[0f401f] | 1 | /**************************************** |
---|
| 2 | * Computer Algebra System SINGULAR * |
---|
| 3 | ****************************************/ |
---|
| 4 | /* |
---|
| 5 | * ABSTRACT - all basic methods to manipulate ideals |
---|
| 6 | */ |
---|
| 7 | |
---|
| 8 | /* includes */ |
---|
[9f7665] | 9 | |
---|
| 10 | #include <kernel/mod2.h> |
---|
| 11 | |
---|
[f11ea16] | 12 | #include <omalloc/omalloc.h> |
---|
| 13 | |
---|
[7fe9e13] | 14 | #ifndef SING_NDEBUG |
---|
[0f401f] | 15 | # define MYTEST 0 |
---|
[7fe9e13] | 16 | #else /* ifndef SING_NDEBUG */ |
---|
[e6e2198] | 17 | # define MYTEST 0 |
---|
[7fe9e13] | 18 | #endif /* ifndef SING_NDEBUG */ |
---|
[0f401f] | 19 | |
---|
| 20 | #include <omalloc/omalloc.h> |
---|
[e6e2198] | 21 | |
---|
| 22 | #include <misc/options.h> |
---|
| 23 | #include <misc/intvec.h> |
---|
| 24 | |
---|
[76cfef] | 25 | #include <coeffs/coeffs.h> |
---|
| 26 | #include <coeffs/numbers.h> |
---|
[f7d39b] | 27 | // #include <coeffs/longrat.h> |
---|
| 28 | |
---|
[e6e2198] | 29 | |
---|
[210e07] | 30 | #include <polys/monomials/ring.h> |
---|
[76cfef] | 31 | #include <polys/matpol.h> |
---|
| 32 | #include <polys/weight.h> |
---|
[210e07] | 33 | #include <polys/sparsmat.h> |
---|
[76cfef] | 34 | #include <polys/prCopy.h> |
---|
[210e07] | 35 | #include <polys/nc/nc.h> |
---|
[0f401f] | 36 | |
---|
[1f637e] | 37 | |
---|
[e6e2198] | 38 | #include <kernel/ideals.h> |
---|
| 39 | |
---|
[f7d39b] | 40 | #include <kernel/polys.h> |
---|
| 41 | |
---|
[57fa2c4] | 42 | #include <kernel/GBEngine/kstd1.h> |
---|
| 43 | #include <kernel/GBEngine/syz.h> |
---|
[e6e2198] | 44 | |
---|
[0f401f] | 45 | |
---|
| 46 | /* #define WITH_OLD_MINOR */ |
---|
| 47 | |
---|
| 48 | /*0 implementation*/ |
---|
| 49 | |
---|
| 50 | /*2 |
---|
| 51 | *returns a minimized set of generators of h1 |
---|
| 52 | */ |
---|
| 53 | ideal idMinBase (ideal h1) |
---|
| 54 | { |
---|
| 55 | ideal h2, h3,h4,e; |
---|
| 56 | int j,k; |
---|
| 57 | int i,l,ll; |
---|
| 58 | intvec * wth; |
---|
| 59 | BOOLEAN homog; |
---|
[4f61c6] | 60 | #ifdef HAVE_RINGS |
---|
| 61 | if(rField_is_Ring(currRing)) |
---|
| 62 | { |
---|
| 63 | WarnS("minbase applies only to the local or homogeneous case over coefficient fields"); |
---|
| 64 | e=idCopy(h1); |
---|
| 65 | return e; |
---|
| 66 | } |
---|
| 67 | #endif |
---|
[ac00e2f] | 68 | homog = idHomModule(h1,currRing->qideal,&wth); |
---|
[4f61c6] | 69 | if (rHasGlobalOrdering(currRing)) |
---|
[0f401f] | 70 | { |
---|
| 71 | if(!homog) |
---|
| 72 | { |
---|
[0fc231] | 73 | WarnS("minbase applies only to the local or homogeneous case over coefficient fields"); |
---|
[0f401f] | 74 | e=idCopy(h1); |
---|
| 75 | return e; |
---|
| 76 | } |
---|
| 77 | else |
---|
| 78 | { |
---|
[ac00e2f] | 79 | ideal re=kMin_std(h1,currRing->qideal,(tHomog)homog,&wth,h2,NULL,0,3); |
---|
[0f401f] | 80 | idDelete(&re); |
---|
| 81 | return h2; |
---|
| 82 | } |
---|
| 83 | } |
---|
| 84 | e=idInit(1,h1->rank); |
---|
| 85 | if (idIs0(h1)) |
---|
| 86 | { |
---|
| 87 | return e; |
---|
| 88 | } |
---|
| 89 | pEnlargeSet(&(e->m),IDELEMS(e),15); |
---|
| 90 | IDELEMS(e) = 16; |
---|
[ac00e2f] | 91 | h2 = kStd(h1,currRing->qideal,isNotHomog,NULL); |
---|
[b7cfaf] | 92 | h3 = idMaxIdeal(1); |
---|
[0f401f] | 93 | h4=idMult(h2,h3); |
---|
| 94 | idDelete(&h3); |
---|
[ac00e2f] | 95 | h3=kStd(h4,currRing->qideal,isNotHomog,NULL); |
---|
[0f401f] | 96 | k = IDELEMS(h3); |
---|
| 97 | while ((k > 0) && (h3->m[k-1] == NULL)) k--; |
---|
| 98 | j = -1; |
---|
| 99 | l = IDELEMS(h2); |
---|
| 100 | while ((l > 0) && (h2->m[l-1] == NULL)) l--; |
---|
| 101 | for (i=l-1; i>=0; i--) |
---|
| 102 | { |
---|
| 103 | if (h2->m[i] != NULL) |
---|
| 104 | { |
---|
| 105 | ll = 0; |
---|
| 106 | while ((ll < k) && ((h3->m[ll] == NULL) |
---|
| 107 | || !pDivisibleBy(h3->m[ll],h2->m[i]))) |
---|
| 108 | ll++; |
---|
| 109 | if (ll >= k) |
---|
| 110 | { |
---|
| 111 | j++; |
---|
| 112 | if (j > IDELEMS(e)-1) |
---|
| 113 | { |
---|
| 114 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
| 115 | IDELEMS(e) += 16; |
---|
| 116 | } |
---|
| 117 | e->m[j] = pCopy(h2->m[i]); |
---|
| 118 | } |
---|
| 119 | } |
---|
| 120 | } |
---|
| 121 | idDelete(&h2); |
---|
| 122 | idDelete(&h3); |
---|
| 123 | idDelete(&h4); |
---|
[ac00e2f] | 124 | if (currRing->qideal!=NULL) |
---|
[0f401f] | 125 | { |
---|
| 126 | h3=idInit(1,e->rank); |
---|
[ac00e2f] | 127 | h2=kNF(h3,currRing->qideal,e); |
---|
[0f401f] | 128 | idDelete(&h3); |
---|
| 129 | idDelete(&e); |
---|
| 130 | e=h2; |
---|
| 131 | } |
---|
| 132 | idSkipZeroes(e); |
---|
| 133 | return e; |
---|
| 134 | } |
---|
| 135 | |
---|
| 136 | |
---|
| 137 | /*2 |
---|
| 138 | *initialized a field with r numbers between beg and end for the |
---|
| 139 | *procedure idNextChoise |
---|
| 140 | */ |
---|
| 141 | ideal idSectWithElim (ideal h1,ideal h2) |
---|
| 142 | // does not destroy h1,h2 |
---|
| 143 | { |
---|
| 144 | if (TEST_OPT_PROT) PrintS("intersect by elimination method\n"); |
---|
| 145 | assume(!idIs0(h1)); |
---|
| 146 | assume(!idIs0(h2)); |
---|
| 147 | assume(IDELEMS(h1)<=IDELEMS(h2)); |
---|
[7b25fe] | 148 | assume(id_RankFreeModule(h1,currRing)==0); |
---|
| 149 | assume(id_RankFreeModule(h2,currRing)==0); |
---|
[0f401f] | 150 | // add a new variable: |
---|
| 151 | int j; |
---|
| 152 | ring origRing=currRing; |
---|
| 153 | ring r=rCopy0(origRing); |
---|
| 154 | r->N++; |
---|
| 155 | r->block0[0]=1; |
---|
| 156 | r->block1[0]= r->N; |
---|
| 157 | omFree(r->order); |
---|
| 158 | r->order=(int*)omAlloc0(3*sizeof(int*)); |
---|
| 159 | r->order[0]=ringorder_dp; |
---|
| 160 | r->order[1]=ringorder_C; |
---|
| 161 | char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr)); |
---|
| 162 | for (j=0;j<r->N-1;j++) names[j]=r->names[j]; |
---|
| 163 | names[r->N-1]=omStrDup("@"); |
---|
| 164 | omFree(r->names); |
---|
| 165 | r->names=names; |
---|
| 166 | rComplete(r,TRUE); |
---|
| 167 | // fetch h1, h2 |
---|
| 168 | ideal h; |
---|
| 169 | h1=idrCopyR(h1,origRing,r); |
---|
| 170 | h2=idrCopyR(h2,origRing,r); |
---|
| 171 | // switch to temp. ring r |
---|
| 172 | rChangeCurrRing(r); |
---|
| 173 | // create 1-t, t |
---|
[861529] | 174 | poly omt=p_One(currRing); |
---|
| 175 | p_SetExp(omt,r->N,1,currRing); |
---|
| 176 | poly t=p_Copy(omt,currRing); |
---|
| 177 | p_Setm(omt,currRing); |
---|
| 178 | omt=p_Neg(omt,currRing); |
---|
| 179 | omt=p_Add_q(omt,pOne(),currRing); |
---|
[0f401f] | 180 | // compute (1-t)*h1 |
---|
[861529] | 181 | h1=(ideal)mp_MultP((matrix)h1,omt,currRing); |
---|
[0f401f] | 182 | // compute t*h2 |
---|
[861529] | 183 | h2=(ideal)mp_MultP((matrix)h2,pCopy(t),currRing); |
---|
[0f401f] | 184 | // (1-t)h1 + t*h2 |
---|
| 185 | h=idInit(IDELEMS(h1)+IDELEMS(h2),1); |
---|
| 186 | int l; |
---|
| 187 | for (l=IDELEMS(h1)-1; l>=0; l--) |
---|
| 188 | { |
---|
| 189 | h->m[l] = h1->m[l]; h1->m[l]=NULL; |
---|
| 190 | } |
---|
| 191 | j=IDELEMS(h1); |
---|
| 192 | for (l=IDELEMS(h2)-1; l>=0; l--) |
---|
| 193 | { |
---|
| 194 | h->m[l+j] = h2->m[l]; h2->m[l]=NULL; |
---|
| 195 | } |
---|
| 196 | idDelete(&h1); |
---|
| 197 | idDelete(&h2); |
---|
| 198 | // eliminate t: |
---|
| 199 | |
---|
| 200 | ideal res=idElimination(h,t); |
---|
[a5d181c] | 201 | // cleanup |
---|
[0f401f] | 202 | idDelete(&h); |
---|
[a5d181c] | 203 | if (res!=NULL) res=idrMoveR(res,r,origRing); |
---|
[0f401f] | 204 | rChangeCurrRing(origRing); |
---|
[5fe834] | 205 | rDelete(r); |
---|
[0f401f] | 206 | return res; |
---|
| 207 | } |
---|
| 208 | /*2 |
---|
| 209 | * h3 := h1 intersect h2 |
---|
| 210 | */ |
---|
| 211 | ideal idSect (ideal h1,ideal h2) |
---|
| 212 | { |
---|
| 213 | int i,j,k,length; |
---|
[7b25fe] | 214 | int flength = id_RankFreeModule(h1,currRing); |
---|
| 215 | int slength = id_RankFreeModule(h2,currRing); |
---|
[a7d85a2] | 216 | int rank=si_max(h1->rank,h2->rank); |
---|
[0f401f] | 217 | if ((idIs0(h1)) || (idIs0(h2))) return idInit(1,rank); |
---|
| 218 | |
---|
| 219 | ideal first,second,temp,temp1,result; |
---|
| 220 | poly p,q; |
---|
| 221 | |
---|
| 222 | if (IDELEMS(h1)<IDELEMS(h2)) |
---|
| 223 | { |
---|
| 224 | first = h1; |
---|
| 225 | second = h2; |
---|
| 226 | } |
---|
| 227 | else |
---|
| 228 | { |
---|
| 229 | first = h2; |
---|
| 230 | second = h1; |
---|
| 231 | int t=flength; flength=slength; slength=t; |
---|
| 232 | } |
---|
| 233 | length = si_max(flength,slength); |
---|
| 234 | if (length==0) |
---|
| 235 | { |
---|
[ac00e2f] | 236 | if ((currRing->qideal==NULL) |
---|
[0f401f] | 237 | && (currRing->OrdSgn==1) |
---|
| 238 | && (!rIsPluralRing(currRing)) |
---|
| 239 | && ((TEST_V_INTERSECT_ELIM) || (!TEST_V_INTERSECT_SYZ))) |
---|
| 240 | return idSectWithElim(first,second); |
---|
| 241 | else length = 1; |
---|
| 242 | } |
---|
| 243 | if (TEST_OPT_PROT) PrintS("intersect by syzygy methods\n"); |
---|
| 244 | j = IDELEMS(first); |
---|
| 245 | |
---|
| 246 | ring orig_ring=currRing; |
---|
[3f07d1] | 247 | ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
[b7cfaf] | 248 | rSetSyzComp(length, syz_ring); |
---|
[0f401f] | 249 | |
---|
| 250 | while ((j>0) && (first->m[j-1]==NULL)) j--; |
---|
| 251 | temp = idInit(j /*IDELEMS(first)*/+IDELEMS(second),length+j); |
---|
| 252 | k = 0; |
---|
| 253 | for (i=0;i<j;i++) |
---|
| 254 | { |
---|
| 255 | if (first->m[i]!=NULL) |
---|
| 256 | { |
---|
| 257 | if (syz_ring==orig_ring) |
---|
| 258 | temp->m[k] = pCopy(first->m[i]); |
---|
| 259 | else |
---|
[861529] | 260 | temp->m[k] = prCopyR(first->m[i], orig_ring, syz_ring); |
---|
[0f401f] | 261 | q = pOne(); |
---|
| 262 | pSetComp(q,i+1+length); |
---|
| 263 | pSetmComp(q); |
---|
[861529] | 264 | if (flength==0) p_Shift(&(temp->m[k]),1,currRing); |
---|
[0f401f] | 265 | p = temp->m[k]; |
---|
| 266 | while (pNext(p)!=NULL) pIter(p); |
---|
| 267 | pNext(p) = q; |
---|
| 268 | k++; |
---|
| 269 | } |
---|
| 270 | } |
---|
| 271 | for (i=0;i<IDELEMS(second);i++) |
---|
| 272 | { |
---|
| 273 | if (second->m[i]!=NULL) |
---|
| 274 | { |
---|
| 275 | if (syz_ring==orig_ring) |
---|
| 276 | temp->m[k] = pCopy(second->m[i]); |
---|
| 277 | else |
---|
[861529] | 278 | temp->m[k] = prCopyR(second->m[i], orig_ring,currRing); |
---|
| 279 | if (slength==0) p_Shift(&(temp->m[k]),1,currRing); |
---|
[0f401f] | 280 | k++; |
---|
| 281 | } |
---|
| 282 | } |
---|
| 283 | intvec *w=NULL; |
---|
[ac00e2f] | 284 | temp1 = kStd(temp,currRing->qideal,testHomog,&w,NULL,length); |
---|
[0f401f] | 285 | if (w!=NULL) delete w; |
---|
| 286 | idDelete(&temp); |
---|
| 287 | if(syz_ring!=orig_ring) |
---|
| 288 | rChangeCurrRing(orig_ring); |
---|
| 289 | |
---|
| 290 | result = idInit(IDELEMS(temp1),rank); |
---|
| 291 | j = 0; |
---|
| 292 | for (i=0;i<IDELEMS(temp1);i++) |
---|
| 293 | { |
---|
| 294 | if ((temp1->m[i]!=NULL) |
---|
| 295 | && (p_GetComp(temp1->m[i],syz_ring)>length)) |
---|
| 296 | { |
---|
| 297 | if(syz_ring==orig_ring) |
---|
| 298 | { |
---|
| 299 | p = temp1->m[i]; |
---|
| 300 | } |
---|
| 301 | else |
---|
| 302 | { |
---|
[b7cfaf] | 303 | p = prMoveR(temp1->m[i], syz_ring,orig_ring); |
---|
[0f401f] | 304 | } |
---|
| 305 | temp1->m[i]=NULL; |
---|
| 306 | while (p!=NULL) |
---|
| 307 | { |
---|
| 308 | q = pNext(p); |
---|
| 309 | pNext(p) = NULL; |
---|
| 310 | k = pGetComp(p)-1-length; |
---|
| 311 | pSetComp(p,0); |
---|
| 312 | pSetmComp(p); |
---|
| 313 | /* Warning! multiply only from the left! it's very important for Plural */ |
---|
| 314 | result->m[j] = pAdd(result->m[j],pMult(p,pCopy(first->m[k]))); |
---|
| 315 | p = q; |
---|
| 316 | } |
---|
| 317 | j++; |
---|
| 318 | } |
---|
| 319 | } |
---|
| 320 | if(syz_ring!=orig_ring) |
---|
| 321 | { |
---|
| 322 | rChangeCurrRing(syz_ring); |
---|
| 323 | idDelete(&temp1); |
---|
| 324 | rChangeCurrRing(orig_ring); |
---|
[5fe834] | 325 | rDelete(syz_ring); |
---|
[0f401f] | 326 | } |
---|
| 327 | else |
---|
| 328 | { |
---|
| 329 | idDelete(&temp1); |
---|
| 330 | } |
---|
| 331 | |
---|
| 332 | idSkipZeroes(result); |
---|
| 333 | if (TEST_OPT_RETURN_SB) |
---|
| 334 | { |
---|
| 335 | w=NULL; |
---|
[ac00e2f] | 336 | temp1=kStd(result,currRing->qideal,testHomog,&w); |
---|
[0f401f] | 337 | if (w!=NULL) delete w; |
---|
| 338 | idDelete(&result); |
---|
| 339 | idSkipZeroes(temp1); |
---|
| 340 | return temp1; |
---|
| 341 | } |
---|
[ac00e2f] | 342 | else //temp1=kInterRed(result,currRing->qideal); |
---|
[0f401f] | 343 | return result; |
---|
| 344 | } |
---|
| 345 | |
---|
| 346 | /*2 |
---|
| 347 | * ideal/module intersection for a list of objects |
---|
| 348 | * given as 'resolvente' |
---|
| 349 | */ |
---|
| 350 | ideal idMultSect(resolvente arg, int length) |
---|
| 351 | { |
---|
| 352 | int i,j=0,k=0,syzComp,l,maxrk=-1,realrki; |
---|
| 353 | ideal bigmat,tempstd,result; |
---|
| 354 | poly p; |
---|
| 355 | int isIdeal=0; |
---|
| 356 | intvec * w=NULL; |
---|
| 357 | |
---|
| 358 | /* find 0-ideals and max rank -----------------------------------*/ |
---|
| 359 | for (i=0;i<length;i++) |
---|
| 360 | { |
---|
| 361 | if (!idIs0(arg[i])) |
---|
| 362 | { |
---|
[7b25fe] | 363 | realrki=id_RankFreeModule(arg[i],currRing); |
---|
[0f401f] | 364 | k++; |
---|
| 365 | j += IDELEMS(arg[i]); |
---|
| 366 | if (realrki>maxrk) maxrk = realrki; |
---|
| 367 | } |
---|
| 368 | else |
---|
| 369 | { |
---|
| 370 | if (arg[i]!=NULL) |
---|
| 371 | { |
---|
| 372 | return idInit(1,arg[i]->rank); |
---|
| 373 | } |
---|
| 374 | } |
---|
| 375 | } |
---|
| 376 | if (maxrk == 0) |
---|
| 377 | { |
---|
| 378 | isIdeal = 1; |
---|
| 379 | maxrk = 1; |
---|
| 380 | } |
---|
| 381 | /* init -----------------------------------------------------------*/ |
---|
| 382 | j += maxrk; |
---|
| 383 | syzComp = k*maxrk; |
---|
| 384 | |
---|
| 385 | ring orig_ring=currRing; |
---|
[3f07d1] | 386 | ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
[b7cfaf] | 387 | rSetSyzComp(syzComp, syz_ring); |
---|
[0f401f] | 388 | |
---|
| 389 | bigmat = idInit(j,(k+1)*maxrk); |
---|
| 390 | /* create unit matrices ------------------------------------------*/ |
---|
| 391 | for (i=0;i<maxrk;i++) |
---|
| 392 | { |
---|
| 393 | for (j=0;j<=k;j++) |
---|
| 394 | { |
---|
| 395 | p = pOne(); |
---|
| 396 | pSetComp(p,i+1+j*maxrk); |
---|
| 397 | pSetmComp(p); |
---|
| 398 | bigmat->m[i] = pAdd(bigmat->m[i],p); |
---|
| 399 | } |
---|
| 400 | } |
---|
| 401 | /* enter given ideals ------------------------------------------*/ |
---|
| 402 | i = maxrk; |
---|
| 403 | k = 0; |
---|
| 404 | for (j=0;j<length;j++) |
---|
| 405 | { |
---|
| 406 | if (arg[j]!=NULL) |
---|
| 407 | { |
---|
| 408 | for (l=0;l<IDELEMS(arg[j]);l++) |
---|
| 409 | { |
---|
| 410 | if (arg[j]->m[l]!=NULL) |
---|
| 411 | { |
---|
| 412 | if (syz_ring==orig_ring) |
---|
| 413 | bigmat->m[i] = pCopy(arg[j]->m[l]); |
---|
| 414 | else |
---|
[861529] | 415 | bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring,currRing); |
---|
| 416 | p_Shift(&(bigmat->m[i]),k*maxrk+isIdeal,currRing); |
---|
[0f401f] | 417 | i++; |
---|
| 418 | } |
---|
| 419 | } |
---|
| 420 | k++; |
---|
| 421 | } |
---|
| 422 | } |
---|
| 423 | /* std computation --------------------------------------------*/ |
---|
[ac00e2f] | 424 | tempstd = kStd(bigmat,currRing->qideal,testHomog,&w,NULL,syzComp); |
---|
[0f401f] | 425 | if (w!=NULL) delete w; |
---|
| 426 | idDelete(&bigmat); |
---|
| 427 | |
---|
| 428 | if(syz_ring!=orig_ring) |
---|
| 429 | rChangeCurrRing(orig_ring); |
---|
| 430 | |
---|
| 431 | /* interprete result ----------------------------------------*/ |
---|
| 432 | result = idInit(IDELEMS(tempstd),maxrk); |
---|
| 433 | k = 0; |
---|
| 434 | for (j=0;j<IDELEMS(tempstd);j++) |
---|
| 435 | { |
---|
| 436 | if ((tempstd->m[j]!=NULL) && (p_GetComp(tempstd->m[j],syz_ring)>syzComp)) |
---|
| 437 | { |
---|
| 438 | if (syz_ring==orig_ring) |
---|
| 439 | p = pCopy(tempstd->m[j]); |
---|
| 440 | else |
---|
[441a2e] | 441 | p = prCopyR(tempstd->m[j], syz_ring,currRing); |
---|
[861529] | 442 | p_Shift(&p,-syzComp-isIdeal,currRing); |
---|
[0f401f] | 443 | result->m[k] = p; |
---|
| 444 | k++; |
---|
| 445 | } |
---|
| 446 | } |
---|
| 447 | /* clean up ----------------------------------------------------*/ |
---|
| 448 | if(syz_ring!=orig_ring) |
---|
| 449 | rChangeCurrRing(syz_ring); |
---|
| 450 | idDelete(&tempstd); |
---|
| 451 | if(syz_ring!=orig_ring) |
---|
| 452 | { |
---|
| 453 | rChangeCurrRing(orig_ring); |
---|
[5fe834] | 454 | rDelete(syz_ring); |
---|
[0f401f] | 455 | } |
---|
| 456 | idSkipZeroes(result); |
---|
| 457 | return result; |
---|
| 458 | } |
---|
| 459 | |
---|
| 460 | /*2 |
---|
| 461 | *computes syzygies of h1, |
---|
| 462 | *if quot != NULL it computes in the quotient ring modulo "quot" |
---|
| 463 | *works always in a ring with ringorder_s |
---|
| 464 | */ |
---|
| 465 | static ideal idPrepare (ideal h1, tHomog hom, int syzcomp, intvec **w) |
---|
| 466 | { |
---|
| 467 | ideal h2, h3; |
---|
| 468 | int i; |
---|
[bca341] | 469 | int j,k; |
---|
[0f401f] | 470 | poly p,q; |
---|
| 471 | |
---|
| 472 | if (idIs0(h1)) return NULL; |
---|
[7b25fe] | 473 | k = id_RankFreeModule(h1,currRing); |
---|
[0f401f] | 474 | h2=idCopy(h1); |
---|
| 475 | i = IDELEMS(h2)-1; |
---|
| 476 | if (k == 0) |
---|
| 477 | { |
---|
[741464] | 478 | id_Shift(h2,1,currRing); |
---|
[0f401f] | 479 | k = 1; |
---|
| 480 | } |
---|
| 481 | if (syzcomp<k) |
---|
| 482 | { |
---|
| 483 | Warn("syzcomp too low, should be %d instead of %d",k,syzcomp); |
---|
| 484 | syzcomp = k; |
---|
[b7cfaf] | 485 | rSetSyzComp(k,currRing); |
---|
[0f401f] | 486 | } |
---|
| 487 | h2->rank = syzcomp+i+1; |
---|
| 488 | |
---|
| 489 | //if (hom==testHomog) |
---|
| 490 | //{ |
---|
[ac00e2f] | 491 | // if(idHomIdeal(h1,currRing->qideal)) |
---|
[0f401f] | 492 | // { |
---|
| 493 | // hom=TRUE; |
---|
| 494 | // } |
---|
| 495 | //} |
---|
| 496 | |
---|
| 497 | #if MYTEST |
---|
| 498 | #ifdef RDEBUG |
---|
| 499 | Print("Prepare::h2: "); |
---|
| 500 | idPrint(h2); |
---|
| 501 | |
---|
| 502 | for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]); |
---|
| 503 | |
---|
| 504 | #endif |
---|
| 505 | #endif |
---|
| 506 | |
---|
| 507 | for (j=0; j<=i; j++) |
---|
| 508 | { |
---|
| 509 | p = h2->m[j]; |
---|
| 510 | q = pOne(); |
---|
| 511 | pSetComp(q,syzcomp+1+j); |
---|
| 512 | pSetmComp(q); |
---|
| 513 | if (p!=NULL) |
---|
| 514 | { |
---|
| 515 | while (pNext(p)) pIter(p); |
---|
| 516 | p->next = q; |
---|
| 517 | } |
---|
| 518 | else |
---|
| 519 | h2->m[j]=q; |
---|
| 520 | } |
---|
| 521 | |
---|
| 522 | #ifdef PDEBUG |
---|
| 523 | for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]); |
---|
| 524 | |
---|
| 525 | #if MYTEST |
---|
| 526 | #ifdef RDEBUG |
---|
| 527 | Print("Prepare::Input: "); |
---|
| 528 | idPrint(h2); |
---|
| 529 | |
---|
| 530 | Print("Prepare::currQuotient: "); |
---|
[ac00e2f] | 531 | idPrint(currRing->qideal); |
---|
[0f401f] | 532 | #endif |
---|
| 533 | #endif |
---|
| 534 | |
---|
| 535 | #endif |
---|
| 536 | |
---|
| 537 | idTest(h2); |
---|
| 538 | |
---|
[ac00e2f] | 539 | h3 = kStd(h2,currRing->qideal,hom,w,NULL,syzcomp); |
---|
[0f401f] | 540 | |
---|
| 541 | #if MYTEST |
---|
| 542 | #ifdef RDEBUG |
---|
| 543 | Print("Prepare::Output: "); |
---|
| 544 | idPrint(h3); |
---|
| 545 | for(j=0;j<IDELEMS(h2);j++) pTest(h3->m[j]); |
---|
| 546 | #endif |
---|
| 547 | #endif |
---|
| 548 | |
---|
| 549 | |
---|
| 550 | idDelete(&h2); |
---|
| 551 | return h3; |
---|
| 552 | } |
---|
| 553 | |
---|
| 554 | /*2 |
---|
| 555 | * compute the syzygies of h1 in R/quot, |
---|
| 556 | * weights of components are in w |
---|
| 557 | * if setRegularity, return the regularity in deg |
---|
| 558 | * do not change h1, w |
---|
| 559 | */ |
---|
| 560 | ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp, |
---|
| 561 | BOOLEAN setRegularity, int *deg) |
---|
| 562 | { |
---|
| 563 | ideal s_h1; |
---|
| 564 | int j, k, length=0,reg; |
---|
| 565 | BOOLEAN isMonomial=TRUE; |
---|
| 566 | int ii, idElemens_h1; |
---|
| 567 | |
---|
| 568 | assume(h1 != NULL); |
---|
| 569 | |
---|
| 570 | idElemens_h1=IDELEMS(h1); |
---|
| 571 | #ifdef PDEBUG |
---|
| 572 | for(ii=0;ii<idElemens_h1 /*IDELEMS(h1)*/;ii++) pTest(h1->m[ii]); |
---|
| 573 | #endif |
---|
| 574 | if (idIs0(h1)) |
---|
| 575 | { |
---|
| 576 | ideal result=idFreeModule(idElemens_h1/*IDELEMS(h1)*/); |
---|
| 577 | return result; |
---|
| 578 | } |
---|
[7b25fe] | 579 | int slength=(int)id_RankFreeModule(h1,currRing); |
---|
| 580 | k=si_max(1,slength /*id_RankFreeModule(h1)*/); |
---|
[0f401f] | 581 | |
---|
| 582 | assume(currRing != NULL); |
---|
| 583 | ring orig_ring=currRing; |
---|
[3f07d1] | 584 | ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
[0f401f] | 585 | |
---|
| 586 | if (setSyzComp) |
---|
[b7cfaf] | 587 | rSetSyzComp(k,syz_ring); |
---|
[0f401f] | 588 | |
---|
| 589 | if (orig_ring != syz_ring) |
---|
| 590 | { |
---|
[441a2e] | 591 | s_h1=idrCopyR_NoSort(h1,orig_ring,syz_ring); |
---|
[0f401f] | 592 | } |
---|
| 593 | else |
---|
| 594 | { |
---|
| 595 | s_h1 = h1; |
---|
| 596 | } |
---|
| 597 | |
---|
| 598 | idTest(s_h1); |
---|
| 599 | |
---|
| 600 | ideal s_h3=idPrepare(s_h1,h,k,w); // main (syz) GB computation |
---|
| 601 | |
---|
| 602 | if (s_h3==NULL) |
---|
| 603 | { |
---|
| 604 | return idFreeModule( idElemens_h1 /*IDELEMS(h1)*/); |
---|
| 605 | } |
---|
| 606 | |
---|
| 607 | if (orig_ring != syz_ring) |
---|
| 608 | { |
---|
| 609 | idDelete(&s_h1); |
---|
| 610 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
| 611 | { |
---|
| 612 | if (s_h3->m[j] != NULL) |
---|
| 613 | { |
---|
| 614 | if (p_MinComp(s_h3->m[j],syz_ring) > k) |
---|
[f9591a] | 615 | p_Shift(&s_h3->m[j], -k,syz_ring); |
---|
[0f401f] | 616 | else |
---|
[f9591a] | 617 | p_Delete(&s_h3->m[j],syz_ring); |
---|
[0f401f] | 618 | } |
---|
| 619 | } |
---|
| 620 | idSkipZeroes(s_h3); |
---|
| 621 | s_h3->rank -= k; |
---|
| 622 | rChangeCurrRing(orig_ring); |
---|
[b7cfaf] | 623 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring); |
---|
[5fe834] | 624 | rDelete(syz_ring); |
---|
[0f401f] | 625 | #ifdef HAVE_PLURAL |
---|
[6a4ba5f] | 626 | if (rIsPluralRing(orig_ring)) |
---|
[0f401f] | 627 | { |
---|
[6a4ba5f] | 628 | id_DelMultiples(s_h3,orig_ring); |
---|
[0f401f] | 629 | idSkipZeroes(s_h3); |
---|
| 630 | } |
---|
| 631 | #endif |
---|
| 632 | idTest(s_h3); |
---|
| 633 | return s_h3; |
---|
| 634 | } |
---|
| 635 | |
---|
| 636 | ideal e = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
| 637 | |
---|
| 638 | for (j=IDELEMS(s_h3)-1; j>=0; j--) |
---|
| 639 | { |
---|
| 640 | if (s_h3->m[j] != NULL) |
---|
| 641 | { |
---|
| 642 | if (p_MinComp(s_h3->m[j],syz_ring) <= k) |
---|
| 643 | { |
---|
| 644 | e->m[j] = s_h3->m[j]; |
---|
| 645 | isMonomial=isMonomial && (pNext(s_h3->m[j])==NULL); |
---|
[f9591a] | 646 | p_Delete(&pNext(s_h3->m[j]),syz_ring); |
---|
[0f401f] | 647 | s_h3->m[j] = NULL; |
---|
| 648 | } |
---|
| 649 | } |
---|
| 650 | } |
---|
| 651 | |
---|
| 652 | idSkipZeroes(s_h3); |
---|
| 653 | idSkipZeroes(e); |
---|
| 654 | |
---|
| 655 | if ((deg != NULL) |
---|
| 656 | && (!isMonomial) |
---|
| 657 | && (!TEST_OPT_NOTREGULARITY) |
---|
| 658 | && (setRegularity) |
---|
| 659 | && (h==isHomog) |
---|
| 660 | && (!rIsPluralRing(currRing)) |
---|
[99ab66] | 661 | #ifdef HAVE_RINGS |
---|
[f230e1c] | 662 | && (!rField_is_Ring(currRing)) |
---|
[99ab66] | 663 | #endif |
---|
[0f401f] | 664 | ) |
---|
| 665 | { |
---|
[1da2a13] | 666 | ring dp_C_ring = rAssure_dp_C(syz_ring); // will do rChangeCurrRing later |
---|
[0f401f] | 667 | if (dp_C_ring != syz_ring) |
---|
[441a2e] | 668 | { |
---|
| 669 | rChangeCurrRing(dp_C_ring); |
---|
[b7cfaf] | 670 | e = idrMoveR_NoSort(e, syz_ring, dp_C_ring); |
---|
[441a2e] | 671 | } |
---|
[0f401f] | 672 | resolvente res = sySchreyerResolvente(e,-1,&length,TRUE, TRUE); |
---|
| 673 | intvec * dummy = syBetti(res,length,®, *w); |
---|
| 674 | *deg = reg+2; |
---|
| 675 | delete dummy; |
---|
| 676 | for (j=0;j<length;j++) |
---|
| 677 | { |
---|
| 678 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
| 679 | } |
---|
| 680 | omFreeSize((ADDRESS)res,length*sizeof(ideal)); |
---|
| 681 | idDelete(&e); |
---|
| 682 | if (dp_C_ring != syz_ring) |
---|
| 683 | { |
---|
| 684 | rChangeCurrRing(syz_ring); |
---|
[5fe834] | 685 | rDelete(dp_C_ring); |
---|
[0f401f] | 686 | } |
---|
| 687 | } |
---|
| 688 | else |
---|
| 689 | { |
---|
| 690 | idDelete(&e); |
---|
| 691 | } |
---|
| 692 | idTest(s_h3); |
---|
[ac00e2f] | 693 | if (currRing->qideal != NULL) |
---|
[0f401f] | 694 | { |
---|
[ac00e2f] | 695 | ideal ts_h3=kStd(s_h3,currRing->qideal,h,w); |
---|
[0f401f] | 696 | idDelete(&s_h3); |
---|
| 697 | s_h3 = ts_h3; |
---|
| 698 | } |
---|
| 699 | return s_h3; |
---|
| 700 | } |
---|
| 701 | |
---|
| 702 | /*2 |
---|
| 703 | */ |
---|
| 704 | ideal idXXX (ideal h1, int k) |
---|
| 705 | { |
---|
| 706 | ideal s_h1; |
---|
| 707 | intvec *w=NULL; |
---|
| 708 | |
---|
| 709 | assume(currRing != NULL); |
---|
| 710 | ring orig_ring=currRing; |
---|
[3f07d1] | 711 | ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
[0f401f] | 712 | |
---|
[b7cfaf] | 713 | rSetSyzComp(k,syz_ring); |
---|
[0f401f] | 714 | |
---|
| 715 | if (orig_ring != syz_ring) |
---|
| 716 | { |
---|
[441a2e] | 717 | s_h1=idrCopyR_NoSort(h1,orig_ring, syz_ring); |
---|
[0f401f] | 718 | } |
---|
| 719 | else |
---|
| 720 | { |
---|
| 721 | s_h1 = h1; |
---|
| 722 | } |
---|
| 723 | |
---|
| 724 | ideal s_h3=kStd(s_h1,NULL,testHomog,&w,NULL,k); |
---|
| 725 | |
---|
| 726 | if (s_h3==NULL) |
---|
| 727 | { |
---|
| 728 | return idFreeModule(IDELEMS(h1)); |
---|
| 729 | } |
---|
| 730 | |
---|
| 731 | if (orig_ring != syz_ring) |
---|
| 732 | { |
---|
| 733 | idDelete(&s_h1); |
---|
| 734 | idSkipZeroes(s_h3); |
---|
| 735 | rChangeCurrRing(orig_ring); |
---|
[b7cfaf] | 736 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring); |
---|
[5fe834] | 737 | rDelete(syz_ring); |
---|
[0f401f] | 738 | idTest(s_h3); |
---|
| 739 | return s_h3; |
---|
| 740 | } |
---|
| 741 | |
---|
| 742 | idSkipZeroes(s_h3); |
---|
| 743 | idTest(s_h3); |
---|
| 744 | return s_h3; |
---|
| 745 | } |
---|
| 746 | |
---|
| 747 | /* |
---|
| 748 | *computes a standard basis for h1 and stores the transformation matrix |
---|
| 749 | * in ma |
---|
| 750 | */ |
---|
| 751 | ideal idLiftStd (ideal h1, matrix* ma, tHomog hi, ideal * syz) |
---|
| 752 | { |
---|
[30664c] | 753 | int i, j, t, inputIsIdeal=id_RankFreeModule(h1,currRing); |
---|
| 754 | long k; |
---|
[bca341] | 755 | poly p=NULL, q; |
---|
[0f401f] | 756 | intvec *w=NULL; |
---|
| 757 | |
---|
| 758 | idDelete((ideal*)ma); |
---|
| 759 | BOOLEAN lift3=FALSE; |
---|
| 760 | if (syz!=NULL) { lift3=TRUE; idDelete(syz); } |
---|
| 761 | if (idIs0(h1)) |
---|
| 762 | { |
---|
| 763 | *ma=mpNew(1,0); |
---|
| 764 | if (lift3) |
---|
| 765 | { |
---|
| 766 | *syz=idFreeModule(IDELEMS(h1)); |
---|
| 767 | } |
---|
| 768 | return idInit(1,h1->rank); |
---|
| 769 | } |
---|
| 770 | |
---|
[d30a399] | 771 | BITSET save2; |
---|
| 772 | SI_SAVE_OPT2(save2); |
---|
[0f401f] | 773 | |
---|
[30664c] | 774 | k=si_max((long)1,id_RankFreeModule(h1,currRing)); |
---|
[0f401f] | 775 | |
---|
[d30a399] | 776 | if ((k==1) && (!lift3)) si_opt_2 |=Sy_bit(V_IDLIFT); |
---|
[0f401f] | 777 | |
---|
| 778 | ring orig_ring = currRing; |
---|
[3f07d1] | 779 | ring syz_ring = rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
[b7cfaf] | 780 | rSetSyzComp(k,syz_ring); |
---|
[0f401f] | 781 | |
---|
| 782 | ideal s_h1=h1; |
---|
| 783 | |
---|
| 784 | if (orig_ring != syz_ring) |
---|
[441a2e] | 785 | s_h1 = idrCopyR_NoSort(h1,orig_ring,syz_ring); |
---|
[0f401f] | 786 | else |
---|
| 787 | s_h1 = h1; |
---|
| 788 | |
---|
| 789 | ideal s_h3=idPrepare(s_h1,hi,k,&w); // main (syz) GB computation |
---|
| 790 | |
---|
| 791 | ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
| 792 | |
---|
| 793 | if (lift3) (*syz)=idInit(IDELEMS(s_h3),IDELEMS(h1)); |
---|
| 794 | |
---|
| 795 | if (w!=NULL) delete w; |
---|
| 796 | i = 0; |
---|
| 797 | |
---|
| 798 | // now sort the result, SB : leave in s_h3 |
---|
| 799 | // T: put in s_h2 |
---|
| 800 | // syz: put in *syz |
---|
| 801 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
| 802 | { |
---|
| 803 | if (s_h3->m[j] != NULL) |
---|
| 804 | { |
---|
| 805 | //if (p_MinComp(s_h3->m[j],syz_ring) <= k) |
---|
| 806 | if (pGetComp(s_h3->m[j]) <= k) // syz_ring == currRing |
---|
| 807 | { |
---|
| 808 | i++; |
---|
| 809 | q = s_h3->m[j]; |
---|
| 810 | while (pNext(q) != NULL) |
---|
| 811 | { |
---|
| 812 | if (pGetComp(pNext(q)) > k) |
---|
| 813 | { |
---|
| 814 | s_h2->m[j] = pNext(q); |
---|
| 815 | pNext(q) = NULL; |
---|
| 816 | } |
---|
| 817 | else |
---|
| 818 | { |
---|
| 819 | pIter(q); |
---|
| 820 | } |
---|
| 821 | } |
---|
[861529] | 822 | if (!inputIsIdeal) p_Shift(&(s_h3->m[j]), -1,currRing); |
---|
[0f401f] | 823 | } |
---|
| 824 | else |
---|
| 825 | { |
---|
| 826 | // we a syzygy here: |
---|
| 827 | if (lift3) |
---|
| 828 | { |
---|
[861529] | 829 | p_Shift(&s_h3->m[j], -k,currRing); |
---|
[0f401f] | 830 | (*syz)->m[j]=s_h3->m[j]; |
---|
| 831 | s_h3->m[j]=NULL; |
---|
| 832 | } |
---|
| 833 | else |
---|
[f9591a] | 834 | p_Delete(&(s_h3->m[j]),currRing); |
---|
[0f401f] | 835 | } |
---|
| 836 | } |
---|
| 837 | } |
---|
| 838 | idSkipZeroes(s_h3); |
---|
| 839 | //extern char * iiStringMatrix(matrix im, int dim,char ch); |
---|
| 840 | //PrintS("SB: ----------------------------------------\n"); |
---|
| 841 | //PrintS(iiStringMatrix((matrix)s_h3,k,'\n')); |
---|
| 842 | //PrintLn(); |
---|
| 843 | //PrintS("T: ----------------------------------------\n"); |
---|
| 844 | //PrintS(iiStringMatrix((matrix)s_h2,h1->rank,'\n')); |
---|
| 845 | //PrintLn(); |
---|
| 846 | |
---|
| 847 | if (lift3) idSkipZeroes(*syz); |
---|
| 848 | |
---|
| 849 | j = IDELEMS(s_h1); |
---|
| 850 | |
---|
| 851 | |
---|
| 852 | if (syz_ring!=orig_ring) |
---|
| 853 | { |
---|
| 854 | idDelete(&s_h1); |
---|
| 855 | rChangeCurrRing(orig_ring); |
---|
| 856 | } |
---|
| 857 | |
---|
| 858 | *ma = mpNew(j,i); |
---|
| 859 | |
---|
| 860 | i = 1; |
---|
| 861 | for (j=0; j<IDELEMS(s_h2); j++) |
---|
| 862 | { |
---|
| 863 | if (s_h2->m[j] != NULL) |
---|
| 864 | { |
---|
[b7cfaf] | 865 | q = prMoveR( s_h2->m[j], syz_ring,orig_ring); |
---|
[0f401f] | 866 | s_h2->m[j] = NULL; |
---|
| 867 | |
---|
[35edb5] | 868 | if (q!=NULL) |
---|
[0f401f] | 869 | { |
---|
[35edb5] | 870 | q=pReverse(q); |
---|
| 871 | while (q != NULL) |
---|
| 872 | { |
---|
| 873 | p = q; |
---|
| 874 | pIter(q); |
---|
| 875 | pNext(p) = NULL; |
---|
| 876 | t=pGetComp(p); |
---|
| 877 | pSetComp(p,0); |
---|
| 878 | pSetmComp(p); |
---|
| 879 | MATELEM(*ma,t-k,i) = pAdd(MATELEM(*ma,t-k,i),p); |
---|
| 880 | } |
---|
[0f401f] | 881 | } |
---|
| 882 | i++; |
---|
| 883 | } |
---|
| 884 | } |
---|
| 885 | idDelete(&s_h2); |
---|
| 886 | |
---|
| 887 | for (i=0; i<IDELEMS(s_h3); i++) |
---|
| 888 | { |
---|
[b7cfaf] | 889 | s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], syz_ring,orig_ring); |
---|
[0f401f] | 890 | } |
---|
| 891 | if (lift3) |
---|
| 892 | { |
---|
| 893 | for (i=0; i<IDELEMS(*syz); i++) |
---|
| 894 | { |
---|
[b7cfaf] | 895 | (*syz)->m[i] = prMoveR_NoSort((*syz)->m[i], syz_ring,orig_ring); |
---|
[0f401f] | 896 | } |
---|
| 897 | } |
---|
| 898 | |
---|
[5fe834] | 899 | if (syz_ring!=orig_ring) rDelete(syz_ring); |
---|
[d30a399] | 900 | SI_RESTORE_OPT2(save2); |
---|
[0f401f] | 901 | return s_h3; |
---|
| 902 | } |
---|
| 903 | |
---|
| 904 | static void idPrepareStd(ideal s_temp, int k) |
---|
| 905 | { |
---|
[7b25fe] | 906 | int j,rk=id_RankFreeModule(s_temp,currRing); |
---|
[0f401f] | 907 | poly p,q; |
---|
| 908 | |
---|
| 909 | if (rk == 0) |
---|
| 910 | { |
---|
| 911 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
| 912 | { |
---|
| 913 | if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1); |
---|
| 914 | } |
---|
| 915 | k = si_max(k,1); |
---|
| 916 | } |
---|
| 917 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
| 918 | { |
---|
| 919 | if (s_temp->m[j]!=NULL) |
---|
| 920 | { |
---|
| 921 | p = s_temp->m[j]; |
---|
| 922 | q = pOne(); |
---|
[ec89bb4] | 923 | //pGetCoeff(q)=nInpNeg(pGetCoeff(q)); //set q to -1 |
---|
[0f401f] | 924 | pSetComp(q,k+1+j); |
---|
| 925 | pSetmComp(q); |
---|
| 926 | while (pNext(p)) pIter(p); |
---|
| 927 | pNext(p) = q; |
---|
| 928 | } |
---|
| 929 | } |
---|
[750754] | 930 | s_temp->rank += k; |
---|
[0f401f] | 931 | } |
---|
| 932 | |
---|
| 933 | /*2 |
---|
| 934 | *computes a representation of the generators of submod with respect to those |
---|
| 935 | * of mod |
---|
| 936 | */ |
---|
| 937 | |
---|
| 938 | ideal idLift(ideal mod, ideal submod,ideal *rest, BOOLEAN goodShape, |
---|
| 939 | BOOLEAN isSB, BOOLEAN divide, matrix *unit) |
---|
| 940 | { |
---|
[6909cfb] | 941 | int lsmod =id_RankFreeModule(submod,currRing), j, k; |
---|
[0f401f] | 942 | int comps_to_add=0; |
---|
| 943 | poly p; |
---|
| 944 | |
---|
| 945 | if (idIs0(submod)) |
---|
| 946 | { |
---|
| 947 | if (unit!=NULL) |
---|
| 948 | { |
---|
| 949 | *unit=mpNew(1,1); |
---|
| 950 | MATELEM(*unit,1,1)=pOne(); |
---|
| 951 | } |
---|
| 952 | if (rest!=NULL) |
---|
| 953 | { |
---|
| 954 | *rest=idInit(1,mod->rank); |
---|
| 955 | } |
---|
| 956 | return idInit(1,mod->rank); |
---|
| 957 | } |
---|
| 958 | if (idIs0(mod)) /* and not idIs0(submod) */ |
---|
| 959 | { |
---|
| 960 | WerrorS("2nd module does not lie in the first"); |
---|
[a5d181c] | 961 | return NULL; |
---|
[0f401f] | 962 | } |
---|
| 963 | if (unit!=NULL) |
---|
| 964 | { |
---|
| 965 | comps_to_add = IDELEMS(submod); |
---|
| 966 | while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL)) |
---|
| 967 | comps_to_add--; |
---|
| 968 | } |
---|
[7b25fe] | 969 | k=si_max(id_RankFreeModule(mod,currRing),id_RankFreeModule(submod,currRing)); |
---|
[0f401f] | 970 | if ((k!=0) && (lsmod==0)) lsmod=1; |
---|
| 971 | k=si_max(k,(int)mod->rank); |
---|
| 972 | if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; } |
---|
| 973 | |
---|
| 974 | ring orig_ring=currRing; |
---|
[3f07d1] | 975 | ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
[b7cfaf] | 976 | rSetSyzComp(k,syz_ring); |
---|
[0f401f] | 977 | |
---|
| 978 | ideal s_mod, s_temp; |
---|
| 979 | if (orig_ring != syz_ring) |
---|
| 980 | { |
---|
[441a2e] | 981 | s_mod = idrCopyR_NoSort(mod,orig_ring,syz_ring); |
---|
| 982 | s_temp = idrCopyR_NoSort(submod,orig_ring,syz_ring); |
---|
[0f401f] | 983 | } |
---|
| 984 | else |
---|
| 985 | { |
---|
| 986 | s_mod = mod; |
---|
| 987 | s_temp = idCopy(submod); |
---|
| 988 | } |
---|
| 989 | ideal s_h3; |
---|
| 990 | if (isSB) |
---|
| 991 | { |
---|
| 992 | s_h3 = idCopy(s_mod); |
---|
| 993 | idPrepareStd(s_h3, k+comps_to_add); |
---|
| 994 | } |
---|
| 995 | else |
---|
| 996 | { |
---|
| 997 | s_h3 = idPrepare(s_mod,(tHomog)FALSE,k+comps_to_add,NULL); |
---|
| 998 | } |
---|
| 999 | if (!goodShape) |
---|
| 1000 | { |
---|
| 1001 | for (j=0;j<IDELEMS(s_h3);j++) |
---|
| 1002 | { |
---|
| 1003 | if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k)) |
---|
[f9591a] | 1004 | p_Delete(&(s_h3->m[j]),currRing); |
---|
[0f401f] | 1005 | } |
---|
| 1006 | } |
---|
| 1007 | idSkipZeroes(s_h3); |
---|
| 1008 | if (lsmod==0) |
---|
| 1009 | { |
---|
[741464] | 1010 | id_Shift(s_temp,1,currRing); |
---|
[0f401f] | 1011 | } |
---|
| 1012 | if (unit!=NULL) |
---|
| 1013 | { |
---|
| 1014 | for(j = 0;j<comps_to_add;j++) |
---|
| 1015 | { |
---|
| 1016 | p = s_temp->m[j]; |
---|
| 1017 | if (p!=NULL) |
---|
| 1018 | { |
---|
| 1019 | while (pNext(p)!=NULL) pIter(p); |
---|
| 1020 | pNext(p) = pOne(); |
---|
| 1021 | pIter(p); |
---|
| 1022 | pSetComp(p,1+j+k); |
---|
| 1023 | pSetmComp(p); |
---|
| 1024 | p = pNeg(p); |
---|
| 1025 | } |
---|
| 1026 | } |
---|
[750754] | 1027 | s_temp->rank += k; |
---|
[0f401f] | 1028 | } |
---|
[ac00e2f] | 1029 | ideal s_result = kNF(s_h3,currRing->qideal,s_temp,k); |
---|
[0f401f] | 1030 | s_result->rank = s_h3->rank; |
---|
| 1031 | ideal s_rest = idInit(IDELEMS(s_result),k); |
---|
| 1032 | idDelete(&s_h3); |
---|
| 1033 | idDelete(&s_temp); |
---|
| 1034 | |
---|
| 1035 | for (j=0;j<IDELEMS(s_result);j++) |
---|
| 1036 | { |
---|
| 1037 | if (s_result->m[j]!=NULL) |
---|
| 1038 | { |
---|
| 1039 | if (pGetComp(s_result->m[j])<=k) |
---|
| 1040 | { |
---|
| 1041 | if (!divide) |
---|
| 1042 | { |
---|
| 1043 | if (isSB) |
---|
| 1044 | { |
---|
| 1045 | WarnS("first module not a standardbasis\n" |
---|
| 1046 | "// ** or second not a proper submodule"); |
---|
| 1047 | } |
---|
| 1048 | else |
---|
| 1049 | WerrorS("2nd module does not lie in the first"); |
---|
| 1050 | idDelete(&s_result); |
---|
| 1051 | idDelete(&s_rest); |
---|
| 1052 | s_result=idInit(IDELEMS(submod),submod->rank); |
---|
| 1053 | break; |
---|
| 1054 | } |
---|
| 1055 | else |
---|
| 1056 | { |
---|
| 1057 | p = s_rest->m[j] = s_result->m[j]; |
---|
| 1058 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p); |
---|
| 1059 | s_result->m[j] = pNext(p); |
---|
| 1060 | pNext(p) = NULL; |
---|
| 1061 | } |
---|
| 1062 | } |
---|
[861529] | 1063 | p_Shift(&(s_result->m[j]),-k,currRing); |
---|
[0f401f] | 1064 | pNeg(s_result->m[j]); |
---|
| 1065 | } |
---|
| 1066 | } |
---|
[9e8bfa] | 1067 | if ((lsmod==0) && (s_rest!=NULL)) |
---|
[0f401f] | 1068 | { |
---|
| 1069 | for (j=IDELEMS(s_rest);j>0;j--) |
---|
| 1070 | { |
---|
| 1071 | if (s_rest->m[j-1]!=NULL) |
---|
| 1072 | { |
---|
[861529] | 1073 | p_Shift(&(s_rest->m[j-1]),-1,currRing); |
---|
[0f401f] | 1074 | s_rest->m[j-1] = s_rest->m[j-1]; |
---|
| 1075 | } |
---|
| 1076 | } |
---|
| 1077 | } |
---|
| 1078 | if(syz_ring!=orig_ring) |
---|
| 1079 | { |
---|
| 1080 | idDelete(&s_mod); |
---|
| 1081 | rChangeCurrRing(orig_ring); |
---|
[b7cfaf] | 1082 | s_result = idrMoveR_NoSort(s_result, syz_ring, orig_ring); |
---|
| 1083 | s_rest = idrMoveR_NoSort(s_rest, syz_ring, orig_ring); |
---|
[5fe834] | 1084 | rDelete(syz_ring); |
---|
[0f401f] | 1085 | } |
---|
| 1086 | if (rest!=NULL) |
---|
| 1087 | *rest = s_rest; |
---|
| 1088 | else |
---|
| 1089 | idDelete(&s_rest); |
---|
| 1090 | //idPrint(s_result); |
---|
| 1091 | if (unit!=NULL) |
---|
| 1092 | { |
---|
| 1093 | *unit=mpNew(comps_to_add,comps_to_add); |
---|
| 1094 | int i; |
---|
| 1095 | for(i=0;i<IDELEMS(s_result);i++) |
---|
| 1096 | { |
---|
| 1097 | poly p=s_result->m[i]; |
---|
| 1098 | poly q=NULL; |
---|
| 1099 | while(p!=NULL) |
---|
| 1100 | { |
---|
| 1101 | if(pGetComp(p)<=comps_to_add) |
---|
| 1102 | { |
---|
| 1103 | pSetComp(p,0); |
---|
| 1104 | if (q!=NULL) |
---|
| 1105 | { |
---|
| 1106 | pNext(q)=pNext(p); |
---|
| 1107 | } |
---|
| 1108 | else |
---|
| 1109 | { |
---|
| 1110 | pIter(s_result->m[i]); |
---|
| 1111 | } |
---|
| 1112 | pNext(p)=NULL; |
---|
| 1113 | MATELEM(*unit,i+1,i+1)=pAdd(MATELEM(*unit,i+1,i+1),p); |
---|
| 1114 | if(q!=NULL) p=pNext(q); |
---|
| 1115 | else p=s_result->m[i]; |
---|
| 1116 | } |
---|
| 1117 | else |
---|
| 1118 | { |
---|
| 1119 | q=p; |
---|
| 1120 | pIter(p); |
---|
| 1121 | } |
---|
| 1122 | } |
---|
[861529] | 1123 | p_Shift(&s_result->m[i],-comps_to_add,currRing); |
---|
[0f401f] | 1124 | } |
---|
| 1125 | } |
---|
| 1126 | return s_result; |
---|
| 1127 | } |
---|
| 1128 | |
---|
| 1129 | /*2 |
---|
| 1130 | *computes division of P by Q with remainder up to (w-weighted) degree n |
---|
| 1131 | *P, Q, and w are not changed |
---|
| 1132 | */ |
---|
| 1133 | void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R,short *w) |
---|
| 1134 | { |
---|
| 1135 | long N=0; |
---|
| 1136 | int i; |
---|
| 1137 | for(i=IDELEMS(Q)-1;i>=0;i--) |
---|
| 1138 | if(w==NULL) |
---|
[31f1850] | 1139 | N=si_max(N,p_Deg(Q->m[i],currRing)); |
---|
[0f401f] | 1140 | else |
---|
[7415540] | 1141 | N=si_max(N,p_DegW(Q->m[i],w,currRing)); |
---|
[0f401f] | 1142 | N+=n; |
---|
| 1143 | |
---|
| 1144 | T=mpNew(IDELEMS(Q),IDELEMS(P)); |
---|
| 1145 | R=idInit(IDELEMS(P),P->rank); |
---|
| 1146 | |
---|
| 1147 | for(i=IDELEMS(P)-1;i>=0;i--) |
---|
| 1148 | { |
---|
| 1149 | poly p; |
---|
| 1150 | if(w==NULL) |
---|
| 1151 | p=ppJet(P->m[i],N); |
---|
| 1152 | else |
---|
| 1153 | p=ppJetW(P->m[i],N,w); |
---|
| 1154 | |
---|
| 1155 | int j=IDELEMS(Q)-1; |
---|
| 1156 | while(p!=NULL) |
---|
| 1157 | { |
---|
| 1158 | if(pDivisibleBy(Q->m[j],p)) |
---|
| 1159 | { |
---|
[441a2e] | 1160 | poly p0=p_DivideM(pHead(p),pHead(Q->m[j]),currRing); |
---|
[0f401f] | 1161 | if(w==NULL) |
---|
| 1162 | p=pJet(pSub(p,ppMult_mm(Q->m[j],p0)),N); |
---|
| 1163 | else |
---|
| 1164 | p=pJetW(pSub(p,ppMult_mm(Q->m[j],p0)),N,w); |
---|
| 1165 | pNormalize(p); |
---|
[7415540] | 1166 | if(((w==NULL)&&(p_Deg(p0,currRing)>n))||((w!=NULL)&&(p_DegW(p0,w,currRing)>n))) |
---|
[f9591a] | 1167 | p_Delete(&p0,currRing); |
---|
[0f401f] | 1168 | else |
---|
| 1169 | MATELEM(T,j+1,i+1)=pAdd(MATELEM(T,j+1,i+1),p0); |
---|
| 1170 | j=IDELEMS(Q)-1; |
---|
| 1171 | } |
---|
| 1172 | else |
---|
| 1173 | { |
---|
| 1174 | if(j==0) |
---|
| 1175 | { |
---|
| 1176 | poly p0=p; |
---|
| 1177 | pIter(p); |
---|
| 1178 | pNext(p0)=NULL; |
---|
[31f1850] | 1179 | if(((w==NULL)&&(p_Deg(p0,currRing)>n)) |
---|
[7415540] | 1180 | ||((w!=NULL)&&(p_DegW(p0,w,currRing)>n))) |
---|
[f9591a] | 1181 | p_Delete(&p0,currRing); |
---|
[0f401f] | 1182 | else |
---|
| 1183 | R->m[i]=pAdd(R->m[i],p0); |
---|
| 1184 | j=IDELEMS(Q)-1; |
---|
| 1185 | } |
---|
| 1186 | else |
---|
| 1187 | j--; |
---|
| 1188 | } |
---|
| 1189 | } |
---|
| 1190 | } |
---|
| 1191 | } |
---|
| 1192 | |
---|
| 1193 | /*2 |
---|
| 1194 | *computes the quotient of h1,h2 : internal routine for idQuot |
---|
| 1195 | *BEWARE: the returned ideals may contain incorrectly ordered polys ! |
---|
| 1196 | * |
---|
| 1197 | */ |
---|
[5b45a4] | 1198 | static ideal idInitializeQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax) |
---|
[0f401f] | 1199 | { |
---|
[5b45a4] | 1200 | idTest(h1); |
---|
| 1201 | idTest(h2); |
---|
[fea494] | 1202 | |
---|
[0f401f] | 1203 | ideal temph1; |
---|
| 1204 | poly p,q = NULL; |
---|
| 1205 | int i,l,ll,k,kkk,kmax; |
---|
| 1206 | int j = 0; |
---|
[7b25fe] | 1207 | int k1 = id_RankFreeModule(h1,currRing); |
---|
| 1208 | int k2 = id_RankFreeModule(h2,currRing); |
---|
[0f401f] | 1209 | tHomog hom=isNotHomog; |
---|
| 1210 | k=si_max(k1,k2); |
---|
| 1211 | if (k==0) |
---|
| 1212 | k = 1; |
---|
| 1213 | if ((k2==0) && (k>1)) *addOnlyOne = FALSE; |
---|
| 1214 | intvec * weights; |
---|
[ac00e2f] | 1215 | hom = (tHomog)idHomModule(h1,currRing->qideal,&weights); |
---|
[a9c298] | 1216 | if /**addOnlyOne &&*/ (/*(*/ !h1IsStb /*)*/) |
---|
[ac00e2f] | 1217 | temph1 = kStd(h1,currRing->qideal,hom,&weights,NULL); |
---|
[0f401f] | 1218 | else |
---|
| 1219 | temph1 = idCopy(h1); |
---|
| 1220 | if (weights!=NULL) delete weights; |
---|
| 1221 | idTest(temph1); |
---|
| 1222 | /*--- making a single vector from h2 ---------------------*/ |
---|
| 1223 | for (i=0; i<IDELEMS(h2); i++) |
---|
| 1224 | { |
---|
| 1225 | if (h2->m[i] != NULL) |
---|
| 1226 | { |
---|
| 1227 | p = pCopy(h2->m[i]); |
---|
| 1228 | if (k2 == 0) |
---|
[861529] | 1229 | p_Shift(&p,j*k+1,currRing); |
---|
[0f401f] | 1230 | else |
---|
[861529] | 1231 | p_Shift(&p,j*k,currRing); |
---|
[0f401f] | 1232 | q = pAdd(q,p); |
---|
| 1233 | j++; |
---|
| 1234 | } |
---|
| 1235 | } |
---|
| 1236 | *kkmax = kmax = j*k+1; |
---|
| 1237 | /*--- adding a monomial for the result (syzygy) ----------*/ |
---|
| 1238 | p = q; |
---|
| 1239 | while (pNext(p)!=NULL) pIter(p); |
---|
| 1240 | pNext(p) = pOne(); |
---|
| 1241 | pIter(p); |
---|
| 1242 | pSetComp(p,kmax); |
---|
| 1243 | pSetmComp(p); |
---|
| 1244 | /*--- constructing the big matrix ------------------------*/ |
---|
| 1245 | ideal h4 = idInit(16,kmax+k-1); |
---|
| 1246 | h4->m[0] = q; |
---|
| 1247 | if (k2 == 0) |
---|
| 1248 | { |
---|
| 1249 | if (k > IDELEMS(h4)) |
---|
| 1250 | { |
---|
| 1251 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
| 1252 | IDELEMS(h4) = k; |
---|
| 1253 | } |
---|
| 1254 | for (i=1; i<k; i++) |
---|
| 1255 | { |
---|
| 1256 | if (h4->m[i-1]!=NULL) |
---|
| 1257 | { |
---|
[fea494] | 1258 | p = p_Copy_noCheck(h4->m[i-1], currRing); p_Shift(&p,1,currRing); |
---|
[741464] | 1259 | // pTest(p); |
---|
[0f401f] | 1260 | h4->m[i] = p; |
---|
| 1261 | } |
---|
| 1262 | } |
---|
| 1263 | } |
---|
| 1264 | idSkipZeroes(h4); |
---|
| 1265 | kkk = IDELEMS(h4); |
---|
| 1266 | i = IDELEMS(temph1); |
---|
| 1267 | for (l=0; l<i; l++) |
---|
| 1268 | { |
---|
| 1269 | if(temph1->m[l]!=NULL) |
---|
| 1270 | { |
---|
| 1271 | for (ll=0; ll<j; ll++) |
---|
| 1272 | { |
---|
| 1273 | p = pCopy(temph1->m[l]); |
---|
| 1274 | if (k1 == 0) |
---|
[861529] | 1275 | p_Shift(&p,ll*k+1,currRing); |
---|
[0f401f] | 1276 | else |
---|
[861529] | 1277 | p_Shift(&p,ll*k,currRing); |
---|
[0f401f] | 1278 | if (kkk >= IDELEMS(h4)) |
---|
| 1279 | { |
---|
| 1280 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
| 1281 | IDELEMS(h4) += 16; |
---|
| 1282 | } |
---|
| 1283 | h4->m[kkk] = p; |
---|
| 1284 | kkk++; |
---|
| 1285 | } |
---|
| 1286 | } |
---|
| 1287 | } |
---|
| 1288 | /*--- if h2 goes in as single vector - the h1-part is just SB ---*/ |
---|
| 1289 | if (*addOnlyOne) |
---|
| 1290 | { |
---|
| 1291 | idSkipZeroes(h4); |
---|
| 1292 | p = h4->m[0]; |
---|
| 1293 | for (i=0;i<IDELEMS(h4)-1;i++) |
---|
| 1294 | { |
---|
| 1295 | h4->m[i] = h4->m[i+1]; |
---|
| 1296 | } |
---|
| 1297 | h4->m[IDELEMS(h4)-1] = p; |
---|
[c96539c] | 1298 | #ifdef HAVE_RINGS |
---|
[9927b9e] | 1299 | if(!rField_is_Ring(currRing)) |
---|
[c96539c] | 1300 | #endif |
---|
[d30a399] | 1301 | si_opt_1 |= Sy_bit(OPT_SB_1); |
---|
[0f401f] | 1302 | } |
---|
| 1303 | idDelete(&temph1); |
---|
[db79f9] | 1304 | //idTest(h4);//see remark at the beginning |
---|
[0f401f] | 1305 | return h4; |
---|
| 1306 | } |
---|
| 1307 | /*2 |
---|
| 1308 | *computes the quotient of h1,h2 |
---|
| 1309 | */ |
---|
| 1310 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal) |
---|
| 1311 | { |
---|
| 1312 | // first check for special case h1:(0) |
---|
| 1313 | if (idIs0(h2)) |
---|
| 1314 | { |
---|
| 1315 | ideal res; |
---|
| 1316 | if (resultIsIdeal) |
---|
| 1317 | { |
---|
| 1318 | res = idInit(1,1); |
---|
| 1319 | res->m[0] = pOne(); |
---|
| 1320 | } |
---|
| 1321 | else |
---|
| 1322 | res = idFreeModule(h1->rank); |
---|
| 1323 | return res; |
---|
| 1324 | } |
---|
[d30a399] | 1325 | BITSET old_test1; |
---|
| 1326 | SI_SAVE_OPT1(old_test1); |
---|
[bca341] | 1327 | int i, kmax; |
---|
[0f401f] | 1328 | BOOLEAN addOnlyOne=TRUE; |
---|
| 1329 | tHomog hom=isNotHomog; |
---|
| 1330 | intvec * weights1; |
---|
| 1331 | |
---|
| 1332 | ideal s_h4 = idInitializeQuot (h1,h2,h1IsStb,&addOnlyOne,&kmax); |
---|
| 1333 | |
---|
[ac00e2f] | 1334 | hom = (tHomog)idHomModule(s_h4,currRing->qideal,&weights1); |
---|
[0f401f] | 1335 | |
---|
| 1336 | ring orig_ring=currRing; |
---|
[3f07d1] | 1337 | ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
[b7cfaf] | 1338 | rSetSyzComp(kmax-1,syz_ring); |
---|
[0f401f] | 1339 | if (orig_ring!=syz_ring) |
---|
[b7cfaf] | 1340 | // s_h4 = idrMoveR_NoSort(s_h4,orig_ring, syz_ring); |
---|
| 1341 | s_h4 = idrMoveR(s_h4,orig_ring, syz_ring); |
---|
[0f401f] | 1342 | idTest(s_h4); |
---|
| 1343 | #if 0 |
---|
| 1344 | void ipPrint_MA0(matrix m, const char *name); |
---|
| 1345 | matrix m=idModule2Matrix(idCopy(s_h4)); |
---|
| 1346 | PrintS("start:\n"); |
---|
| 1347 | ipPrint_MA0(m,"Q"); |
---|
| 1348 | idDelete((ideal *)&m); |
---|
| 1349 | PrintS("last elem:");wrp(s_h4->m[IDELEMS(s_h4)-1]);PrintLn(); |
---|
| 1350 | #endif |
---|
| 1351 | ideal s_h3; |
---|
| 1352 | if (addOnlyOne) |
---|
| 1353 | { |
---|
[ac00e2f] | 1354 | s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,0/*kmax-1*/,IDELEMS(s_h4)-1); |
---|
[0f401f] | 1355 | } |
---|
| 1356 | else |
---|
| 1357 | { |
---|
[ac00e2f] | 1358 | s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,kmax-1); |
---|
[0f401f] | 1359 | } |
---|
[d30a399] | 1360 | SI_RESTORE_OPT1(old_test1); |
---|
[0f401f] | 1361 | #if 0 |
---|
| 1362 | // only together with the above debug stuff |
---|
| 1363 | idSkipZeroes(s_h3); |
---|
| 1364 | m=idModule2Matrix(idCopy(s_h3)); |
---|
| 1365 | Print("result, kmax=%d:\n",kmax); |
---|
| 1366 | ipPrint_MA0(m,"S"); |
---|
| 1367 | idDelete((ideal *)&m); |
---|
| 1368 | #endif |
---|
| 1369 | idTest(s_h3); |
---|
| 1370 | if (weights1!=NULL) delete weights1; |
---|
| 1371 | idDelete(&s_h4); |
---|
| 1372 | |
---|
| 1373 | for (i=0;i<IDELEMS(s_h3);i++) |
---|
| 1374 | { |
---|
| 1375 | if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax)) |
---|
| 1376 | { |
---|
| 1377 | if (resultIsIdeal) |
---|
[861529] | 1378 | p_Shift(&s_h3->m[i],-kmax,currRing); |
---|
[0f401f] | 1379 | else |
---|
[861529] | 1380 | p_Shift(&s_h3->m[i],-kmax+1,currRing); |
---|
[0f401f] | 1381 | } |
---|
| 1382 | else |
---|
[f9591a] | 1383 | p_Delete(&s_h3->m[i],currRing); |
---|
[0f401f] | 1384 | } |
---|
| 1385 | if (resultIsIdeal) |
---|
| 1386 | s_h3->rank = 1; |
---|
| 1387 | else |
---|
| 1388 | s_h3->rank = h1->rank; |
---|
| 1389 | if(syz_ring!=orig_ring) |
---|
| 1390 | { |
---|
| 1391 | rChangeCurrRing(orig_ring); |
---|
[b7cfaf] | 1392 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring); |
---|
[5fe834] | 1393 | rDelete(syz_ring); |
---|
[0f401f] | 1394 | } |
---|
| 1395 | idSkipZeroes(s_h3); |
---|
| 1396 | idTest(s_h3); |
---|
| 1397 | return s_h3; |
---|
| 1398 | } |
---|
| 1399 | |
---|
| 1400 | /*2 |
---|
| 1401 | * eliminate delVar (product of vars) in h1 |
---|
| 1402 | */ |
---|
| 1403 | ideal idElimination (ideal h1,poly delVar,intvec *hilb) |
---|
| 1404 | { |
---|
| 1405 | int i,j=0,k,l; |
---|
| 1406 | ideal h,hh, h3; |
---|
| 1407 | int *ord,*block0,*block1; |
---|
| 1408 | int ordersize=2; |
---|
| 1409 | int **wv; |
---|
| 1410 | tHomog hom; |
---|
| 1411 | intvec * w; |
---|
| 1412 | ring tmpR; |
---|
| 1413 | ring origR = currRing; |
---|
| 1414 | |
---|
| 1415 | if (delVar==NULL) |
---|
| 1416 | { |
---|
| 1417 | return idCopy(h1); |
---|
| 1418 | } |
---|
[ac00e2f] | 1419 | if ((currRing->qideal!=NULL) && rIsPluralRing(origR)) |
---|
[0f401f] | 1420 | { |
---|
| 1421 | WerrorS("cannot eliminate in a qring"); |
---|
[a5d181c] | 1422 | return NULL; |
---|
[0f401f] | 1423 | } |
---|
| 1424 | if (idIs0(h1)) return idInit(1,h1->rank); |
---|
| 1425 | #ifdef HAVE_PLURAL |
---|
| 1426 | if (rIsPluralRing(origR)) |
---|
| 1427 | /* in the NC case, we have to check the admissibility of */ |
---|
| 1428 | /* the subalgebra to be intersected with */ |
---|
| 1429 | { |
---|
| 1430 | if ((ncRingType(origR) != nc_skew) && (ncRingType(origR) != nc_exterior)) /* in (quasi)-commutative algebras every subalgebra is admissible */ |
---|
| 1431 | { |
---|
| 1432 | if (nc_CheckSubalgebra(delVar,origR)) |
---|
| 1433 | { |
---|
| 1434 | WerrorS("no elimination is possible: subalgebra is not admissible"); |
---|
[a5d181c] | 1435 | return NULL; |
---|
[0f401f] | 1436 | } |
---|
| 1437 | } |
---|
| 1438 | } |
---|
| 1439 | #endif |
---|
| 1440 | hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL |
---|
| 1441 | h3=idInit(16,h1->rank); |
---|
| 1442 | for (k=0;; k++) |
---|
| 1443 | { |
---|
| 1444 | if (origR->order[k]!=0) ordersize++; |
---|
| 1445 | else break; |
---|
| 1446 | } |
---|
| 1447 | #if 0 |
---|
| 1448 | if (rIsPluralRing(origR)) // we have too keep the odering: it may be needed |
---|
| 1449 | // for G-algebra |
---|
| 1450 | { |
---|
| 1451 | for (k=0;k<ordersize-1; k++) |
---|
| 1452 | { |
---|
| 1453 | block0[k+1] = origR->block0[k]; |
---|
| 1454 | block1[k+1] = origR->block1[k]; |
---|
| 1455 | ord[k+1] = origR->order[k]; |
---|
| 1456 | if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]); |
---|
| 1457 | } |
---|
| 1458 | } |
---|
| 1459 | else |
---|
| 1460 | { |
---|
| 1461 | block0[1] = 1; |
---|
[1f637e] | 1462 | block1[1] = (currRing->N); |
---|
[0f401f] | 1463 | if (origR->OrdSgn==1) ord[1] = ringorder_wp; |
---|
| 1464 | else ord[1] = ringorder_ws; |
---|
[1f637e] | 1465 | wv[1]=(int*)omAlloc0((currRing->N)*sizeof(int)); |
---|
| 1466 | double wNsqr = (double)2.0 / (double)(currRing->N); |
---|
[0f401f] | 1467 | wFunctional = wFunctionalBuch; |
---|
[1f637e] | 1468 | int *x= (int * )omAlloc(2 * ((currRing->N) + 1) * sizeof(int)); |
---|
[0f401f] | 1469 | int sl=IDELEMS(h1) - 1; |
---|
| 1470 | wCall(h1->m, sl, x, wNsqr); |
---|
[1f637e] | 1471 | for (sl = (currRing->N); sl!=0; sl--) |
---|
| 1472 | wv[1][sl-1] = x[sl + (currRing->N) + 1]; |
---|
| 1473 | omFreeSize((ADDRESS)x, 2 * ((currRing->N) + 1) * sizeof(int)); |
---|
[0f401f] | 1474 | |
---|
| 1475 | ord[2]=ringorder_C; |
---|
| 1476 | ord[3]=0; |
---|
| 1477 | } |
---|
| 1478 | #else |
---|
| 1479 | #endif |
---|
| 1480 | if ((hom==TRUE) && (origR->OrdSgn==1) && (!rIsPluralRing(origR))) |
---|
| 1481 | { |
---|
| 1482 | #if 1 |
---|
| 1483 | // we change to an ordering: |
---|
| 1484 | // aa(1,1,1,...,0,0,0),wp(...),C |
---|
| 1485 | // this seems to be better than version 2 below, |
---|
| 1486 | // according to Tst/../elimiate_[3568].tat (- 17 %) |
---|
| 1487 | ord=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1488 | block0=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1489 | block1=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1490 | wv=(int**) omAlloc0(4*sizeof(int**)); |
---|
| 1491 | block0[0] = block0[1] = 1; |
---|
| 1492 | block1[0] = block1[1] = rVar(origR); |
---|
| 1493 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
| 1494 | // use this special ordering: like ringorder_a, except that pFDeg, pWeights |
---|
| 1495 | // ignore it |
---|
| 1496 | ord[0] = ringorder_aa; |
---|
| 1497 | for (j=0;j<rVar(origR);j++) |
---|
| 1498 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
| 1499 | BOOLEAN wp=FALSE; |
---|
| 1500 | for (j=0;j<rVar(origR);j++) |
---|
| 1501 | if (pWeight(j+1,origR)!=1) { wp=TRUE;break; } |
---|
| 1502 | if (wp) |
---|
| 1503 | { |
---|
| 1504 | wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
| 1505 | for (j=0;j<rVar(origR);j++) |
---|
| 1506 | wv[1][j]=pWeight(j+1,origR); |
---|
| 1507 | ord[1] = ringorder_wp; |
---|
| 1508 | } |
---|
| 1509 | else |
---|
| 1510 | ord[1] = ringorder_dp; |
---|
| 1511 | #else |
---|
| 1512 | // we change to an ordering: |
---|
| 1513 | // a(w1,...wn),wp(1,...0.....),C |
---|
| 1514 | ord=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1515 | block0=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1516 | block1=(int*)omAlloc0(4*sizeof(int)); |
---|
| 1517 | wv=(int**) omAlloc0(4*sizeof(int**)); |
---|
| 1518 | block0[0] = block0[1] = 1; |
---|
| 1519 | block1[0] = block1[1] = rVar(origR); |
---|
| 1520 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
| 1521 | wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
| 1522 | ord[0] = ringorder_a; |
---|
| 1523 | for (j=0;j<rVar(origR);j++) |
---|
| 1524 | wv[0][j]=pWeight(j+1,origR); |
---|
| 1525 | ord[1] = ringorder_wp; |
---|
| 1526 | for (j=0;j<rVar(origR);j++) |
---|
| 1527 | if (pGetExp(delVar,j+1)!=0) wv[1][j]=1; |
---|
| 1528 | #endif |
---|
| 1529 | ord[2] = ringorder_C; |
---|
| 1530 | ord[3] = 0; |
---|
| 1531 | } |
---|
| 1532 | else |
---|
| 1533 | { |
---|
| 1534 | // we change to an ordering: |
---|
| 1535 | // aa(....),orig_ordering |
---|
| 1536 | ord=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
| 1537 | block0=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
| 1538 | block1=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
| 1539 | wv=(int**) omAlloc0(ordersize*sizeof(int**)); |
---|
| 1540 | for (k=0;k<ordersize-1; k++) |
---|
| 1541 | { |
---|
| 1542 | block0[k+1] = origR->block0[k]; |
---|
| 1543 | block1[k+1] = origR->block1[k]; |
---|
| 1544 | ord[k+1] = origR->order[k]; |
---|
| 1545 | if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]); |
---|
| 1546 | } |
---|
| 1547 | block0[0] = 1; |
---|
| 1548 | block1[0] = rVar(origR); |
---|
| 1549 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
| 1550 | for (j=0;j<rVar(origR);j++) |
---|
| 1551 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
| 1552 | // use this special ordering: like ringorder_a, except that pFDeg, pWeights |
---|
| 1553 | // ignore it |
---|
| 1554 | ord[0] = ringorder_aa; |
---|
| 1555 | } |
---|
| 1556 | // fill in tmp ring to get back the data later on |
---|
| 1557 | tmpR = rCopy0(origR,FALSE,FALSE); // qring==NULL |
---|
| 1558 | //rUnComplete(tmpR); |
---|
| 1559 | tmpR->p_Procs=NULL; |
---|
| 1560 | tmpR->order = ord; |
---|
| 1561 | tmpR->block0 = block0; |
---|
| 1562 | tmpR->block1 = block1; |
---|
| 1563 | tmpR->wvhdl = wv; |
---|
| 1564 | rComplete(tmpR, 1); |
---|
| 1565 | |
---|
| 1566 | #ifdef HAVE_PLURAL |
---|
| 1567 | /* update nc structure on tmpR */ |
---|
| 1568 | if (rIsPluralRing(origR)) |
---|
| 1569 | { |
---|
| 1570 | if ( nc_rComplete(origR, tmpR, false) ) // no quotient ideal! |
---|
| 1571 | { |
---|
| 1572 | Werror("no elimination is possible: ordering condition is violated"); |
---|
| 1573 | // cleanup |
---|
| 1574 | rDelete(tmpR); |
---|
| 1575 | if (w!=NULL) |
---|
| 1576 | delete w; |
---|
[a5d181c] | 1577 | return NULL; |
---|
[0f401f] | 1578 | } |
---|
| 1579 | } |
---|
| 1580 | #endif |
---|
| 1581 | // change into the new ring |
---|
[1f637e] | 1582 | //pChangeRing((currRing->N),currRing->OrdSgn,ord,block0,block1,wv); |
---|
[0f401f] | 1583 | rChangeCurrRing(tmpR); |
---|
| 1584 | |
---|
| 1585 | //h = idInit(IDELEMS(h1),h1->rank); |
---|
| 1586 | // fetch data from the old ring |
---|
| 1587 | //for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR); |
---|
| 1588 | h=idrCopyR(h1,origR,currRing); |
---|
| 1589 | if (origR->qideal!=NULL) |
---|
| 1590 | { |
---|
| 1591 | WarnS("eliminate in q-ring: experimental"); |
---|
| 1592 | ideal q=idrCopyR(origR->qideal,origR,currRing); |
---|
| 1593 | ideal s=idSimpleAdd(h,q); |
---|
| 1594 | idDelete(&h); |
---|
| 1595 | idDelete(&q); |
---|
| 1596 | h=s; |
---|
| 1597 | } |
---|
| 1598 | // compute kStd |
---|
| 1599 | #if 1 |
---|
| 1600 | //rWrite(tmpR);PrintLn(); |
---|
[d30a399] | 1601 | //BITSET save1; |
---|
| 1602 | //SI_SAVE_OPT1(save1); |
---|
| 1603 | //si_opt_1 |=1; |
---|
[0f401f] | 1604 | //Print("h: %d gen, rk=%d\n",IDELEMS(h),h->rank); |
---|
| 1605 | //extern char * showOption(); |
---|
| 1606 | //Print("%s\n",showOption()); |
---|
| 1607 | hh = kStd(h,NULL,hom,&w,hilb); |
---|
[d30a399] | 1608 | //SI_RESTORE_OPT1(save1); |
---|
[0f401f] | 1609 | idDelete(&h); |
---|
| 1610 | #else |
---|
| 1611 | extern ideal kGroebner(ideal F, ideal Q); |
---|
| 1612 | hh=kGroebner(h,NULL); |
---|
| 1613 | #endif |
---|
| 1614 | // go back to the original ring |
---|
| 1615 | rChangeCurrRing(origR); |
---|
| 1616 | i = IDELEMS(hh)-1; |
---|
| 1617 | while ((i >= 0) && (hh->m[i] == NULL)) i--; |
---|
| 1618 | j = -1; |
---|
| 1619 | // fetch data from temp ring |
---|
| 1620 | for (k=0; k<=i; k++) |
---|
| 1621 | { |
---|
[1f637e] | 1622 | l=(currRing->N); |
---|
[0f401f] | 1623 | while ((l>0) && (p_GetExp( hh->m[k],l,tmpR)*pGetExp(delVar,l)==0)) l--; |
---|
| 1624 | if (l==0) |
---|
| 1625 | { |
---|
| 1626 | j++; |
---|
| 1627 | if (j >= IDELEMS(h3)) |
---|
| 1628 | { |
---|
| 1629 | pEnlargeSet(&(h3->m),IDELEMS(h3),16); |
---|
| 1630 | IDELEMS(h3) += 16; |
---|
| 1631 | } |
---|
[b7cfaf] | 1632 | h3->m[j] = prMoveR( hh->m[k], tmpR,origR); |
---|
[0f401f] | 1633 | hh->m[k] = NULL; |
---|
| 1634 | } |
---|
| 1635 | } |
---|
| 1636 | id_Delete(&hh, tmpR); |
---|
| 1637 | idSkipZeroes(h3); |
---|
| 1638 | rDelete(tmpR); |
---|
| 1639 | if (w!=NULL) |
---|
| 1640 | delete w; |
---|
| 1641 | return h3; |
---|
| 1642 | } |
---|
| 1643 | |
---|
[7356be] | 1644 | #ifdef WITH_OLD_MINOR |
---|
[0f401f] | 1645 | /*2 |
---|
| 1646 | * compute the which-th ar-minor of the matrix a |
---|
| 1647 | */ |
---|
| 1648 | poly idMinor(matrix a, int ar, unsigned long which, ideal R) |
---|
| 1649 | { |
---|
[cd4f24] | 1650 | int i,j/*,k,size*/; |
---|
[0f401f] | 1651 | unsigned long curr; |
---|
| 1652 | int *rowchoise,*colchoise; |
---|
| 1653 | BOOLEAN rowch,colch; |
---|
[cd4f24] | 1654 | // ideal result; |
---|
[0f401f] | 1655 | matrix tmp; |
---|
| 1656 | poly p,q; |
---|
| 1657 | |
---|
| 1658 | i = binom(a->rows(),ar); |
---|
| 1659 | j = binom(a->cols(),ar); |
---|
| 1660 | |
---|
| 1661 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1662 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
[cd4f24] | 1663 | // if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
| 1664 | // else size=i*j; |
---|
| 1665 | // result=idInit(size,1); |
---|
[0f401f] | 1666 | tmp=mpNew(ar,ar); |
---|
[cd4f24] | 1667 | // k = 0; /* the index in result*/ |
---|
[0f401f] | 1668 | curr = 0; /* index of current minor */ |
---|
| 1669 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
| 1670 | while (!rowch) |
---|
| 1671 | { |
---|
| 1672 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
| 1673 | while (!colch) |
---|
| 1674 | { |
---|
| 1675 | if (curr == which) |
---|
| 1676 | { |
---|
| 1677 | for (i=1; i<=ar; i++) |
---|
| 1678 | { |
---|
| 1679 | for (j=1; j<=ar; j++) |
---|
| 1680 | { |
---|
| 1681 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
| 1682 | } |
---|
| 1683 | } |
---|
[441a2e] | 1684 | p = mp_DetBareiss(tmp,currRing); |
---|
[0f401f] | 1685 | if (p!=NULL) |
---|
| 1686 | { |
---|
| 1687 | if (R!=NULL) |
---|
| 1688 | { |
---|
| 1689 | q = p; |
---|
[ac00e2f] | 1690 | p = kNF(R,currRing->qideal,q); |
---|
[f9591a] | 1691 | p_Delete(&q,currRing); |
---|
[0f401f] | 1692 | } |
---|
| 1693 | /*delete the matrix tmp*/ |
---|
| 1694 | for (i=1; i<=ar; i++) |
---|
| 1695 | { |
---|
| 1696 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
| 1697 | } |
---|
| 1698 | idDelete((ideal*)&tmp); |
---|
| 1699 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
| 1700 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
| 1701 | return (p); |
---|
| 1702 | } |
---|
| 1703 | } |
---|
| 1704 | curr++; |
---|
| 1705 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
| 1706 | } |
---|
| 1707 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
| 1708 | } |
---|
| 1709 | return (poly) 1; |
---|
| 1710 | } |
---|
| 1711 | |
---|
| 1712 | /*2 |
---|
| 1713 | * compute all ar-minors of the matrix a |
---|
| 1714 | */ |
---|
| 1715 | ideal idMinors(matrix a, int ar, ideal R) |
---|
| 1716 | { |
---|
[cd4f24] | 1717 | int i,j,/*k,*/size; |
---|
[0f401f] | 1718 | int *rowchoise,*colchoise; |
---|
| 1719 | BOOLEAN rowch,colch; |
---|
| 1720 | ideal result; |
---|
| 1721 | matrix tmp; |
---|
| 1722 | poly p,q; |
---|
| 1723 | |
---|
| 1724 | i = binom(a->rows(),ar); |
---|
| 1725 | j = binom(a->cols(),ar); |
---|
| 1726 | |
---|
| 1727 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1728 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1729 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
| 1730 | else size=i*j; |
---|
| 1731 | result=idInit(size,1); |
---|
| 1732 | tmp=mpNew(ar,ar); |
---|
[cd4f24] | 1733 | // k = 0; /* the index in result*/ |
---|
[0f401f] | 1734 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
| 1735 | while (!rowch) |
---|
| 1736 | { |
---|
| 1737 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
| 1738 | while (!colch) |
---|
| 1739 | { |
---|
| 1740 | for (i=1; i<=ar; i++) |
---|
| 1741 | { |
---|
| 1742 | for (j=1; j<=ar; j++) |
---|
| 1743 | { |
---|
| 1744 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
| 1745 | } |
---|
| 1746 | } |
---|
[441a2e] | 1747 | p = mp_DetBareiss(tmp,vcurrRing); |
---|
[0f401f] | 1748 | if (p!=NULL) |
---|
| 1749 | { |
---|
| 1750 | if (R!=NULL) |
---|
| 1751 | { |
---|
| 1752 | q = p; |
---|
[ac00e2f] | 1753 | p = kNF(R,currRing->qideal,q); |
---|
[f9591a] | 1754 | p_Delete(&q,currRing); |
---|
[0f401f] | 1755 | } |
---|
| 1756 | if (p!=NULL) |
---|
| 1757 | { |
---|
| 1758 | if (k>=size) |
---|
| 1759 | { |
---|
| 1760 | pEnlargeSet(&result->m,size,32); |
---|
| 1761 | size += 32; |
---|
| 1762 | } |
---|
| 1763 | result->m[k] = p; |
---|
| 1764 | k++; |
---|
| 1765 | } |
---|
| 1766 | } |
---|
| 1767 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
| 1768 | } |
---|
| 1769 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
| 1770 | } |
---|
| 1771 | /*delete the matrix tmp*/ |
---|
| 1772 | for (i=1; i<=ar; i++) |
---|
| 1773 | { |
---|
| 1774 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
| 1775 | } |
---|
| 1776 | idDelete((ideal*)&tmp); |
---|
| 1777 | if (k==0) |
---|
| 1778 | { |
---|
| 1779 | k=1; |
---|
| 1780 | result->m[0]=NULL; |
---|
| 1781 | } |
---|
| 1782 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
| 1783 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
| 1784 | pEnlargeSet(&result->m,size,k-size); |
---|
| 1785 | IDELEMS(result) = k; |
---|
| 1786 | return (result); |
---|
| 1787 | } |
---|
| 1788 | #else |
---|
[49b748] | 1789 | |
---|
| 1790 | |
---|
| 1791 | /// compute all ar-minors of the matrix a |
---|
| 1792 | /// the caller of mpRecMin |
---|
| 1793 | /// the elements of the result are not in R (if R!=NULL) |
---|
[0f401f] | 1794 | ideal idMinors(matrix a, int ar, ideal R) |
---|
| 1795 | { |
---|
[f13c85] | 1796 | |
---|
[49b748] | 1797 | const ring origR=currRing; |
---|
| 1798 | id_Test((ideal)a, origR); |
---|
[0f401f] | 1799 | |
---|
[49b748] | 1800 | const int r = a->nrows; |
---|
| 1801 | const int c = a->ncols; |
---|
[f13c85] | 1802 | |
---|
[0f401f] | 1803 | if((ar<=0) || (ar>r) || (ar>c)) |
---|
| 1804 | { |
---|
| 1805 | Werror("%d-th minor, matrix is %dx%d",ar,r,c); |
---|
| 1806 | return NULL; |
---|
| 1807 | } |
---|
[f13c85] | 1808 | |
---|
| 1809 | ideal h = id_Matrix2Module(mp_Copy(a,origR),origR); |
---|
[49b748] | 1810 | long bound = sm_ExpBound(h,c,r,ar,origR); |
---|
| 1811 | id_Delete(&h, origR); |
---|
[f13c85] | 1812 | |
---|
[49b748] | 1813 | ring tmpR = sm_RingChange(origR,bound); |
---|
[f13c85] | 1814 | |
---|
[49b748] | 1815 | matrix b = mpNew(r,c); |
---|
[f13c85] | 1816 | |
---|
[49b748] | 1817 | for (int i=r*c-1;i>=0;i--) |
---|
| 1818 | if (a->m[i] != NULL) |
---|
[46008c] | 1819 | b->m[i] = prCopyR(a->m[i],origR,tmpR); |
---|
[f13c85] | 1820 | |
---|
[49b748] | 1821 | id_Test( (ideal)b, tmpR); |
---|
[f13c85] | 1822 | |
---|
[0f401f] | 1823 | if (R!=NULL) |
---|
| 1824 | { |
---|
[49b748] | 1825 | R = idrCopyR(R,origR,tmpR); // TODO: overwrites R? memory leak? |
---|
[0f401f] | 1826 | //if (ar>1) // otherwise done in mpMinorToResult |
---|
| 1827 | //{ |
---|
[ac00e2f] | 1828 | // matrix bb=(matrix)kNF(R,currRing->qideal,(ideal)b); |
---|
[0f401f] | 1829 | // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols; |
---|
| 1830 | // idDelete((ideal*)&b); b=bb; |
---|
| 1831 | //} |
---|
[49b748] | 1832 | id_Test( R, tmpR); |
---|
[0f401f] | 1833 | } |
---|
[f13c85] | 1834 | |
---|
| 1835 | |
---|
[49b748] | 1836 | ideal result = idInit(32,1); |
---|
| 1837 | |
---|
| 1838 | int elems = 0; |
---|
[f13c85] | 1839 | |
---|
[49b748] | 1840 | if(ar>1) |
---|
| 1841 | mp_RecMin(ar-1,result,elems,b,r,c,NULL,R,tmpR); |
---|
| 1842 | else |
---|
| 1843 | mp_MinorToResult(result,elems,b,r,c,R,tmpR); |
---|
[f13c85] | 1844 | |
---|
[49b748] | 1845 | id_Test( (ideal)b, tmpR); |
---|
[f13c85] | 1846 | |
---|
[49b748] | 1847 | id_Delete((ideal *)&b, tmpR); |
---|
[f13c85] | 1848 | |
---|
[0f401f] | 1849 | if (R!=NULL) idDelete(&R); |
---|
[f13c85] | 1850 | |
---|
[0f401f] | 1851 | idSkipZeroes(result); |
---|
| 1852 | rChangeCurrRing(origR); |
---|
[441a2e] | 1853 | result = idrMoveR(result,tmpR,origR); |
---|
[d16ea9] | 1854 | sm_KillModifiedRing(tmpR); |
---|
[0f401f] | 1855 | idTest(result); |
---|
| 1856 | return result; |
---|
| 1857 | } |
---|
| 1858 | #endif |
---|
| 1859 | |
---|
| 1860 | /*2 |
---|
| 1861 | *returns TRUE if id1 is a submodule of id2 |
---|
| 1862 | */ |
---|
| 1863 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
| 1864 | { |
---|
| 1865 | int i; |
---|
| 1866 | poly p; |
---|
| 1867 | |
---|
| 1868 | if (idIs0(id1)) return TRUE; |
---|
| 1869 | for (i=0;i<IDELEMS(id1);i++) |
---|
| 1870 | { |
---|
| 1871 | if (id1->m[i] != NULL) |
---|
| 1872 | { |
---|
[ac00e2f] | 1873 | p = kNF(id2,currRing->qideal,id1->m[i]); |
---|
[0f401f] | 1874 | if (p != NULL) |
---|
| 1875 | { |
---|
[f9591a] | 1876 | p_Delete(&p,currRing); |
---|
[0f401f] | 1877 | return FALSE; |
---|
| 1878 | } |
---|
| 1879 | } |
---|
| 1880 | } |
---|
| 1881 | return TRUE; |
---|
| 1882 | } |
---|
| 1883 | |
---|
| 1884 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
| 1885 | { |
---|
| 1886 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
| 1887 | if (idIs0(m)) return TRUE; |
---|
| 1888 | |
---|
| 1889 | int cmax=-1; |
---|
| 1890 | int i; |
---|
| 1891 | poly p=NULL; |
---|
| 1892 | int length=IDELEMS(m); |
---|
| 1893 | polyset P=m->m; |
---|
| 1894 | for (i=length-1;i>=0;i--) |
---|
| 1895 | { |
---|
| 1896 | p=P[i]; |
---|
| 1897 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
| 1898 | } |
---|
| 1899 | if (w != NULL) |
---|
| 1900 | if (w->length()+1 < cmax) |
---|
| 1901 | { |
---|
| 1902 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
| 1903 | return FALSE; |
---|
| 1904 | } |
---|
| 1905 | |
---|
| 1906 | if(w!=NULL) |
---|
[e1215e] | 1907 | p_SetModDeg(w, currRing); |
---|
[0f401f] | 1908 | |
---|
| 1909 | for (i=length-1;i>=0;i--) |
---|
| 1910 | { |
---|
| 1911 | p=P[i]; |
---|
| 1912 | if (p!=NULL) |
---|
| 1913 | { |
---|
[b7cfaf] | 1914 | int d=currRing->pFDeg(p,currRing); |
---|
[0f401f] | 1915 | loop |
---|
| 1916 | { |
---|
| 1917 | pIter(p); |
---|
| 1918 | if (p==NULL) break; |
---|
[b7cfaf] | 1919 | if (d!=currRing->pFDeg(p,currRing)) |
---|
[0f401f] | 1920 | { |
---|
| 1921 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
| 1922 | if(w!=NULL) |
---|
[e1215e] | 1923 | p_SetModDeg(NULL, currRing); |
---|
[0f401f] | 1924 | return FALSE; |
---|
| 1925 | } |
---|
| 1926 | } |
---|
| 1927 | } |
---|
| 1928 | } |
---|
| 1929 | |
---|
| 1930 | if(w!=NULL) |
---|
[e1215e] | 1931 | p_SetModDeg(NULL, currRing); |
---|
[0f401f] | 1932 | |
---|
| 1933 | return TRUE; |
---|
| 1934 | } |
---|
| 1935 | |
---|
| 1936 | ideal idSeries(int n,ideal M,matrix U,intvec *w) |
---|
| 1937 | { |
---|
| 1938 | for(int i=IDELEMS(M)-1;i>=0;i--) |
---|
| 1939 | { |
---|
| 1940 | if(U==NULL) |
---|
| 1941 | M->m[i]=pSeries(n,M->m[i],NULL,w); |
---|
| 1942 | else |
---|
| 1943 | { |
---|
| 1944 | M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w); |
---|
| 1945 | MATELEM(U,i+1,i+1)=NULL; |
---|
| 1946 | } |
---|
| 1947 | } |
---|
| 1948 | if(U!=NULL) |
---|
| 1949 | idDelete((ideal*)&U); |
---|
| 1950 | return M; |
---|
| 1951 | } |
---|
| 1952 | |
---|
| 1953 | matrix idDiff(matrix i, int k) |
---|
| 1954 | { |
---|
| 1955 | int e=MATCOLS(i)*MATROWS(i); |
---|
| 1956 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
| 1957 | r->rank=i->rank; |
---|
| 1958 | int j; |
---|
| 1959 | for(j=0; j<e; j++) |
---|
| 1960 | { |
---|
| 1961 | r->m[j]=pDiff(i->m[j],k); |
---|
| 1962 | } |
---|
| 1963 | return r; |
---|
| 1964 | } |
---|
| 1965 | |
---|
| 1966 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
| 1967 | { |
---|
| 1968 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
| 1969 | int i,j; |
---|
| 1970 | for(i=0; i<IDELEMS(I); i++) |
---|
| 1971 | { |
---|
| 1972 | for(j=0; j<IDELEMS(J); j++) |
---|
| 1973 | { |
---|
| 1974 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
| 1975 | } |
---|
| 1976 | } |
---|
| 1977 | return r; |
---|
| 1978 | } |
---|
| 1979 | |
---|
| 1980 | /*3 |
---|
| 1981 | *handles for some ideal operations the ring/syzcomp managment |
---|
| 1982 | *returns all syzygies (componentwise-)shifted by -syzcomp |
---|
| 1983 | *or -syzcomp-1 (in case of ideals as input) |
---|
| 1984 | static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE) |
---|
| 1985 | { |
---|
| 1986 | ring orig_ring=currRing; |
---|
[3f07d1] | 1987 | ring syz_ring=rAssure_SyzComp(orig_ring, TRUE); rChangeCurrRing(syz_ring); |
---|
| 1988 | rSetSyzComp(length, syz_ring); |
---|
[0f401f] | 1989 | |
---|
| 1990 | ideal s_temp; |
---|
| 1991 | if (orig_ring!=syz_ring) |
---|
[b7cfaf] | 1992 | s_temp=idrMoveR_NoSort(arg,orig_ring, syz_ring); |
---|
[0f401f] | 1993 | else |
---|
| 1994 | s_temp=arg; |
---|
| 1995 | |
---|
[ac00e2f] | 1996 | ideal s_temp1 = kStd(s_temp,currRing->qideal,testHomog,&w,NULL,length); |
---|
[0f401f] | 1997 | if (w!=NULL) delete w; |
---|
| 1998 | |
---|
| 1999 | if (syz_ring!=orig_ring) |
---|
| 2000 | { |
---|
| 2001 | idDelete(&s_temp); |
---|
| 2002 | rChangeCurrRing(orig_ring); |
---|
| 2003 | } |
---|
| 2004 | |
---|
| 2005 | idDelete(&temp); |
---|
| 2006 | ideal temp1=idRingCopy(s_temp1,syz_ring); |
---|
| 2007 | |
---|
| 2008 | if (syz_ring!=orig_ring) |
---|
| 2009 | { |
---|
| 2010 | rChangeCurrRing(syz_ring); |
---|
| 2011 | idDelete(&s_temp1); |
---|
| 2012 | rChangeCurrRing(orig_ring); |
---|
[5fe834] | 2013 | rDelete(syz_ring); |
---|
[0f401f] | 2014 | } |
---|
| 2015 | |
---|
| 2016 | for (i=0;i<IDELEMS(temp1);i++) |
---|
| 2017 | { |
---|
| 2018 | if ((temp1->m[i]!=NULL) |
---|
| 2019 | && (pGetComp(temp1->m[i])<=length)) |
---|
| 2020 | { |
---|
| 2021 | pDelete(&(temp1->m[i])); |
---|
| 2022 | } |
---|
| 2023 | else |
---|
| 2024 | { |
---|
[861529] | 2025 | p_Shift(&(temp1->m[i]),-length,currRing); |
---|
[0f401f] | 2026 | } |
---|
| 2027 | } |
---|
| 2028 | temp1->rank = rk; |
---|
| 2029 | idSkipZeroes(temp1); |
---|
| 2030 | |
---|
| 2031 | return temp1; |
---|
| 2032 | } |
---|
| 2033 | */ |
---|
| 2034 | /*2 |
---|
| 2035 | * represents (h1+h2)/h2=h1/(h1 intersect h2) |
---|
| 2036 | */ |
---|
| 2037 | //ideal idModulo (ideal h2,ideal h1) |
---|
| 2038 | ideal idModulo (ideal h2,ideal h1, tHomog hom, intvec ** w) |
---|
| 2039 | { |
---|
| 2040 | intvec *wtmp=NULL; |
---|
| 2041 | |
---|
[bca341] | 2042 | int i,k,rk,flength=0,slength,length; |
---|
[0f401f] | 2043 | poly p,q; |
---|
| 2044 | |
---|
| 2045 | if (idIs0(h2)) |
---|
| 2046 | return idFreeModule(si_max(1,h2->ncols)); |
---|
| 2047 | if (!idIs0(h1)) |
---|
[7b25fe] | 2048 | flength = id_RankFreeModule(h1,currRing); |
---|
| 2049 | slength = id_RankFreeModule(h2,currRing); |
---|
[0f401f] | 2050 | length = si_max(flength,slength); |
---|
| 2051 | if (length==0) |
---|
| 2052 | { |
---|
| 2053 | length = 1; |
---|
| 2054 | } |
---|
| 2055 | ideal temp = idInit(IDELEMS(h2),length+IDELEMS(h2)); |
---|
| 2056 | if ((w!=NULL)&&((*w)!=NULL)) |
---|
| 2057 | { |
---|
| 2058 | //Print("input weights:");(*w)->show(1);PrintLn(); |
---|
| 2059 | int d; |
---|
| 2060 | int k; |
---|
| 2061 | wtmp=new intvec(length+IDELEMS(h2)); |
---|
| 2062 | for (i=0;i<length;i++) |
---|
| 2063 | ((*wtmp)[i])=(**w)[i]; |
---|
| 2064 | for (i=0;i<IDELEMS(h2);i++) |
---|
| 2065 | { |
---|
| 2066 | poly p=h2->m[i]; |
---|
| 2067 | if (p!=NULL) |
---|
| 2068 | { |
---|
[31f1850] | 2069 | d = p_Deg(p,currRing); |
---|
[0f401f] | 2070 | k= pGetComp(p); |
---|
| 2071 | if (slength>0) k--; |
---|
| 2072 | d +=((**w)[k]); |
---|
| 2073 | ((*wtmp)[i+length]) = d; |
---|
| 2074 | } |
---|
| 2075 | } |
---|
| 2076 | //Print("weights:");wtmp->show(1);PrintLn(); |
---|
| 2077 | } |
---|
| 2078 | for (i=0;i<IDELEMS(h2);i++) |
---|
| 2079 | { |
---|
| 2080 | temp->m[i] = pCopy(h2->m[i]); |
---|
| 2081 | q = pOne(); |
---|
| 2082 | pSetComp(q,i+1+length); |
---|
| 2083 | pSetmComp(q); |
---|
| 2084 | if(temp->m[i]!=NULL) |
---|
| 2085 | { |
---|
[861529] | 2086 | if (slength==0) p_Shift(&(temp->m[i]),1,currRing); |
---|
[0f401f] | 2087 | p = temp->m[i]; |
---|
| 2088 | while (pNext(p)!=NULL) pIter(p); |
---|
[80b62c4] | 2089 | pNext(p) = q; // will be sorted later correctly |
---|
[0f401f] | 2090 | } |
---|
| 2091 | else |
---|
| 2092 | temp->m[i]=q; |
---|
| 2093 | } |
---|
| 2094 | rk = k = IDELEMS(h2); |
---|
| 2095 | if (!idIs0(h1)) |
---|
| 2096 | { |
---|
| 2097 | pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1)); |
---|
| 2098 | IDELEMS(temp) += IDELEMS(h1); |
---|
| 2099 | for (i=0;i<IDELEMS(h1);i++) |
---|
| 2100 | { |
---|
| 2101 | if (h1->m[i]!=NULL) |
---|
| 2102 | { |
---|
| 2103 | temp->m[k] = pCopy(h1->m[i]); |
---|
[861529] | 2104 | if (flength==0) p_Shift(&(temp->m[k]),1,currRing); |
---|
[0f401f] | 2105 | k++; |
---|
| 2106 | } |
---|
| 2107 | } |
---|
| 2108 | } |
---|
| 2109 | |
---|
| 2110 | ring orig_ring=currRing; |
---|
[3f07d1] | 2111 | ring syz_ring=rAssure_SyzComp(orig_ring, TRUE); rChangeCurrRing(syz_ring); |
---|
[80b62c4] | 2112 | // we can use OPT_RETURN_SB only, if syz_ring==orig_ring, |
---|
| 2113 | // therefore we disable OPT_RETURN_SB for modulo: |
---|
| 2114 | // (see tr. #701) |
---|
| 2115 | //if (TEST_OPT_RETURN_SB) |
---|
| 2116 | // rSetSyzComp(IDELEMS(h2)+length, syz_ring); |
---|
| 2117 | //else |
---|
[fe09c54] | 2118 | rSetSyzComp(length, syz_ring); |
---|
[0f401f] | 2119 | ideal s_temp; |
---|
| 2120 | |
---|
| 2121 | if (syz_ring != orig_ring) |
---|
| 2122 | { |
---|
[b7cfaf] | 2123 | s_temp = idrMoveR_NoSort(temp, orig_ring, syz_ring); |
---|
[0f401f] | 2124 | } |
---|
| 2125 | else |
---|
| 2126 | { |
---|
| 2127 | s_temp = temp; |
---|
| 2128 | } |
---|
| 2129 | |
---|
| 2130 | idTest(s_temp); |
---|
[ac00e2f] | 2131 | ideal s_temp1 = kStd(s_temp,currRing->qideal,hom,&wtmp,NULL,length); |
---|
[0f401f] | 2132 | |
---|
| 2133 | //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn(); |
---|
| 2134 | if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL)) |
---|
| 2135 | { |
---|
| 2136 | delete *w; |
---|
| 2137 | *w=new intvec(IDELEMS(h2)); |
---|
| 2138 | for (i=0;i<IDELEMS(h2);i++) |
---|
| 2139 | ((**w)[i])=(*wtmp)[i+length]; |
---|
| 2140 | } |
---|
| 2141 | if (wtmp!=NULL) delete wtmp; |
---|
| 2142 | |
---|
| 2143 | for (i=0;i<IDELEMS(s_temp1);i++) |
---|
| 2144 | { |
---|
| 2145 | if ((s_temp1->m[i]!=NULL) |
---|
[d30a399] | 2146 | && (((int)pGetComp(s_temp1->m[i]))<=length)) |
---|
[0f401f] | 2147 | { |
---|
[f9591a] | 2148 | p_Delete(&(s_temp1->m[i]),currRing); |
---|
[0f401f] | 2149 | } |
---|
| 2150 | else |
---|
| 2151 | { |
---|
[861529] | 2152 | p_Shift(&(s_temp1->m[i]),-length,currRing); |
---|
[0f401f] | 2153 | } |
---|
| 2154 | } |
---|
| 2155 | s_temp1->rank = rk; |
---|
| 2156 | idSkipZeroes(s_temp1); |
---|
| 2157 | |
---|
| 2158 | if (syz_ring!=orig_ring) |
---|
| 2159 | { |
---|
| 2160 | rChangeCurrRing(orig_ring); |
---|
[b7cfaf] | 2161 | s_temp1 = idrMoveR_NoSort(s_temp1, syz_ring, orig_ring); |
---|
[5fe834] | 2162 | rDelete(syz_ring); |
---|
[0f401f] | 2163 | // Hmm ... here seems to be a memory leak |
---|
| 2164 | // However, simply deleting it causes memory trouble |
---|
| 2165 | // idDelete(&s_temp); |
---|
| 2166 | } |
---|
| 2167 | else |
---|
| 2168 | { |
---|
| 2169 | idDelete(&temp); |
---|
| 2170 | } |
---|
| 2171 | idTest(s_temp1); |
---|
| 2172 | return s_temp1; |
---|
| 2173 | } |
---|
| 2174 | |
---|
| 2175 | /* |
---|
| 2176 | *computes module-weights for liftings of homogeneous modules |
---|
| 2177 | */ |
---|
| 2178 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
| 2179 | { |
---|
| 2180 | if (idIs0(mod)) return new intvec(2); |
---|
| 2181 | int i=IDELEMS(mod); |
---|
| 2182 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
| 2183 | intvec *result = new intvec(i+1); |
---|
| 2184 | while (i>0) |
---|
| 2185 | { |
---|
[b7cfaf] | 2186 | (*result)[i]=currRing->pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])]; |
---|
[0f401f] | 2187 | } |
---|
| 2188 | return result; |
---|
| 2189 | } |
---|
| 2190 | |
---|
| 2191 | /*2 |
---|
| 2192 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
| 2193 | *with x_max,...,x_1) |
---|
| 2194 | */ |
---|
| 2195 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
| 2196 | { |
---|
| 2197 | int i; |
---|
| 2198 | ideal result; |
---|
| 2199 | |
---|
| 2200 | if (idIs0(kBase)) return NULL; |
---|
| 2201 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
| 2202 | *convert = idSort(kBase,FALSE); |
---|
| 2203 | for (i=0;i<(*convert)->length();i++) |
---|
| 2204 | { |
---|
| 2205 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
| 2206 | } |
---|
| 2207 | return result; |
---|
| 2208 | } |
---|
| 2209 | |
---|
| 2210 | /*2 |
---|
| 2211 | *returns the index of a given monom in the list of the special kbase |
---|
| 2212 | */ |
---|
| 2213 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
| 2214 | { |
---|
| 2215 | int j=IDELEMS(kbase); |
---|
| 2216 | |
---|
| 2217 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
| 2218 | if (j==0) return -1; |
---|
[1f637e] | 2219 | int i=(currRing->N); |
---|
[0f401f] | 2220 | while (i>0) |
---|
| 2221 | { |
---|
| 2222 | loop |
---|
| 2223 | { |
---|
| 2224 | if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1; |
---|
| 2225 | if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break; |
---|
| 2226 | j--; |
---|
| 2227 | if (j==0) return -1; |
---|
| 2228 | } |
---|
| 2229 | if (i==1) |
---|
| 2230 | { |
---|
| 2231 | while(j>0) |
---|
| 2232 | { |
---|
| 2233 | if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1; |
---|
| 2234 | if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1; |
---|
| 2235 | j--; |
---|
| 2236 | } |
---|
| 2237 | } |
---|
| 2238 | i--; |
---|
| 2239 | } |
---|
| 2240 | return -1; |
---|
| 2241 | } |
---|
| 2242 | |
---|
| 2243 | /*2 |
---|
| 2244 | *decomposes the monom in a part of coefficients described by the |
---|
| 2245 | *complement of how and a monom in variables occuring in how, the |
---|
| 2246 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
| 2247 | *exists) |
---|
| 2248 | */ |
---|
| 2249 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
| 2250 | { |
---|
| 2251 | int i; |
---|
| 2252 | poly coeff=pOne(), base=pOne(); |
---|
| 2253 | |
---|
[1f637e] | 2254 | for (i=1;i<=(currRing->N);i++) |
---|
[0f401f] | 2255 | { |
---|
| 2256 | if (pGetExp(how,i)>0) |
---|
| 2257 | { |
---|
| 2258 | pSetExp(base,i,pGetExp(monom,i)); |
---|
| 2259 | } |
---|
| 2260 | else |
---|
| 2261 | { |
---|
| 2262 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
| 2263 | } |
---|
| 2264 | } |
---|
| 2265 | pSetComp(base,pGetComp(monom)); |
---|
| 2266 | pSetm(base); |
---|
| 2267 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
| 2268 | pSetm(coeff); |
---|
| 2269 | *pos = idIndexOfKBase(base,kbase); |
---|
| 2270 | if (*pos<0) |
---|
[f9591a] | 2271 | p_Delete(&coeff,currRing); |
---|
| 2272 | p_Delete(&base,currRing); |
---|
[0f401f] | 2273 | return coeff; |
---|
| 2274 | } |
---|
| 2275 | |
---|
| 2276 | /*2 |
---|
| 2277 | *returns a matrix A of coefficients with kbase*A=arg |
---|
| 2278 | *if all monomials in variables of how occur in kbase |
---|
| 2279 | *the other are deleted |
---|
| 2280 | */ |
---|
| 2281 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
| 2282 | { |
---|
| 2283 | matrix result; |
---|
| 2284 | ideal tempKbase; |
---|
| 2285 | poly p,q; |
---|
| 2286 | intvec * convert; |
---|
| 2287 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
| 2288 | #if 0 |
---|
| 2289 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
| 2290 | if (idIs0(arg)) |
---|
| 2291 | return mpNew(i,1); |
---|
| 2292 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
| 2293 | result = mpNew(i,j); |
---|
| 2294 | #else |
---|
| 2295 | result = mpNew(i, j); |
---|
| 2296 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
| 2297 | #endif |
---|
| 2298 | |
---|
| 2299 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
| 2300 | for (k=0;k<j;k++) |
---|
| 2301 | { |
---|
| 2302 | p = arg->m[k]; |
---|
| 2303 | while (p!=NULL) |
---|
| 2304 | { |
---|
| 2305 | q = idDecompose(p,how,tempKbase,&pos); |
---|
| 2306 | if (pos>=0) |
---|
| 2307 | { |
---|
| 2308 | MATELEM(result,(*convert)[pos],k+1) = |
---|
| 2309 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
| 2310 | } |
---|
| 2311 | else |
---|
[f9591a] | 2312 | p_Delete(&q,currRing); |
---|
[0f401f] | 2313 | pIter(p); |
---|
| 2314 | } |
---|
| 2315 | } |
---|
| 2316 | idDelete(&tempKbase); |
---|
| 2317 | return result; |
---|
| 2318 | } |
---|
| 2319 | |
---|
| 2320 | static void idDeleteComps(ideal arg,int* red_comp,int del) |
---|
| 2321 | // red_comp is an array [0..args->rank] |
---|
| 2322 | { |
---|
| 2323 | int i,j; |
---|
| 2324 | poly p; |
---|
| 2325 | |
---|
| 2326 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
| 2327 | { |
---|
| 2328 | p = arg->m[i]; |
---|
| 2329 | while (p!=NULL) |
---|
| 2330 | { |
---|
| 2331 | j = pGetComp(p); |
---|
| 2332 | if (red_comp[j]!=j) |
---|
| 2333 | { |
---|
| 2334 | pSetComp(p,red_comp[j]); |
---|
| 2335 | pSetmComp(p); |
---|
| 2336 | } |
---|
| 2337 | pIter(p); |
---|
| 2338 | } |
---|
| 2339 | } |
---|
| 2340 | (arg->rank) -= del; |
---|
| 2341 | } |
---|
| 2342 | |
---|
| 2343 | /*2 |
---|
| 2344 | * returns the presentation of an isomorphic, minimally |
---|
| 2345 | * embedded module (arg represents the quotient!) |
---|
| 2346 | */ |
---|
| 2347 | ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w) |
---|
| 2348 | { |
---|
| 2349 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
| 2350 | int i,next_gen,next_comp; |
---|
| 2351 | ideal res=arg; |
---|
| 2352 | if (!inPlace) res = idCopy(arg); |
---|
[7b25fe] | 2353 | res->rank=si_max(res->rank,id_RankFreeModule(res,currRing)); |
---|
[0f401f] | 2354 | int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int)); |
---|
| 2355 | for (i=res->rank;i>=0;i--) red_comp[i]=i; |
---|
| 2356 | |
---|
| 2357 | int del=0; |
---|
| 2358 | loop |
---|
| 2359 | { |
---|
[d16ea9] | 2360 | next_gen = id_ReadOutPivot(res, &next_comp, currRing); |
---|
[0f401f] | 2361 | if (next_gen<0) break; |
---|
| 2362 | del++; |
---|
| 2363 | syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res)); |
---|
| 2364 | for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--; |
---|
| 2365 | if ((w !=NULL)&&(*w!=NULL)) |
---|
| 2366 | { |
---|
| 2367 | for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i]; |
---|
| 2368 | } |
---|
| 2369 | } |
---|
| 2370 | |
---|
| 2371 | idDeleteComps(res,red_comp,del); |
---|
| 2372 | idSkipZeroes(res); |
---|
| 2373 | omFree(red_comp); |
---|
| 2374 | |
---|
| 2375 | if ((w !=NULL)&&(*w!=NULL) &&(del>0)) |
---|
| 2376 | { |
---|
[424492] | 2377 | int nl=si_max((*w)->length()-del,1); |
---|
| 2378 | intvec *wtmp=new intvec(nl); |
---|
[0f401f] | 2379 | for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i]; |
---|
| 2380 | delete *w; |
---|
| 2381 | *w=wtmp; |
---|
| 2382 | } |
---|
| 2383 | return res; |
---|
| 2384 | } |
---|
| 2385 | |
---|
[76cfef] | 2386 | #include <polys/clapsing.h> |
---|
[0f401f] | 2387 | |
---|
[7e6bfe] | 2388 | #if 0 |
---|
[0f401f] | 2389 | poly id_GCD(poly f, poly g, const ring r) |
---|
| 2390 | { |
---|
| 2391 | ring save_r=currRing; |
---|
| 2392 | rChangeCurrRing(r); |
---|
| 2393 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
| 2394 | intvec *w = NULL; |
---|
| 2395 | ideal S=idSyzygies(I,testHomog,&w); |
---|
| 2396 | if (w!=NULL) delete w; |
---|
| 2397 | poly gg=pTakeOutComp(&(S->m[0]),2); |
---|
| 2398 | idDelete(&S); |
---|
[b7cfaf] | 2399 | poly gcd_p=singclap_pdivide(f,gg,r); |
---|
[f9591a] | 2400 | p_Delete(&gg,r); |
---|
[0f401f] | 2401 | rChangeCurrRing(save_r); |
---|
| 2402 | return gcd_p; |
---|
| 2403 | } |
---|
[7e6bfe] | 2404 | #else |
---|
| 2405 | poly id_GCD(poly f, poly g, const ring r) |
---|
| 2406 | { |
---|
| 2407 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
| 2408 | intvec *w = NULL; |
---|
| 2409 | |
---|
[a5d181c] | 2410 | ring save_r = currRing; rChangeCurrRing(r); ideal S=idSyzygies(I,testHomog,&w); rChangeCurrRing(save_r); |
---|
| 2411 | |
---|
[7e6bfe] | 2412 | if (w!=NULL) delete w; |
---|
| 2413 | poly gg=p_TakeOutComp(&(S->m[0]), 2, r); |
---|
| 2414 | id_Delete(&S, r); |
---|
| 2415 | poly gcd_p=singclap_pdivide(f,gg, r); |
---|
| 2416 | p_Delete(&gg, r); |
---|
[a5d181c] | 2417 | |
---|
[7e6bfe] | 2418 | return gcd_p; |
---|
| 2419 | } |
---|
| 2420 | #endif |
---|
[0f401f] | 2421 | |
---|
[f11ea16] | 2422 | #if 0 |
---|
| 2423 | /*2 |
---|
| 2424 | * xx,q: arrays of length 0..rl-1 |
---|
| 2425 | * xx[i]: SB mod q[i] |
---|
| 2426 | * assume: char=0 |
---|
| 2427 | * assume: q[i]!=0 |
---|
| 2428 | * destroys xx |
---|
| 2429 | */ |
---|
| 2430 | ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring R) |
---|
| 2431 | { |
---|
| 2432 | int cnt=IDELEMS(xx[0])*xx[0]->nrows; |
---|
| 2433 | ideal result=idInit(cnt,xx[0]->rank); |
---|
| 2434 | result->nrows=xx[0]->nrows; // for lifting matrices |
---|
| 2435 | result->ncols=xx[0]->ncols; // for lifting matrices |
---|
| 2436 | int i,j; |
---|
| 2437 | poly r,h,hh,res_p; |
---|
| 2438 | number *x=(number *)omAlloc(rl*sizeof(number)); |
---|
| 2439 | for(i=cnt-1;i>=0;i--) |
---|
| 2440 | { |
---|
| 2441 | res_p=NULL; |
---|
| 2442 | loop |
---|
| 2443 | { |
---|
| 2444 | r=NULL; |
---|
| 2445 | for(j=rl-1;j>=0;j--) |
---|
| 2446 | { |
---|
| 2447 | h=xx[j]->m[i]; |
---|
| 2448 | if ((h!=NULL) |
---|
| 2449 | &&((r==NULL)||(p_LmCmp(r,h,R)==-1))) |
---|
| 2450 | r=h; |
---|
| 2451 | } |
---|
| 2452 | if (r==NULL) break; |
---|
| 2453 | h=p_Head(r, R); |
---|
| 2454 | for(j=rl-1;j>=0;j--) |
---|
| 2455 | { |
---|
| 2456 | hh=xx[j]->m[i]; |
---|
| 2457 | if ((hh!=NULL) && (p_LmCmp(r,hh, R)==0)) |
---|
| 2458 | { |
---|
| 2459 | x[j]=p_GetCoeff(hh, R); |
---|
| 2460 | hh=p_LmFreeAndNext(hh, R); |
---|
| 2461 | xx[j]->m[i]=hh; |
---|
| 2462 | } |
---|
| 2463 | else |
---|
| 2464 | x[j]=n_Init(0, R->cf); // is R->cf really n_Q???, yes! |
---|
| 2465 | } |
---|
[a5d181c] | 2466 | |
---|
[7938a0f] | 2467 | number n=n_ChineseRemainder(x,q,rl, R->cf); |
---|
[f11ea16] | 2468 | |
---|
| 2469 | for(j=rl-1;j>=0;j--) |
---|
| 2470 | { |
---|
| 2471 | x[j]=NULL; // nlInit(0...) takes no memory |
---|
| 2472 | } |
---|
| 2473 | if (n_IsZero(n, R->cf)) p_Delete(&h, R); |
---|
| 2474 | else |
---|
| 2475 | { |
---|
| 2476 | p_SetCoeff(h,n, R); |
---|
| 2477 | //Print("new mon:");pWrite(h); |
---|
| 2478 | res_p=p_Add_q(res_p, h, R); |
---|
| 2479 | } |
---|
| 2480 | } |
---|
| 2481 | result->m[i]=res_p; |
---|
| 2482 | } |
---|
| 2483 | omFree(x); |
---|
| 2484 | for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]), R); |
---|
| 2485 | omFree(xx); |
---|
| 2486 | return result; |
---|
| 2487 | } |
---|
| 2488 | #endif |
---|
[0f401f] | 2489 | /* currently unsed: |
---|
| 2490 | ideal idChineseRemainder(ideal *xx, intvec *iv) |
---|
| 2491 | { |
---|
| 2492 | int rl=iv->length(); |
---|
| 2493 | number *q=(number *)omAlloc(rl*sizeof(number)); |
---|
| 2494 | int i; |
---|
| 2495 | for(i=0; i<rl; i++) |
---|
| 2496 | { |
---|
| 2497 | q[i]=nInit((*iv)[i]); |
---|
| 2498 | } |
---|
| 2499 | return idChineseRemainder(xx,q,rl); |
---|
| 2500 | } |
---|
| 2501 | */ |
---|
| 2502 | /* |
---|
| 2503 | * lift ideal with coeffs over Z (mod N) to Q via Farey |
---|
| 2504 | */ |
---|
[f9591a] | 2505 | ideal id_Farey(ideal x, number N, const ring r) |
---|
[0f401f] | 2506 | { |
---|
| 2507 | int cnt=IDELEMS(x)*x->nrows; |
---|
| 2508 | ideal result=idInit(cnt,x->rank); |
---|
| 2509 | result->nrows=x->nrows; // for lifting matrices |
---|
| 2510 | result->ncols=x->ncols; // for lifting matrices |
---|
| 2511 | |
---|
| 2512 | int i; |
---|
| 2513 | for(i=cnt-1;i>=0;i--) |
---|
| 2514 | { |
---|
[0b0bc3] | 2515 | result->m[i]=p_Farey(x->m[i],N,r); |
---|
[0f401f] | 2516 | } |
---|
| 2517 | return result; |
---|
| 2518 | } |
---|
[38fc181] | 2519 | |
---|
| 2520 | |
---|
| 2521 | |
---|
| 2522 | |
---|
| 2523 | // uses glabl vars via pSetModDeg |
---|
| 2524 | /* |
---|
| 2525 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
| 2526 | { |
---|
| 2527 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
| 2528 | if (idIs0(m)) return TRUE; |
---|
| 2529 | |
---|
| 2530 | int cmax=-1; |
---|
| 2531 | int i; |
---|
| 2532 | poly p=NULL; |
---|
| 2533 | int length=IDELEMS(m); |
---|
| 2534 | poly* P=m->m; |
---|
| 2535 | for (i=length-1;i>=0;i--) |
---|
| 2536 | { |
---|
| 2537 | p=P[i]; |
---|
| 2538 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
| 2539 | } |
---|
| 2540 | if (w != NULL) |
---|
| 2541 | if (w->length()+1 < cmax) |
---|
| 2542 | { |
---|
| 2543 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
| 2544 | return FALSE; |
---|
| 2545 | } |
---|
| 2546 | |
---|
| 2547 | if(w!=NULL) |
---|
| 2548 | p_SetModDeg(w, currRing); |
---|
| 2549 | |
---|
| 2550 | for (i=length-1;i>=0;i--) |
---|
| 2551 | { |
---|
| 2552 | p=P[i]; |
---|
| 2553 | poly q=p; |
---|
| 2554 | if (p!=NULL) |
---|
| 2555 | { |
---|
| 2556 | int d=p_FDeg(p,currRing); |
---|
| 2557 | loop |
---|
| 2558 | { |
---|
| 2559 | pIter(p); |
---|
| 2560 | if (p==NULL) break; |
---|
| 2561 | if (d!=p_FDeg(p,currRing)) |
---|
| 2562 | { |
---|
| 2563 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
| 2564 | if(w!=NULL) |
---|
| 2565 | p_SetModDeg(NULL, currRing); |
---|
| 2566 | return FALSE; |
---|
| 2567 | } |
---|
| 2568 | } |
---|
| 2569 | } |
---|
| 2570 | } |
---|
| 2571 | |
---|
| 2572 | if(w!=NULL) |
---|
| 2573 | p_SetModDeg(NULL, currRing); |
---|
| 2574 | |
---|
| 2575 | return TRUE; |
---|
| 2576 | } |
---|
| 2577 | */ |
---|
| 2578 | |
---|
[9234fb] | 2579 | /// keeps the first k (>= 1) entries of the given ideal |
---|
| 2580 | /// (Note that the kept polynomials may be zero.) |
---|
| 2581 | void idKeepFirstK(ideal id, const int k) |
---|
| 2582 | { |
---|
[ae78cf] | 2583 | for (int i = IDELEMS(id)-1; i >= k; i--) |
---|
| 2584 | { |
---|
| 2585 | if (id->m[i] != NULL) pDelete(&id->m[i]); |
---|
| 2586 | } |
---|
[a9c298] | 2587 | int kk=k; |
---|
| 2588 | if (k==0) kk=1; /* ideals must have at least one element(0)*/ |
---|
| 2589 | pEnlargeSet(&(id->m), IDELEMS(id), kk-IDELEMS(id)); |
---|
| 2590 | IDELEMS(id) = kk; |
---|
[9234fb] | 2591 | } |
---|
[38fc181] | 2592 | |
---|
[c81bf7] | 2593 | /* |
---|
| 2594 | * compare the leading terms of a and b |
---|
| 2595 | */ |
---|
| 2596 | static int tCompare(const poly a, const poly b) |
---|
| 2597 | { |
---|
[b0a811] | 2598 | if (b == NULL) return(a != NULL); |
---|
[c81bf7] | 2599 | if (a == NULL) return(-1); |
---|
| 2600 | |
---|
| 2601 | /* a != NULL && b != NULL */ |
---|
| 2602 | int r = pLmCmp(a, b); |
---|
| 2603 | if (r != 0) return(r); |
---|
| 2604 | number h = nSub(pGetCoeff(a), pGetCoeff(b)); |
---|
| 2605 | r = -1 + nIsZero(h) + 2*nGreaterZero(h); /* -1: <, 0:==, 1: > */ |
---|
| 2606 | nDelete(&h); |
---|
| 2607 | return(r); |
---|
| 2608 | } |
---|
| 2609 | |
---|
| 2610 | /* |
---|
| 2611 | * compare a and b (rev-lex on terms) |
---|
| 2612 | */ |
---|
| 2613 | static int pCompare(const poly a, const poly b) |
---|
| 2614 | { |
---|
| 2615 | int r = tCompare(a, b); |
---|
| 2616 | if (r != 0) return(r); |
---|
| 2617 | |
---|
| 2618 | poly aa = a; |
---|
| 2619 | poly bb = b; |
---|
| 2620 | while (r == 0 && aa != NULL && bb != NULL) |
---|
| 2621 | { |
---|
| 2622 | pIter(aa); |
---|
| 2623 | pIter(bb); |
---|
| 2624 | r = tCompare(aa, bb); |
---|
| 2625 | } |
---|
| 2626 | return(r); |
---|
| 2627 | } |
---|
| 2628 | |
---|
| 2629 | typedef struct |
---|
| 2630 | { |
---|
| 2631 | poly p; |
---|
| 2632 | int index; |
---|
| 2633 | } poly_sort; |
---|
| 2634 | |
---|
| 2635 | int pCompare_qsort(const void *a, const void *b) |
---|
| 2636 | { |
---|
| 2637 | int res = pCompare(((poly_sort *)a)->p, ((poly_sort *)b)->p); |
---|
| 2638 | return(res); |
---|
| 2639 | } |
---|
| 2640 | |
---|
| 2641 | void idSort_qsort(poly_sort *id_sort, int idsize) |
---|
| 2642 | { |
---|
| 2643 | qsort(id_sort, idsize, sizeof(poly_sort), pCompare_qsort); |
---|
| 2644 | } |
---|
| 2645 | |
---|
| 2646 | /*2 |
---|
| 2647 | * ideal id = (id[i]) |
---|
| 2648 | * if id[i] = id[j] then id[j] is deleted for j > i |
---|
| 2649 | */ |
---|
| 2650 | void idDelEquals(ideal id) |
---|
| 2651 | { |
---|
| 2652 | int idsize = IDELEMS(id); |
---|
| 2653 | poly_sort *id_sort = (poly_sort *)omAlloc0(idsize*sizeof(poly_sort)); |
---|
| 2654 | for (int i = 0; i < idsize; i++) |
---|
| 2655 | { |
---|
| 2656 | id_sort[i].p = id->m[i]; |
---|
| 2657 | id_sort[i].index = i; |
---|
| 2658 | } |
---|
| 2659 | idSort_qsort(id_sort, idsize); |
---|
| 2660 | int index, index_i, index_j; |
---|
| 2661 | int i = 0; |
---|
| 2662 | for (int j = 1; j < idsize; j++) |
---|
| 2663 | { |
---|
[b0a811] | 2664 | if (id_sort[i].p != NULL && pEqualPolys(id_sort[i].p, id_sort[j].p)) |
---|
[c81bf7] | 2665 | { |
---|
| 2666 | index_i = id_sort[i].index; |
---|
| 2667 | index_j = id_sort[j].index; |
---|
| 2668 | if (index_j > index_i) |
---|
| 2669 | { |
---|
| 2670 | index = index_j; |
---|
| 2671 | } |
---|
| 2672 | else |
---|
| 2673 | { |
---|
| 2674 | index = index_i; |
---|
| 2675 | i = j; |
---|
| 2676 | } |
---|
[b0a811] | 2677 | pDelete(&id->m[index]); |
---|
[c81bf7] | 2678 | } |
---|
| 2679 | else |
---|
| 2680 | { |
---|
| 2681 | i = j; |
---|
| 2682 | } |
---|
| 2683 | } |
---|
| 2684 | omFreeSize((ADDRESS)(id_sort), idsize*sizeof(poly_sort)); |
---|
| 2685 | } |
---|