My Project  UNKNOWN_GIT_VERSION
Functions
maps_ip.h File Reference
#include "kernel/mod2.h"
#include "polys/matpol.h"
#include "kernel/structs.h"
#include "kernel/ideals.h"
#include "kernel/polys.h"

Go to the source code of this file.

Functions

poly pSubstPoly (poly p, int var, poly image)
 
poly pSubstPar (poly p, int par, poly image)
 
ideal idSubstPoly (ideal id, int n, poly e)
 
ideal idSubstPar (ideal id, int n, poly e)
 
BOOLEAN maApplyFetch (int what, map theMap, leftv res, leftv w, ring preimage_r, int *perm, int *par_perm, int P, nMapFunc nMap)
 

Function Documentation

◆ idSubstPar()

ideal idSubstPar ( ideal  id,
int  n,
poly  e 
)

Definition at line 385 of file maps_ip.cc.

386 {
387  int k=MATROWS((matrix)id)*MATCOLS((matrix)id);
388  ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id));
389 
390  res->rank = id->rank;
391  for(k--;k>=0;k--)
392  {
393  res->m[k]=pSubstPar(id->m[k],n,e);
394  }
395  return res;
396 }
int k
Definition: cfEzgcd.cc:92
poly * m
Definition: matpol.h:18
CanonicalForm res
Definition: facAbsFact.cc:64
poly pSubstPar(poly p, int par, poly image)
Definition: maps_ip.cc:265
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition: matpol.cc:37
#define MATCOLS(i)
Definition: matpol.h:27
#define MATROWS(i)
Definition: matpol.h:26

◆ idSubstPoly()

ideal idSubstPoly ( ideal  id,
int  n,
poly  e 
)

Definition at line 418 of file maps_ip.cc.

419 {
420 
421 #ifdef HAVE_PLURAL
422  if (rIsPluralRing(currRing))
423  {
424  int k=MATROWS((matrix)id)*MATCOLS((matrix)id);
425  ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id));
426  res->rank = id->rank;
427  for(k--;k>=0;k--)
428  {
429  res->m[k]=pSubst(pCopy(id->m[k]),n,e);
430  }
431  return res;
432  }
433 #endif
434  return id_SubstPoly(id,n,e,currRing,currRing,ndCopyMap);
435 }
#define pSubst(p, n, e)
Definition: polys.h:360
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
Definition: numbers.cc:252
int k
Definition: cfEzgcd.cc:92
poly * m
Definition: matpol.h:18
CanonicalForm res
Definition: facAbsFact.cc:64
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
Definition: ring.h:398
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition: matpol.cc:37
#define MATCOLS(i)
Definition: matpol.h:27
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13
ideal id_SubstPoly(ideal id, int var, poly image, const ring preimage_r, const ring image_r, const nMapFunc nMap)
Definition: subst_maps.cc:68
#define MATROWS(i)
Definition: matpol.h:26
#define pCopy(p)
return a copy of the poly
Definition: polys.h:180

◆ maApplyFetch()

BOOLEAN maApplyFetch ( int  what,
map  theMap,
leftv  res,
leftv  w,
ring  preimage_r,
int *  perm,
int *  par_perm,
int  P,
nMapFunc  nMap 
)

Definition at line 46 of file maps_ip.cc.

48 {
49  BOOLEAN use_mult=FALSE;
50 #ifdef HAVE_PLURAL
51  if ((what==IMAP_CMD)
53  && rIsPluralRing(preimage_r))
54  {
55  assume(perm!=NULL);
56  int i=1;
57  while((i<currRing->N)&&(perm[i]==0)) i++;
58  if (i<currRing->N)
59  {
60  int prev_nonnull=i;
61  i++;
62  for(;i<=currRing->N;i++)
63  {
64  if (perm[prev_nonnull] > perm[i])
65  {
66  if (TEST_V_ALLWARN)
67  {
68  Warn("imap not usable for permuting variables, use map (%s <-> %s)",currRing->names[prev_nonnull-1],currRing->names[i-1]);
69  }
70  use_mult=TRUE;
71  break;
72  }
73  else
74  prev_nonnull=i;
75  }
76  }
77  }
78 #endif
79  int i;
80  int N = preimage_r->N;
81 #if 0
82  Print("N=%d what=%s ",N,Tok2Cmdname(what));
83  if (perm!=NULL) for(i=1;i<=N;i++) Print("%d -> %d ",i,perm[i]);
84  PrintS("\n");
85  Print("P=%d ",P);
86  if (par_perm!=NULL) for(i=0;i<P;i++) Print("%d -> %d ",i,par_perm[i]);
87  PrintS("\n");
88 #endif
89 
90  void *data=w->Data();
91  res->rtyp = w->rtyp;
92  switch (w->rtyp)
93  {
94  case NUMBER_CMD:
95  if (P!=0)
96  {
97 // poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst);
98  res->data= (void *) n_PermNumber((number)data, par_perm, P, preimage_r, currRing);
99  res->rtyp=POLY_CMD;
100  if (nCoeff_is_algExt(currRing->cf))
101  res->data=(void *)p_MinPolyNormalize((poly)res->data, currRing);
102  pTest((poly) res->data);
103  }
104  else
105  {
106  assume( nMap != NULL );
107  number a = nMap((number)data, preimage_r->cf, currRing->cf);
108  if (nCoeff_is_Extension(currRing->cf))
109  {
110  n_Normalize(a, currRing->cf);
111 /*
112  number a = (number)res->data;
113  number one = nInit(1);
114  number product = nMult(a, one );
115  nDelete(&one);
116  nDelete(&a);
117  res->data=(void *)product;
118  */
119  }
120  #ifdef LDEBUG
121  n_Test(a, currRing->cf);
122  #endif
123  res->data=(void *)a;
124 
125  }
126  break;
127  case BUCKET_CMD:
128  if ((what==FETCH_CMD)&& (preimage_r->cf==currRing->cf))
129  res->data=(void *)prCopyR(sBucketPeek((sBucket_pt)data), preimage_r, currRing);
130  else
131  if ( (what==IMAP_CMD) || /*(*/ (what==FETCH_CMD) /*)*/) /* && (nMap!=nCopy)*/
132  res->data=(void *)p_PermPoly(sBucketPeek((sBucket_pt)data),perm,preimage_r,currRing, nMap,par_perm,P,use_mult);
133  else /*if (what==MAP_CMD)*/
134  {
135  matrix s=mpNew(N,maMaxDeg_P(sBucketPeek((sBucket_pt)data), preimage_r));
136  res->data=(void *)maEval(theMap, sBucketPeek((sBucket_pt)data), preimage_r, nMap, (ideal)s, currRing);
137  idDelete((ideal *)&s);
138  }
139  if (nCoeff_is_Extension(currRing->cf))
140  res->data=(void *)p_MinPolyNormalize(sBucketPeek((sBucket_pt)data), currRing);
141  break;
142  case POLY_CMD:
143  case VECTOR_CMD:
144  if ((what==FETCH_CMD)&& (preimage_r->cf==currRing->cf))
145  res->data=(void *)prCopyR( (poly)data, preimage_r, currRing);
146  else
147  if ( (what==IMAP_CMD) || /*(*/ (what==FETCH_CMD) /*)*/) /* && (nMap!=nCopy)*/
148  res->data=(void *)p_PermPoly((poly)data,perm,preimage_r,currRing, nMap,par_perm,P,use_mult);
149  else /*if (what==MAP_CMD)*/
150  {
151  p_Test((poly)data,preimage_r);
152  matrix s=mpNew(N,maMaxDeg_P((poly)data, preimage_r));
153  res->data=(void *)maEval(theMap, (poly)data, preimage_r, nMap, (ideal)s, currRing);
154  idDelete((ideal *)&s);
155  }
156  if (nCoeff_is_Extension(currRing->cf))
157  res->data=(void *)p_MinPolyNormalize((poly)res->data, currRing);
158  pTest((poly)res->data);
159  break;
160  case MODUL_CMD:
161  case MATRIX_CMD:
162  case IDEAL_CMD:
163  case MAP_CMD:
164  {
165  int C=((matrix)data)->cols();
166  int R;
167  if (w->rtyp==MAP_CMD) R=1;
168  else R=((matrix)data)->rows();
169  matrix m=mpNew(R,C);
170  char *tmpR=NULL;
171  if(w->rtyp==MAP_CMD)
172  {
173  tmpR=((map)data)->preimage;
174  ((matrix)data)->rank=((matrix)data)->rows();
175  }
176  if ((what==FETCH_CMD)&& (preimage_r->cf == currRing->cf))
177  {
178  for (i=R*C-1;i>=0;i--)
179  {
180  m->m[i]=prCopyR(((ideal)data)->m[i], preimage_r, currRing);
181  pTest(m->m[i]);
182  }
183  }
184  else if ((what==IMAP_CMD) || (what==FETCH_CMD))
185  {
186  for (i=R*C-1;i>=0;i--)
187  {
188  m->m[i]=p_PermPoly(((ideal)data)->m[i],perm,preimage_r,currRing,
189  nMap,par_perm,P,use_mult);
190  pTest(m->m[i]);
191  }
192  }
193  else /* (what==MAP_CMD) */
194  {
195  assume(what==MAP_CMD);
196  matrix s=mpNew(N,maMaxDeg_Ma((ideal)data,preimage_r));
197  for (i=R*C-1;i>=0;i--)
198  {
199  m->m[i]=maEval(theMap, ((ideal)data)->m[i], preimage_r, nMap, (ideal)s, currRing);
200  pTest(m->m[i]);
201  }
202  idDelete((ideal *)&s);
203  }
204  if (nCoeff_is_algExt(currRing->cf))
205  {
206  for (i=R*C-1;i>=0;i--)
207  {
208  m->m[i]=p_MinPolyNormalize(m->m[i], currRing);
209  pTest(m->m[i]);
210  }
211  }
212  if(w->rtyp==MAP_CMD)
213  {
214  ((map)data)->preimage=tmpR;
215  ((map)m)->preimage=omStrDup(tmpR);
216  }
217  else
218  {
219  m->rank=((matrix)data)->rank;
220  }
221  res->data=(char *)m;
222  idTest((ideal) m);
223  break;
224  }
225 
226  case LIST_CMD:
227  {
228  lists l=(lists)data;
230  ml->Init(l->nr+1);
231  for(i=0;i<=l->nr;i++)
232  {
233  if (((l->m[i].rtyp>BEGIN_RING)&&(l->m[i].rtyp<END_RING))
234  ||(l->m[i].rtyp==LIST_CMD))
235  {
236  if (maApplyFetch(what,theMap,&ml->m[i],&l->m[i],
237  preimage_r,perm,par_perm,P,nMap))
238  {
239  ml->Clean();
241  res->rtyp=0;
242  return TRUE;
243  }
244  }
245  else
246  {
247  ml->m[i].Copy(&l->m[i]);
248  }
249  }
250  res->data=(char *)ml;
251  break;
252  }
253  default:
254  {
255  return TRUE;
256  }
257  }
258  return FALSE;
259 }
#define omAllocBin(bin)
Definition: omAllocDecl.h:205
CanonicalForm map(const CanonicalForm &primElem, const Variable &alpha, const CanonicalForm &F, const Variable &beta)
map from to such that is mapped onto
Definition: cf_map_ext.cc:400
const CanonicalForm int s
Definition: facAbsFact.cc:55
sleftv * m
Definition: lists.h:45
#define Print
Definition: emacs.cc:80
poly prCopyR(poly p, ring src_r, ring dest_r)
Definition: prCopy.cc:35
#define idDelete(H)
delete an ideal
Definition: ideals.h:29
Definition: lists.h:22
#define FALSE
Definition: auxiliary.h:94
#define pTest(p)
Definition: polys.h:409
int maMaxDeg_Ma(ideal a, ring preimage_r)
Definition: maps.cc:254
#define TRUE
Definition: auxiliary.h:98
BOOLEAN maApplyFetch(int what, map theMap, leftv res, leftv w, ring preimage_r, int *perm, int *par_perm, int P, nMapFunc nMap)
Definition: maps_ip.cc:46
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
Definition: coeffs.h:578
void * ADDRESS
Definition: auxiliary.h:133
poly p_PermPoly(poly p, const int *perm, const ring oldRing, const ring dst, nMapFunc nMap, const int *par_perm, int OldPar, BOOLEAN use_mult)
Definition: p_polys.cc:4028
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
Definition: coeffs.h:932
CanonicalForm res
Definition: facAbsFact.cc:64
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:48
#define assume(x)
Definition: mod2.h:390
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
Definition: ring.h:398
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
Definition: coeffs.h:738
void Copy(leftv e)
Definition: subexpr.cc:720
int m
Definition: cfEzgcd.cc:121
int i
Definition: cfEzgcd.cc:125
void PrintS(const char *s)
Definition: reporter.cc:284
#define p_Test(p, r)
Definition: p_polys.h:164
INLINE_THIS void Init(int l=0)
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition: matpol.cc:37
poly p_MinPolyNormalize(poly p, const ring r)
Definition: maps.cc:324
#define NULL
Definition: omList.c:10
slists * lists
Definition: mpr_numeric.h:146
poly n_PermNumber(const number z, const int *par_perm, const int, const ring src, const ring dst)
Definition: p_polys.cc:3924
const char * Tok2Cmdname(int tok)
Definition: gentable.cc:140
#define R
Definition: sirandom.c:26
const CanonicalForm & w
Definition: facAbsFact.cc:55
int maMaxDeg_P(poly p, ring preimage_r)
Definition: maps.cc:292
void Clean(ring r=currRing)
Definition: lists.h:25
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13
poly sBucketPeek(sBucket_pt b)
Definition: sbuckets.cc:455
Definition: tok.h:118
omBin slists_bin
Definition: lists.cc:23
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
Definition: coeffs.h:868
#define omFreeBin(addr, bin)
Definition: omAllocDecl.h:259
int BOOLEAN
Definition: auxiliary.h:85
#define TEST_V_ALLWARN
Definition: options.h:140
ip_smatrix * matrix
Definition: matpol.h:31
int l
Definition: cfEzgcd.cc:93
poly maEval(map theMap, poly p, ring preimage_r, nMapFunc nMap, ideal s, const ring dst_r)
Definition: maps.cc:117
#define idTest(id)
Definition: ideals.h:47
#define Warn
Definition: emacs.cc:77
#define omStrDup(s)
Definition: omAllocDecl.h:263

◆ pSubstPar()

poly pSubstPar ( poly  p,
int  par,
poly  image 
)

Definition at line 265 of file maps_ip.cc.

266 {
267  const ring R = currRing->cf->extRing;
268  ideal theMapI = idInit(rPar(currRing),1);
269  nMapFunc nMap = n_SetMap(R->cf, currRing->cf);
270  int i;
271  for(i = rPar(currRing);i>0;i--)
272  {
273  if (i != par)
274  theMapI->m[i-1]= p_NSet(n_Param(i, currRing), currRing);
275  else
276  theMapI->m[i-1] = p_Copy(image, currRing);
277  p_Test(theMapI->m[i-1],currRing);
278  }
279  //iiWriteMatrix((matrix)theMapI,"map:",1,currRing,0);
280 
281  map theMap=(map)theMapI;
282  theMap->preimage=NULL;
283 
285  sleftv tmpW;
286  poly res=NULL;
287 
289  if (currRing->cf->rep==n_rep_rat_fct )
290  {
291  while (p!=NULL)
292  {
293  memset(v,0,sizeof(sleftv));
294 
295  number d = n_GetDenom(pGetCoeff(p), currRing->cf);
296  p_Test((poly)NUM((fraction)d), R);
297 
298  if ( n_IsOne (d, currRing->cf) )
299  {
300  n_Delete(&d, currRing->cf); d = NULL;
301  }
302  else if (!p_IsConstant((poly)NUM((fraction)d), R))
303  {
304  WarnS("ignoring denominators of coefficients...");
305  n_Delete(&d, currRing->cf); d = NULL;
306  }
307 
308  number num = n_GetNumerator(pGetCoeff(p), currRing->cf);
309  memset(&tmpW,0,sizeof(sleftv));
310  tmpW.rtyp = POLY_CMD;
311  p_Test((poly)NUM((fraction)num), R);
312 
313  tmpW.data = NUM ((fraction)num); // a copy of this poly will be used
314 
315  p_Normalize(NUM((fraction)num),R);
316  if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,R,NULL,NULL,0,nMap))
317  {
318  WerrorS("map failed");
319  v->data=NULL;
320  }
321  n_Delete(&num, currRing->cf);
322  //TODO check for memory leaks
323  poly pp = pHead(p);
324  //PrintS("map:");pWrite(pp);
325  if( d != NULL )
326  {
327  pSetCoeff(pp, n_Invers(d, currRing->cf));
328  n_Delete(&d, currRing->cf); // d = NULL;
329  }
330  else
331  pSetCoeff(pp, nInit(1));
332 
333  //PrintS("->");pWrite((poly)(v->data));
334  poly ppp = pMult((poly)(v->data),pp);
335  //PrintS("->");pWrite(ppp);
336  res=pAdd(res,ppp);
337  pIter(p);
338  }
339  }
340  else if (currRing->cf->rep==n_rep_poly )
341  {
342  while (p!=NULL)
343  {
344  memset(v,0,sizeof(sleftv));
345 
346  number num = n_GetNumerator(pGetCoeff(p), currRing->cf);
347  memset(&tmpW,0,sizeof(sleftv));
348  tmpW.rtyp = POLY_CMD;
349  p_Test((poly)num, R);
350 
351 
352  p_Normalize((poly)num,R);
353  if (num==NULL) num=(number)R->qideal->m[0];
354  tmpW.data = num; // a copy of this poly will be used
355  if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,R,NULL,NULL,0,nMap))
356  {
357  WerrorS("map failed");
358  v->data=NULL;
359  }
360  if (num!=(number)R->qideal->m[0]) n_Delete(&num, currRing->cf);
361  //TODO check for memory leaks
362  poly pp = pHead(p);
363  //PrintS("map:");pWrite(pp);
364  pSetCoeff(pp,n_Init(1,currRing->cf));
365  //PrintS("cf->");pWrite((poly)(v->data));
366  poly ppp = pMult((poly)(v->data),pp);
367  //PrintS("->");pWrite(ppp);
368  res=pAdd(res,ppp);
369  pIter(p);
370  }
371  }
372  else
373  {
374  WerrorS("cannot apply subst for these coeffcients");
375  }
376  idDelete((ideal *)(&theMap));
378  return res;
379 }
#define omAllocBin(bin)
Definition: omAllocDecl.h:205
CanonicalForm map(const CanonicalForm &primElem, const Variable &alpha, const CanonicalForm &F, const Variable &beta)
map from to such that is mapped onto
Definition: cf_map_ext.cc:400
static FORCE_INLINE number n_GetNumerator(number &n, const coeffs r)
return the numerator of n (if elements of r are by nature not fractional, result is n)
Definition: coeffs.h:608
Class used for (list of) interpreter objects.
Definition: subexpr.h:82
#define pAdd(p, q)
Definition: polys.h:198
#define idDelete(H)
delete an ideal
Definition: ideals.h:29
CanonicalForm num(const CanonicalForm &f)
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
Definition: coeffs.h:468
static int rPar(const ring r)
(r->cf->P)
Definition: ring.h:589
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
Definition: p_polys.cc:1435
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
Definition: coeffs.h:538
BOOLEAN maApplyFetch(int what, map theMap, leftv res, leftv w, ring preimage_r, int *perm, int *par_perm, int P, nMapFunc nMap)
Definition: maps_ip.cc:46
void * ADDRESS
Definition: auxiliary.h:133
sleftv * leftv
Definition: structs.h:60
void WerrorS(const char *s)
Definition: feFopen.cc:24
(fraction), see transext.h
Definition: coeffs.h:114
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition: monomials.h:45
#define WarnS
Definition: emacs.cc:78
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:813
(poly), see algext.h
Definition: coeffs.h:113
void * data
Definition: subexpr.h:88
static FORCE_INLINE number n_Param(const int iParameter, const coeffs r)
return the (iParameter^th) parameter as a NEW number NOTE: parameter numbering: 1....
Definition: coeffs.h:805
#define pIter(p)
Definition: monomials.h:38
if(yy_init)
Definition: libparse.cc:1418
CanonicalForm res
Definition: facAbsFact.cc:64
static BOOLEAN p_IsConstant(const poly p, const ring r)
Definition: p_polys.h:1929
CanonicalForm pp(const CanonicalForm &)
CanonicalForm pp ( const CanonicalForm & f )
Definition: cf_gcd.cc:248
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:73
static FORCE_INLINE number n_Invers(number a, const coeffs r)
return the multiplicative inverse of 'a'; raise an error if 'a' is not invertible
Definition: coeffs.h:564
omBin sleftv_bin
Definition: subexpr.cc:47
int i
Definition: cfEzgcd.cc:125
#define pHead(p)
returns newly allocated copy of Lm(p), coef is copied, next=NULL, p might be NULL
Definition: polys.h:67
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
Definition: coeffs.h:721
#define p_Test(p, r)
Definition: p_polys.h:164
void p_Normalize(poly p, const ring r)
Definition: p_polys.cc:3723
ideal idInit(int idsize, int rank)
initialise an ideal / module
Definition: simpleideals.cc:37
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:37
#define NULL
Definition: omList.c:10
Definition: readcf.cc:164
#define pMult(p, q)
Definition: polys.h:202
#define R
Definition: sirandom.c:26
int rtyp
Definition: subexpr.h:91
static FORCE_INLINE number n_GetDenom(number &n, const coeffs r)
return the denominator of n (if elements of r are by nature not fractional, result is 1)
Definition: coeffs.h:603
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:455
int p
Definition: cfModGcd.cc:4019
#define omFreeBin(addr, bin)
Definition: omAllocDecl.h:259
#define nInit(i)
Definition: numbers.h:25
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition: polys.h:31

◆ pSubstPoly()

poly pSubstPoly ( poly  p,
int  var,
poly  image 
)

Definition at line 402 of file maps_ip.cc.

403 {
404  if (p==NULL) return NULL;
405 #ifdef HAVE_PLURAL
406  if (rIsPluralRing(currRing))
407  {
408  return pSubst(pCopy(p),var,image);
409  }
410 #endif
411  return p_SubstPoly(p,var,image,currRing,currRing,ndCopyMap);
412 }
#define pSubst(p, n, e)
Definition: polys.h:360
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
Definition: numbers.cc:252
poly p_SubstPoly(poly p, int var, poly image, const ring preimage_r, const ring image_r, const nMapFunc nMap, matrix cache=NULL)
Definition: subst_maps.cc:39
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
Definition: ring.h:398
#define NULL
Definition: omList.c:10
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13
int p
Definition: cfModGcd.cc:4019
#define pCopy(p)
return a copy of the poly
Definition: polys.h:180