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maps_ip.cc
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1 /****************************************
2 * Computer Algebra System SINGULAR *
3 ****************************************/
4 /*
5 * ABSTRACT - the mapping of polynomials to other rings
6 */
7 #define TRANSEXT_PRIVATES
8 
9 #include "kernel/mod2.h"
10 
11 #include "coeffs/numbers.h"
12 #include "coeffs/coeffs.h"
13 
14 #include "polys/monomials/ring.h"
15 #include "polys/monomials/maps.h"
16 #include "polys/matpol.h"
17 #include "polys/prCopy.h"
19 
20 //#include "polys/ext_fields/longtrans.h"
21 // #include "kernel/longalg.h"
22 
23 #include "misc/options.h"
24 #include "kernel/GBEngine/kstd1.h"
25 #include "kernel/maps/gen_maps.h"
26 
27 #include "maps_ip.h"
28 #include "ipid.h"
29 
30 
31 #include "lists.h"
32 #include "tok.h"
33 
34 /* debug output: Tok2Cmdname in maApplyFetch*/
35 #include "ipshell.h"
36 
37 /*2
38 * maps the expression w to res,
39 * switch what: MAP_CMD: use theMap for mapping, N for preimage ring
40 * //FETCH_CMD: use pOrdPoly for mapping
41 * IMAP_CMD: use perm for mapping, N for preimage ring
42 * default: map only poly-structures,
43 * use perm and par_perm, N and P,
44 */
45 BOOLEAN maApplyFetch(int what,map theMap,leftv res, leftv w, ring preimage_r,
46  int *perm, int *par_perm, int P, nMapFunc nMap)
47 {
48  BOOLEAN use_mult=FALSE;
49 #ifdef HAVE_PLURAL
50  if ((what==IMAP_CMD)
52  && rIsPluralRing(preimage_r))
53  {
54  assume(perm!=NULL);
55  int i=1;
56  while((i<currRing->N)&&(perm[i]==0)) i++;
57  if (i<currRing->N)
58  {
59  int prev_nonnull=i;
60  i++;
61  for(;i<=currRing->N;i++)
62  {
63  if (perm[prev_nonnull] > perm[i])
64  {
65  if (TEST_V_ALLWARN)
66  {
67  Warn("imap not usable for permuting variables, use map (%s <-> %s)",currRing->names[prev_nonnull-1],currRing->names[i-1]);
68  }
69  use_mult=TRUE;
70  break;
71  }
72  else
73  prev_nonnull=i;
74  }
75  }
76  }
77 #endif
78  int i;
79  int N = preimage_r->N;
80 #if 0
81  Print("N=%d what=%s ",N,Tok2Cmdname(what));
82  if (perm!=NULL) for(i=1;i<=N;i++) Print("%d -> %d ",i,perm[i]);
83  PrintS("\n");
84  Print("P=%d ",P);
85  if (par_perm!=NULL) for(i=0;i<P;i++) Print("%d -> %d ",i,par_perm[i]);
86  PrintS("\n");
87 #endif
88 
89  void *data=w->Data();
90  res->rtyp = w->rtyp;
91  switch (w->rtyp)
92  {
93  case NUMBER_CMD:
94  if (P!=0)
95  {
96 // poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst);
97  res->data= (void *) n_PermNumber((number)data, par_perm, P, preimage_r, currRing);
98  res->rtyp=POLY_CMD;
99  if (nCoeff_is_algExt(currRing->cf))
100  res->data=(void *)p_MinPolyNormalize((poly)res->data, currRing);
101  pTest((poly) res->data);
102  }
103  else
104  {
105  assume( nMap != NULL );
106  number a = nMap((number)data, preimage_r->cf, currRing->cf);
107  if (nCoeff_is_Extension(currRing->cf))
108  {
109  n_Normalize(a, currRing->cf);
110 /*
111  number a = (number)res->data;
112  number one = nInit(1);
113  number product = nMult(a, one );
114  nDelete(&one);
115  nDelete(&a);
116  res->data=(void *)product;
117  */
118  }
119  #ifdef LDEBUG
120  n_Test(a, currRing->cf);
121  #endif
122  res->data=(void *)a;
123 
124  }
125  break;
126  case BUCKET_CMD:
127  if ((what==FETCH_CMD)&& (preimage_r->cf==currRing->cf))
128  res->data=(void *)prCopyR(sBucketPeek((sBucket_pt)data), preimage_r, currRing);
129  else
130  if ( (what==IMAP_CMD) || /*(*/ (what==FETCH_CMD) /*)*/) /* && (nMap!=nCopy)*/
131  res->data=(void *)p_PermPoly(sBucketPeek((sBucket_pt)data),perm,preimage_r,currRing, nMap,par_perm,P,use_mult);
132  else /*if (what==MAP_CMD)*/
133  {
134  res->data=(void*)maMapPoly(sBucketPeek((sBucket_pt)data),preimage_r,(ideal)theMap,currRing,nMap);
135  }
136  if (nCoeff_is_Extension(currRing->cf))
137  res->data=(void *)p_MinPolyNormalize(sBucketPeek((sBucket_pt)data), currRing);
138  break;
139  case POLY_CMD:
140  case VECTOR_CMD:
141  if ((what==FETCH_CMD)&& (preimage_r->cf==currRing->cf))
142  res->data=(void *)prCopyR( (poly)data, preimage_r, currRing);
143  else
144  if ( (what==IMAP_CMD) || /*(*/ (what==FETCH_CMD) /*)*/) /* && (nMap!=nCopy)*/
145  res->data=(void *)p_PermPoly((poly)data,perm,preimage_r,currRing, nMap,par_perm,P,use_mult);
146  else /*if (what==MAP_CMD)*/
147  {
148  p_Test((poly)data,preimage_r);
149  res->data=(void*)maMapPoly((poly)data,preimage_r,(ideal)theMap,currRing,nMap);
150  }
151  if (nCoeff_is_Extension(currRing->cf))
152  res->data=(void *)p_MinPolyNormalize((poly)res->data, currRing);
153  pTest((poly)res->data);
154  break;
155  case MODUL_CMD:
156  case MATRIX_CMD:
157  case IDEAL_CMD:
158  case MAP_CMD:
159  {
160  int C=((matrix)data)->cols();
161  int R;
162  if (w->rtyp==MAP_CMD) R=1;
163  else R=((matrix)data)->rows();
164  matrix m=mpNew(R,C);
165  char *tmpR=NULL;
166  if(w->rtyp==MAP_CMD)
167  {
168  tmpR=((map)data)->preimage;
169  ((matrix)data)->rank=((matrix)data)->rows();
170  }
171  if ((what==FETCH_CMD)&& (preimage_r->cf == currRing->cf))
172  {
173  for (i=R*C-1;i>=0;i--)
174  {
175  m->m[i]=prCopyR(((ideal)data)->m[i], preimage_r, currRing);
176  pTest(m->m[i]);
177  }
178  }
179  else if ((what==IMAP_CMD) || (what==FETCH_CMD))
180  {
181  for (i=R*C-1;i>=0;i--)
182  {
183  m->m[i]=p_PermPoly(((ideal)data)->m[i],perm,preimage_r,currRing,
184  nMap,par_perm,P,use_mult);
185  pTest(m->m[i]);
186  }
187  }
188  else /* (what==MAP_CMD) */
189  {
190  assume(what==MAP_CMD);
191  matrix s=mpNew(N,maMaxDeg_Ma((ideal)data,preimage_r));
192  for (i=R*C-1;i>=0;i--)
193  {
194  m->m[i]=maEval(theMap, ((ideal)data)->m[i], preimage_r, nMap, (ideal)s, currRing);
195  pTest(m->m[i]);
196  }
197  idDelete((ideal *)&s);
198  }
199  if (nCoeff_is_algExt(currRing->cf))
200  {
201  for (i=R*C-1;i>=0;i--)
202  {
203  m->m[i]=p_MinPolyNormalize(m->m[i], currRing);
204  pTest(m->m[i]);
205  }
206  }
207  if(w->rtyp==MAP_CMD)
208  {
209  ((map)data)->preimage=tmpR;
210  ((map)m)->preimage=omStrDup(tmpR);
211  }
212  else
213  {
214  m->rank=((matrix)data)->rank;
215  }
216  res->data=(char *)m;
217  idTest((ideal) m);
218  break;
219  }
220 
221  case LIST_CMD:
222  {
223  lists l=(lists)data;
225  ml->Init(l->nr+1);
226  for(i=0;i<=l->nr;i++)
227  {
228  if (((l->m[i].rtyp>BEGIN_RING)&&(l->m[i].rtyp<END_RING))
229  ||(l->m[i].rtyp==LIST_CMD))
230  {
231  if (maApplyFetch(what,theMap,&ml->m[i],&l->m[i],
232  preimage_r,perm,par_perm,P,nMap))
233  {
234  ml->Clean();
236  res->rtyp=0;
237  return TRUE;
238  }
239  }
240  else
241  {
242  ml->m[i].Copy(&l->m[i]);
243  }
244  }
245  res->data=(char *)ml;
246  break;
247  }
248  default:
249  {
250  return TRUE;
251  }
252  }
253  return FALSE;
254 }
255 
256 /*2
257 * substitutes the parameter par (from 1..N) by image,
258 * does not destroy p and image
259 */
260 poly pSubstPar(poly p, int par, poly image)
261 {
262  const ring R = currRing->cf->extRing;
263  ideal theMapI = idInit(rPar(currRing),1);
264  nMapFunc nMap = n_SetMap(R->cf, currRing->cf);
265  int i;
266  for(i = rPar(currRing);i>0;i--)
267  {
268  if (i != par)
269  theMapI->m[i-1]= p_NSet(n_Param(i, currRing), currRing);
270  else
271  theMapI->m[i-1] = p_Copy(image, currRing);
272  p_Test(theMapI->m[i-1],currRing);
273  }
274  //iiWriteMatrix((matrix)theMapI,"map:",1,currRing,0);
275 
276  map theMap=(map)theMapI;
277  theMap->preimage=NULL;
278 
280  sleftv tmpW;
281  poly res=NULL;
282 
284  if (currRing->cf->rep==n_rep_rat_fct )
285  {
286  while (p!=NULL)
287  {
288  memset(v,0,sizeof(sleftv));
289 
290  number d = n_GetDenom(pGetCoeff(p), currRing->cf);
291  p_Test((poly)NUM((fraction)d), R);
292 
293  if ( n_IsOne (d, currRing->cf) )
294  {
295  n_Delete(&d, currRing->cf); d = NULL;
296  }
297  else if (!p_IsConstant((poly)NUM((fraction)d), R))
298  {
299  WarnS("ignoring denominators of coefficients...");
300  n_Delete(&d, currRing->cf); d = NULL;
301  }
302 
303  number num = n_GetNumerator(pGetCoeff(p), currRing->cf);
304  memset(&tmpW,0,sizeof(sleftv));
305  tmpW.rtyp = POLY_CMD;
306  p_Test((poly)NUM((fraction)num), R);
307 
308  tmpW.data = NUM ((fraction)num); // a copy of this poly will be used
309 
310  p_Normalize(NUM((fraction)num),R);
311  if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,R,NULL,NULL,0,nMap))
312  {
313  WerrorS("map failed");
314  v->data=NULL;
315  }
316  n_Delete(&num, currRing->cf);
317  //TODO check for memory leaks
318  poly pp = pHead(p);
319  //PrintS("map:");pWrite(pp);
320  if( d != NULL )
321  {
322  pSetCoeff(pp, n_Invers(d, currRing->cf));
323  n_Delete(&d, currRing->cf); // d = NULL;
324  }
325  else
326  pSetCoeff(pp, nInit(1));
327 
328  //PrintS("->");pWrite((poly)(v->data));
329  poly ppp = pMult((poly)(v->data),pp);
330  //PrintS("->");pWrite(ppp);
331  res=pAdd(res,ppp);
332  pIter(p);
333  }
334  }
335  else if (currRing->cf->rep==n_rep_poly )
336  {
337  while (p!=NULL)
338  {
339  memset(v,0,sizeof(sleftv));
340 
341  number num = n_GetNumerator(pGetCoeff(p), currRing->cf);
342  memset(&tmpW,0,sizeof(sleftv));
343  tmpW.rtyp = POLY_CMD;
344  p_Test((poly)num, R);
345 
346 
347  p_Normalize((poly)num,R);
348  if (num==NULL) num=(number)R->qideal->m[0];
349  tmpW.data = num; // a copy of this poly will be used
350  if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,R,NULL,NULL,0,nMap))
351  {
352  WerrorS("map failed");
353  v->data=NULL;
354  }
355  if (num!=(number)R->qideal->m[0]) n_Delete(&num, currRing->cf);
356  //TODO check for memory leaks
357  poly pp = pHead(p);
358  //PrintS("map:");pWrite(pp);
359  pSetCoeff(pp,n_Init(1,currRing->cf));
360  //PrintS("cf->");pWrite((poly)(v->data));
361  poly ppp = pMult((poly)(v->data),pp);
362  //PrintS("->");pWrite(ppp);
363  res=pAdd(res,ppp);
364  pIter(p);
365  }
366  }
367  else
368  {
369  WerrorS("cannot apply subst for these coeffcients");
370  }
371  idDelete((ideal *)(&theMap));
373  return res;
374 }
375 
376 /*2
377 * substitute the n-th parameter by the poly e in id
378 * does not destroy id and e
379 */
380 ideal idSubstPar(ideal id, int n, poly e)
381 {
382  int k=MATROWS((matrix)id)*MATCOLS((matrix)id);
383  ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id));
384 
385  res->rank = id->rank;
386  for(k--;k>=0;k--)
387  {
388  res->m[k]=pSubstPar(id->m[k],n,e);
389  }
390  return res;
391 }
392 
393 /*2
394 * substitutes the variable var (from 1..N) by image,
395 * does not destroy p and image
396 */
397 poly pSubstPoly(poly p, int var, poly image)
398 {
399  if (p==NULL) return NULL;
400 #ifdef HAVE_PLURAL
401  if (rIsPluralRing(currRing))
402  {
403  return pSubst(pCopy(p),var,image);
404  }
405 #endif
406  return p_SubstPoly(p,var,image,currRing,currRing,ndCopyMap);
407 }
408 
409 /*2
410 * substitute the n-th variable by the poly e in id
411 * does not destroy id and e
412 */
413 ideal idSubstPoly(ideal id, int n, poly e)
414 {
415 
416 #ifdef HAVE_PLURAL
417  if (rIsPluralRing(currRing))
418  {
419  int k=MATROWS((matrix)id)*MATCOLS((matrix)id);
420  ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id));
421  res->rank = id->rank;
422  for(k--;k>=0;k--)
423  {
424  res->m[k]=pSubst(pCopy(id->m[k]),n,e);
425  }
426  return res;
427  }
428 #endif
429  return id_SubstPoly(id,n,e,currRing,currRing,ndCopyMap);
430 }
int BOOLEAN
Definition: auxiliary.h:87
#define TRUE
Definition: auxiliary.h:100
#define FALSE
Definition: auxiliary.h:96
void * ADDRESS
Definition: auxiliary.h:135
CanonicalForm pp(const CanonicalForm &)
CanonicalForm pp ( const CanonicalForm & f )
Definition: cf_gcd.cc:248
CanonicalForm num(const CanonicalForm &f)
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:49
int l
Definition: cfEzgcd.cc:93
int m
Definition: cfEzgcd.cc:121
int i
Definition: cfEzgcd.cc:125
int k
Definition: cfEzgcd.cc:92
int p
Definition: cfModGcd.cc:4019
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
poly * m
Definition: matpol.h:18
Class used for (list of) interpreter objects.
Definition: subexpr.h:83
int rtyp
Definition: subexpr.h:91
void Copy(leftv e)
Definition: subexpr.cc:714
void * data
Definition: subexpr.h:88
Definition: lists.h:24
sleftv * m
Definition: lists.h:46
void Clean(ring r=currRing)
Definition: lists.h:26
INLINE_THIS void Init(int l=0)
Coefficient rings, fields and other domains suitable for Singular polynomials.
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
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
static FORCE_INLINE BOOLEAN nCoeff_is_Extension(const coeffs r)
Definition: coeffs.h:868
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
Definition: coeffs.h:738
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
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
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:455
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
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
Definition: coeffs.h:932
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
@ n_rep_poly
(poly), see algext.h
Definition: coeffs.h:113
@ n_rep_rat_fct
(fraction), see transext.h
Definition: coeffs.h:114
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 void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
Definition: coeffs.h:578
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
Definition: coeffs.h:468
#define Print
Definition: emacs.cc:80
#define Warn
Definition: emacs.cc:77
#define WarnS
Definition: emacs.cc:78
const CanonicalForm int s
Definition: facAbsFact.cc:55
CanonicalForm res
Definition: facAbsFact.cc:64
const CanonicalForm & w
Definition: facAbsFact.cc:55
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:37
void WerrorS(const char *s)
Definition: feFopen.cc:24
poly maMapPoly(const poly map_p, const ring map_r, const ideal image_id, const ring image_r, const nMapFunc nMap)
polynomial map for poly (vector) map_p: the poly (vector) to map map_r: the base ring for map_p image...
Definition: gen_maps.cc:159
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
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
const char * Tok2Cmdname(int tok)
Definition: gentable.cc:140
@ END_RING
Definition: grammar.cc:310
@ IDEAL_CMD
Definition: grammar.cc:284
@ MATRIX_CMD
Definition: grammar.cc:286
@ BUCKET_CMD
Definition: grammar.cc:283
@ IMAP_CMD
Definition: grammar.cc:298
@ MAP_CMD
Definition: grammar.cc:285
@ BEGIN_RING
Definition: grammar.cc:282
@ MODUL_CMD
Definition: grammar.cc:287
@ VECTOR_CMD
Definition: grammar.cc:292
@ NUMBER_CMD
Definition: grammar.cc:288
@ POLY_CMD
Definition: grammar.cc:289
@ FETCH_CMD
Definition: grammar.cc:295
#define idDelete(H)
delete an ideal
Definition: ideals.h:29
#define idTest(id)
Definition: ideals.h:47
EXTERN_VAR omBin sleftv_bin
Definition: ipid.h:140
if(yy_init)
Definition: libparse.cc:1420
VAR omBin slists_bin
Definition: lists.cc:23
poly maEval(map theMap, poly p, ring preimage_r, nMapFunc nMap, ideal s, const ring dst_r)
Definition: maps.cc:115
int maMaxDeg_Ma(ideal a, ring preimage_r)
Definition: maps.cc:329
poly p_MinPolyNormalize(poly p, const ring r)
Definition: maps.cc:399
poly pSubstPoly(poly p, int var, poly image)
Definition: maps_ip.cc:397
ideal idSubstPoly(ideal id, int n, poly e)
Definition: maps_ip.cc:413
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:45
ideal idSubstPar(ideal id, int n, poly e)
Definition: maps_ip.cc:380
poly pSubstPar(poly p, int par, poly image)
Definition: maps_ip.cc:260
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition: matpol.cc:37
ip_smatrix * matrix
Definition: matpol.h:43
#define MATROWS(i)
Definition: matpol.h:26
#define MATCOLS(i)
Definition: matpol.h:27
#define assume(x)
Definition: mod2.h:390
#define pIter(p)
Definition: monomials.h:37
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition: monomials.h:44
slists * lists
Definition: mpr_numeric.h:146
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
Definition: numbers.cc:251
#define nInit(i)
Definition: numbers.h:24
#define omStrDup(s)
Definition: omAllocDecl.h:263
#define omAllocBin(bin)
Definition: omAllocDecl.h:205
#define omFreeBin(addr, bin)
Definition: omAllocDecl.h:259
#define NULL
Definition: omList.c:12
#define TEST_V_ALLWARN
Definition: options.h:139
poly n_PermNumber(const number z, const int *par_perm, const int, const ring src, const ring dst)
Definition: p_polys.cc:3933
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:4036
void p_Normalize(poly p, const ring r)
Definition: p_polys.cc:3732
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
Definition: p_polys.cc:1455
static BOOLEAN p_IsConstant(const poly p, const ring r)
Definition: p_polys.h:1931
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:811
#define p_Test(p, r)
Definition: p_polys.h:162
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13
#define pAdd(p, q)
Definition: polys.h:199
#define pTest(p)
Definition: polys.h:411
#define pHead(p)
returns newly allocated copy of Lm(p), coef is copied, next=NULL, p might be NULL
Definition: polys.h:67
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition: polys.h:31
#define pMult(p, q)
Definition: polys.h:203
#define pSubst(p, n, e)
Definition: polys.h:362
#define pCopy(p)
return a copy of the poly
Definition: polys.h:181
poly prCopyR(poly p, ring src_r, ring dest_r)
Definition: prCopy.cc:34
void PrintS(const char *s)
Definition: reporter.cc:284
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
Definition: ring.h:397
static int rPar(const ring r)
(r->cf->P)
Definition: ring.h:594
poly sBucketPeek(sBucket_pt b)
Definition: sbuckets.cc:455
ideal idInit(int idsize, int rank)
initialise an ideal / module
Definition: simpleideals.cc:35
#define R
Definition: sirandom.c:27
sleftv * leftv
Definition: structs.h:62
@ LIST_CMD
Definition: tok.h:118