * sizeof(int *));
 
  // ringorder a for the first block: var 1..nv
  r->order[0]  = ringorder_a;
  r->block0[0] = 1;
  r->block1[0] = nv;
 
 // ringorder Wp for the second block: var 1..nv
  r->order[1]  = ringorder_a;
  r->block0[1] = 1;
  r->block1[1] = nv;
 
  // ringorder lp for the third block: var 1..nv
  r->order[2]  = ringorder_lp;
  r->block0[2] = 1;
  r->block1[2] = nv;
 
  // ringorder C for the 4th block
  // it is very important within "idLift",
  // especially, by ring syz_ring=rCurrRingAssure_SyzComp();
  // therefore, nb  must be (nBlocks(currRing)  + 1)
  r->order[3]  = ringorder_C;
 
  // the last block: everything is 0
  r->order[4]  = (rRingOrder_t)0;
 
  // complete ring intializations
 
  rComplete(r);
 
  //rChangeCurrRing(r);
  return r;
}

Variable Documentation

ngleich

VAR int ngleich

Definition at line 4505 of file walk.cc.

nnflow

VAR int nnflow

Definition at line 6944 of file walk.cc.

nstep

VAR int nstep

kstd2.cc

Definition at line 80 of file walk.cc.

Overflow_Error

VAR BOOLEAN Overflow_Error = FALSE

Definition at line 88 of file walk.cc.

pSetm_error

EXTERN_VAR BOOLEAN pSetm_error

Definition at line 84 of file walk.cc.

Xcall

VAR int Xcall

Definition at line 6945 of file walk.cc.

Xivinput

VAR intvec* Xivinput

Definition at line 4509 of file walk.cc.

Xivlp

VAR intvec* Xivlp

Definition at line 4510 of file walk.cc.

XivNull

VAR intvec* XivNull

Definition at line 6927 of file walk.cc.

xn

VAR int xn

Definition at line 4508 of file walk.cc.

Xngleich

VAR int Xngleich

Definition at line 6946 of file walk.cc.

Xnlev

VAR int Xnlev

Definition at line 1511 of file walk.cc.

Xsigma

VAR intvec* Xsigma

Definition at line 4506 of file walk.cc.

Xtau

VAR intvec* Xtau

Definition at line 4507 of file walk.cc.