tgb_internal.h

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#ifndef TGB_INTERNAL_H
#define TGB_INTERNAL_H
//!\file tgb_internal.h
/****************************************
*  Computer Algebra System SINGULAR     *
****************************************/
/*
 * ABSTRACT: tgb internal .h file
*/
#define USE_NORO 1
 
#include "omalloc/omalloc.h"
 
//#define TGB_DEBUG
#define FULLREDUCTIONS
//#define HALFREDUCTIONS
//#define HOMOGENEOUS_EXAMPLE
#define REDTAIL_S
#define PAR_N 100
#define PAR_N_F4 5000
#define AC_NEW_MIN 2
#define AC_FLATTEN 1
 
//#define FIND_DETERMINISTIC
//#define REDTAIL_PROT
//#define QUICK_SPOLY_TEST
#ifdef USE_NORO
#define NORO_CACHE 1
#define NORO_SPARSE_ROWS_PRE 1
#define NORO_NON_POLY 1
#include <algorithm>
#endif
#ifdef NORO_CACHE
//#include <map>
#include <vector>
#endif
#ifdef HAVE_BOOST_DYNAMIC_BITSET_HPP
#define  HAVE_BOOST 1
#endif
//#define HAVE_BOOST 1
//#define USE_STDVECBOOL 1
#ifdef HAVE_BOOST
#include <vector>
using boost::dynamic_bitset;
using std::vector;
#endif
#ifdef USE_STDVECBOOL
#include <vector>
using std::vector;
#endif
#include <stdlib.h>
 
#include "misc/options.h"
 
#include "coeffs/modulop.h"
 
#include "polys/monomials/p_polys.h"
#include "polys/monomials/ring.h"
#include "polys/kbuckets.h"
 
#include "kernel/ideals.h"
#include "kernel/polys.h"
 
#include "kernel/GBEngine/kutil.h"
#include "kernel/GBEngine/kInline.h"
#include "kernel/GBEngine/kstd1.h"
 
#include "coeffs/modulop_inl.h" // npInit, npMult
 
class PolySimple
{
public:
  PolySimple(poly p)
  {
    impl=p;
  }
  PolySimple()
  {
    impl=NULL;
  }
  PolySimple(const PolySimple& a)
  {
    //impl=p_Copy(a.impl,currRing);
    impl=a.impl;
  }
  PolySimple& operator=(const PolySimple& p2)
  {
    //p_Delete(&impl,currRing);
    //impl=p_Copy(p2.impl,currRing);
    impl=p2.impl;
    return *this;
  }
  ~PolySimple()
  {
    //p_Delete(&impl,currRing);
  }
  bool operator< (const PolySimple& other) const
  {
    return pLmCmp(impl,other.impl)<0;
  }
  bool operator==(const PolySimple& other)
  {
    return pLmEqual(impl,other.impl);
  }
  poly impl;
 
};
template<class number_type> class DataNoroCacheNode;
/*class MonRedRes{
public:
  poly p;
  number coef;
  BOOLEAN changed;
  int len;
  BOOLEAN onlyBorrowed;
  bool operator<(const MonRedRes& other) const
  {
    int cmp=p_LmCmp(p,other.p,currRing);
    if ((cmp<0)||((cmp==0)&&((onlyBorrowed)&&(!(other.onlyBorrowed)))))
    {
      return true;
    } else return false;
  }
  DataNoroCacheNode* ref;
  MonRedRes()
  {
    ref=NULL;
    p=NULL;
  }
};*/
template <class number_type> class MonRedResNP
{
public:
  number coef;
 
 
  DataNoroCacheNode<number_type>* ref;
  MonRedResNP()
  {
    ref=NULL;
  }
};
struct sorted_pair_node
{
  //criterium, which is stable 0. small lcm 1. small i 2. small j
  wlen_type expected_length;
  poly lcm_of_lm;
  int i;
  int j;
  int deg;
 
 
};
#ifdef NORO_CACHE
#ifndef NORO_NON_POLY
class NoroPlaceHolder
{
public:
  DataNoroCacheNode* ref;
  number coef;
};
#endif
#endif
//static ideal debug_Ideal;
 
 
struct poly_list_node
{
  poly p;
  poly_list_node* next;
};
 
struct int_pair_node
{
  int_pair_node* next;
  int a;
  int b;
};
struct monom_poly
{
  poly m;
  poly f;
};
struct mp_array_list
{
  monom_poly* mp;
  int size;
  mp_array_list* next;
};
 
 
struct poly_array_list
{
  poly* p;
  int size;
  poly_array_list* next;
};
class slimgb_alg
{
  public:
    slimgb_alg(ideal I, int syz_comp,BOOLEAN F4,int deg_pos);
                void introduceDelayedPairs(poly* pa,int s);
    virtual ~slimgb_alg();
    void cleanDegs(int lower, int upper);
#ifndef HAVE_BOOST
#ifdef USE_STDVECBOOL
  vector<vector<bool> > states;
#else
  char** states;
#endif
#else
  vector<dynamic_bitset<> > states;
#endif
  ideal add_later;
  ideal S;
  ring r;
  int* lengths;
  wlen_type* weighted_lengths;
  long* short_Exps;
  kStrategy strat;
  int* T_deg;
  int* T_deg_full;
  poly tmp_lm;
  poly* tmp_pair_lm;
  sorted_pair_node** tmp_spn;
  poly* expandS;
  poly* gcd_of_terms;
  int_pair_node* soon_free;
  sorted_pair_node** apairs;
  #if 0
  BOOLEAN* modifiedS;
  #endif
  #ifdef TGB_RESORT_PAIRS
  bool* replaced;
  #endif
  poly_list_node* to_destroy;
  //for F4
  mp_array_list* F;
  poly_array_list* F_minus;
 
  //end for F4
  unsigned int reduction_steps;
  int n;
  //! array_lengths should be greater equal n;
  int syz_comp;
  int array_lengths;
  int normal_forms;
  int current_degree;
  int Rcounter;
  int last_index;
  int max_pairs;
  int pair_top;
  int easy_product_crit;
  int extended_product_crit;
  int average_length;
  int lastDpBlockStart;
  int lastCleanedDeg;
  int deg_pos;
  BOOLEAN use_noro;
  BOOLEAN use_noro_last_block;
  BOOLEAN isDifficultField;
  BOOLEAN completed;
  BOOLEAN is_homog;
  BOOLEAN tailReductions;
  BOOLEAN eliminationProblem;
  BOOLEAN F4_mode;
  BOOLEAN nc;
  #ifdef TGB_RESORT_PAIRS
  BOOLEAN used_b;
  #endif
  inline unsigned long pTotaldegree(poly p)
  {
      pTest(p);
      //assume(pDeg(p,r)==::p_Totaldegree(p,r));
      assume(((unsigned long)::p_Totaldegree(p,r))==p->exp[deg_pos]);
      return p->exp[deg_pos];
      //return ::pTotaldegree(p,this->r);
  }
  inline int pTotaldegree_full(poly p)
  {
    int rr=0;
    while(p!=NULL)
    {
      int d=this->pTotaldegree(p);
      if (d>rr) rr=d;
      pIter(p);
    }
    return rr;
  }
};
class red_object
{
 public:
  kBucket_pt bucket;
  poly p;
  unsigned long sev;
  void flatten();
  void validate();
  wlen_type initial_quality;
  void adjust_coefs(number c_r, number c_ac_r);
  wlen_type guess_quality(slimgb_alg* c);
  int clear_to_poly();
  void canonicalize();
};
 
 
enum calc_state
  {
    UNCALCULATED,
    HASTREP//,
    //UNIMPORTANT,
    //SOONTREP
  };
template <class len_type, class set_type>  int pos_helper(kStrategy strat, poly p, len_type len, set_type setL, polyset set);
void free_sorted_pair_node(sorted_pair_node* s, const ring r);
ideal do_t_rep_gb(ring r,ideal arg_I, int syz_comp, BOOLEAN F4_mode,int deg_pos);
void now_t_rep(const int & arg_i, const int & arg_j, slimgb_alg* c);
 
void clean_top_of_pair_list(slimgb_alg* c);
int slim_nsize(number n, ring r);
sorted_pair_node* quick_pop_pair(slimgb_alg* c);
sorted_pair_node* top_pair(slimgb_alg* c);
sorted_pair_node** add_to_basis_ideal_quotient(poly h, slimgb_alg* c, int* ip);//, BOOLEAN new_pairs=TRUE);
sorted_pair_node**  spn_merge(sorted_pair_node** p, int pn,sorted_pair_node **q, int qn,slimgb_alg* c);
int kFindDivisibleByInS_easy(kStrategy strat,const red_object & obj);
int tgb_pair_better_gen2(const void* ap,const void* bp);
int kFindDivisibleByInS_easy(kStrategy strat,poly p, long sev);
/**
   makes on each red_object in a region a single_step
 **/
class reduction_step
{
 public:
  /// we assume that all occurring red_objects have same lm, and all
  /// occ. lm's in r[l...u] are the same, only reductor does not occur
  virtual void reduce(red_object* r, int l, int u);
  //int reduction_id;
  virtual ~reduction_step();
  slimgb_alg* c;
  int reduction_id;
};
class simple_reducer:public reduction_step
{
 public:
  poly p;
  kBucket_pt fill_back;
  int p_len;
  int reducer_deg;
  simple_reducer(poly pp, int pp_len,int pp_reducer_deg, slimgb_alg* pp_c =NULL)
  {
    this->p=pp;
    this->reducer_deg=pp_reducer_deg;
    assume(pp_len==(int)pLength(pp));
    this->p_len=pp_len;
    this->c=pp_c;
  }
  virtual void pre_reduce(red_object* r, int l, int u);
  virtual void reduce(red_object* r, int l, int u);
  ~simple_reducer();
 
 
  virtual void do_reduce(red_object & ro);
};
 
//class sum_canceling_reducer:public reduction_step {
//  void reduce(red_object* r, int l, int u);
//};
struct find_erg
{
  poly expand;
  int expand_length;
  int to_reduce_u;
  int to_reduce_l;
  int reduce_by;//index of reductor
  BOOLEAN fromS;//else from los
 
};
 
template <class len_type, class set_type>  int pos_helper(kStrategy strat, poly p, len_type len, set_type setL, polyset set)
{
  //Print("POSHELER:%d",sizeof(wlen_type));
  int length=strat->sl;
  int i;
  int an = 0;
  int en= length;
 
  if ((len>setL[length])
      || ((len==setL[length]) && (pLmCmp(set[length],p)== -1)))
    return length+1;
 
  loop
  {
    if (an >= en-1)
    {
      if ((len<setL[an])
          || ((len==setL[an]) && (pLmCmp(set[an],p) == 1))) return an;
      return en;
    }
    i=(an+en) / 2;
    if ((len<setL[i])
        || ((len==setL[i]) && (pLmCmp(set[i],p) == 1))) en=i;
    //else if ((len>setL[i])
    //|| ((len==setL[i]) && (pLmCmp(set[i],p) == -1))) an=i;
    else an=i;
  }
 
}
#ifdef NORO_CACHE
#define slim_prec_cast(a) (unsigned int) (unsigned long) (a)
#define F4mat_to_number_type(a) (number_type) slim_prec_cast(a)
typedef unsigned short tgb_uint16;
typedef unsigned char tgb_uint8;
typedef unsigned int tgb_uint32;
class NoroCacheNode
{
public:
  NoroCacheNode** branches;
  int branches_len;
 
 
  NoroCacheNode()
  {
    branches=NULL;
    branches_len=0;
 
  }
  NoroCacheNode* setNode(int branch, NoroCacheNode* node)
  {
    if (branch>=branches_len)
    {
      if (branches==NULL)
      {
        branches_len=branch+1;
        branches_len=si_max(branches_len,3);
        branches=(NoroCacheNode**) omAlloc(branches_len*sizeof(NoroCacheNode*));
        int i;
        for(i=0;i<branches_len;i++)
        {
          branches[i]=NULL;
        }
      }
      else
      {
        int branches_len_old=branches_len;
        branches_len=branch+1;
        branches=(NoroCacheNode**) omrealloc(branches,branches_len*sizeof(NoroCacheNode*));
        int i;
        for(i=branches_len_old;i<branches_len;i++)
        {
          branches[i]=NULL;
        }
      }
    }
    assume(branches[branch]==NULL);
    branches[branch]=node;
    return node;
  }
  NoroCacheNode* getBranch(int branch)
  {
    if (branch<branches_len) return branches[branch];
    return NULL;
  }
  virtual ~NoroCacheNode()
  {
    int i;
    for(i=0;i<branches_len;i++)
    {
      delete branches[i];
    }
    omfree(branches);
  }
  NoroCacheNode* getOrInsertBranch(int branch)
  {
    if ((branch<branches_len)&&(branches[branch]))
      return branches[branch];
    else
    {
      return setNode(branch,new NoroCacheNode());
    }
  }
};
class DenseRow{
public:
  number* array;
  int begin;
  int end;
  DenseRow()
  {
    array=NULL;
  }
  ~DenseRow()
  {
    omfree(array);
  }
};
template <class number_type> class SparseRow
{
public:
  int* idx_array;
  number_type* coef_array;
  int len;
  SparseRow()
  {
    len=0;
    idx_array=NULL;
    coef_array=NULL;
  }
  SparseRow<number_type>(int n)
  {
    len=n;
    idx_array=(int*) omAlloc(n*sizeof(int));
    coef_array=(number_type*) omAlloc(n*sizeof(number_type));
  }
  SparseRow<number_type>(int n, const number_type* source)
  {
    len=n;
    idx_array=NULL;
    coef_array=(number_type*) omAlloc(n*sizeof(number_type));
    memcpy(coef_array,source,n*sizeof(number_type));
  }
  ~SparseRow<number_type>()
  {
    omfree(idx_array);
    omfree(coef_array);
  }
};
 
template <class number_type> class DataNoroCacheNode:public NoroCacheNode
{
public:
 
  int value_len;
  poly value_poly;
  #ifdef NORO_SPARSE_ROWS_PRE
  SparseRow<number_type>* row;
  #else
  DenseRow* row;
  #endif
  int term_index;
  DataNoroCacheNode(poly p, int len)
  {
    value_len=len;
    value_poly=p;
    row=NULL;
    term_index=-1;
  }
  #ifdef NORO_SPARSE_ROWS_PRE
  DataNoroCacheNode(SparseRow<number_type>* row)
  {
    if (row!=NULL)
      value_len=row->len;
    else
      value_len=0;
    value_poly=NULL;
    this->row=row;
    term_index=-1;
  }
  #endif
  ~DataNoroCacheNode()
  {
    //p_Delete(&value_poly,currRing);
    if (row) delete row;
  }
};
template <class number_type> class TermNoroDataNode
{
public:
  DataNoroCacheNode<number_type>* node;
  poly t;
};
 
template <class number_type> class NoroCache
{
public:
  poly temp_term;
#ifndef NORO_NON_POLY
  void evaluatePlaceHolder(number* row,std::vector<NoroPlaceHolder>& place_holders);
  void evaluateRows();
  void evaluateRows(int level, NoroCacheNode* node);
#endif
  void collectIrreducibleMonomials( std::vector<DataNoroCacheNode<number_type>* >& res);
  void collectIrreducibleMonomials(int level,  NoroCacheNode* node, std::vector<DataNoroCacheNode<number_type>* >& res);
 
#ifdef NORO_RED_ARRAY_RESERVER
  int reserved;
  poly* recursionPolyBuffer;
#endif
  static const int backLinkCode=-222;
  DataNoroCacheNode<number_type>* insert(poly term, poly nf, int len)
  {
    //assume(impl.find(p_Copy(term,currRing))==impl.end());
    //assume(len==pLength(nf));
    assume(npIsOne(p_GetCoeff(term,currRing),currRing->cf));
    if (term==nf)
    {
      term=p_Copy(term,currRing);
 
      ressources.push_back(term);
      nIrreducibleMonomials++;
      return treeInsertBackLink(term);
 
    }
    else
    {
      if (nf)
      {
        //nf=p_Copy(nf,currRing);
        assume(p_LmCmp(nf,term,currRing)==-1);
        ressources.push_back(nf);
      }
      return treeInsert(term,nf,len);
 
    }
 
    //impl[term]=std::pair<PolySimple,int> (nf,len);
  }
  #ifdef NORO_SPARSE_ROWS_PRE
  DataNoroCacheNode<number_type>* insert(poly term, SparseRow<number_type>* srow)
  {
    //assume(impl.find(p_Copy(term,currRing))==impl.end());
    //assume(len==pLength(nf));
 
      return treeInsert(term,srow);
 
 
    //impl[term]=std::pair<PolySimple,int> (nf,len);
  }
  #endif
  DataNoroCacheNode<number_type>* insertAndTransferOwnerShip(poly t, ring /*r*/)
  {
    ressources.push_back(t);
    DataNoroCacheNode<number_type>* res=treeInsertBackLink(t);
    res->term_index=nIrreducibleMonomials;
    nIrreducibleMonomials++;
    return res;
  }
  poly lookup(poly term, BOOLEAN& succ, int & len);
  DataNoroCacheNode<number_type>* getCacheReference(poly term);
  NoroCache()
  {
    buffer=NULL;
#ifdef NORO_RED_ARRAY_RESERVER
    reserved=0;
    recursionPolyBuffer=(poly*)omAlloc(1000000*sizeof(poly));
#endif
    nIrreducibleMonomials=0;
    nReducibleMonomials=0;
    temp_term=pOne();
    tempBufferSize=3000;
    tempBuffer=omAlloc(tempBufferSize);
  }
  void ensureTempBufferSize(size_t size)
  {
    if (tempBufferSize<size)
    {
      tempBufferSize=2*size;
      omFree(tempBuffer);
      tempBuffer=omAlloc(tempBufferSize);
    }
  }
#ifdef NORO_RED_ARRAY_RESERVER
  poly* reserve(int n)
  {
    poly* res=recursionPolyBuffer+reserved;
    reserved+=n;
    return res;
  }
  void free(int n)
  {
    reserved-=n;
  }
#endif
  ~NoroCache()
  {
    int s=ressources.size();
    int i;
    for(i=0;i<s;i++)
    {
      p_Delete(&ressources[i].impl,currRing);
    }
    p_Delete(&temp_term,currRing);
#ifdef NORO_RED_ARRAY_RESERVER
    omfree(recursionPolyBuffer);
#endif
   omFree(tempBuffer);
  }
 
  int nIrreducibleMonomials;
  int nReducibleMonomials;
  void* tempBuffer;
  size_t tempBufferSize;
protected:
  DataNoroCacheNode<number_type>* treeInsert(poly term,poly nf,int len)
  {
    int i;
    nReducibleMonomials++;
    int nvars=(currRing->N);
    NoroCacheNode* parent=&root;
    for(i=1;i<nvars;i++)
    {
      parent=parent->getOrInsertBranch(p_GetExp(term,i,currRing));
    }
    return (DataNoroCacheNode<number_type>*) parent->setNode(p_GetExp(term,nvars,currRing),new DataNoroCacheNode<number_type>(nf,len));
  }
  #ifdef NORO_SPARSE_ROWS_PRE
  DataNoroCacheNode<number_type>* treeInsert(poly term,SparseRow<number_type>* srow)
  {
    int i;
    nReducibleMonomials++;
    int nvars=(currRing->N);
    NoroCacheNode* parent=&root;
    for(i=1;i<nvars;i++)
    {
      parent=parent->getOrInsertBranch(p_GetExp(term,i,currRing));
    }
    return (DataNoroCacheNode<number_type>*) parent->setNode(p_GetExp(term,nvars,currRing),new DataNoroCacheNode<number_type>(srow));
  }
  #endif
  DataNoroCacheNode<number_type>* treeInsertBackLink(poly term)
  {
    int i;
    int nvars=(currRing->N);
    NoroCacheNode* parent=&root;
    for(i=1;i<nvars;i++)
    {
      parent=parent->getOrInsertBranch(p_GetExp(term,i,currRing));
    }
    return (DataNoroCacheNode<number_type>*) parent->setNode(p_GetExp(term,nvars,currRing),new DataNoroCacheNode<number_type>(term,backLinkCode));
  }
 
  //@TODO descruct nodes;
  typedef std::vector<PolySimple> poly_vec;
  poly_vec ressources;
  //typedef std::map<PolySimple,std::pair<PolySimple,int> > cache_map;
  //cache_map impl;
  NoroCacheNode root;
  number* buffer;
};
template<class number_type> SparseRow<number_type> * noro_red_to_non_poly_t(poly p, int &len, NoroCache<number_type>* cache,slimgb_alg* c);
template<class number_type> MonRedResNP<number_type> noro_red_mon_to_non_poly(poly t,  NoroCache<number_type> * cache,slimgb_alg* c)
{
  MonRedResNP<number_type> res_holder;
 
 
    DataNoroCacheNode<number_type>* ref=cache->getCacheReference(t);
    if (ref!=NULL)
    {
      res_holder.coef=p_GetCoeff(t,c->r);
 
      res_holder.ref=ref;
      p_Delete(&t,c->r);
      return res_holder;
    }
 
  unsigned long sev=p_GetShortExpVector(t,currRing);
  int i=kFindDivisibleByInS_easy(c->strat,t,sev);
  if (i>=0)
  {
    number coef_bak=p_GetCoeff(t,c->r);
 
    p_SetCoeff(t,npInit(1,c->r->cf),c->r);
    assume(npIsOne(p_GetCoeff(c->strat->S[i],c->r),c->r->cf));
    number coefstrat=p_GetCoeff(c->strat->S[i],c->r);
 
 
    poly exp_diff=cache->temp_term;
    p_ExpVectorDiff(exp_diff,t,c->strat->S[i],c->r);
    p_SetCoeff(exp_diff,npNegM(npInversM(coefstrat,c->r->cf),c->r->cf),c->r);
    p_Setm(exp_diff,c->r);
    assume(c->strat->S[i]!=NULL);
 
    poly res;
    res=pp_Mult_mm(pNext(c->strat->S[i]),exp_diff,c->r);
 
    int len=c->strat->lenS[i]-1;
    SparseRow<number_type>* srow;
    srow=noro_red_to_non_poly_t<number_type>(res,len,cache,c);
    ref=cache->insert(t,srow);
    p_Delete(&t,c->r);
 
 
    res_holder.coef=coef_bak;
    res_holder.ref=ref;
    return res_holder;
 
  } else {
    number coef_bak=p_GetCoeff(t,c->r);
    number one=npInit(1, c->r->cf);
    p_SetCoeff(t,one,c->r);
 
    res_holder.ref=cache->insertAndTransferOwnerShip(t,c->r);
    assume(res_holder.ref!=NULL);
    res_holder.coef=coef_bak;
 
    return res_holder;
 
  }
 
}
/*
poly tree_add(poly* a,int begin, int end,ring r)
{
  int d=end-begin;
  switch(d)
  {
    case 0:
      return NULL;
    case 1:
      return a[begin];
    case 2:
      return p_Add_q(a[begin],a[begin+1],r);
    default:
      int s=d/2;
      return p_Add_q(tree_add(a,begin,begin+s,r),tree_add(a,begin+s,end,r),r);
  }
}
*/
 
template<class number_type> SparseRow<number_type>* convert_to_sparse_row(number_type* temp_array,int temp_size,int non_zeros)
{
SparseRow<number_type>* res=new SparseRow<number_type>(non_zeros);
//int pos=0;
//Print("denseness:%f\n",((double) non_zeros/(double) temp_size));
number_type* it_coef=res->coef_array;
int* it_idx=res->idx_array;
#if 0
for(i=0;i<cache->nIrreducibleMonomials;i++)
{
  if (!(0==temp_array[i]))
  {
 
    res->idx_array[pos]=i;
    res->coef_array[pos]=temp_array[i];
 
    pos++;
    non_zeros--;
    if (non_zeros==0) break;
  }
 
}
#else
int64* start=(int64*) ((void*)temp_array);
int64* end;
const int multiple=sizeof(int64)/sizeof(number_type);
if (temp_size==0) end=start;
 
else
{
  int temp_size_rounded=temp_size+(multiple-(temp_size%multiple));
  assume(temp_size_rounded>=temp_size);
  assume(temp_size_rounded%multiple==0);
  assume(temp_size_rounded<temp_size+multiple);
  number_type* nt_end=temp_array+temp_size_rounded;
  end=(int64*)((void*)nt_end);
}
int64* it=start;
while(it!=end)
{
  if UNLIKELY((*it)!=0)
  {
    int small_i;
    const int temp_index=((number_type*)((void*) it))-temp_array;
    const int bound=temp_index+multiple;
    number_type c;
    for(small_i=temp_index;small_i<bound;small_i++)
    {
      if((c=temp_array[small_i])!=0)
      {
        //res->idx_array[pos]=small_i;
        //res->coef_array[pos]=temp_array[small_i];
        (*(it_idx++))=small_i;
        (*(it_coef++))=c;
        //pos++;
        non_zeros--;
 
      }
      if UNLIKELY(non_zeros==0) break;
    }
 
  }
  ++it;
}
#endif
return res;
}
#ifdef SING_NDEBUG
template <class number_type> void add_coef_times_sparse(number_type* const temp_array,
int /*temp_size*/,SparseRow<number_type>* row, number coef)
#else
template <class number_type> void add_coef_times_sparse(number_type* const temp_array,
int temp_size,SparseRow<number_type>* row, number coef)
#endif
{
  int j;
  number_type* const coef_array=row->coef_array;
  int* const idx_array=row->idx_array;
  const int len=row->len;
  tgb_uint32 buffer[256];
  const tgb_uint32 prime=n_GetChar(currRing->cf);
  const tgb_uint32 c=F4mat_to_number_type(coef);
  assume(!(npIsZero(coef,currRing->cf)));
  for(j=0;j<len;j=j+256)
  {
    const int bound=std::min(j+256,len);
    int i;
    int bpos=0;
    for(i=j;i<bound;i++)
    {
      buffer[bpos++]=coef_array[i];
    }
    int bpos_bound=bound-j;
    for(i=0;i<bpos_bound;i++)
    {
       buffer[i]*=c;
     }
    for(i=0;i<bpos_bound;i++)
    {
       buffer[i]=buffer[i]%prime;
    }
    bpos=0;
    for(i=j;i<bound;i++)
    {
      int idx=idx_array[i];
      assume(bpos<256);
      assume(!(npIsZero((number)(long) buffer[bpos],currRing->cf)));
      temp_array[idx]=F4mat_to_number_type(npAddM((number)(long) temp_array[idx], (number)(long) buffer[bpos++],currRing->cf));
      #ifndef SING_NDEBUG
      assume(idx<temp_size);
      #endif
    }
 
  }
}
#ifdef SING_NDEBUG
template <class number_type> void add_coef_times_dense(number_type* const temp_array,
int /*temp_size*/,const number_type* row, int len,number coef)
#else
template <class number_type> void add_coef_times_dense(number_type* const temp_array,
int temp_size,const number_type* row, int len,number coef)
#endif
{
  int j;
  const number_type* const coef_array=row;
  //int* const idx_array=row->idx_array;
  //const int len=temp_size;
  tgb_uint32 buffer[256];
  const tgb_uint32 prime=n_GetChar(currRing->cf);
  const tgb_uint32 c=F4mat_to_number_type(coef);
  assume(!(npIsZero(coef,currRing->cf)));
  for(j=0;j<len;j=j+256)
  {
    const int bound=std::min(j+256,len);
    int i;
    int bpos=0;
    for(i=j;i<bound;i++)
    {
      buffer[bpos++]=coef_array[i];
    }
    int bpos_bound=bound-j;
    for(i=0;i<bpos_bound;i++)
    {
       buffer[i]*=c;
     }
    for(i=0;i<bpos_bound;i++)
    {
       buffer[i]=buffer[i]%prime;
    }
    bpos=0;
    for(i=j;i<bound;i++)
    {
      //int idx=idx_array[i];
      assume(bpos<256);
      //assume(!(npIsZero((number) buffer[bpos])));
      temp_array[i]=F4mat_to_number_type(npAddM((number)(long) temp_array[i], (number)(long) buffer[bpos++],currRing->cf));
      #ifndef SING_NDEBUG
      assume(i<temp_size);
      #endif
    }
 
  }
}
#ifdef SING_NDEBUG
template <class number_type> void add_dense(number_type* const temp_array,
int /*temp_size*/,const number_type* row, int len)
#else
template <class number_type> void add_dense(number_type* const temp_array,
int temp_size,const number_type* row, int len)
#endif
{
  //int j;
  //const number_type* const coef_array=row;
  //int* const idx_array=row->idx_array;
  //const int len=temp_size;
  //tgb_uint32 buffer[256];
  //const tgb_uint32 prime=npPrimeM;
  //const tgb_uint32 c=F4mat_to_number_type(coef);
 
  int i;
  for(i=0;i<len;i++)
  {
    temp_array[i]=F4mat_to_number_type(npAddM((number)(long) temp_array[i], (number)(long) row[i],currRing->cf));
    #ifndef SING_NDEBUG
    assume(i<temp_size);
    #endif
  }
 
}
#ifdef SING_NDEBUG
template <class number_type> void sub_dense(number_type* const temp_array,
int /*temp_size*/,const number_type* row, int len)
#else
template <class number_type> void sub_dense(number_type* const temp_array,
int temp_size,const number_type* row, int len)
#endif
{
  //int j;
  //const number_type* const coef_array=row;
  //int* const idx_array=row->idx_array;
  //const int len=temp_size;
  //tgb_uint32 buffer[256];
  //const tgb_uint32 prime=npPrimeM;
  //const tgb_uint32 c=F4mat_to_number_type(coef);
 
  int i;
  for(i=0;i<len;i++)
  {
    temp_array[i]=F4mat_to_number_type(npSubM((number)(long) temp_array[i], (number)(long) row[i],currRing->cf));
    #ifndef SING_NDEBUG
    assume(i<temp_size);
    #endif
  }
}
 
#ifdef SING_NDEBUG
template <class number_type> void add_sparse(number_type* const temp_array,int /*temp_size*/,SparseRow<number_type>* row)
#else
template <class number_type> void add_sparse(number_type* const temp_array,int temp_size,SparseRow<number_type>* row)
#endif
{
  int j;
 
          number_type* const coef_array=row->coef_array;
          int* const idx_array=row->idx_array;
          const int len=row->len;
        for(j=0;j<len;j++)
        {
          int idx=idx_array[j];
          temp_array[idx]=F4mat_to_number_type(   (number_type)(long)npAddM((number) (long)temp_array[idx],(number)(long) coef_array[j],currRing->cf));
          #ifndef SING_NDEBUG
          assume(idx<temp_size);
          #endif
        }
}
#ifdef SING_NDEBUG
template <class number_type> void sub_sparse(number_type* const temp_array,int /*temp_size*/,SparseRow<number_type>* row)
#else
template <class number_type> void sub_sparse(number_type* const temp_array,int temp_size,SparseRow<number_type>* row)
#endif
{
  int j;
 
          number_type* const coef_array=row->coef_array;
          int* const idx_array=row->idx_array;
          const int len=row->len;
        for(j=0;j<len;j++)
        {
          int idx=idx_array[j];
          temp_array[idx]=F4mat_to_number_type(  (number_type)(long) npSubM((number) (long)temp_array[idx],(number)(long) coef_array[j],currRing->cf));
          #ifndef SING_NDEBUG
          assume(idx<temp_size);
          #endif
        }
}
template <class number_type> SparseRow<number_type>* noro_red_to_non_poly_dense(MonRedResNP<number_type>* mon, int len,NoroCache<number_type>* cache)
{
  size_t temp_size_bytes=cache->nIrreducibleMonomials*sizeof(number_type)+8;//use 8bit int for testing
   assume(sizeof(int64)==8);
   cache->ensureTempBufferSize(temp_size_bytes);
   number_type* temp_array=(number_type*) cache->tempBuffer;//omalloc(cache->nIrreducibleMonomials*sizeof(number_type));
   int temp_size=cache->nIrreducibleMonomials;
   memset(temp_array,0,temp_size_bytes);
   number minus_one=npInit(-1,currRing->cf);
   int i;
   for(i=0;i<len;i++)
   {
     MonRedResNP<number_type> red=mon[i];
     if ( /*(*/ red.ref /*)*/ )
     {
       if (red.ref->row)
       {
         SparseRow<number_type>* row=red.ref->row;
         number coef=red.coef;
         if (row->idx_array)
         {
           if (!((coef==(number)1L)||(coef==minus_one)))
           {
             add_coef_times_sparse(temp_array,temp_size,row,coef);
           }
           else
           {
             if (coef==(number)1L)
             {
               add_sparse(temp_array,temp_size,row);
             }
             else
             {
               sub_sparse(temp_array,temp_size,row);
             }
           }
         }
         else
         //TODO: treat, 1,-1
         if (!((coef==(number)1L)||(coef==minus_one)))
         {
          add_coef_times_dense(temp_array,temp_size,row->coef_array,row->len,coef);
         }
         else
         {
           if (coef==(number)1L)
             add_dense(temp_array,temp_size,row->coef_array,row->len);
           else
           {
             assume(coef==minus_one);
             sub_dense(temp_array,temp_size,row->coef_array,row->len);
             //add_coef_times_dense(temp_array,temp_size,row->coef_array,row->len,coef);
           }
         }
       }
       else
       {
         if (red.ref->value_len==NoroCache<number_type>::backLinkCode)
         {
           temp_array[red.ref->term_index]=F4mat_to_number_type( npAddM((number)(long) temp_array[red.ref->term_index],red.coef,currRing->cf));
         }
         else
         {
           //PrintS("third case\n");
         }
       }
     }
   }
   int non_zeros=0;
   for(i=0;i<cache->nIrreducibleMonomials;i++)
   {
     //if (!(temp_array[i]==0))
     //{
     //  non_zeros++;
     //}
     assume(((temp_array[i]!=0)==0)|| (((temp_array[i]!=0)==1)));
     non_zeros+=(temp_array[i]!=0);
   }
 
   if (non_zeros==0)
   {
     //omfree(mon);
     return NULL;
   }
   SparseRow<number_type>* res=new SparseRow<number_type>(temp_size,temp_array);//convert_to_sparse_row(temp_array,temp_size, non_zeros);
 
   //omfree(temp_array);
 
 
   return res;
}
template<class number_type> class CoefIdx
{
public:
  number_type coef;
  int idx;
  bool operator<(const CoefIdx<number_type>& other) const
  {
    return (idx<other.idx);
  }
};
template<class number_type> void write_coef_times_xx_idx_to_buffer(CoefIdx<number_type>* const pairs,int& pos,int* const idx_array, number_type* const coef_array,const int rlen, const number coef)
{
  int j;
  for(j=0;j<rlen;j++)
  {
    assume(coef_array[j]!=0);
    CoefIdx<number_type> ci;
    ci.coef=F4mat_to_number_type(npMultM((number)(long) coef,(number)(long) coef_array[j],currRing->cf));
    ci.idx=idx_array[j];
    pairs[pos++]=ci;
  }
}
template<class number_type> void write_coef_times_xx_idx_to_buffer_dense(CoefIdx<number_type>* const pairs,int& pos, number_type* const coef_array,const int rlen, const number coef)
{
  int j;
 
  for(j=0;j<rlen;j++)
  {
    if (coef_array[j]!=0)
    {
      assume(coef_array[j]!=0);
      CoefIdx<number_type> ci;
      ci.coef=F4mat_to_number_type(npMultM((number)(long) coef,(number)(long) coef_array[j],currRing->cf));
      assume(ci.coef!=0);
      ci.idx=j;
      pairs[pos++]=ci;
    }
  }
}
template<class number_type> void write_coef_idx_to_buffer_dense(CoefIdx<number_type>* const pairs,int& pos, number_type* const coef_array,const int rlen)
{
  int j;
 
  for(j=0;j<rlen;j++)
  {
    if (coef_array[j]!=0)
    {
      assume(coef_array[j]!=0);
      CoefIdx<number_type> ci;
      ci.coef=coef_array[j];
      assume(ci.coef!=0);
      ci.idx=j;
      pairs[pos++]=ci;
    }
  }
}
 
template<class number_type> void write_minus_coef_idx_to_buffer_dense(CoefIdx<number_type>* const pairs,int& pos, number_type* const coef_array,const int rlen)
{
  int j;
 
  for(j=0;j<rlen;j++)
  {
    if (coef_array[j]!=0)
    {
      assume(coef_array[j]!=0);
      CoefIdx<number_type> ci;
      ci.coef=F4mat_to_number_type(npNegM((number)(long) coef_array[j],currRing->cf)); // FIXME: inplace negation! // TODO: check if this is not a bug!?
      assume(ci.coef!=0);
      ci.idx=j;
      pairs[pos++]=ci;
    }
  }
}
template<class number_type> void write_coef_idx_to_buffer(CoefIdx<number_type>* const pairs,int& pos,int* const idx_array, number_type* const coef_array,const int rlen)
{
  int j;
  for(j=0;j<rlen;j++)
  {
    assume(coef_array[j]!=0);
    CoefIdx<number_type> ci;
    ci.coef=coef_array[j];
    ci.idx=idx_array[j];
    pairs[pos++]=ci;
  }
}
 
template<class number_type> void write_minus_coef_idx_to_buffer(CoefIdx<number_type>* const pairs,int& pos,int* const idx_array, number_type* const coef_array,const int rlen)
{
  int j;
  for(j=0;j<rlen;j++)
  {
    assume(coef_array[j]!=0);
    CoefIdx<number_type> ci;
    ci.coef=F4mat_to_number_type(npNegM((number)(unsigned long)coef_array[j],currRing->cf));  // FIXME: inplace negation! // TODO: check if this is not a bug!?
    ci.idx=idx_array[j];
    pairs[pos++]=ci;
  }
}
template <class number_type> SparseRow<number_type>* noro_red_to_non_poly_sparse(MonRedResNP<number_type>* mon, int len,NoroCache<number_type>* cache)
{
  int i;
  int together=0;
  for(i=0;i<len;i++)
  {
    MonRedResNP<number_type> red=mon[i];
    if ((red.ref) &&( red.ref->row))
    {
      together+=red.ref->row->len;
    }
    else
    {
      if ((red.ref) &&(red.ref->value_len==NoroCache<number_type>::backLinkCode))
      together++;
    }
  }
  //PrintS("here\n");
  if (together==0) return 0;
  //PrintS("there\n");
  cache->ensureTempBufferSize(together*sizeof(CoefIdx<number_type>));
  CoefIdx<number_type>* pairs=(CoefIdx<number_type>*) cache->tempBuffer; //omalloc(together*sizeof(CoefIdx<number_type>));
  int pos=0;
  const number one=npInit(1, currRing->cf);
  const number minus_one=npInit(-1, currRing->cf);
  for(i=0;i<len;i++)
  {
    MonRedResNP<number_type> red=mon[i];
    if ((red.ref) &&( red.ref->row))
    {
      //together+=red.ref->row->len;
      int* idx_array=red.ref->row->idx_array;
      number_type* coef_array=red.ref->row->coef_array;
      int rlen=red.ref->row->len;
      number coef=red.coef;
      if (idx_array)
      {
        if ((coef!=one)&&(coef!=minus_one))
        {
          write_coef_times_xx_idx_to_buffer(pairs,pos,idx_array, coef_array,rlen, coef);
        }
        else
        {
          if (coef==one)
          {
            write_coef_idx_to_buffer(pairs,pos,idx_array, coef_array,rlen);
          }
          else
          {
            assume(coef==minus_one);
            write_minus_coef_idx_to_buffer(pairs,pos,idx_array, coef_array,rlen);
          }
        }
      }
      else
      {
        if ((coef!=one)&&(coef!=minus_one))
        {
          write_coef_times_xx_idx_to_buffer_dense(pairs,pos,coef_array,rlen,coef);
        }
        else
        {
          if (coef==one)
            write_coef_idx_to_buffer_dense(pairs,pos,coef_array,rlen);
          else
          {
            assume(coef==minus_one);
            write_minus_coef_idx_to_buffer_dense(pairs,pos,coef_array,rlen);
          }
        }
      }
    }
    else
    {
      if ((red.ref) &&(red.ref->value_len==NoroCache<number_type>::backLinkCode))
      {
        CoefIdx<number_type> ci;
        ci.coef=F4mat_to_number_type(red.coef);
        ci.idx=red.ref->term_index;
        pairs[pos++]=ci;
      }
    }
  }
  assume(pos<=together);
  together=pos;
 
  std::sort(pairs,pairs+together);
 
  int act=0;
 
  assume(pairs[0].coef!=0);
  for(i=1;i<together;i++)
  {
    if (pairs[i].idx!=pairs[act].idx)
    {
      if (pairs[act].coef!=0)
      {
        act=act+1;
      }
      pairs[act]=pairs[i];
    }
    else
    {
      pairs[act].coef=F4mat_to_number_type(npAddM((number)(long)pairs[act].coef,(number)(long)pairs[i].coef,currRing->cf));
    }
  }
 
  if (pairs[act].coef==0)
  {
    act--;
  }
  int sparse_row_len=act+1;
  //Print("res len:%d",sparse_row_len);
  if (sparse_row_len==0) {return NULL;}
  SparseRow<number_type>* res=new SparseRow<number_type>(sparse_row_len);
  {
    number_type* coef_array=res->coef_array;
    int* idx_array=res->idx_array;
    for(i=0;i<sparse_row_len;i++)
    {
      idx_array[i]=pairs[i].idx;
      coef_array[i]=pairs[i].coef;
    }
  }
  //omfree(pairs);
 
  return res;
}
template<class number_type> SparseRow<number_type> * noro_red_to_non_poly_t(poly p, int &len, NoroCache<number_type>* cache,slimgb_alg* c)
{
  assume(len==(int)pLength(p));
  if (p==NULL)
  {
    len=0;
    return NULL;
  }
 
  MonRedResNP<number_type>* mon=(MonRedResNP<number_type>*) omalloc(len*sizeof(MonRedResNP<number_type>));
  int i=0;
  double max_density=0.0;
  while(p!=NULL)
  {
    poly t=p;
    pIter(p);
    pNext(t)=NULL;
 
    MonRedResNP<number_type> red=noro_red_mon_to_non_poly(t,cache,c);
    if ((red.ref) && (red.ref->row))
    {
      double act_density=(double) red.ref->row->len;
      act_density/=(double) cache->nIrreducibleMonomials;
      max_density=std::max(act_density,max_density);
    }
    mon[i]=red;
    i++;
  }
 
  assume(i==len);
  len=i;
  bool dense=true;
  if (max_density<0.3) dense=false;
  if (dense)
  {
    SparseRow<number_type>* res=noro_red_to_non_poly_dense(mon,len,cache);
    omfree(mon);
    return res;
  }
  else
  {
    SparseRow<number_type>* res=noro_red_to_non_poly_sparse(mon,len,cache);
    omfree(mon);
    return res;
  }
  //in the loop before nIrreducibleMonomials increases, so position here is important
 
}
#endif
int terms_sort_crit(const void* a, const void* b);
//void simplest_gauss_modp(number* a, int nrows,int ncols);
// a: a[0,0],a[0,1]....a[nrows-1,ncols-1]
// assume: field is Zp
#ifdef USE_NORO
 
 
template <class number_type > void write_poly_to_row(number_type* row, poly h, poly*terms, int tn)
{
  //poly* base=row;
  while(h!=NULL)
  {
    //Print("h:%i\n",h);
    number coef=pGetCoeff(h);
    poly* ptr_to_h=(poly*) bsearch(&h,terms,tn,sizeof(poly),terms_sort_crit);
    assume(ptr_to_h!=NULL);
    int pos=ptr_to_h-terms;
    row[pos]=F4mat_to_number_type(coef);
    //number_type_array[base+pos]=coef;
    pIter(h);
  }
}
template <class number_type > poly row_to_poly(number_type* row, poly* terms, int tn, ring r)
{
  poly h=NULL;
  int j;
  number_type zero=0;//;npInit(0);
  for(j=tn-1;j>=0;j--)
  {
    if (!(zero==(row[j])))
    {
      poly t=terms[j];
      t=p_LmInit(t,r);
      p_SetCoeff(t,(number)(long) row[j],r);
      pNext(t)=h;
      h=t;
    }
 
  }
  return h;
}
template <class number_type > int modP_lastIndexRow(number_type* row,int ncols)
{
  int lastIndex;
  const number_type zero=0;//npInit(0);
  for(lastIndex=ncols-1;lastIndex>=0;lastIndex--)
  {
    if (!(row[lastIndex]==zero))
    {
      return lastIndex;
    }
  }
  return -1;
}
template <class number_type> int term_nodes_sort_crit(const void* a, const void* b)
{
  return -pLmCmp(((TermNoroDataNode<number_type>*) a)->t,((TermNoroDataNode<number_type>*) b)->t);
}
 
template <class number_type>class ModPMatrixBackSubstProxyOnArray;
template <class number_type > class ModPMatrixProxyOnArray
{
public:
  friend class ModPMatrixBackSubstProxyOnArray<number_type>;
 
  int ncols,nrows;
  ModPMatrixProxyOnArray(number_type* array, int nnrows, int nncols)
  {
    this->ncols=nncols;
    this->nrows=nnrows;
    rows=(number_type**) omalloc((size_t)nnrows*sizeof(number_type*));
    startIndices=(int*)omalloc((size_t)nnrows*sizeof(int));
    int i;
    for(i=0;i<nnrows;i++)
    {
      rows[i]=array+((long)i*(long)nncols);
      updateStartIndex(i,-1);
    }
  }
  ~ModPMatrixProxyOnArray()
  {
    omfree(rows);
    omfree(startIndices);
  }
 
  void permRows(int i, int j)
  {
    number_type* h=rows[i];
    rows[i]=rows[j];
    rows[j]=h;
    int hs=startIndices[i];
    startIndices[i]=startIndices[j];
    startIndices[j]=hs;
  }
  void multiplyRow(int row, number_type coef)
  {
    int i;
    number_type* row_array=rows[row];
    if(currRing->cf->ch<=NV_MAX_PRIME)
    {
      for(i=startIndices[row];i<ncols;i++)
      {
        row_array[i]=F4mat_to_number_type(npMult((number)(long) row_array[i],(number)(long) coef,currRing->cf));
      }
    }
    else
    {
      for(i=startIndices[row];i<ncols;i++)
      {
        row_array[i]=F4mat_to_number_type(nvMult((number)(long) row_array[i],(number)(long) coef,currRing->cf));
      }
    }
  }
  void reduceOtherRowsForward(int r)
  {
    //assume rows "under r" have bigger or equal start index
    number_type* row_array=rows[r];
    number_type zero=F4mat_to_number_type((number)0 /*npInit(0, currRing)*/);
    int start=startIndices[r];
    number_type coef=row_array[start];
    assume(start<ncols);
    int other_row;
    assume(!(npIsZero((number)(long) row_array[start],currRing->cf)));
    if (!(npIsOne((number)(long) coef,currRing->cf)))
      multiplyRow(r,F4mat_to_number_type(npInversM((number)(long) coef,currRing->cf)));
    assume(npIsOne((number)(long) row_array[start],currRing->cf));
    int lastIndex=modP_lastIndexRow(row_array, ncols);
    number minus_one=npInit(-1, currRing->cf);
    if(currRing->cf->ch<=NV_MAX_PRIME)
    {
      for (other_row=r+1;other_row<nrows;other_row++)
      {
        assume(startIndices[other_row]>=start);
        if (startIndices[other_row]==start)
        {
          int i;
          number_type* other_row_array=rows[other_row];
          number coef2=npNegM((number)(long) other_row_array[start],currRing->cf);
          if (coef2==minus_one)
          {
            for(i=start;i<=lastIndex;i++)
            {
              if (row_array[i]!=zero)
              {
                other_row_array[i]=F4mat_to_number_type(npSubM((number)(long) other_row_array[i], (number)(long) row_array[i],currRing->cf));
              }
            }
          }
          else
          {
            for(i=start;i<=lastIndex;i++)
            {
              if (row_array[i]!=zero)
              {
                other_row_array[i]=F4mat_to_number_type(npAddM(npMult(coef2,(number)(long) row_array[i],currRing->cf),(number)(long) other_row_array[i],currRing->cf));
              }
            }
          }
          updateStartIndex(other_row,start);
          assume(npIsZero((number)(long) other_row_array[start],currRing->cf));
        }
      }
    }
    else /* ch>NV_MAX_PRIME*/
    {
      for (other_row=r+1;other_row<nrows;other_row++)
      {
        assume(startIndices[other_row]>=start);
        if (startIndices[other_row]==start)
        {
          int i;
          number_type* other_row_array=rows[other_row];
          number coef2=npNegM((number)(long) other_row_array[start],currRing->cf);
          if (coef2==minus_one)
          {
            for(i=start;i<=lastIndex;i++)
            {
              if (row_array[i]!=zero)
              {
                other_row_array[i]=F4mat_to_number_type(npSubM((number)(long) other_row_array[i], (number)(long) row_array[i],currRing->cf));
              }
            }
          }
          else
          {
            for(i=start;i<=lastIndex;i++)
            {
              if (row_array[i]!=zero)
              {
                other_row_array[i]=F4mat_to_number_type(npAddM(nvMult(coef2,(number)(long) row_array[i],currRing->cf),(number)(long) other_row_array[i],currRing->cf));
              }
            }
          }
          updateStartIndex(other_row,start);
          assume(npIsZero((number)(long) other_row_array[start],currRing->cf));
        }
      }
    }
}
void updateStartIndex(int row,int lower_bound)
{
  number_type* row_array=rows[row];
  assume((lower_bound<0)||(npIsZero((number)(long) row_array[lower_bound],currRing->cf)));
  int i;
  //number_type zero=npInit(0);
  for(i=lower_bound+1;i<ncols;i++)
  {
    if (!(row_array[i]==0))
      break;
  }
  startIndices[row]=i;
}
int getStartIndex(int row)
{
  return startIndices[row];
}
BOOLEAN findPivot(int &r, int &c)
{
  //row>=r, col>=c
 
  while(c<ncols)
  {
    int i;
    for(i=r;i<nrows;i++)
    {
      assume(startIndices[i]>=c);
      if (startIndices[i]==c)
      {
        //r=i;
        if (r!=i)
          permRows(r,i);
        return TRUE;
      }
    }
    c++;
  }
  return FALSE;
}
protected:
  number_type** rows;
  int* startIndices;
};
template <class number_type > class ModPMatrixBackSubstProxyOnArray
{
  int *startIndices;
  number_type** rows;
  int *lastReducibleIndices;
  int ncols;
  int nrows;
  int nonZeroUntil;
public:
  void multiplyRow(int row, number_type coef)
  {
    int i;
    number_type* row_array=rows[row];
    if (currRing->cf->ch<=NV_MAX_PRIME)
    {
      for(i=startIndices[row];i<ncols;i++)
      {
        row_array[i]=F4mat_to_number_type(npMult((number)(long) row_array[i],(number)(long) coef,currRing->cf));
      }
    }
    else
    {
      for(i=startIndices[row];i<ncols;i++)
      {
        row_array[i]=F4mat_to_number_type(nvMult((number)(long) row_array[i],(number)(long) coef,currRing->cf));
      }
    }
  }
  ModPMatrixBackSubstProxyOnArray<number_type> (ModPMatrixProxyOnArray<number_type> & p)
  {
//  (number_type* array, int nrows, int ncols, int* startIndices, number_type** rows){
    //we borrow some parameters ;-)
    //we assume, that nobody changes the order of the rows
    this->startIndices=p.startIndices;
    this->rows=p.rows;
    this->ncols=p.ncols;
    this->nrows=p.nrows;
    lastReducibleIndices=(int*) omalloc(nrows*sizeof(int));
    nonZeroUntil=0;
    while(nonZeroUntil<nrows)
    {
      if (startIndices[nonZeroUntil]<ncols)
      {
        nonZeroUntil++;
      }
      else break;
    }
    if (TEST_OPT_PROT)
      Print("rank:%i\n",nonZeroUntil);
    nonZeroUntil--;
    int i;
    for(i=0;i<=nonZeroUntil;i++)
    {
      assume(startIndices[i]<ncols);
      assume(!(npIsZero((number)(long) rows[i][startIndices[i]],currRing->cf)));
      assume(startIndices[i]>=i);
      updateLastReducibleIndex(i,nonZeroUntil+1);
    }
  }
  void updateLastReducibleIndex(int r, int upper_bound)
  {
    number_type* row_array=rows[r];
    if (upper_bound>nonZeroUntil) upper_bound=nonZeroUntil+1;
    int i;
    const number_type zero=0;//npInit(0);
    for(i=upper_bound-1;i>r;i--)
    {
      int start=startIndices[i];
      assume(start<ncols);
      if (!(row_array[start]==zero))
      {
        lastReducibleIndices[r]=start;
        return;
      }
    }
    lastReducibleIndices[r]=-1;
  }
  void backwardSubstitute(int r)
  {
    int start=startIndices[r];
    assume(start<ncols);
    number_type zero=0;//npInit(0);
    number_type* row_array=rows[r];
    assume((!(npIsZero((number)(long) row_array[start],currRing->cf))));
    assume(start<ncols);
    int other_row;
    if (!(npIsOne((number)(long) row_array[r],currRing->cf)))
    {
      //it should be one, but this safety is not expensive
      multiplyRow(r, F4mat_to_number_type(npInversM((number)(long) row_array[start],currRing->cf)));
    }
    int lastIndex=modP_lastIndexRow(row_array, ncols);
    assume(lastIndex<ncols);
    assume(lastIndex>=0);
    if(currRing->cf->ch<=NV_MAX_PRIME)
    {
      for(other_row=r-1;other_row>=0;other_row--)
      {
        assume(lastReducibleIndices[other_row]<=start);
        if (lastReducibleIndices[other_row]==start)
        {
          number_type* other_row_array=rows[other_row];
          number coef=npNegM((number)(long) other_row_array[start],currRing->cf);
          assume(!(npIsZero(coef,currRing->cf)));
          int i;
          assume(start>startIndices[other_row]);
          for(i=start;i<=lastIndex;i++)
          {
            if (row_array[i]!=zero)
            {
              other_row_array[i]=F4mat_to_number_type(npAddM(npMult(coef,(number)(long)row_array[i],currRing->cf),(number)(long)other_row_array[i],currRing->cf));
            }
          }
          updateLastReducibleIndex(other_row,r);
        }
      }
    }
    else
    {
      for(other_row=r-1;other_row>=0;other_row--)
      {
        assume(lastReducibleIndices[other_row]<=start);
        if (lastReducibleIndices[other_row]==start)
        {
          number_type* other_row_array=rows[other_row];
          number coef=npNegM((number)(long) other_row_array[start],currRing->cf);
          assume(!(npIsZero(coef,currRing->cf)));
          int i;
          assume(start>startIndices[other_row]);
          for(i=start;i<=lastIndex;i++)
          {
            if (row_array[i]!=zero)
            {
              other_row_array[i]=F4mat_to_number_type(npAddM(nvMult(coef,(number)(long)row_array[i],currRing->cf),(number)(long)other_row_array[i],currRing->cf));
            }
          }
          updateLastReducibleIndex(other_row,r);
        }
      }
    }
  }
  ~ModPMatrixBackSubstProxyOnArray<number_type>()
  {
    omfree(lastReducibleIndices);
  }
  void backwardSubstitute()
  {
    int i;
    for(i=nonZeroUntil;i>0;i--)
    {
      backwardSubstitute(i);
    }
  }
};
template <class number_type > void simplest_gauss_modp(number_type* a, int nrows,int ncols)
{
  //use memmoves for changing rows
  //if (TEST_OPT_PROT)
  //    PrintS("StartGauss\n");
  ModPMatrixProxyOnArray<number_type> mat(a,nrows,ncols);
 
  int c=0;
  int r=0;
  while(mat.findPivot(r,c))
  {
    //int pivot=find_pivot()
      mat.reduceOtherRowsForward(r);
    r++;
    c++;
  }
  ModPMatrixBackSubstProxyOnArray<number_type> backmat(mat);
  backmat.backwardSubstitute();
  //backward substitutions
  //if (TEST_OPT_PROT)
  //PrintS("StopGauss\n");
}
//int term_nodes_sort_crit(const void* a, const void* b);
template <class number_type> void noro_step(poly*p,int &pn,slimgb_alg* c)
{
  //Print("Input rows %d\n",pn);
  int j;
  if (TEST_OPT_PROT)
  {
    Print("Input rows %d\n",pn);
  }
 
  NoroCache<number_type> cache;
 
  SparseRow<number_type> ** srows=(SparseRow<number_type>**) omAlloc(pn*sizeof(SparseRow<number_type>*));
  int non_zeros=0;
  for(j=0;j<pn;j++)
  {
    poly h=p[j];
    int h_len=pLength(h);
    //number coef;
    srows[non_zeros]=noro_red_to_non_poly_t<number_type>(h,h_len,&cache,c);
    if (srows[non_zeros]!=NULL) non_zeros++;
  }
  std::vector<DataNoroCacheNode<number_type>*> irr_nodes;
  cache.collectIrreducibleMonomials(irr_nodes);
  //now can build up terms array
  //Print("historic irred Mon%d\n",cache.nIrreducibleMonomials);
  int n=irr_nodes.size();//cache.countIrreducibleMonomials();
  cache.nIrreducibleMonomials=n;
  if (TEST_OPT_PROT)
  {
    Print("Irred Mon:%d\n",n);
    Print("red Mon:%d\n",cache.nReducibleMonomials);
  }
  TermNoroDataNode<number_type>* term_nodes=(TermNoroDataNode<number_type>*) omalloc(n*sizeof(TermNoroDataNode<number_type>));
 
  for(j=0;j<n;j++)
  {
    assume(irr_nodes[j]!=NULL);
    assume(irr_nodes[j]->value_len==NoroCache<number_type>::backLinkCode);
    term_nodes[j].t=irr_nodes[j]->value_poly;
    assume(term_nodes[j].t!=NULL);
    term_nodes[j].node=irr_nodes[j];
  }
 
  qsort(term_nodes,n,sizeof(TermNoroDataNode<number_type>),term_nodes_sort_crit<number_type>);
  poly* terms=(poly*) omalloc(n*sizeof(poly));
 
  int* old_to_new_indices=(int*) omalloc(cache.nIrreducibleMonomials*sizeof(int));
  for(j=0;j<n;j++)
  {
    old_to_new_indices[term_nodes[j].node->term_index]=j;
    term_nodes[j].node->term_index=j;
    terms[j]=term_nodes[j].t;
  }
 
  //if (TEST_OPT_PROT)
  //  Print("Evaluate Rows \n");
  pn=non_zeros;
  number_type* number_array=(number_type*) omalloc0(((size_t)n)*pn*sizeof(number_type));
 
  for(j=0;j<pn;j++)
  {
    int i;
    number_type* row=number_array+((long)n)*(long)j;
    /*for(i=0;i<n;i++)
    {
      row[i]=zero;
    }*/
 
    SparseRow<number_type>* srow=srows[j];
 
    if (srow)
    {
      int* const idx_array=srow->idx_array;
      number_type* const coef_array=srow->coef_array;
      const int len=srow->len;
      if (srow->idx_array)
      {
        for(i=0;i<len;i++)
        {
         int idx=old_to_new_indices[idx_array[i]];
         row[idx]=F4mat_to_number_type(coef_array[i]);
        }
      }
      else
      {
        for(i=0;i<len;i++)
        {
          row[old_to_new_indices[i]]=F4mat_to_number_type(coef_array[i]);
        }
      }
      delete srow;
    }
  }
 
  //static int export_n=0;
  //export_mat(number_array,pn,n,"mat%i.py",++export_n);
  simplest_gauss_modp(number_array,pn,n);
 
  int p_pos=0;
  for(j=0;j<pn;j++)
  {
    poly h=row_to_poly(number_array+((long)j)*((long)n),terms,n,c->r);
    if(h!=NULL)
    {
      p[p_pos++]=h;
    }
  }
  pn=p_pos;
  omfree(terms);
  omfree(term_nodes);
  omfree(number_array);
  #ifdef NORO_NON_POLY
  omfree(srows);
  omfree(old_to_new_indices);
  #endif
  //don't forget the rank
 
}
 
template <class number_type> void NoroCache<number_type>::collectIrreducibleMonomials( std::vector<DataNoroCacheNode<number_type> *>& res)
{
  int i;
  for(i=0;i<root.branches_len;i++)
  {
    collectIrreducibleMonomials(1,root.branches[i],res);
  }
}
template <class number_type> void NoroCache<number_type>::collectIrreducibleMonomials(int level, NoroCacheNode* node, std::vector<DataNoroCacheNode<number_type>*>& res)
{
  assume(level>=0);
  if (node==NULL) return;
  if (level<(currRing->N))
  {
    int i;
    for(i=0;i<node->branches_len;i++)
    {
      collectIrreducibleMonomials(level+1,node->branches[i],res);
    }
  }
  else
  {
    DataNoroCacheNode<number_type>* dn=(DataNoroCacheNode<number_type>*) node;
    if (dn->value_len==backLinkCode)
    {
      res.push_back(dn);
    }
  }
}
 
template<class number_type> DataNoroCacheNode<number_type>* NoroCache<number_type>::getCacheReference(poly term)
{
  int i;
  NoroCacheNode* parent=&root;
  for(i=1;i<(currRing->N);i++)
  {
    parent=parent->getBranch(p_GetExp(term,i,currRing));
    if (!(parent))
    {
      return NULL;
    }
  }
  DataNoroCacheNode<number_type>* res_holder=(DataNoroCacheNode<number_type>*) parent->getBranch(p_GetExp(term,i,currRing));
  return res_holder;
}
template<class number_type> poly NoroCache<number_type>::lookup(poly term, BOOLEAN& succ, int & len)
{
  int i;
  NoroCacheNode* parent=&root;
  for(i=1;i<(currRing->N);i++)
  {
    parent=parent->getBranch(p_GetExp(term,i,currRing));
    if (!(parent))
    {
      succ=FALSE;
      return NULL;
    }
  }
  DataNoroCacheNode<number_type>* res_holder=(DataNoroCacheNode<number_type>*) parent->getBranch(p_GetExp(term,i,currRing));
  if (res_holder)
  {
    succ=TRUE;
    if ( /*(*/ res_holder->value_len==backLinkCode /*)*/ )
    {
      len=1;
      return term;
    }
    len=res_holder->value_len;
    return res_holder->value_poly;
  } else {
    succ=FALSE;
    return NULL;
  }
}
#endif
 
#endif