maps.cc

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/****************************************
*  Computer Algebra System SINGULAR     *
****************************************/
/*
* ABSTRACT - the mapping of polynomials to other rings
*/
 
#include "misc/auxiliary.h"
#include "misc/options.h"
 
#include "coeffs/coeffs.h"
#include "coeffs/numbers.h"
 
#include "polys/monomials/p_polys.h"
#include "polys/monomials/ring.h"
#include "polys/simpleideals.h"
#include "polys/prCopy.h"
#include "polys/monomials/maps.h"
 
#ifdef HAVE_PLURAL
#include "polys/nc/nc.h"
#endif
 
// This is a very dirty way to "normalize" numbers w.r.t. a
// MinPoly
 
#define MAX_MAP_DEG 128
 
/*2
* copy a map
*/
map maCopy(map theMap, const ring r)
{
  int i;
  map m=(map)idInit(IDELEMS(theMap),0);
  for (i=IDELEMS(theMap)-1; i>=0; i--)
      m->m[i] = p_Copy(theMap->m[i],r);
  m->preimage=omStrDup(theMap->preimage);
  return m;
}
 
 
/*2
* return the image of var(v)^pExp, where var(v) maps to p
*/
poly maEvalVariable(poly p, int v,int pExp, ideal s, const ring dst_r)
{
  if (pExp==1)
    return p_Copy(p,dst_r);
 
  poly res;
 
  if((s!=NULL)&&(pExp<MAX_MAP_DEG))
  {
    int j=2;
    poly p0=p;
    // find starting point
    if(MATELEM(s,v,1)==NULL)
    {
      MATELEM(s,v,1)=p_Copy(p/*theMap->m[v-1]*/,dst_r);
    }
    else
    {
      while((j<=pExp)&&(MATELEM(s,v,j)!=NULL))
      {
        j++;
      }
      p0=MATELEM(s,v,j-1);
    }
    // multiply
    for(;j<=pExp;j++)
    {
      p0=MATELEM(s,v,j)=pp_Mult_qq(p0, p,dst_r);
      p_Normalize(p0, dst_r);
    }
    res=p_Copy(p0/*MATELEM(s,v,pExp)*/,dst_r);
  }
  else //if ((p->next!=NULL)&&(p->next->next==NULL))
  {
    res=p_Power(p_Copy(p,dst_r),pExp,dst_r);
  }
  return res;
}
 
static poly maEvalMonom(map theMap, poly p,ring preimage_r, ideal s,
           nMapFunc nMap, const ring dst_r)
{
    p_Test(p,preimage_r);
    poly q=p_NSet(nMap(pGetCoeff(p),preimage_r->cf,dst_r->cf),dst_r);
 
    int i;
    for(i=1;i<=preimage_r->N; i++)
    {
      int pExp=p_GetExp( p,i,preimage_r);
      if (pExp != 0)
      {
        if (theMap->m[i-1]!=NULL)
        {
          poly p1=theMap->m[i-1];
          poly pp=maEvalVariable(p1,i,pExp,s,dst_r);
          q = p_Mult_q(q,pp,dst_r);
        }
        else
        {
          p_Delete(&q,dst_r);
          break;
        }
      }
    }
    int modulComp = p_GetComp( p,preimage_r);
    if (q!=NULL) p_SetCompP(q,modulComp,dst_r);
  return q;
}
 
poly maEval(map theMap, poly p,ring preimage_r,nMapFunc nMap, ideal s, const ring dst_r)
{
  poly result = NULL;
  int i;
 
//  for(i=1; i<=preimage_r->N; i++)
//  {
//    pTest(theMap->m[i-1]);
//  }
//  while (p!=NULL)
//  {
//    poly q=maEvalMonom(theMap,p,preimage_r,s);
//    result = pAdd(result,q);
//    pIter(p);
//  }
  if (p!=NULL)
  {
    int l = pLength(p)-1;
    poly* monoms;
    if (l>0)
    {
      monoms = (poly*) omAlloc(l*sizeof(poly));
 
      for (i=0; i<l; i++)
      {
        monoms[i]=maEvalMonom(theMap,p,preimage_r,s, nMap, dst_r);
        pIter(p);
      }
    }
    result=maEvalMonom(theMap,p,preimage_r,s, nMap, dst_r);
    if (l>0)
    {
      for(i = l-1; i>=0; i--)
      {
        result=p_Add_q(result, monoms[i], dst_r);
      }
      omFreeSize((ADDRESS)monoms,l*sizeof(poly));
    }
 
    assume(dst_r != NULL);
    assume(dst_r->cf != NULL);
 
    if (nCoeff_is_algExt(dst_r->cf))
      result = p_MinPolyNormalize(result, dst_r);
  }
  return result;
}
 
void maFindPerm(char const * const * const preim_names, int preim_n, char const * const * const preim_par, int preim_p,
                char const * const * const names,       int n,       char const * const * const par,       int nop,
                int * perm, int *par_perm, n_coeffType ch)
{
  int i,j;
  /* find correspondig vars */
  for (i=0; i<preim_n; i++)
  {
    for(j=0; j<n; j++)
    {
      if (strcmp(preim_names[i],names[j])==0)
      {
        if (BVERBOSE(V_IMAP))
          Print("// var %s: nr %d -> nr %d\n",preim_names[i],i+1,j+1);
        /* var i+1 from preimage ring is var j+1  (index j+1) from image ring */
        perm[i+1]=j+1;
        break;
      }
    }
    if ((perm[i+1]==0)&&(par!=NULL)
        // do not consider par of Fq
         && (ch!=n_GF))
    {
      for(j=0; j<nop; j++)
      {
        if (strcmp(preim_names[i],par[j])==0)
        {
          if (BVERBOSE(V_IMAP))
            Print("// var %s: nr %d -> par %d\n",preim_names[i],i+1,j+1);
          /* var i+1 from preimage ring is par j+1 (index j) from image ring */
          perm[i+1]=-(j+1);
        }
      }
    }
  }
  if (par_perm!=NULL)
  {
    for (i=0; i<preim_p; i++)
    {
      for(j=0; j<n; j++)
      {
        if (strcmp(preim_par[i],names[j])==0)
        {
          if (BVERBOSE(V_IMAP))
            Print("// par %s: par %d -> nr %d\n",preim_par[i],i+1,j+1);
          /*par i+1 from preimage ring is var j+1  (index j+1) from image ring*/
          par_perm[i]=j+1;
          break;
        }
      }
      if ((par!=NULL) && (par_perm[i]==0))
      {
        for(j=0; j<nop; j++)
        {
          if (strcmp(preim_par[i],par[j])==0)
          {
            if (BVERBOSE(V_IMAP))
              Print("// par %s: nr %d -> par %d\n",preim_par[i],i+1,j+1);
            /*par i+1 from preimage ring is par j+1 (index j) from image ring */
            par_perm[i]=-(j+1);
          }
        }
      }
    }
  }
}
 
#ifdef HAVE_SHIFTBBA
void maFindPermLP(char const * const * const preim_names, int preim_n, char const * const * const preim_par, int preim_p,
                char const * const * const names,       int n,       char const * const * const par,       int nop,
                int * perm, int *par_perm, n_coeffType ch, int lV)
{
  int i,j,b;
  /* find correspondig vars */
  for  (b=0;b<preim_n/lV;b++)
  {
    for (i=b*lV; i<(b+1)*lV; i++)
    {
      int cnt=0;
      for(j=0; j<n; j++)
      {
        if (strcmp(preim_names[i],names[j])==0)
        {
          if (cnt==b)
          {
            if (BVERBOSE(V_IMAP))
              Print("// var %s: nr %d -> nr %d\n",preim_names[i],i+1,j+1);
            /* var i+1 from preimage ring is var j+1  (index j+1) from image ring */
            perm[i+1]=j+1;
            break;
          }
          else cnt++;
        }
      }
      if ((perm[i+1]==0)&&(par!=NULL)
        // do not consider par of Fq
         && (ch!=n_GF))
      {
        for(j=0; j<nop; j++)
        {
          if (strcmp(preim_names[i],par[j])==0)
          {
            if (BVERBOSE(V_IMAP))
              Print("// var %s: nr %d -> par %d\n",preim_names[i],i+1,j+1);
            /* var i+1 from preimage ring is par j+1 (index j) from image ring */
            perm[i+1]=-(j+1);
          }
        }
      }
    }
  }
  if (par_perm!=NULL)
  {
    for (i=0; i<preim_p; i++)
    {
      for(j=0; j<n; j++)
      {
        if (strcmp(preim_par[i],names[j])==0)
        {
          if (BVERBOSE(V_IMAP))
            Print("// par %s: par %d -> nr %d\n",preim_par[i],i+1,j+1);
          /*par i+1 from preimage ring is var j+1  (index j+1) from image ring*/
          par_perm[i]=j+1;
          break;
        }
      }
      if ((par!=NULL) && (par_perm[i]==0))
      {
        for(j=0; j<nop; j++)
        {
          if (strcmp(preim_par[i],par[j])==0)
          {
            if (BVERBOSE(V_IMAP))
              Print("// par %s: nr %d -> par %d\n",preim_par[i],i+1,j+1);
            /*par i+1 from preimage ring is par j+1 (index j) from image ring */
            par_perm[i]=-(j+1);
          }
        }
      }
    }
  }
}
 
void maFetchPermLP(const ring preimage_r, const ring dst_r, int * perm)
/* perm=(int *)omAlloc0(preimage_r->N+1 * sizeof(int)); */
{
  for (int i = 0; i < preimage_r->N + 1; i++) { perm[i] = 0; }
 
  int preimage_lV = preimage_r->isLPring;
  int r_lV = dst_r->isLPring;
 
  int preimage_ncgens = preimage_r->LPncGenCount;
  int r_ncges = dst_r->LPncGenCount;
 
  int preimage_vars = preimage_lV - preimage_ncgens;
  int r_vars = r_lV - r_ncges;
 
  // for each block
  for (int i = 0; i < si_min(preimage_r->N / preimage_lV, dst_r->N / r_lV); i++)
  {
    // align variables
    for (int j = 1; j <= si_min(preimage_vars, r_vars); j++)
    {
      perm[(i * preimage_lV) + j] = (i * r_lV) + j;
    }
 
    // align ncgens
    for (int j = 1; j <= si_min(preimage_ncgens, r_ncges); j++)
    {
      perm[(i * preimage_lV) + preimage_vars + j] = (i * r_lV) + r_vars + j;
    }
  }
}
#endif
 
/*2
* embeds poly p from the subring r into the current ring
*/
poly maIMap(ring r, poly p, const ring dst_r)
{
  /* the simplest case:*/
  if(r==dst_r) return p_Copy(p,dst_r);
  nMapFunc nMap=n_SetMap(r->cf,dst_r->cf);
  int *perm=(int *)omAlloc0((r->N+1)*sizeof(int));
  //int *par_perm=(int *)omAlloc0(rPar(r)*sizeof(int));
  maFindPerm(r->names, rVar(r), rParameter(r), rPar(r),
             dst_r->names, rVar(dst_r),rParameter(dst_r), rPar(dst_r),
             perm,NULL, dst_r->cf->type);
  poly res=p_PermPoly(p,perm,r,dst_r, nMap /*,par_perm,rPar(r)*/);
  omFreeSize((ADDRESS)perm,(r->N+1)*sizeof(int));
  //omFreeSize((ADDRESS)par_perm,rPar(r)*sizeof(int));
  return res;
}
 
/*3
* find the max. degree in one variable, but not larger than MAX_MAP_DEG
*/
int maMaxDeg_Ma(ideal a,ring preimage_r)
{
  int i,j;
  int N = preimage_r->N;
  poly p;
  int *m=(int *)omAlloc0(N*sizeof(int));
 
  for (i=MATROWS(a)*MATCOLS(a)-1;i>=0;i--)
  {
    p=a->m[i];
    //pTest(p); // cannot test p because it is from another ring
    while(p!=NULL)
    {
      for(j=N-1;j>=0;j--)
      {
        m[j]=si_max(m[j],(int)p_GetExp( p,j+1,preimage_r));
        if (m[j]>=MAX_MAP_DEG)
        {
          i=MAX_MAP_DEG;
          goto max_deg_fertig_id;
        }
      }
      pIter(p);
    }
  }
  i=m[0];
  for(j=N-1;j>0;j--)
  {
    i=si_max(i,m[j]);
  }
max_deg_fertig_id:
  omFreeSize((ADDRESS)m,N*sizeof(int));
  return i;
}
 
/*3
* find the max. degree in one variable, but not larger than MAX_MAP_DEG
*/
int maMaxDeg_P(poly p,ring preimage_r)
{
  int i,j;
  int N = preimage_r->N;
  int *m=(int *)omAlloc0(N*sizeof(int));
 
//  pTest(p);
  while(p!=NULL)
  {
    for(j=N-1;j>=0;j--)
    {
      m[j]=si_max(m[j],(int)p_GetExp(p,j+1,preimage_r));
      if (m[j]>=MAX_MAP_DEG)
      {
        i=MAX_MAP_DEG;
        goto max_deg_fertig_p;
      }
    }
    pIter(p);
  }
  i=m[0];
  for(j=N-1;j>0;j--)
  {
    i=si_max(i,m[j]);
  }
max_deg_fertig_p:
  omFreeSize((ADDRESS)m,N*sizeof(int));
  return i;
}
 
// This is a very dirty way to cancel monoms whose number equals the
// MinPoly
poly p_MinPolyNormalize(poly p, const ring r)
{
  const coeffs C = r->cf;
  number one = n_Init(1, C);
  spolyrec rp;
 
  poly q = &rp;
 
  while (p != NULL)
  {
    // this returns 0, if p == MinPoly
    number product = n_Mult(p_GetCoeff(p, r), one, C);
    if ((product == NULL)||(n_IsZero(product, C)))
    {
      p_LmDelete(&p, r);
    }
    else
    {
      p_SetCoeff(p, product, r);
      pNext(q) = p;
      q = p;
      p = pNext(p);
    }
  }
  pNext(q) = NULL;
  n_Delete(&one, C);
  return rp.next;
}