source: git/Singular/maps_ip.cc @ 020ef9

/****************************************
*  Computer Algebra System SINGULAR     *
****************************************/
/* $Id$ */
/*
* ABSTRACT - the mapping of polynomials to other rings
*/

#include <Singular/mod2.h>
#include <Singular/tok.h>
#include <kernel/febase.h>
#include <kernel/polys.h>
#include <kernel/numbers.h>
#include <kernel/ring.h>
#include <kernel/ideals.h>
#include <kernel/matpol.h>
#include <omalloc.h>
#include <kernel/kstd1.h>
#include <kernel/longalg.h>
#include <Singular/lists.h>
#include <kernel/maps.h>
#include <Singular/maps_ip.h>
#include <kernel/prCopy.h>

// define this if you want to use the fast_map routine for mapping ideals
//#define FAST_MAP

#ifdef FAST_MAP
#include <kernel/maps.h>
#endif


/*2
* maps the expression w to res,
* switch what: MAP_CMD: use theMap for mapping, N for preimage ring
*              //FETCH_CMD: use pOrdPoly for mapping
*              IMAP_CMD: use perm for mapping, N for preimage ring
*              default: map only poly-structures,
*                       use perm and par_perm, N and P,
*/
BOOLEAN maApplyFetch(int what,map theMap,leftv res, leftv w, ring preimage_r,
                     int *perm, int *par_perm, int P, nMapFunc nMap)
{
  int i;
  int N = preimage_r->N;
  //Print("N=%d what=%s ",N,Tok2Cmdname(what));
  //if (perm!=NULL) for(i=1;i<=N;i++) Print("%d -> %d ",i,perm[i]);
  //PrintS("\n");
  //Print("P=%d ",P);
  //if (par_perm!=NULL) for(i=0;i<P;i++) Print("%d -> %d ",i,par_perm[i]);
  //PrintS("\n");
  void *data=w->Data();
  res->rtyp = w->rtyp;
  switch (w->rtyp)
  {
    case NUMBER_CMD:
      if (P!=0)
      {
        res->data=(void *)naPermNumber((number)data,par_perm,P, preimage_r);
        res->rtyp=POLY_CMD;
        if (currRing->minpoly!=NULL)
          res->data=(void *)pMinPolyNormalize((poly)res->data);
        pTest((poly) res->data);
      }
      else
      {
        res->data=(void *)nMap((number)data);
        if (currRing->minpoly!=NULL)
        {
          number a=(number)res->data;
          nNormalize(a);
          res->data=(void *)a;
        }
        #ifdef LDEBUG
        nTest((number) res->data);
        #endif
      }
      break;
    case POLY_CMD:
    case VECTOR_CMD:
      if ((what==FETCH_CMD)&& (nMap==nCopy))
        res->data=(void *)prCopyR( (poly)data, preimage_r);
      else
      if ((what==IMAP_CMD) || ((what==FETCH_CMD) /* && (nMap!=nCopy)*/))
        res->data=(void *)pPermPoly((poly)data,perm,preimage_r,nMap,par_perm,P);
      else /*if (what==MAP_CMD)*/
      {
        matrix s=mpNew(N,maMaxDeg_P((poly)data, preimage_r));
        res->data=(void *)maEval(theMap,(poly)data,preimage_r,nMap,s);
        idDelete((ideal *)&s);
      }
      if (currRing->minpoly!=NULL)
        res->data=(void *)pMinPolyNormalize((poly)res->data);
      pTest((poly)res->data);
      break;
    case MODUL_CMD:
    case MATRIX_CMD:
    case IDEAL_CMD:
    case MAP_CMD:
    {
      int C=((matrix)data)->cols();
      int R;
      if (w->rtyp==MAP_CMD) R=1;
      else R=((matrix)data)->rows();
      matrix m=mpNew(R,C);
      char *tmpR=NULL;
      if(w->rtyp==MAP_CMD)
      {
        tmpR=((map)data)->preimage;
        ((matrix)data)->rank=((matrix)data)->rows();
      }
      if ((what==FETCH_CMD)&& (nMap==nCopy))
      {
        for (i=R*C-1;i>=0;i--)
        {
          m->m[i]=prCopyR(((ideal)data)->m[i], preimage_r);
          pTest(m->m[i]);
        }
      }
      else
      if ((what==IMAP_CMD) || ((what==FETCH_CMD) /* && (nMap!=nCopy)*/))
      {
        for (i=R*C-1;i>=0;i--)
        {
          m->m[i]=pPermPoly(((ideal)data)->m[i],perm,preimage_r,nMap,par_perm,P);
          pTest(m->m[i]);
        }
      }
      else /* if(what==MAP_CMD) */
      {
        matrix s=mpNew(N,maMaxDeg_Ma((ideal)data,preimage_r));
        for (i=R*C-1;i>=0;i--)
        {
          m->m[i]=maEval(theMap,((ideal)data)->m[i],preimage_r,nMap,s);
          pTest(m->m[i]);
        }
        idDelete((ideal *)&s);
      }
      if (currRing->minpoly!=NULL)
      {
        for (i=R*C-1;i>=0;i--)
        {
          m->m[i]=pMinPolyNormalize(m->m[i]);
          pTest(m->m[i]);
        }
      }
      if(w->rtyp==MAP_CMD)
      {
        ((map)data)->preimage=tmpR;
        ((map)m)->preimage=omStrDup(tmpR);
      }
      else
      {
        m->rank=((matrix)data)->rank;
      }
      res->data=(char *)m;
      idTest((ideal) m);
      break;
    }

    case LIST_CMD:
    {
      lists l=(lists)data;
      lists ml=(lists)omAllocBin(slists_bin);
      ml->Init(l->nr+1);
      for(i=0;i<=l->nr;i++)
      {
        if (((l->m[i].rtyp>BEGIN_RING)&&(l->m[i].rtyp<END_RING))
        ||(l->m[i].rtyp==LIST_CMD))
        {
          if (maApplyFetch(what,theMap,&ml->m[i],&l->m[i],
                           preimage_r,perm,par_perm,P,nMap))
          {
            ml->Clean();
            omFreeBin((ADDRESS)ml, slists_bin);
            res->rtyp=0;
            return TRUE;
          }
        }
        else
        {
          ml->m[i].Copy(&l->m[i]);
        }
      }
      res->data=(char *)ml;
      break;
    }
    default:
    {
      return TRUE;
    }
  }
  return FALSE;
}

/*2
* substitutes the parameter par (from 1..N) by image,
* does not destroy p and  image
*/
poly pSubstPar(poly p, int par, poly image)
{
  ideal theMapI=idInit(rPar(currRing),1);
  nMapFunc nMap=nSetMap(currRing->algring);

  int i;
  poly pp;
  for(i=rPar(currRing);i>0;i--)
  {
    if (i!=par)
    {
      pp=theMapI->m[i-1]=pOne();
      lnumber n=(lnumber)pGetCoeff(pp);
      p_SetExp(n->z,i,1,currRing->algring);
      p_Setm(n->z,currRing->algring);
    }
    else
      theMapI->m[i-1]=pCopy(image);
  }

  map theMap=(map)theMapI;
  theMap->preimage=NULL;

  leftv v=(leftv)omAllocBin(sleftv_bin);
  sleftv tmpW;
  poly res=NULL;
  while (p!=NULL)
  {
    memset(&tmpW,0,sizeof(sleftv));
    memset(v,0,sizeof(sleftv));
    tmpW.rtyp=POLY_CMD;
    lnumber n=(lnumber)pGetCoeff(p);
    tmpW.data=n->z;
    if (n->n!=NULL) WarnS("ignoring denominators of coefficients...");
    if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,currRing->algring,NULL,NULL,0,nMap))
    {
      WerrorS("map failed");
      v->data=NULL;
    }
    pp=pHead(p);
    //PrintS("map:");pWrite(pp);
    pSetCoeff(pp,nInit(1));
    //PrintS("->");pWrite((poly)(v->data));
    poly ppp=pMult((poly)(v->data),pp);
    //PrintS("->");pWrite(ppp);
    res=pAdd(res,ppp);
    pIter(p);
  }
  idDelete((ideal *)(&theMap));
  omFreeBin((ADDRESS)v, sleftv_bin);
  return res;
}

/*2
* substitute the n-th parameter by the poly e in id
* does not destroy id and e
*/
ideal  idSubstPar(ideal id, int n, poly e)
{
  int k=MATROWS((matrix)id)*MATCOLS((matrix)id);
  ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id));

  res->rank = id->rank;
  for(k--;k>=0;k--)
  {
    res->m[k]=pSubstPar(id->m[k],n,e);
  }
  return res;
}

/*2
* substitutes the variable var (from 1..N) by image,
* does not destroy p and  image
*/
poly pSubstPoly(poly p, int var, poly image)
{
  if (p==NULL) return NULL;
#ifdef HAVE_PLURAL
  if (rIsPluralRing(currRing))
  {
    return pSubst(pCopy(p),var,image);
  }
#endif
  map theMap=(map)idMaxIdeal(1);
  theMap->preimage=NULL;
  pDelete(&(theMap->m[var-1]));
  theMap->m[var-1]=pCopy(image);

  poly res=NULL;
#ifdef FAST_MAP
  if (pGetComp(p)==0)
  {
    ideal src_id=idInit(1,1);
    src_id->m[0]=p;
    ideal res_id=fast_map(src_id,currRing,(ideal)theMap,currRing);
    res=res_id->m[0];
    res_id->m[0]=NULL; idDelete(&res_id);
    src_id->m[0]=NULL; idDelete(&src_id);
  }
  else
#endif
  {
    sleftv tmpW;
    memset(&tmpW,0,sizeof(sleftv));
    tmpW.rtyp=POLY_CMD;
    tmpW.data=p;
    leftv v=(leftv)omAlloc0Bin(sleftv_bin);
    if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,currRing,NULL,NULL,0,nCopy))
    {
      WerrorS("map failed");
      v->data=NULL;
    }
    res=(poly)(v->data);
    omFreeBin((ADDRESS)v, sleftv_bin);
  }
  idDelete((ideal *)(&theMap));
  return res;
}

/*2
* substitute the n-th variable by the poly e in id
* does not destroy id and e
*/
ideal  idSubstPoly(ideal id, int n, poly e)
{

#ifdef HAVE_PLURAL
  if (rIsPluralRing(currRing))
  {
    int k=MATROWS((matrix)id)*MATCOLS((matrix)id);
    ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id));
    res->rank = id->rank;
    for(k--;k>=0;k--)
    {
      res->m[k]=pSubst(pCopy(id->m[k]),n,e);
    }
    return res;
  }
#endif
  map theMap=(map)idMaxIdeal(1);
  theMap->preimage=NULL;
  pDelete(&(theMap->m[n-1]));
  theMap->m[n-1]=pCopy(e);

  leftv v=(leftv)omAlloc0Bin(sleftv_bin);
  sleftv tmpW;
  memset(&tmpW,0,sizeof(sleftv));
  tmpW.rtyp=IDEAL_CMD;
  tmpW.data=id;
  if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,currRing,NULL,NULL,0,nCopy))
  {
    WerrorS("map failed");
    v->data=NULL;
  }
  ideal res=(ideal)(v->data);
  idDelete((ideal *)(&theMap));
  omFreeBin((ADDRESS)v, sleftv_bin);
  return res;
}