[35aab3] | 1 | /**************************************** |
---|
| 2 | * Computer Algebra System SINGULAR * |
---|
| 3 | ****************************************/ |
---|
[341696] | 4 | /* $Id$ */ |
---|
[35aab3] | 5 | /* |
---|
| 6 | * ABSTRACT - all basic methods to manipulate ideals |
---|
| 7 | */ |
---|
| 8 | |
---|
[2ad10e9] | 9 | |
---|
[35aab3] | 10 | /* includes */ |
---|
[2ad10e9] | 11 | #include "config.h" |
---|
| 12 | #include <misc/auxiliary.h> |
---|
[af598e] | 13 | |
---|
[f71e8c5] | 14 | #include <omalloc/omalloc.h> |
---|
[af598e] | 15 | |
---|
| 16 | #include <misc/options.h> |
---|
[f5c2d02] | 17 | #include <misc/intvec.h> |
---|
[af598e] | 18 | |
---|
[7829fb] | 19 | // #include <coeffs/longrat.h> |
---|
| 20 | #include "matpol.h" |
---|
| 21 | |
---|
[af598e] | 22 | #include "monomials/p_polys.h" |
---|
| 23 | #include "weight.h" |
---|
[a2d993] | 24 | #include "sbuckets.h" |
---|
[529fa4] | 25 | #include "clapsing.h" |
---|
[35aab3] | 26 | |
---|
[7829fb] | 27 | #include "simpleideals.h" |
---|
| 28 | |
---|
[fba6f18] | 29 | omBin sip_sideal_bin = omGetSpecBin(sizeof(sip_sideal)); |
---|
[9765f3] | 30 | |
---|
[2f5547] | 31 | static poly * idpower; |
---|
| 32 | /*collects the monomials in makemonoms, must be allocated befor*/ |
---|
| 33 | static int idpowerpoint; |
---|
| 34 | /*index of the actual monomial in idpower*/ |
---|
| 35 | static poly * givenideal; |
---|
| 36 | /*the ideal from which a power is computed*/ |
---|
| 37 | |
---|
[35aab3] | 38 | /*2 |
---|
| 39 | * initialise an ideal |
---|
| 40 | */ |
---|
| 41 | ideal idInit(int idsize, int rank) |
---|
| 42 | { |
---|
| 43 | /*- initialise an ideal -*/ |
---|
| 44 | ideal hh = (ideal )omAllocBin(sip_sideal_bin); |
---|
| 45 | hh->nrows = 1; |
---|
| 46 | hh->rank = rank; |
---|
| 47 | IDELEMS(hh) = idsize; |
---|
| 48 | if (idsize>0) |
---|
| 49 | { |
---|
| 50 | hh->m = (poly *)omAlloc0(idsize*sizeof(poly)); |
---|
| 51 | } |
---|
| 52 | else |
---|
| 53 | hh->m=NULL; |
---|
| 54 | return hh; |
---|
| 55 | } |
---|
| 56 | |
---|
[e9c3b2] | 57 | #ifdef PDEBUG |
---|
[e070895] | 58 | // this is only for outputting an ideal within the debugger |
---|
[645a19] | 59 | void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint) |
---|
[35aab3] | 60 | { |
---|
[645a19] | 61 | assume( debugPrint >= 0 ); |
---|
[bead81] | 62 | |
---|
[52e2f6] | 63 | if( id == NULL ) |
---|
[f44fb9] | 64 | PrintS("(NULL)"); |
---|
[52e2f6] | 65 | else |
---|
[35aab3] | 66 | { |
---|
[6867f5] | 67 | Print("Module of rank %ld,real rank %ld and %d generators.\n", |
---|
[f71e8c5] | 68 | id->rank,id_RankFreeModule(id, lmRing, tailRing),IDELEMS(id)); |
---|
[645a19] | 69 | |
---|
| 70 | int j = (id->ncols*id->nrows) - 1; |
---|
| 71 | while ((j > 0) && (id->m[j]==NULL)) j--; |
---|
| 72 | for (int i = 0; i <= j; i++) |
---|
[35aab3] | 73 | { |
---|
[645a19] | 74 | Print("generator %d: ",i); p_DebugPrint(id->m[i], lmRing, tailRing, debugPrint); |
---|
[35aab3] | 75 | } |
---|
| 76 | } |
---|
| 77 | } |
---|
[e070895] | 78 | #endif |
---|
[35aab3] | 79 | |
---|
[dd5534] | 80 | /* index of generator with leading term in ground ring (if any); |
---|
| 81 | otherwise -1 */ |
---|
[f71e8c5] | 82 | int id_PosConstant(ideal id, const ring r) |
---|
[dd5534] | 83 | { |
---|
| 84 | int k; |
---|
| 85 | for (k = IDELEMS(id)-1; k>=0; k--) |
---|
| 86 | { |
---|
[f71e8c5] | 87 | if (p_LmIsConstantComp(id->m[k], r) == TRUE) |
---|
[dd5534] | 88 | return k; |
---|
| 89 | } |
---|
| 90 | return -1; |
---|
| 91 | } |
---|
| 92 | |
---|
[35aab3] | 93 | /*2 |
---|
| 94 | * initialise the maximal ideal (at 0) |
---|
| 95 | */ |
---|
[f71e8c5] | 96 | ideal id_MaxIdeal (const ring r) |
---|
[35aab3] | 97 | { |
---|
| 98 | int l; |
---|
| 99 | ideal hh=NULL; |
---|
| 100 | |
---|
[f71e8c5] | 101 | hh=idInit(rVar(r),1); |
---|
| 102 | for (l=0; l<rVar(r); l++) |
---|
[35aab3] | 103 | { |
---|
[f71e8c5] | 104 | hh->m[l] = p_One(r); |
---|
| 105 | p_SetExp(hh->m[l],l+1,1,r); |
---|
| 106 | p_Setm(hh->m[l],r); |
---|
[35aab3] | 107 | } |
---|
| 108 | return hh; |
---|
| 109 | } |
---|
| 110 | |
---|
| 111 | /*2 |
---|
| 112 | * deletes an ideal/matrix |
---|
| 113 | */ |
---|
| 114 | void id_Delete (ideal * h, ring r) |
---|
| 115 | { |
---|
| 116 | int j,elems; |
---|
| 117 | if (*h == NULL) |
---|
| 118 | return; |
---|
| 119 | elems=j=(*h)->nrows*(*h)->ncols; |
---|
| 120 | if (j>0) |
---|
| 121 | { |
---|
| 122 | do |
---|
| 123 | { |
---|
| 124 | p_Delete(&((*h)->m[--j]), r); |
---|
| 125 | } |
---|
| 126 | while (j>0); |
---|
| 127 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
---|
| 128 | } |
---|
| 129 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
---|
| 130 | *h=NULL; |
---|
| 131 | } |
---|
| 132 | |
---|
| 133 | |
---|
| 134 | /*2 |
---|
| 135 | * Shallowdeletes an ideal/matrix |
---|
| 136 | */ |
---|
| 137 | void id_ShallowDelete (ideal *h, ring r) |
---|
| 138 | { |
---|
| 139 | int j,elems; |
---|
| 140 | if (*h == NULL) |
---|
| 141 | return; |
---|
| 142 | elems=j=(*h)->nrows*(*h)->ncols; |
---|
| 143 | if (j>0) |
---|
| 144 | { |
---|
| 145 | do |
---|
| 146 | { |
---|
| 147 | p_ShallowDelete(&((*h)->m[--j]), r); |
---|
| 148 | } |
---|
| 149 | while (j>0); |
---|
| 150 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
---|
| 151 | } |
---|
| 152 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
---|
| 153 | *h=NULL; |
---|
| 154 | } |
---|
| 155 | |
---|
| 156 | /*2 |
---|
| 157 | *gives an ideal the minimal possible size |
---|
| 158 | */ |
---|
| 159 | void idSkipZeroes (ideal ide) |
---|
| 160 | { |
---|
| 161 | int k; |
---|
| 162 | int j = -1; |
---|
| 163 | BOOLEAN change=FALSE; |
---|
| 164 | for (k=0; k<IDELEMS(ide); k++) |
---|
| 165 | { |
---|
| 166 | if (ide->m[k] != NULL) |
---|
| 167 | { |
---|
| 168 | j++; |
---|
| 169 | if (change) |
---|
| 170 | { |
---|
| 171 | ide->m[j] = ide->m[k]; |
---|
| 172 | } |
---|
| 173 | } |
---|
| 174 | else |
---|
| 175 | { |
---|
| 176 | change=TRUE; |
---|
| 177 | } |
---|
| 178 | } |
---|
| 179 | if (change) |
---|
| 180 | { |
---|
| 181 | if (j == -1) |
---|
| 182 | j = 0; |
---|
| 183 | else |
---|
| 184 | { |
---|
| 185 | for (k=j+1; k<IDELEMS(ide); k++) |
---|
| 186 | ide->m[k] = NULL; |
---|
| 187 | } |
---|
| 188 | pEnlargeSet(&(ide->m),IDELEMS(ide),j+1-IDELEMS(ide)); |
---|
| 189 | IDELEMS(ide) = j+1; |
---|
| 190 | } |
---|
| 191 | } |
---|
| 192 | |
---|
[2b3caae] | 193 | /*2 |
---|
| 194 | * copies the first k (>= 1) entries of the given ideal |
---|
| 195 | * and returns these as a new ideal |
---|
| 196 | * (Note that the copied polynomials may be zero.) |
---|
| 197 | */ |
---|
[f71e8c5] | 198 | ideal id_CopyFirstK (const ideal ide, const int k,const ring r) |
---|
[2b3caae] | 199 | { |
---|
| 200 | ideal newI = idInit(k, 0); |
---|
| 201 | for (int i = 0; i < k; i++) |
---|
[f71e8c5] | 202 | newI->m[i] = p_Copy(ide->m[i],r); |
---|
[2b3caae] | 203 | return newI; |
---|
| 204 | } |
---|
| 205 | |
---|
[35aab3] | 206 | /*2 |
---|
| 207 | * ideal id = (id[i]) |
---|
| 208 | * result is leadcoeff(id[i]) = 1 |
---|
| 209 | */ |
---|
[9aa29b] | 210 | void id_Norm(ideal id, const ring r) |
---|
[35aab3] | 211 | { |
---|
[699567] | 212 | for (int i=IDELEMS(id)-1; i>=0; i--) |
---|
[35aab3] | 213 | { |
---|
| 214 | if (id->m[i] != NULL) |
---|
| 215 | { |
---|
[9aa29b] | 216 | p_Norm(id->m[i],r); |
---|
[35aab3] | 217 | } |
---|
| 218 | } |
---|
| 219 | } |
---|
| 220 | |
---|
| 221 | /*2 |
---|
[dd5534] | 222 | * ideal id = (id[i]), c any unit |
---|
[35aab3] | 223 | * if id[i] = c*id[j] then id[j] is deleted for j > i |
---|
| 224 | */ |
---|
[f5c2d02] | 225 | void id_DelMultiples(ideal id, const ring r) |
---|
[35aab3] | 226 | { |
---|
[699567] | 227 | int i, j; |
---|
| 228 | int k = IDELEMS(id)-1; |
---|
| 229 | for (i=k; i>=0; i--) |
---|
[35aab3] | 230 | { |
---|
| 231 | if (id->m[i]!=NULL) |
---|
| 232 | { |
---|
[699567] | 233 | for (j=k; j>i; j--) |
---|
[35aab3] | 234 | { |
---|
[dd5534] | 235 | if (id->m[j]!=NULL) |
---|
[35aab3] | 236 | { |
---|
[dd5534] | 237 | #ifdef HAVE_RINGS |
---|
[f5c2d02] | 238 | if (rField_is_Ring(r)) |
---|
[dd5534] | 239 | { |
---|
| 240 | /* if id[j] = c*id[i] then delete id[j]. |
---|
| 241 | In the below cases of a ground field, we |
---|
| 242 | check whether id[i] = c*id[j] and, if so, |
---|
| 243 | delete id[j] for historical reasons (so |
---|
| 244 | that previous output does not change) */ |
---|
[f5c2d02] | 245 | if (p_ComparePolys(id->m[j], id->m[i],r)) p_Delete(&id->m[j],r); |
---|
[dd5534] | 246 | } |
---|
| 247 | else |
---|
| 248 | { |
---|
[f5c2d02] | 249 | if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r); |
---|
[dd5534] | 250 | } |
---|
| 251 | #else |
---|
[f5c2d02] | 252 | if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r); |
---|
[3d0808] | 253 | #endif |
---|
[35aab3] | 254 | } |
---|
| 255 | } |
---|
| 256 | } |
---|
| 257 | } |
---|
| 258 | } |
---|
| 259 | |
---|
| 260 | /*2 |
---|
| 261 | * ideal id = (id[i]) |
---|
| 262 | * if id[i] = id[j] then id[j] is deleted for j > i |
---|
| 263 | */ |
---|
[4a08e7] | 264 | void id_DelEquals(ideal id, const ring r) |
---|
[35aab3] | 265 | { |
---|
[7ac29f] | 266 | int i, j; |
---|
| 267 | int k = IDELEMS(id)-1; |
---|
| 268 | for (i=k; i>=0; i--) |
---|
[35aab3] | 269 | { |
---|
[7ac29f] | 270 | if (id->m[i]!=NULL) |
---|
[35aab3] | 271 | { |
---|
[7ac29f] | 272 | for (j=k; j>i; j--) |
---|
[35aab3] | 273 | { |
---|
[7ac29f] | 274 | if ((id->m[j]!=NULL) |
---|
[4a08e7] | 275 | && (p_EqualPolys(id->m[i], id->m[j],r))) |
---|
[7ac29f] | 276 | { |
---|
[4a08e7] | 277 | p_Delete(&id->m[j],r); |
---|
[7ac29f] | 278 | } |
---|
[35aab3] | 279 | } |
---|
| 280 | } |
---|
| 281 | } |
---|
| 282 | } |
---|
| 283 | |
---|
| 284 | // |
---|
[a8b44d] | 285 | // Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i |
---|
[35aab3] | 286 | // |
---|
[119853] | 287 | void id_DelLmEquals(ideal id, const ring r) |
---|
[35aab3] | 288 | { |
---|
[7ac29f] | 289 | int i, j; |
---|
| 290 | int k = IDELEMS(id)-1; |
---|
| 291 | for (i=k; i>=0; i--) |
---|
[35aab3] | 292 | { |
---|
[73df93] | 293 | if (id->m[i] != NULL) |
---|
[35aab3] | 294 | { |
---|
[7ac29f] | 295 | for (j=k; j>i; j--) |
---|
[35aab3] | 296 | { |
---|
[7ac29f] | 297 | if ((id->m[j] != NULL) |
---|
[119853] | 298 | && p_LmEqual(id->m[i], id->m[j],r) |
---|
[a8b44d] | 299 | #ifdef HAVE_RINGS |
---|
[c9c118] | 300 | && n_IsUnit(pGetCoeff(id->m[i]),r->cf) && n_IsUnit(pGetCoeff(id->m[j]),r->cf) |
---|
[a8b44d] | 301 | #endif |
---|
| 302 | ) |
---|
[35aab3] | 303 | { |
---|
[119853] | 304 | p_Delete(&id->m[j],r); |
---|
[35aab3] | 305 | } |
---|
| 306 | } |
---|
| 307 | } |
---|
| 308 | } |
---|
| 309 | } |
---|
| 310 | |
---|
[a8b44d] | 311 | // |
---|
| 312 | // delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., |
---|
| 313 | // delete id[i], if LT(i) == coeff*mon*LT(j) |
---|
| 314 | // |
---|
[3d0808] | 315 | void id_DelDiv(ideal id, const ring r) |
---|
[35aab3] | 316 | { |
---|
[7ac29f] | 317 | int i, j; |
---|
| 318 | int k = IDELEMS(id)-1; |
---|
| 319 | for (i=k; i>=0; i--) |
---|
[35aab3] | 320 | { |
---|
[73df93] | 321 | if (id->m[i] != NULL) |
---|
[35aab3] | 322 | { |
---|
[7ac29f] | 323 | for (j=k; j>i; j--) |
---|
[35aab3] | 324 | { |
---|
[7ac29f] | 325 | if (id->m[j]!=NULL) |
---|
[35aab3] | 326 | { |
---|
[a8b44d] | 327 | #ifdef HAVE_RINGS |
---|
[3d0808] | 328 | if (rField_is_Ring(r)) |
---|
[a8b44d] | 329 | { |
---|
[3d0808] | 330 | if (p_DivisibleByRingCase(id->m[i], id->m[j],r)) |
---|
[a8b44d] | 331 | { |
---|
[3d0808] | 332 | p_Delete(&id->m[j],r); |
---|
| 333 | } |
---|
| 334 | else if (p_DivisibleByRingCase(id->m[j], id->m[i],r)) |
---|
| 335 | { |
---|
| 336 | p_Delete(&id->m[i],r); |
---|
| 337 | break; |
---|
[a8b44d] | 338 | } |
---|
| 339 | } |
---|
| 340 | else |
---|
| 341 | { |
---|
| 342 | #endif |
---|
| 343 | /* the case of a ground field: */ |
---|
[3d0808] | 344 | if (p_DivisibleBy(id->m[i], id->m[j],r)) |
---|
[7ac29f] | 345 | { |
---|
[3d0808] | 346 | p_Delete(&id->m[j],r); |
---|
[7ac29f] | 347 | } |
---|
[3d0808] | 348 | else if (p_DivisibleBy(id->m[j], id->m[i],r)) |
---|
[7ac29f] | 349 | { |
---|
[3d0808] | 350 | p_Delete(&id->m[i],r); |
---|
[7ac29f] | 351 | break; |
---|
| 352 | } |
---|
[a8b44d] | 353 | #ifdef HAVE_RINGS |
---|
| 354 | } |
---|
[3d0808] | 355 | #endif |
---|
[35aab3] | 356 | } |
---|
| 357 | } |
---|
| 358 | } |
---|
| 359 | } |
---|
| 360 | } |
---|
| 361 | |
---|
| 362 | /*2 |
---|
| 363 | *test if the ideal has only constant polynomials |
---|
| 364 | */ |
---|
[2e7dee] | 365 | BOOLEAN id_IsConstant(ideal id, const ring r) |
---|
[35aab3] | 366 | { |
---|
| 367 | int k; |
---|
| 368 | for (k = IDELEMS(id)-1; k>=0; k--) |
---|
| 369 | { |
---|
[6f3273] | 370 | if (!p_IsConstantPoly(id->m[k],r)) |
---|
[35aab3] | 371 | return FALSE; |
---|
| 372 | } |
---|
| 373 | return TRUE; |
---|
| 374 | } |
---|
| 375 | |
---|
| 376 | /*2 |
---|
| 377 | * copy an ideal |
---|
| 378 | */ |
---|
[2e7dee] | 379 | ideal id_Copy(ideal h1, const ring r) |
---|
[d523f3] | 380 | { |
---|
| 381 | int i; |
---|
| 382 | ideal h2; |
---|
| 383 | |
---|
| 384 | //#ifdef TEST |
---|
| 385 | if (h1 == NULL) |
---|
| 386 | { |
---|
| 387 | h2=idInit(1,1); |
---|
| 388 | } |
---|
| 389 | else |
---|
| 390 | //#endif |
---|
| 391 | { |
---|
| 392 | h2=idInit(IDELEMS(h1),h1->rank); |
---|
| 393 | for (i=IDELEMS(h1)-1; i>=0; i--) |
---|
| 394 | h2->m[i] = p_Copy(h1->m[i],r); |
---|
| 395 | } |
---|
| 396 | return h2; |
---|
| 397 | } |
---|
[35aab3] | 398 | |
---|
| 399 | #ifdef PDEBUG |
---|
[91a72f] | 400 | void id_DBTest(ideal h1, int level, const char *f,const int l, const ring r) |
---|
[35aab3] | 401 | { |
---|
| 402 | int i; |
---|
| 403 | |
---|
| 404 | if (h1 != NULL) |
---|
| 405 | { |
---|
| 406 | // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix |
---|
| 407 | omCheckAddrSize(h1,sizeof(*h1)); |
---|
| 408 | omdebugAddrSize(h1->m,h1->ncols*h1->nrows*sizeof(poly)); |
---|
| 409 | /* to be able to test matrices: */ |
---|
| 410 | for (i=(h1->ncols*h1->nrows)-1; i>=0; i--) |
---|
[91a72f] | 411 | _p_Test(h1->m[i], r, level); |
---|
| 412 | int new_rk=id_RankFreeModule(h1,r); |
---|
[35aab3] | 413 | if(new_rk > h1->rank) |
---|
| 414 | { |
---|
| 415 | dReportError("wrong rank %d (should be %d) in %s:%d\n", |
---|
| 416 | h1->rank, new_rk, f,l); |
---|
| 417 | omPrintAddrInfo(stderr, h1, " for ideal"); |
---|
| 418 | h1->rank=new_rk; |
---|
| 419 | } |
---|
| 420 | } |
---|
| 421 | } |
---|
| 422 | #endif |
---|
| 423 | |
---|
| 424 | /*3 |
---|
| 425 | * for idSort: compare a and b revlex inclusive module comp. |
---|
| 426 | */ |
---|
[2e4757c] | 427 | static int p_Comp_RevLex(poly a, poly b,BOOLEAN nolex, const ring R) |
---|
[35aab3] | 428 | { |
---|
| 429 | if (b==NULL) return 1; |
---|
| 430 | if (a==NULL) return -1; |
---|
| 431 | |
---|
[3d0808] | 432 | if (nolex) |
---|
[2c872b] | 433 | { |
---|
[2e4757c] | 434 | int r=p_LmCmp(a,b,R); |
---|
[2c872b] | 435 | if (r!=0) return r; |
---|
[2e4757c] | 436 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf); |
---|
| 437 | r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */ |
---|
| 438 | n_Delete(&h, R->cf); |
---|
[2c872b] | 439 | return r; |
---|
| 440 | } |
---|
[2e4757c] | 441 | int l=rVar(R); |
---|
| 442 | while ((l>0) && (p_GetExp(a,l,R)==p_GetExp(b,l,R))) l--; |
---|
[35aab3] | 443 | if (l==0) |
---|
| 444 | { |
---|
[2e4757c] | 445 | if (p_GetComp(a,R)==p_GetComp(b,R)) |
---|
[2c872b] | 446 | { |
---|
[2e4757c] | 447 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf); |
---|
| 448 | int r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */ |
---|
| 449 | n_Delete(&h,R->cf); |
---|
[2c872b] | 450 | return r; |
---|
| 451 | } |
---|
[2e4757c] | 452 | if (p_GetComp(a,R)>p_GetComp(b,R)) return 1; |
---|
[35aab3] | 453 | } |
---|
[2e4757c] | 454 | else if (p_GetExp(a,l,R)>p_GetExp(b,l,R)) |
---|
[35aab3] | 455 | return 1; |
---|
| 456 | return -1; |
---|
| 457 | } |
---|
| 458 | |
---|
| 459 | /*2 |
---|
| 460 | *sorts the ideal w.r.t. the actual ringordering |
---|
| 461 | *uses lex-ordering when nolex = FALSE |
---|
| 462 | */ |
---|
[91a72f] | 463 | intvec *id_Sort(ideal id,BOOLEAN nolex, const ring r) |
---|
[35aab3] | 464 | { |
---|
| 465 | poly p,q; |
---|
| 466 | intvec * result = new intvec(IDELEMS(id)); |
---|
| 467 | int i, j, actpos=0, newpos, l; |
---|
| 468 | int diff, olddiff, lastcomp, newcomp; |
---|
| 469 | BOOLEAN notFound; |
---|
| 470 | |
---|
| 471 | for (i=0;i<IDELEMS(id);i++) |
---|
| 472 | { |
---|
| 473 | if (id->m[i]!=NULL) |
---|
| 474 | { |
---|
| 475 | notFound = TRUE; |
---|
| 476 | newpos = actpos / 2; |
---|
| 477 | diff = (actpos+1) / 2; |
---|
| 478 | diff = (diff+1) / 2; |
---|
[91a72f] | 479 | lastcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r); |
---|
[35aab3] | 480 | if (lastcomp<0) |
---|
| 481 | { |
---|
| 482 | newpos -= diff; |
---|
| 483 | } |
---|
| 484 | else if (lastcomp>0) |
---|
| 485 | { |
---|
| 486 | newpos += diff; |
---|
| 487 | } |
---|
| 488 | else |
---|
| 489 | { |
---|
| 490 | notFound = FALSE; |
---|
| 491 | } |
---|
| 492 | //while ((newpos>=0) && (newpos<actpos) && (notFound)) |
---|
| 493 | while (notFound && (newpos>=0) && (newpos<actpos)) |
---|
| 494 | { |
---|
[91a72f] | 495 | newcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r); |
---|
[35aab3] | 496 | olddiff = diff; |
---|
| 497 | if (diff>1) |
---|
| 498 | { |
---|
| 499 | diff = (diff+1) / 2; |
---|
| 500 | if ((newcomp==1) |
---|
| 501 | && (actpos-newpos>1) |
---|
| 502 | && (diff>1) |
---|
| 503 | && (newpos+diff>=actpos)) |
---|
| 504 | { |
---|
| 505 | diff = actpos-newpos-1; |
---|
| 506 | } |
---|
| 507 | else if ((newcomp==-1) |
---|
| 508 | && (diff>1) |
---|
| 509 | && (newpos<diff)) |
---|
| 510 | { |
---|
| 511 | diff = newpos; |
---|
| 512 | } |
---|
| 513 | } |
---|
| 514 | if (newcomp<0) |
---|
| 515 | { |
---|
| 516 | if ((olddiff==1) && (lastcomp>0)) |
---|
| 517 | notFound = FALSE; |
---|
| 518 | else |
---|
| 519 | newpos -= diff; |
---|
| 520 | } |
---|
| 521 | else if (newcomp>0) |
---|
| 522 | { |
---|
| 523 | if ((olddiff==1) && (lastcomp<0)) |
---|
| 524 | { |
---|
| 525 | notFound = FALSE; |
---|
| 526 | newpos++; |
---|
| 527 | } |
---|
| 528 | else |
---|
| 529 | { |
---|
| 530 | newpos += diff; |
---|
| 531 | } |
---|
| 532 | } |
---|
| 533 | else |
---|
| 534 | { |
---|
| 535 | notFound = FALSE; |
---|
| 536 | } |
---|
| 537 | lastcomp = newcomp; |
---|
| 538 | if (diff==0) notFound=FALSE; /*hs*/ |
---|
| 539 | } |
---|
| 540 | if (newpos<0) newpos = 0; |
---|
| 541 | if (newpos>actpos) newpos = actpos; |
---|
[91a72f] | 542 | while ((newpos<actpos) && (p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r)==0)) |
---|
[35aab3] | 543 | newpos++; |
---|
| 544 | for (j=actpos;j>newpos;j--) |
---|
| 545 | { |
---|
| 546 | (*result)[j] = (*result)[j-1]; |
---|
| 547 | } |
---|
| 548 | (*result)[newpos] = i; |
---|
| 549 | actpos++; |
---|
| 550 | } |
---|
| 551 | } |
---|
| 552 | for (j=0;j<actpos;j++) (*result)[j]++; |
---|
| 553 | return result; |
---|
| 554 | } |
---|
| 555 | |
---|
| 556 | /*2 |
---|
| 557 | * concat the lists h1 and h2 without zeros |
---|
| 558 | */ |
---|
[2f5936] | 559 | ideal id_SimpleAdd (ideal h1,ideal h2, const ring R) |
---|
[35aab3] | 560 | { |
---|
| 561 | int i,j,r,l; |
---|
| 562 | ideal result; |
---|
| 563 | |
---|
[2f5936] | 564 | if (h1==NULL) return id_Copy(h2,R); |
---|
| 565 | if (h2==NULL) return id_Copy(h1,R); |
---|
[35aab3] | 566 | j = IDELEMS(h1)-1; |
---|
| 567 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
| 568 | i = IDELEMS(h2)-1; |
---|
| 569 | while ((i >= 0) && (h2->m[i] == NULL)) i--; |
---|
| 570 | r = si_max(h1->rank,h2->rank); |
---|
| 571 | if (i+j==(-2)) |
---|
| 572 | return idInit(1,r); |
---|
| 573 | else |
---|
| 574 | result=idInit(i+j+2,r); |
---|
| 575 | for (l=j; l>=0; l--) |
---|
| 576 | { |
---|
[2f5936] | 577 | result->m[l] = p_Copy(h1->m[l],R); |
---|
[35aab3] | 578 | } |
---|
| 579 | r = i+j+1; |
---|
| 580 | for (l=i; l>=0; l--, r--) |
---|
| 581 | { |
---|
[2f5936] | 582 | result->m[r] = p_Copy(h2->m[l],R); |
---|
[35aab3] | 583 | } |
---|
| 584 | return result; |
---|
| 585 | } |
---|
| 586 | |
---|
[e070895] | 587 | /*2 |
---|
[ded085] | 588 | * insert h2 into h1 (if h2 is not the zero polynomial) |
---|
| 589 | * return TRUE iff h2 was indeed inserted |
---|
[e070895] | 590 | */ |
---|
[ded085] | 591 | BOOLEAN idInsertPoly (ideal h1, poly h2) |
---|
[e070895] | 592 | { |
---|
[ded085] | 593 | if (h2==NULL) return FALSE; |
---|
[e070895] | 594 | int j = IDELEMS(h1)-1; |
---|
| 595 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
| 596 | j++; |
---|
| 597 | if (j==IDELEMS(h1)) |
---|
| 598 | { |
---|
| 599 | pEnlargeSet(&(h1->m),IDELEMS(h1),16); |
---|
| 600 | IDELEMS(h1)+=16; |
---|
| 601 | } |
---|
| 602 | h1->m[j]=h2; |
---|
[ded085] | 603 | return TRUE; |
---|
[e070895] | 604 | } |
---|
| 605 | |
---|
[1a68d1d] | 606 | /*2 |
---|
[2b3caae] | 607 | * insert h2 into h1 depending on the two boolean parameters: |
---|
| 608 | * - if zeroOk is true, then h2 will also be inserted when it is zero |
---|
| 609 | * - if duplicateOk is true, then h2 will also be inserted when it is |
---|
| 610 | * already present in h1 |
---|
[ded085] | 611 | * return TRUE iff h2 was indeed inserted |
---|
[1a68d1d] | 612 | */ |
---|
[2f5936] | 613 | BOOLEAN id_InsertPolyWithTests (ideal h1, const int validEntries, |
---|
| 614 | const poly h2, const bool zeroOk, const bool duplicateOk, const ring r) |
---|
[1a68d1d] | 615 | { |
---|
[2b3caae] | 616 | if ((!zeroOk) && (h2 == NULL)) return FALSE; |
---|
| 617 | if (!duplicateOk) |
---|
[1a68d1d] | 618 | { |
---|
[2b3caae] | 619 | bool h2FoundInH1 = false; |
---|
| 620 | int i = 0; |
---|
| 621 | while ((i < validEntries) && (!h2FoundInH1)) |
---|
| 622 | { |
---|
[2f5936] | 623 | h2FoundInH1 = p_EqualPolys(h1->m[i], h2,r); |
---|
[2b3caae] | 624 | i++; |
---|
| 625 | } |
---|
| 626 | if (h2FoundInH1) return FALSE; |
---|
[1a68d1d] | 627 | } |
---|
[2b3caae] | 628 | if (validEntries == IDELEMS(h1)) |
---|
| 629 | { |
---|
| 630 | pEnlargeSet(&(h1->m), IDELEMS(h1), 16); |
---|
| 631 | IDELEMS(h1) += 16; |
---|
| 632 | } |
---|
| 633 | h1->m[validEntries] = h2; |
---|
| 634 | return TRUE; |
---|
[1a68d1d] | 635 | } |
---|
| 636 | |
---|
[35aab3] | 637 | /*2 |
---|
| 638 | * h1 + h2 |
---|
| 639 | */ |
---|
[2f5936] | 640 | ideal id_Add (ideal h1,ideal h2, const ring r) |
---|
[35aab3] | 641 | { |
---|
[2f5936] | 642 | ideal result = id_SimpleAdd(h1,h2,r); |
---|
| 643 | id_Compactify(result,r); |
---|
[35c62a9] | 644 | return result; |
---|
[35aab3] | 645 | } |
---|
| 646 | |
---|
| 647 | /*2 |
---|
| 648 | * h1 * h2 |
---|
| 649 | */ |
---|
[a665eb] | 650 | ideal id_Mult (ideal h1,ideal h2, const ring r) |
---|
[35aab3] | 651 | { |
---|
| 652 | int i,j,k; |
---|
| 653 | ideal hh; |
---|
| 654 | |
---|
| 655 | j = IDELEMS(h1); |
---|
| 656 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
---|
| 657 | i = IDELEMS(h2); |
---|
| 658 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
---|
| 659 | j = j * i; |
---|
| 660 | if (j == 0) |
---|
| 661 | hh = idInit(1,1); |
---|
| 662 | else |
---|
| 663 | hh=idInit(j,1); |
---|
| 664 | if (h1->rank<h2->rank) |
---|
| 665 | hh->rank = h2->rank; |
---|
| 666 | else |
---|
| 667 | hh->rank = h1->rank; |
---|
| 668 | if (j==0) return hh; |
---|
| 669 | k = 0; |
---|
| 670 | for (i=0; i<IDELEMS(h1); i++) |
---|
| 671 | { |
---|
| 672 | if (h1->m[i] != NULL) |
---|
| 673 | { |
---|
| 674 | for (j=0; j<IDELEMS(h2); j++) |
---|
| 675 | { |
---|
| 676 | if (h2->m[j] != NULL) |
---|
| 677 | { |
---|
[a665eb] | 678 | hh->m[k] = pp_Mult_qq(h1->m[i],h2->m[j],r); |
---|
[35aab3] | 679 | k++; |
---|
| 680 | } |
---|
| 681 | } |
---|
| 682 | } |
---|
| 683 | } |
---|
| 684 | { |
---|
[a665eb] | 685 | id_Compactify(hh,r); |
---|
[10ea45f] | 686 | return hh; |
---|
[35aab3] | 687 | } |
---|
| 688 | } |
---|
| 689 | |
---|
| 690 | /*2 |
---|
| 691 | *returns true if h is the zero ideal |
---|
| 692 | */ |
---|
| 693 | BOOLEAN idIs0 (ideal h) |
---|
| 694 | { |
---|
| 695 | int i; |
---|
| 696 | |
---|
| 697 | if (h == NULL) return TRUE; |
---|
[9dd6270] | 698 | i = IDELEMS(h)-1; |
---|
| 699 | while ((i >= 0) && (h->m[i] == NULL)) |
---|
[35aab3] | 700 | { |
---|
| 701 | i--; |
---|
| 702 | } |
---|
[9dd6270] | 703 | if (i < 0) |
---|
[35aab3] | 704 | return TRUE; |
---|
| 705 | else |
---|
| 706 | return FALSE; |
---|
| 707 | } |
---|
| 708 | |
---|
| 709 | /*2 |
---|
| 710 | * return the maximal component number found in any polynomial in s |
---|
| 711 | */ |
---|
[2f5547] | 712 | long id_RankFreeModule (ideal s, ring lmRing, ring tailRing) |
---|
[35aab3] | 713 | { |
---|
| 714 | if (s!=NULL) |
---|
| 715 | { |
---|
| 716 | int j=0; |
---|
| 717 | |
---|
| 718 | if (rRing_has_Comp(tailRing) && rRing_has_Comp(lmRing)) |
---|
| 719 | { |
---|
| 720 | int l=IDELEMS(s); |
---|
| 721 | poly *p=s->m; |
---|
| 722 | int k; |
---|
| 723 | for (; l != 0; l--) |
---|
| 724 | { |
---|
| 725 | if (*p!=NULL) |
---|
| 726 | { |
---|
| 727 | pp_Test(*p, lmRing, tailRing); |
---|
| 728 | k = p_MaxComp(*p, lmRing, tailRing); |
---|
| 729 | if (k>j) j = k; |
---|
| 730 | } |
---|
| 731 | p++; |
---|
| 732 | } |
---|
| 733 | } |
---|
| 734 | return j; |
---|
| 735 | } |
---|
| 736 | return -1; |
---|
| 737 | } |
---|
| 738 | |
---|
| 739 | BOOLEAN idIsModule(ideal id, ring r) |
---|
| 740 | { |
---|
| 741 | if (id != NULL && rRing_has_Comp(r)) |
---|
| 742 | { |
---|
| 743 | int j, l = IDELEMS(id); |
---|
| 744 | for (j=0; j<l; j++) |
---|
| 745 | { |
---|
| 746 | if (id->m[j] != NULL && p_GetComp(id->m[j], r) > 0) return TRUE; |
---|
| 747 | } |
---|
| 748 | } |
---|
| 749 | return FALSE; |
---|
| 750 | } |
---|
| 751 | |
---|
| 752 | |
---|
| 753 | /*2 |
---|
| 754 | *returns true if id is homogenous with respect to the aktual weights |
---|
| 755 | */ |
---|
[a665eb] | 756 | BOOLEAN id_HomIdeal (ideal id, ideal Q, const ring r) |
---|
[35aab3] | 757 | { |
---|
| 758 | int i; |
---|
| 759 | BOOLEAN b; |
---|
| 760 | if ((id == NULL) || (IDELEMS(id) == 0)) return TRUE; |
---|
| 761 | i = 0; |
---|
| 762 | b = TRUE; |
---|
| 763 | while ((i < IDELEMS(id)) && b) |
---|
| 764 | { |
---|
[a665eb] | 765 | b = p_IsHomogeneous(id->m[i],r); |
---|
[35aab3] | 766 | i++; |
---|
| 767 | } |
---|
| 768 | if ((b) && (Q!=NULL) && (IDELEMS(Q)>0)) |
---|
| 769 | { |
---|
| 770 | i=0; |
---|
| 771 | while ((i < IDELEMS(Q)) && b) |
---|
| 772 | { |
---|
[a665eb] | 773 | b = p_IsHomogeneous(Q->m[i],r); |
---|
[35aab3] | 774 | i++; |
---|
| 775 | } |
---|
| 776 | } |
---|
| 777 | return b; |
---|
| 778 | } |
---|
| 779 | |
---|
| 780 | /*2 |
---|
| 781 | *initialized a field with r numbers between beg and end for the |
---|
| 782 | *procedure idNextChoise |
---|
| 783 | */ |
---|
| 784 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise) |
---|
| 785 | { |
---|
| 786 | /*returns the first choise of r numbers between beg and end*/ |
---|
| 787 | int i; |
---|
| 788 | for (i=0; i<r; i++) |
---|
| 789 | { |
---|
| 790 | choise[i] = 0; |
---|
| 791 | } |
---|
| 792 | if (r <= end-beg+1) |
---|
| 793 | for (i=0; i<r; i++) |
---|
| 794 | { |
---|
| 795 | choise[i] = beg+i; |
---|
| 796 | } |
---|
| 797 | if (r > end-beg+1) |
---|
| 798 | *endch = TRUE; |
---|
| 799 | else |
---|
| 800 | *endch = FALSE; |
---|
| 801 | } |
---|
| 802 | |
---|
| 803 | /*2 |
---|
| 804 | *returns the next choise of r numbers between beg and end |
---|
| 805 | */ |
---|
| 806 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise) |
---|
| 807 | { |
---|
| 808 | int i = r-1,j; |
---|
| 809 | while ((i >= 0) && (choise[i] == end)) |
---|
| 810 | { |
---|
| 811 | i--; |
---|
| 812 | end--; |
---|
| 813 | } |
---|
| 814 | if (i == -1) |
---|
| 815 | *endch = TRUE; |
---|
| 816 | else |
---|
| 817 | { |
---|
| 818 | choise[i]++; |
---|
| 819 | for (j=i+1; j<r; j++) |
---|
| 820 | { |
---|
| 821 | choise[j] = choise[i]+j-i; |
---|
| 822 | } |
---|
| 823 | *endch = FALSE; |
---|
| 824 | } |
---|
| 825 | } |
---|
| 826 | |
---|
| 827 | /*2 |
---|
| 828 | *takes the field choise of d numbers between beg and end, cancels the t-th |
---|
| 829 | *entree and searches for the ordinal number of that d-1 dimensional field |
---|
| 830 | * w.r.t. the algorithm of construction |
---|
| 831 | */ |
---|
| 832 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise) |
---|
| 833 | { |
---|
| 834 | int * localchoise,i,result=0; |
---|
| 835 | BOOLEAN b=FALSE; |
---|
| 836 | |
---|
| 837 | if (d<=1) return 1; |
---|
| 838 | localchoise=(int*)omAlloc((d-1)*sizeof(int)); |
---|
| 839 | idInitChoise(d-1,begin,end,&b,localchoise); |
---|
| 840 | while (!b) |
---|
| 841 | { |
---|
| 842 | result++; |
---|
| 843 | i = 0; |
---|
| 844 | while ((i<t) && (localchoise[i]==choise[i])) i++; |
---|
| 845 | if (i>=t) |
---|
| 846 | { |
---|
| 847 | i = t+1; |
---|
| 848 | while ((i<d) && (localchoise[i-1]==choise[i])) i++; |
---|
| 849 | if (i>=d) |
---|
[f71e8c5] | 850 | { |
---|
| 851 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
| 852 | return result; |
---|
[35aab3] | 853 | } |
---|
| 854 | } |
---|
[f71e8c5] | 855 | idGetNextChoise(d-1,end,&b,localchoise); |
---|
[35aab3] | 856 | } |
---|
[f71e8c5] | 857 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
| 858 | return 0; |
---|
[35aab3] | 859 | } |
---|
| 860 | |
---|
| 861 | /*2 |
---|
[f71e8c5] | 862 | *computes the binomial coefficient |
---|
[35aab3] | 863 | */ |
---|
[f71e8c5] | 864 | int binom (int n,int r) |
---|
| 865 | { |
---|
| 866 | int i,result; |
---|
[35aab3] | 867 | |
---|
[f71e8c5] | 868 | if (r==0) return 1; |
---|
| 869 | if (n-r<r) return binom(n,n-r); |
---|
| 870 | result = n-r+1; |
---|
| 871 | for (i=2;i<=r;i++) |
---|
[35aab3] | 872 | { |
---|
[f71e8c5] | 873 | result *= n-r+i; |
---|
| 874 | if (result<0) |
---|
[35aab3] | 875 | { |
---|
[f71e8c5] | 876 | WarnS("overflow in binomials"); |
---|
| 877 | return 0; |
---|
[35aab3] | 878 | } |
---|
[f71e8c5] | 879 | result /= i; |
---|
[35aab3] | 880 | } |
---|
[f71e8c5] | 881 | return result; |
---|
[35aab3] | 882 | } |
---|
[f71e8c5] | 883 | |
---|
[35aab3] | 884 | /*2 |
---|
[f71e8c5] | 885 | *the free module of rank i |
---|
[35aab3] | 886 | */ |
---|
[2f5547] | 887 | ideal id_FreeModule (int i, const ring r) |
---|
[35aab3] | 888 | { |
---|
[f71e8c5] | 889 | int j; |
---|
| 890 | ideal h; |
---|
| 891 | |
---|
| 892 | h=idInit(i,i); |
---|
| 893 | for (j=0; j<i; j++) |
---|
[35aab3] | 894 | { |
---|
[2f5936] | 895 | h->m[j] = p_One(r); |
---|
[2f5547] | 896 | p_SetComp(h->m[j],j+1,r); |
---|
| 897 | p_SetmComp(h->m[j],r); |
---|
[35aab3] | 898 | } |
---|
[f71e8c5] | 899 | return h; |
---|
| 900 | } |
---|
[35aab3] | 901 | |
---|
| 902 | /*2 |
---|
| 903 | *computes recursively all monomials of a certain degree |
---|
| 904 | *in every step the actvar-th entry in the exponential |
---|
| 905 | *vector is incremented and the other variables are |
---|
| 906 | *computed by recursive calls of makemonoms |
---|
| 907 | *if the last variable is reached, the difference to the |
---|
| 908 | *degree is computed directly |
---|
| 909 | *vars is the number variables |
---|
| 910 | *actvar is the actual variable to handle |
---|
| 911 | *deg is the degree of the monomials to compute |
---|
| 912 | *monomdeg is the actual degree of the monomial in consideration |
---|
| 913 | */ |
---|
[2f5547] | 914 | static void makemonoms(int vars,int actvar,int deg,int monomdeg, const ring r) |
---|
[35aab3] | 915 | { |
---|
| 916 | poly p; |
---|
| 917 | int i=0; |
---|
| 918 | |
---|
| 919 | if ((idpowerpoint == 0) && (actvar ==1)) |
---|
| 920 | { |
---|
[2f5936] | 921 | idpower[idpowerpoint] = p_One(r); |
---|
[35aab3] | 922 | monomdeg = 0; |
---|
| 923 | } |
---|
| 924 | while (i<=deg) |
---|
| 925 | { |
---|
| 926 | if (deg == monomdeg) |
---|
| 927 | { |
---|
[2f5547] | 928 | p_Setm(idpower[idpowerpoint],r); |
---|
[35aab3] | 929 | idpowerpoint++; |
---|
| 930 | return; |
---|
| 931 | } |
---|
| 932 | if (actvar == vars) |
---|
| 933 | { |
---|
[2f5547] | 934 | p_SetExp(idpower[idpowerpoint],actvar,deg-monomdeg,r); |
---|
| 935 | p_Setm(idpower[idpowerpoint],r); |
---|
| 936 | p_Test(idpower[idpowerpoint],r); |
---|
[35aab3] | 937 | idpowerpoint++; |
---|
| 938 | return; |
---|
| 939 | } |
---|
| 940 | else |
---|
| 941 | { |
---|
[2f5547] | 942 | p = p_Copy(idpower[idpowerpoint],r); |
---|
| 943 | makemonoms(vars,actvar+1,deg,monomdeg,r); |
---|
[35aab3] | 944 | idpower[idpowerpoint] = p; |
---|
| 945 | } |
---|
| 946 | monomdeg++; |
---|
[2f5547] | 947 | p_SetExp(idpower[idpowerpoint],actvar,p_GetExp(idpower[idpowerpoint],actvar,r)+1,r); |
---|
| 948 | p_Setm(idpower[idpowerpoint],r); |
---|
| 949 | p_Test(idpower[idpowerpoint],r); |
---|
[35aab3] | 950 | i++; |
---|
| 951 | } |
---|
| 952 | } |
---|
| 953 | |
---|
| 954 | /*2 |
---|
| 955 | *returns the deg-th power of the maximal ideal of 0 |
---|
| 956 | */ |
---|
[a665eb] | 957 | ideal id_MaxIdeal(int deg, const ring r) |
---|
[35aab3] | 958 | { |
---|
| 959 | if (deg < 0) |
---|
| 960 | { |
---|
| 961 | WarnS("maxideal: power must be non-negative"); |
---|
| 962 | } |
---|
| 963 | if (deg < 1) |
---|
| 964 | { |
---|
| 965 | ideal I=idInit(1,1); |
---|
[2f5936] | 966 | I->m[0]=p_One(r); |
---|
[35aab3] | 967 | return I; |
---|
| 968 | } |
---|
| 969 | if (deg == 1) |
---|
| 970 | { |
---|
[2f5547] | 971 | return id_MaxIdeal(r); |
---|
[35aab3] | 972 | } |
---|
| 973 | |
---|
[a665eb] | 974 | int vars = rVar(r); |
---|
[35aab3] | 975 | int i = binom(vars+deg-1,deg); |
---|
| 976 | if (i<=0) return idInit(1,1); |
---|
| 977 | ideal id=idInit(i,1); |
---|
| 978 | idpower = id->m; |
---|
| 979 | idpowerpoint = 0; |
---|
[2f5547] | 980 | makemonoms(vars,1,deg,0,r); |
---|
[35aab3] | 981 | idpower = NULL; |
---|
| 982 | idpowerpoint = 0; |
---|
| 983 | return id; |
---|
| 984 | } |
---|
| 985 | |
---|
| 986 | /*2 |
---|
| 987 | *computes recursively all generators of a certain degree |
---|
| 988 | *of the ideal "givenideal" |
---|
| 989 | *elms is the number elements in the given ideal |
---|
| 990 | *actelm is the actual element to handle |
---|
| 991 | *deg is the degree of the power to compute |
---|
| 992 | *gendeg is the actual degree of the generator in consideration |
---|
| 993 | */ |
---|
[2f5547] | 994 | static void makepotence(int elms,int actelm,int deg,int gendeg, const ring r) |
---|
[35aab3] | 995 | { |
---|
| 996 | poly p; |
---|
| 997 | int i=0; |
---|
| 998 | |
---|
| 999 | if ((idpowerpoint == 0) && (actelm ==1)) |
---|
| 1000 | { |
---|
[2f5936] | 1001 | idpower[idpowerpoint] = p_One(r); |
---|
[35aab3] | 1002 | gendeg = 0; |
---|
| 1003 | } |
---|
| 1004 | while (i<=deg) |
---|
| 1005 | { |
---|
| 1006 | if (deg == gendeg) |
---|
| 1007 | { |
---|
| 1008 | idpowerpoint++; |
---|
| 1009 | return; |
---|
| 1010 | } |
---|
| 1011 | if (actelm == elms) |
---|
| 1012 | { |
---|
[2f5547] | 1013 | p=p_Power(p_Copy(givenideal[actelm-1],r),deg-gendeg,r); |
---|
| 1014 | idpower[idpowerpoint]=p_Mult_q(idpower[idpowerpoint],p,r); |
---|
[35aab3] | 1015 | idpowerpoint++; |
---|
| 1016 | return; |
---|
| 1017 | } |
---|
| 1018 | else |
---|
| 1019 | { |
---|
[2f5547] | 1020 | p = p_Copy(idpower[idpowerpoint],r); |
---|
| 1021 | makepotence(elms,actelm+1,deg,gendeg,r); |
---|
[35aab3] | 1022 | idpower[idpowerpoint] = p; |
---|
| 1023 | } |
---|
| 1024 | gendeg++; |
---|
[2f5547] | 1025 | idpower[idpowerpoint]=p_Mult_q(idpower[idpowerpoint],p_Copy(givenideal[actelm-1],r),r); |
---|
[35aab3] | 1026 | i++; |
---|
| 1027 | } |
---|
| 1028 | } |
---|
| 1029 | |
---|
| 1030 | /*2 |
---|
| 1031 | *returns the deg-th power of the ideal gid |
---|
| 1032 | */ |
---|
| 1033 | //ideal idPower(ideal gid,int deg) |
---|
| 1034 | //{ |
---|
| 1035 | // int i; |
---|
| 1036 | // ideal id; |
---|
| 1037 | // |
---|
| 1038 | // if (deg < 1) deg = 1; |
---|
| 1039 | // i = binom(IDELEMS(gid)+deg-1,deg); |
---|
| 1040 | // id=idInit(i,1); |
---|
| 1041 | // idpower = id->m; |
---|
| 1042 | // givenideal = gid->m; |
---|
| 1043 | // idpowerpoint = 0; |
---|
| 1044 | // makepotence(IDELEMS(gid),1,deg,0); |
---|
| 1045 | // idpower = NULL; |
---|
| 1046 | // givenideal = NULL; |
---|
| 1047 | // idpowerpoint = 0; |
---|
| 1048 | // return id; |
---|
| 1049 | //} |
---|
[a2d993] | 1050 | static void id_NextPotence(ideal given, ideal result, |
---|
| 1051 | int begin, int end, int deg, int restdeg, poly ap, const ring r) |
---|
[35aab3] | 1052 | { |
---|
| 1053 | poly p; |
---|
| 1054 | int i; |
---|
| 1055 | |
---|
[a2d993] | 1056 | p = p_Power(p_Copy(given->m[begin],r),restdeg,r); |
---|
[35aab3] | 1057 | i = result->nrows; |
---|
[a2d993] | 1058 | result->m[i] = p_Mult_q(p_Copy(ap,r),p,r); |
---|
[35aab3] | 1059 | //PrintS("."); |
---|
| 1060 | (result->nrows)++; |
---|
| 1061 | if (result->nrows >= IDELEMS(result)) |
---|
| 1062 | { |
---|
| 1063 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
| 1064 | IDELEMS(result) += 16; |
---|
| 1065 | } |
---|
| 1066 | if (begin == end) return; |
---|
| 1067 | for (i=restdeg-1;i>0;i--) |
---|
| 1068 | { |
---|
[a2d993] | 1069 | p = p_Power(p_Copy(given->m[begin],r),i,r); |
---|
| 1070 | p = p_Mult_q(p_Copy(ap,r),p,r); |
---|
| 1071 | id_NextPotence(given, result, begin+1, end, deg, restdeg-i, p,r); |
---|
| 1072 | p_Delete(&p,r); |
---|
[35aab3] | 1073 | } |
---|
[a2d993] | 1074 | id_NextPotence(given, result, begin+1, end, deg, restdeg, ap,r); |
---|
[35aab3] | 1075 | } |
---|
| 1076 | |
---|
[2f5936] | 1077 | ideal id_Power(ideal given,int exp, const ring r) |
---|
[35aab3] | 1078 | { |
---|
| 1079 | ideal result,temp; |
---|
| 1080 | poly p1; |
---|
| 1081 | int i; |
---|
| 1082 | |
---|
| 1083 | if (idIs0(given)) return idInit(1,1); |
---|
[2f5936] | 1084 | temp = id_Copy(given,r); |
---|
[35aab3] | 1085 | idSkipZeroes(temp); |
---|
| 1086 | i = binom(IDELEMS(temp)+exp-1,exp); |
---|
| 1087 | result = idInit(i,1); |
---|
| 1088 | result->nrows = 0; |
---|
| 1089 | //Print("ideal contains %d elements\n",i); |
---|
[2f5936] | 1090 | p1=p_One(r); |
---|
[a2d993] | 1091 | id_NextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1,r); |
---|
[2f5936] | 1092 | p_Delete(&p1,r); |
---|
| 1093 | id_Delete(&temp,r); |
---|
[35aab3] | 1094 | result->nrows = 1; |
---|
[2f5936] | 1095 | id_DelEquals(result,r); |
---|
[ff2fd1] | 1096 | idSkipZeroes(result); |
---|
[35aab3] | 1097 | return result; |
---|
| 1098 | } |
---|
| 1099 | |
---|
| 1100 | /*2 |
---|
| 1101 | *skips all zeroes and double elements, searches also for units |
---|
| 1102 | */ |
---|
[2f5936] | 1103 | void id_Compactify(ideal id, const ring r) |
---|
[35aab3] | 1104 | { |
---|
| 1105 | int i,j; |
---|
| 1106 | BOOLEAN b=FALSE; |
---|
| 1107 | |
---|
| 1108 | i = IDELEMS(id)-1; |
---|
| 1109 | while ((! b) && (i>=0)) |
---|
| 1110 | { |
---|
[2f5936] | 1111 | b=p_IsUnit(id->m[i],r); |
---|
[35aab3] | 1112 | i--; |
---|
| 1113 | } |
---|
| 1114 | if (b) |
---|
| 1115 | { |
---|
[2f5936] | 1116 | for(i=IDELEMS(id)-1;i>=0;i--) p_Delete(&id->m[i],r); |
---|
| 1117 | id->m[0]=p_One(r); |
---|
[35aab3] | 1118 | } |
---|
| 1119 | else |
---|
| 1120 | { |
---|
[2f5936] | 1121 | id_DelMultiples(id,r); |
---|
[35aab3] | 1122 | } |
---|
[962de7] | 1123 | idSkipZeroes(id); |
---|
[35aab3] | 1124 | } |
---|
| 1125 | |
---|
| 1126 | /*2 |
---|
| 1127 | * returns the ideals of initial terms |
---|
| 1128 | */ |
---|
[a2d993] | 1129 | ideal id_Head(ideal h,const ring r) |
---|
[35aab3] | 1130 | { |
---|
| 1131 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
| 1132 | int i; |
---|
| 1133 | |
---|
| 1134 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
| 1135 | { |
---|
[a2d993] | 1136 | if (h->m[i]!=NULL) m->m[i]=p_Head(h->m[i],r); |
---|
[35aab3] | 1137 | } |
---|
| 1138 | return m; |
---|
| 1139 | } |
---|
| 1140 | |
---|
[a2d993] | 1141 | ideal id_Homogen(ideal h, int varnum,const ring r) |
---|
[35aab3] | 1142 | { |
---|
| 1143 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
| 1144 | int i; |
---|
| 1145 | |
---|
| 1146 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
| 1147 | { |
---|
[a2d993] | 1148 | m->m[i]=p_Homogen(h->m[i],varnum,r); |
---|
[35aab3] | 1149 | } |
---|
| 1150 | return m; |
---|
| 1151 | } |
---|
| 1152 | |
---|
| 1153 | /*------------------type conversions----------------*/ |
---|
[a2d993] | 1154 | ideal id_Vec2Ideal(poly vec, const ring R) |
---|
[35aab3] | 1155 | { |
---|
| 1156 | ideal result=idInit(1,1); |
---|
| 1157 | omFree((ADDRESS)result->m); |
---|
| 1158 | result->m=NULL; // remove later |
---|
[a2d993] | 1159 | p_Vec2Polys(vec, &(result->m), &(IDELEMS(result)),R); |
---|
[35aab3] | 1160 | return result; |
---|
| 1161 | } |
---|
| 1162 | |
---|
| 1163 | |
---|
| 1164 | // converts mat to module, destroys mat |
---|
[a2d993] | 1165 | ideal id_Matrix2Module(matrix mat, const ring R) |
---|
[35aab3] | 1166 | { |
---|
| 1167 | int mc=MATCOLS(mat); |
---|
| 1168 | int mr=MATROWS(mat); |
---|
| 1169 | ideal result = idInit(si_max(mc,1),si_max(mr,1)); |
---|
| 1170 | int i,j, l; |
---|
| 1171 | poly h; |
---|
| 1172 | poly p; |
---|
[a2d993] | 1173 | sBucket_pt bucket = sBucketCreate(R); |
---|
[35aab3] | 1174 | |
---|
| 1175 | for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */ |
---|
| 1176 | { |
---|
| 1177 | for (i=1;i<=mr /*MATROWS(mat)*/;i++) |
---|
| 1178 | { |
---|
| 1179 | h = MATELEM(mat,i,j+1); |
---|
| 1180 | if (h!=NULL) |
---|
| 1181 | { |
---|
[ca3e7b] | 1182 | l=pLength(h); |
---|
[35aab3] | 1183 | MATELEM(mat,i,j+1)=NULL; |
---|
[a2d993] | 1184 | p_SetCompP(h,i, R); |
---|
[35aab3] | 1185 | sBucket_Merge_p(bucket, h, l); |
---|
| 1186 | } |
---|
| 1187 | } |
---|
| 1188 | sBucketClearMerge(bucket, &(result->m[j]), &l); |
---|
| 1189 | } |
---|
[cbeafc2] | 1190 | sBucketDestroy(&bucket); |
---|
[35aab3] | 1191 | |
---|
| 1192 | // obachman: need to clean this up |
---|
[a2d993] | 1193 | id_Delete((ideal*) &mat,R); |
---|
[35aab3] | 1194 | return result; |
---|
| 1195 | } |
---|
| 1196 | |
---|
| 1197 | /*2 |
---|
| 1198 | * converts a module into a matrix, destroyes the input |
---|
| 1199 | */ |
---|
[a2d993] | 1200 | matrix id_Module2Matrix(ideal mod, const ring R) |
---|
[35aab3] | 1201 | { |
---|
| 1202 | matrix result = mpNew(mod->rank,IDELEMS(mod)); |
---|
| 1203 | int i,cp; |
---|
| 1204 | poly p,h; |
---|
| 1205 | |
---|
| 1206 | for(i=0;i<IDELEMS(mod);i++) |
---|
| 1207 | { |
---|
[d0164d9] | 1208 | p=pReverse(mod->m[i]); |
---|
[35aab3] | 1209 | mod->m[i]=NULL; |
---|
| 1210 | while (p!=NULL) |
---|
| 1211 | { |
---|
| 1212 | h=p; |
---|
| 1213 | pIter(p); |
---|
| 1214 | pNext(h)=NULL; |
---|
| 1215 | // cp = si_max(1,pGetComp(h)); // if used for ideals too |
---|
[a2d993] | 1216 | cp = p_GetComp(h,R); |
---|
| 1217 | p_SetComp(h,0,R); |
---|
| 1218 | p_SetmComp(h,R); |
---|
[35aab3] | 1219 | #ifdef TEST |
---|
| 1220 | if (cp>mod->rank) |
---|
| 1221 | { |
---|
[6867f5] | 1222 | Print("## inv. rank %ld -> %d\n",mod->rank,cp); |
---|
[35aab3] | 1223 | int k,l,o=mod->rank; |
---|
| 1224 | mod->rank=cp; |
---|
| 1225 | matrix d=mpNew(mod->rank,IDELEMS(mod)); |
---|
| 1226 | for (l=1; l<=o; l++) |
---|
| 1227 | { |
---|
| 1228 | for (k=1; k<=IDELEMS(mod); k++) |
---|
| 1229 | { |
---|
| 1230 | MATELEM(d,l,k)=MATELEM(result,l,k); |
---|
| 1231 | MATELEM(result,l,k)=NULL; |
---|
| 1232 | } |
---|
| 1233 | } |
---|
[a2d993] | 1234 | id_Delete((ideal *)&result,R); |
---|
[35aab3] | 1235 | result=d; |
---|
| 1236 | } |
---|
| 1237 | #endif |
---|
[a2d993] | 1238 | MATELEM(result,cp,i+1) = p_Add_q(MATELEM(result,cp,i+1),h,R); |
---|
[35aab3] | 1239 | } |
---|
| 1240 | } |
---|
| 1241 | // obachman 10/99: added the following line, otherwise memory leack! |
---|
[a2d993] | 1242 | id_Delete(&mod,R); |
---|
[35aab3] | 1243 | return result; |
---|
| 1244 | } |
---|
| 1245 | |
---|
[a2d993] | 1246 | matrix id_Module2formatedMatrix(ideal mod,int rows, int cols, const ring R) |
---|
[35aab3] | 1247 | { |
---|
| 1248 | matrix result = mpNew(rows,cols); |
---|
[a2d993] | 1249 | int i,cp,r=id_RankFreeModule(mod,R),c=IDELEMS(mod); |
---|
[35aab3] | 1250 | poly p,h; |
---|
| 1251 | |
---|
| 1252 | if (r>rows) r = rows; |
---|
| 1253 | if (c>cols) c = cols; |
---|
| 1254 | for(i=0;i<c;i++) |
---|
| 1255 | { |
---|
[bafaec0] | 1256 | p=pReverse(mod->m[i]); |
---|
[35aab3] | 1257 | mod->m[i]=NULL; |
---|
| 1258 | while (p!=NULL) |
---|
| 1259 | { |
---|
| 1260 | h=p; |
---|
| 1261 | pIter(p); |
---|
| 1262 | pNext(h)=NULL; |
---|
[a2d993] | 1263 | cp = p_GetComp(h,R); |
---|
[35aab3] | 1264 | if (cp<=r) |
---|
| 1265 | { |
---|
[a2d993] | 1266 | p_SetComp(h,0,R); |
---|
| 1267 | p_SetmComp(h,R); |
---|
| 1268 | MATELEM(result,cp,i+1) = p_Add_q(MATELEM(result,cp,i+1),h,R); |
---|
[35aab3] | 1269 | } |
---|
| 1270 | else |
---|
[a2d993] | 1271 | p_Delete(&h,R); |
---|
[35aab3] | 1272 | } |
---|
| 1273 | } |
---|
[a2d993] | 1274 | id_Delete(&mod,R); |
---|
[35aab3] | 1275 | return result; |
---|
| 1276 | } |
---|
| 1277 | |
---|
| 1278 | /*2 |
---|
| 1279 | * substitute the n-th variable by the monomial e in id |
---|
| 1280 | * destroy id |
---|
| 1281 | */ |
---|
[a2d993] | 1282 | ideal id_Subst(ideal id, int n, poly e, const ring r) |
---|
[35aab3] | 1283 | { |
---|
| 1284 | int k=MATROWS((matrix)id)*MATCOLS((matrix)id); |
---|
| 1285 | ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id)); |
---|
| 1286 | |
---|
| 1287 | res->rank = id->rank; |
---|
| 1288 | for(k--;k>=0;k--) |
---|
| 1289 | { |
---|
[a2d993] | 1290 | res->m[k]=p_Subst(id->m[k],n,e,r); |
---|
[35aab3] | 1291 | id->m[k]=NULL; |
---|
| 1292 | } |
---|
[a2d993] | 1293 | id_Delete(&id,r); |
---|
[35aab3] | 1294 | return res; |
---|
| 1295 | } |
---|
| 1296 | |
---|
[a2d993] | 1297 | BOOLEAN id_HomModule(ideal m, ideal Q, intvec **w, const ring R) |
---|
[35aab3] | 1298 | { |
---|
| 1299 | if (w!=NULL) *w=NULL; |
---|
[a2d993] | 1300 | if ((Q!=NULL) && (!id_HomIdeal(Q,NULL,R))) return FALSE; |
---|
[43ebb1] | 1301 | if (idIs0(m)) |
---|
| 1302 | { |
---|
[a12776] | 1303 | if (w!=NULL) (*w)=new intvec(m->rank); |
---|
[43ebb1] | 1304 | return TRUE; |
---|
| 1305 | } |
---|
[35aab3] | 1306 | |
---|
[4e63600] | 1307 | long cmax=1,order=0,ord,* diff,diffmin=32000; |
---|
| 1308 | int *iscom; |
---|
| 1309 | int i,j; |
---|
[35aab3] | 1310 | poly p=NULL; |
---|
[1f5db38] | 1311 | pFDegProc d; |
---|
[a2d993] | 1312 | if (R->pLexOrder && (R->order[0]==ringorder_lp)) |
---|
[99bdcf] | 1313 | d=p_Totaldegree; |
---|
[bead81] | 1314 | else |
---|
[9765f3] | 1315 | d=R->pFDeg; |
---|
[35aab3] | 1316 | int length=IDELEMS(m); |
---|
[a2d993] | 1317 | poly* P=m->m; |
---|
| 1318 | poly* F=(poly*)omAlloc(length*sizeof(poly)); |
---|
[35aab3] | 1319 | for (i=length-1;i>=0;i--) |
---|
| 1320 | { |
---|
| 1321 | p=F[i]=P[i]; |
---|
[a2d993] | 1322 | cmax=si_max(cmax,(long)p_MaxComp(p,R)); |
---|
[35aab3] | 1323 | } |
---|
[4e63600] | 1324 | cmax++; |
---|
| 1325 | diff = (long *)omAlloc0(cmax*sizeof(long)); |
---|
[35aab3] | 1326 | if (w!=NULL) *w=new intvec(cmax-1); |
---|
| 1327 | iscom = (int *)omAlloc0(cmax*sizeof(int)); |
---|
| 1328 | i=0; |
---|
| 1329 | while (i<=length) |
---|
| 1330 | { |
---|
| 1331 | if (i<length) |
---|
| 1332 | { |
---|
| 1333 | p=F[i]; |
---|
[a2d993] | 1334 | while ((p!=NULL) && (iscom[p_GetComp(p,R)]==0)) pIter(p); |
---|
[35aab3] | 1335 | } |
---|
| 1336 | if ((p==NULL) && (i<length)) |
---|
| 1337 | { |
---|
| 1338 | i++; |
---|
| 1339 | } |
---|
| 1340 | else |
---|
| 1341 | { |
---|
[4e63600] | 1342 | if (p==NULL) /* && (i==length) */ |
---|
[35aab3] | 1343 | { |
---|
| 1344 | i=0; |
---|
| 1345 | while ((i<length) && (F[i]==NULL)) i++; |
---|
| 1346 | if (i>=length) break; |
---|
| 1347 | p = F[i]; |
---|
| 1348 | } |
---|
[1f5db38] | 1349 | //if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
| 1350 | // order=pTotaldegree(p); |
---|
| 1351 | //else |
---|
[35aab3] | 1352 | // order = p->order; |
---|
[1f5db38] | 1353 | // order = pFDeg(p,currRing); |
---|
[a2d993] | 1354 | order = d(p,R) +diff[p_GetComp(p,R)]; |
---|
[1f5db38] | 1355 | //order += diff[pGetComp(p)]; |
---|
[35aab3] | 1356 | p = F[i]; |
---|
| 1357 | //Print("Actual p=F[%d]: ",i);pWrite(p); |
---|
| 1358 | F[i] = NULL; |
---|
| 1359 | i=0; |
---|
| 1360 | } |
---|
| 1361 | while (p!=NULL) |
---|
| 1362 | { |
---|
[a2d993] | 1363 | if (R->pLexOrder && (R->order[0]==ringorder_lp)) |
---|
| 1364 | ord=p_Totaldegree(p,R); |
---|
[4e63600] | 1365 | else |
---|
[35aab3] | 1366 | // ord = p->order; |
---|
[9765f3] | 1367 | ord = R->pFDeg(p,R); |
---|
[a2d993] | 1368 | if (iscom[p_GetComp(p,R)]==0) |
---|
[35aab3] | 1369 | { |
---|
[a2d993] | 1370 | diff[p_GetComp(p,R)] = order-ord; |
---|
| 1371 | iscom[p_GetComp(p,R)] = 1; |
---|
[35aab3] | 1372 | /* |
---|
| 1373 | *PrintS("new diff: "); |
---|
| 1374 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
| 1375 | *PrintLn(); |
---|
| 1376 | *PrintS("new iscom: "); |
---|
| 1377 | *for (j=0;j<cmax;j++) Print("%d ",iscom[j]); |
---|
| 1378 | *PrintLn(); |
---|
| 1379 | *Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]); |
---|
| 1380 | */ |
---|
| 1381 | } |
---|
| 1382 | else |
---|
| 1383 | { |
---|
| 1384 | /* |
---|
| 1385 | *PrintS("new diff: "); |
---|
| 1386 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
| 1387 | *PrintLn(); |
---|
| 1388 | *Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]); |
---|
| 1389 | */ |
---|
[a2d993] | 1390 | if (order != (ord+diff[p_GetComp(p,R)])) |
---|
[35aab3] | 1391 | { |
---|
| 1392 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
[4e63600] | 1393 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
[35aab3] | 1394 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
| 1395 | delete *w;*w=NULL; |
---|
| 1396 | return FALSE; |
---|
| 1397 | } |
---|
| 1398 | } |
---|
| 1399 | pIter(p); |
---|
| 1400 | } |
---|
| 1401 | } |
---|
| 1402 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
| 1403 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
[4e63600] | 1404 | for (i=1;i<cmax;i++) (**w)[i-1]=(int)(diff[i]); |
---|
[35aab3] | 1405 | for (i=1;i<cmax;i++) |
---|
| 1406 | { |
---|
| 1407 | if (diff[i]<diffmin) diffmin=diff[i]; |
---|
| 1408 | } |
---|
| 1409 | if (w!=NULL) |
---|
| 1410 | { |
---|
| 1411 | for (i=1;i<cmax;i++) |
---|
| 1412 | { |
---|
[4e63600] | 1413 | (**w)[i-1]=(int)(diff[i]-diffmin); |
---|
[35aab3] | 1414 | } |
---|
| 1415 | } |
---|
[4e63600] | 1416 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
[35aab3] | 1417 | return TRUE; |
---|
| 1418 | } |
---|
| 1419 | |
---|
[a2d993] | 1420 | // uses glabl vars via pSetModDeg |
---|
| 1421 | //BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
| 1422 | //{ |
---|
| 1423 | // if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
| 1424 | // if (idIs0(m)) return TRUE; |
---|
| 1425 | // |
---|
| 1426 | // int cmax=-1; |
---|
| 1427 | // int i; |
---|
| 1428 | // poly p=NULL; |
---|
| 1429 | // int length=IDELEMS(m); |
---|
| 1430 | // poly* P=m->m; |
---|
| 1431 | // for (i=length-1;i>=0;i--) |
---|
| 1432 | // { |
---|
| 1433 | // p=P[i]; |
---|
| 1434 | // if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
| 1435 | // } |
---|
| 1436 | // if (w != NULL) |
---|
| 1437 | // if (w->length()+1 < cmax) |
---|
| 1438 | // { |
---|
| 1439 | // // Print("length: %d - %d \n", w->length(),cmax); |
---|
| 1440 | // return FALSE; |
---|
| 1441 | // } |
---|
| 1442 | // |
---|
| 1443 | // if(w!=NULL) |
---|
| 1444 | // pSetModDeg(w); |
---|
| 1445 | // |
---|
| 1446 | // for (i=length-1;i>=0;i--) |
---|
| 1447 | // { |
---|
| 1448 | // p=P[i]; |
---|
| 1449 | // poly q=p; |
---|
| 1450 | // if (p!=NULL) |
---|
| 1451 | // { |
---|
| 1452 | // int d=pFDeg(p,currRing); |
---|
| 1453 | // loop |
---|
| 1454 | // { |
---|
| 1455 | // pIter(p); |
---|
| 1456 | // if (p==NULL) break; |
---|
| 1457 | // if (d!=pFDeg(p,currRing)) |
---|
| 1458 | // { |
---|
| 1459 | // //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
| 1460 | // if(w!=NULL) |
---|
| 1461 | // pSetModDeg(NULL); |
---|
| 1462 | // return FALSE; |
---|
| 1463 | // } |
---|
| 1464 | // } |
---|
| 1465 | // } |
---|
| 1466 | // } |
---|
| 1467 | // |
---|
| 1468 | // if(w!=NULL) |
---|
| 1469 | // pSetModDeg(NULL); |
---|
| 1470 | // |
---|
| 1471 | // return TRUE; |
---|
| 1472 | //} |
---|
[30b8381] | 1473 | |
---|
[a2d993] | 1474 | ideal id_Jet(ideal i,int d, const ring R) |
---|
[35aab3] | 1475 | { |
---|
| 1476 | ideal r=idInit((i->nrows)*(i->ncols),i->rank); |
---|
| 1477 | r->nrows = i-> nrows; |
---|
| 1478 | r->ncols = i-> ncols; |
---|
| 1479 | //r->rank = i-> rank; |
---|
| 1480 | int k; |
---|
| 1481 | for(k=(i->nrows)*(i->ncols)-1;k>=0; k--) |
---|
| 1482 | { |
---|
[a2d993] | 1483 | r->m[k]=pp_Jet(i->m[k],d,R); |
---|
[35aab3] | 1484 | } |
---|
| 1485 | return r; |
---|
| 1486 | } |
---|
| 1487 | |
---|
[a2d993] | 1488 | ideal id_JetW(ideal i,int d, intvec * iv, const ring R) |
---|
[35aab3] | 1489 | { |
---|
| 1490 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
| 1491 | if (ecartWeights!=NULL) |
---|
| 1492 | { |
---|
| 1493 | WerrorS("cannot compute weighted jets now"); |
---|
| 1494 | } |
---|
| 1495 | else |
---|
| 1496 | { |
---|
[a2d993] | 1497 | short *w=iv2array(iv,R); |
---|
[35aab3] | 1498 | int k; |
---|
| 1499 | for(k=0; k<IDELEMS(i); k++) |
---|
| 1500 | { |
---|
[a2d993] | 1501 | r->m[k]=pp_JetW(i->m[k],d,w,R); |
---|
[35aab3] | 1502 | } |
---|
[a2d993] | 1503 | omFreeSize((ADDRESS)w,(rVar(R)+1)*sizeof(short)); |
---|
[35aab3] | 1504 | } |
---|
| 1505 | return r; |
---|
| 1506 | } |
---|
| 1507 | |
---|
| 1508 | /*3 |
---|
[b8f199] | 1509 | * searches for the next unit in the components of the module arg and |
---|
| 1510 | * returns the first one; |
---|
[35aab3] | 1511 | */ |
---|
[2f5936] | 1512 | static int id_ReadOutPivot(ideal arg,int* comp, const ring r) |
---|
[35aab3] | 1513 | { |
---|
[1d138c] | 1514 | if (idIs0(arg)) return -1; |
---|
[8421b8] | 1515 | int i=0,j, generator=-1; |
---|
| 1516 | int rk_arg=arg->rank; //idRankFreeModule(arg); |
---|
| 1517 | int * componentIsUsed =(int *)omAlloc((rk_arg+1)*sizeof(int)); |
---|
[fc7902] | 1518 | poly p; |
---|
[35aab3] | 1519 | |
---|
[8421b8] | 1520 | while ((generator<0) && (i<IDELEMS(arg))) |
---|
[35aab3] | 1521 | { |
---|
[8421b8] | 1522 | memset(componentIsUsed,0,(rk_arg+1)*sizeof(int)); |
---|
[35aab3] | 1523 | p = arg->m[i]; |
---|
| 1524 | while (p!=NULL) |
---|
| 1525 | { |
---|
[2f5936] | 1526 | j = p_GetComp(p,r); |
---|
[8421b8] | 1527 | if (componentIsUsed[j]==0) |
---|
[35aab3] | 1528 | { |
---|
[b8f199] | 1529 | #ifdef HAVE_RINGS |
---|
[2f5936] | 1530 | if (p_LmIsConstantComp(p,r) && |
---|
| 1531 | (!rField_is_Ring(r) || n_IsUnit(pGetCoeff(p),r->cf))) |
---|
[b8f199] | 1532 | { |
---|
| 1533 | #else |
---|
[2f5936] | 1534 | if (p_LmIsConstantComp(p,r)) |
---|
[35aab3] | 1535 | { |
---|
[b8f199] | 1536 | #endif |
---|
[35aab3] | 1537 | generator = i; |
---|
[8421b8] | 1538 | componentIsUsed[j] = 1; |
---|
[35aab3] | 1539 | } |
---|
| 1540 | else |
---|
| 1541 | { |
---|
[8421b8] | 1542 | componentIsUsed[j] = -1; |
---|
[35aab3] | 1543 | } |
---|
| 1544 | } |
---|
[8421b8] | 1545 | else if (componentIsUsed[j]>0) |
---|
[35aab3] | 1546 | { |
---|
[8421b8] | 1547 | (componentIsUsed[j])++; |
---|
[35aab3] | 1548 | } |
---|
| 1549 | pIter(p); |
---|
| 1550 | } |
---|
| 1551 | i++; |
---|
| 1552 | } |
---|
| 1553 | i = 0; |
---|
| 1554 | *comp = -1; |
---|
| 1555 | for (j=0;j<=rk_arg;j++) |
---|
| 1556 | { |
---|
[8421b8] | 1557 | if (componentIsUsed[j]>0) |
---|
[35aab3] | 1558 | { |
---|
[8421b8] | 1559 | if ((*comp==-1) || (componentIsUsed[j]<i)) |
---|
[35aab3] | 1560 | { |
---|
| 1561 | *comp = j; |
---|
[8421b8] | 1562 | i= componentIsUsed[j]; |
---|
[35aab3] | 1563 | } |
---|
| 1564 | } |
---|
| 1565 | } |
---|
[8421b8] | 1566 | omFree(componentIsUsed); |
---|
[35aab3] | 1567 | return generator; |
---|
| 1568 | } |
---|
| 1569 | |
---|
[955025] | 1570 | #if 0 |
---|
[35aab3] | 1571 | static void idDeleteComp(ideal arg,int red_comp) |
---|
| 1572 | { |
---|
| 1573 | int i,j; |
---|
| 1574 | poly p; |
---|
| 1575 | |
---|
| 1576 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
| 1577 | { |
---|
| 1578 | p = arg->m[i]; |
---|
| 1579 | while (p!=NULL) |
---|
| 1580 | { |
---|
| 1581 | j = pGetComp(p); |
---|
| 1582 | if (j>red_comp) |
---|
| 1583 | { |
---|
| 1584 | pSetComp(p,j-1); |
---|
| 1585 | pSetm(p); |
---|
| 1586 | } |
---|
| 1587 | pIter(p); |
---|
| 1588 | } |
---|
| 1589 | } |
---|
| 1590 | (arg->rank)--; |
---|
| 1591 | } |
---|
[955025] | 1592 | #endif |
---|
| 1593 | |
---|
[a2d993] | 1594 | intvec * id_QHomWeight(ideal id, const ring r) |
---|
[35aab3] | 1595 | { |
---|
| 1596 | poly head, tail; |
---|
| 1597 | int k; |
---|
| 1598 | int in=IDELEMS(id)-1, ready=0, all=0, |
---|
[a665eb] | 1599 | coldim=rVar(r), rowmax=2*coldim; |
---|
[35aab3] | 1600 | if (in<0) return NULL; |
---|
| 1601 | intvec *imat=new intvec(rowmax+1,coldim,0); |
---|
| 1602 | |
---|
| 1603 | do |
---|
| 1604 | { |
---|
| 1605 | head = id->m[in--]; |
---|
| 1606 | if (head!=NULL) |
---|
| 1607 | { |
---|
| 1608 | tail = pNext(head); |
---|
| 1609 | while (tail!=NULL) |
---|
| 1610 | { |
---|
| 1611 | all++; |
---|
| 1612 | for (k=1;k<=coldim;k++) |
---|
[a2d993] | 1613 | IMATELEM(*imat,all,k) = p_GetExpDiff(head,tail,k,r); |
---|
[35aab3] | 1614 | if (all==rowmax) |
---|
| 1615 | { |
---|
| 1616 | ivTriangIntern(imat, ready, all); |
---|
| 1617 | if (ready==coldim) |
---|
| 1618 | { |
---|
| 1619 | delete imat; |
---|
| 1620 | return NULL; |
---|
| 1621 | } |
---|
| 1622 | } |
---|
| 1623 | pIter(tail); |
---|
| 1624 | } |
---|
| 1625 | } |
---|
| 1626 | } while (in>=0); |
---|
| 1627 | if (all>ready) |
---|
| 1628 | { |
---|
| 1629 | ivTriangIntern(imat, ready, all); |
---|
| 1630 | if (ready==coldim) |
---|
| 1631 | { |
---|
| 1632 | delete imat; |
---|
| 1633 | return NULL; |
---|
| 1634 | } |
---|
| 1635 | } |
---|
| 1636 | intvec *result = ivSolveKern(imat, ready); |
---|
| 1637 | delete imat; |
---|
| 1638 | return result; |
---|
| 1639 | } |
---|
| 1640 | |
---|
[a2d993] | 1641 | BOOLEAN id_IsZeroDim(ideal I, const ring r) |
---|
[35aab3] | 1642 | { |
---|
[a665eb] | 1643 | BOOLEAN *UsedAxis=(BOOLEAN *)omAlloc0(rVar(r)*sizeof(BOOLEAN)); |
---|
[35aab3] | 1644 | int i,n; |
---|
| 1645 | poly po; |
---|
| 1646 | BOOLEAN res=TRUE; |
---|
| 1647 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
| 1648 | { |
---|
| 1649 | po=I->m[i]; |
---|
[a2d993] | 1650 | if ((po!=NULL) &&((n=p_IsPurePower(po,r))!=0)) UsedAxis[n-1]=TRUE; |
---|
[35aab3] | 1651 | } |
---|
[a665eb] | 1652 | for(i=rVar(r)-1;i>=0;i--) |
---|
[35aab3] | 1653 | { |
---|
| 1654 | if(UsedAxis[i]==FALSE) {res=FALSE; break;} // not zero-dim. |
---|
| 1655 | } |
---|
[a665eb] | 1656 | omFreeSize(UsedAxis,rVar(r)*sizeof(BOOLEAN)); |
---|
[35aab3] | 1657 | return res; |
---|
| 1658 | } |
---|
| 1659 | |
---|
[2f5936] | 1660 | void id_Normalize(ideal I,const ring r) |
---|
[35aab3] | 1661 | { |
---|
[2f5936] | 1662 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
[35aab3] | 1663 | int i; |
---|
| 1664 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
| 1665 | { |
---|
[2f5936] | 1666 | p_Normalize(I->m[i],r); |
---|
[35aab3] | 1667 | } |
---|
| 1668 | } |
---|
[225d94] | 1669 | |
---|
[2ad10e9] | 1670 | // #include <kernel/clapsing.h> |
---|
[225d94] | 1671 | |
---|
[2f6fc61] | 1672 | #ifdef HAVE_FACTORY |
---|
[af598e] | 1673 | #if 0 |
---|
[225d94] | 1674 | poly id_GCD(poly f, poly g, const ring r) |
---|
| 1675 | { |
---|
[a665eb] | 1676 | ring save_r=r; |
---|
[225d94] | 1677 | rChangeCurrRing(r); |
---|
| 1678 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
| 1679 | intvec *w = NULL; |
---|
[af598e] | 1680 | |
---|
[225d94] | 1681 | ideal S=idSyzygies(I,testHomog,&w); |
---|
[af598e] | 1682 | |
---|
[225d94] | 1683 | if (w!=NULL) delete w; |
---|
| 1684 | poly gg=pTakeOutComp(&(S->m[0]),2); |
---|
| 1685 | idDelete(&S); |
---|
| 1686 | poly gcd_p=singclap_pdivide(f,gg); |
---|
| 1687 | pDelete(&gg); |
---|
| 1688 | rChangeCurrRing(save_r); |
---|
| 1689 | return gcd_p; |
---|
| 1690 | } |
---|
[2f6fc61] | 1691 | #endif |
---|
[af598e] | 1692 | #endif |
---|
[bba835] | 1693 | |
---|
| 1694 | /*2 |
---|
| 1695 | * xx,q: arrays of length 0..rl-1 |
---|
| 1696 | * xx[i]: SB mod q[i] |
---|
| 1697 | * assume: char=0 |
---|
| 1698 | * assume: q[i]!=0 |
---|
| 1699 | * destroys xx |
---|
| 1700 | */ |
---|
[2f6fc61] | 1701 | #ifdef HAVE_FACTORY |
---|
[af598e] | 1702 | ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring R) |
---|
[bba835] | 1703 | { |
---|
[07969d] | 1704 | int cnt=IDELEMS(xx[0])*xx[0]->nrows; |
---|
| 1705 | ideal result=idInit(cnt,xx[0]->rank); |
---|
| 1706 | result->nrows=xx[0]->nrows; // for lifting matrices |
---|
| 1707 | result->ncols=xx[0]->ncols; // for lifting matrices |
---|
[bba835] | 1708 | int i,j; |
---|
[cbc7e3] | 1709 | poly r,h,hh,res_p; |
---|
[bba835] | 1710 | number *x=(number *)omAlloc(rl*sizeof(number)); |
---|
[07969d] | 1711 | for(i=cnt-1;i>=0;i--) |
---|
[bba835] | 1712 | { |
---|
| 1713 | res_p=NULL; |
---|
| 1714 | loop |
---|
| 1715 | { |
---|
| 1716 | r=NULL; |
---|
| 1717 | for(j=rl-1;j>=0;j--) |
---|
| 1718 | { |
---|
| 1719 | h=xx[j]->m[i]; |
---|
[4d8843] | 1720 | if ((h!=NULL) |
---|
[af598e] | 1721 | &&((r==NULL)||(p_LmCmp(r,h,R)==-1))) |
---|
[4d8843] | 1722 | r=h; |
---|
[bba835] | 1723 | } |
---|
| 1724 | if (r==NULL) break; |
---|
[af598e] | 1725 | h=p_Head(r, R); |
---|
[bba835] | 1726 | for(j=rl-1;j>=0;j--) |
---|
| 1727 | { |
---|
[cbc7e3] | 1728 | hh=xx[j]->m[i]; |
---|
[af598e] | 1729 | if ((hh!=NULL) && (p_LmCmp(r,hh, R)==0)) |
---|
[cbc7e3] | 1730 | { |
---|
[af598e] | 1731 | x[j]=p_GetCoeff(hh, R); |
---|
| 1732 | hh=p_LmFreeAndNext(hh, R); |
---|
[cbc7e3] | 1733 | xx[j]->m[i]=hh; |
---|
[bba835] | 1734 | } |
---|
| 1735 | else |
---|
[af598e] | 1736 | x[j]=nlInit(0, R->cf); // is R->cf really n_Q??? |
---|
[bba835] | 1737 | } |
---|
[af598e] | 1738 | |
---|
[529fa4] | 1739 | number n=nChineseRemainder(x,q,rl, R->cf); |
---|
[af598e] | 1740 | |
---|
[bba835] | 1741 | for(j=rl-1;j>=0;j--) |
---|
| 1742 | { |
---|
[38f763] | 1743 | x[j]=NULL; // nlInit(0...) takes no memory |
---|
[bba835] | 1744 | } |
---|
[529fa4] | 1745 | if (n_IsZero(n, R->cf)) p_Delete(&h, R); |
---|
[a8ef67] | 1746 | else |
---|
| 1747 | { |
---|
[af598e] | 1748 | p_SetCoeff(h,n, R); |
---|
[a8ef67] | 1749 | //Print("new mon:");pWrite(h); |
---|
[af598e] | 1750 | res_p=p_Add_q(res_p, h, R); |
---|
[a8ef67] | 1751 | } |
---|
[bba835] | 1752 | } |
---|
| 1753 | result->m[i]=res_p; |
---|
| 1754 | } |
---|
| 1755 | omFree(x); |
---|
[af598e] | 1756 | for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]), R); |
---|
[bba835] | 1757 | omFree(xx); |
---|
| 1758 | return result; |
---|
| 1759 | } |
---|
[2f6fc61] | 1760 | #endif |
---|
[90a60f] | 1761 | |
---|
| 1762 | /*2 |
---|
| 1763 | * transpose a module |
---|
| 1764 | */ |
---|
| 1765 | ideal id_Transp(ideal a, const ring rRing) |
---|
| 1766 | { |
---|
| 1767 | int r = a->rank, c = IDELEMS(a); |
---|
| 1768 | ideal b = idInit(r,c); |
---|
| 1769 | |
---|
| 1770 | for (int i=c; i>0; i--) |
---|
| 1771 | { |
---|
| 1772 | poly p=a->m[i-1]; |
---|
| 1773 | while(p!=NULL) |
---|
| 1774 | { |
---|
| 1775 | poly h=p_Head(p, rRing); |
---|
| 1776 | int co=p_GetComp(h, rRing)-1; |
---|
| 1777 | p_SetComp(h, i, rRing); |
---|
| 1778 | p_Setm(h, rRing); |
---|
| 1779 | b->m[co] = p_Add_q(b->m[co], h, rRing); |
---|
| 1780 | pIter(p); |
---|
| 1781 | } |
---|
| 1782 | } |
---|
| 1783 | return b; |
---|
| 1784 | } |
---|
| 1785 | |
---|
| 1786 | |
---|
| 1787 | |
---|
| 1788 | /*2 |
---|
| 1789 | * The following is needed to compute the image of certain map used in |
---|
| 1790 | * the computation of cohomologies via BGG |
---|
| 1791 | * let M = { w_1, ..., w_k }, k = size(M) == ncols(M), n = nvars(currRing). |
---|
| 1792 | * assuming that nrows(M) <= m*n; the procedure computes: |
---|
| 1793 | * transpose(M) * transpose( var(1) I_m | ... | var(n) I_m ) :== transpose(module{f_1, ... f_k}), |
---|
| 1794 | * where f_i = \sum_{j=1}^{m} (w_i, v_j) gen(j), (w_i, v_j) is a `scalar` multiplication. |
---|
| 1795 | * that is, if w_i = (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) then |
---|
| 1796 | |
---|
| 1797 | (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) |
---|
| 1798 | * var_1 ... var_1 | var_2 ... var_2 | ... | var_n ... var(n) |
---|
| 1799 | * gen_1 ... gen_m | gen_1 ... gen_m | ... | gen_1 ... gen_m |
---|
| 1800 | + => |
---|
| 1801 | f_i = |
---|
| 1802 | |
---|
| 1803 | a^1_1 * var(1) * gen(1) + ... + a^1_m * var(1) * gen(m) + |
---|
| 1804 | a^2_1 * var(2) * gen(1) + ... + a^2_m * var(2) * gen(m) + |
---|
| 1805 | ... |
---|
| 1806 | a^n_1 * var(n) * gen(1) + ... + a^n_m * var(n) * gen(m); |
---|
| 1807 | |
---|
| 1808 | NOTE: for every f_i we run only ONCE along w_i saving partial sums into a temporary array of polys of size m |
---|
| 1809 | */ |
---|
[9c1b63] | 1810 | ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing) |
---|
[90a60f] | 1811 | { |
---|
| 1812 | // #ifdef DEBU |
---|
| 1813 | // WarnS("tensorModuleMult!!!!"); |
---|
| 1814 | |
---|
| 1815 | assume(m > 0); |
---|
| 1816 | assume(M != NULL); |
---|
| 1817 | |
---|
| 1818 | const int n = rRing->N; |
---|
| 1819 | |
---|
| 1820 | assume(M->rank <= m * n); |
---|
| 1821 | |
---|
| 1822 | const int k = IDELEMS(M); |
---|
| 1823 | |
---|
| 1824 | ideal idTemp = idInit(k,m); // = {f_1, ..., f_k } |
---|
| 1825 | |
---|
| 1826 | for( int i = 0; i < k; i++ ) // for every w \in M |
---|
| 1827 | { |
---|
| 1828 | poly pTempSum = NULL; |
---|
| 1829 | |
---|
| 1830 | poly w = M->m[i]; |
---|
| 1831 | |
---|
| 1832 | while(w != NULL) // for each term of w... |
---|
| 1833 | { |
---|
| 1834 | poly h = p_Head(w, rRing); |
---|
| 1835 | |
---|
| 1836 | const int gen = p_GetComp(h, rRing); // 1 ... |
---|
| 1837 | |
---|
| 1838 | assume(gen > 0); |
---|
| 1839 | assume(gen <= n*m); |
---|
| 1840 | |
---|
| 1841 | // TODO: write a formula with %, / instead of while! |
---|
| 1842 | /* |
---|
| 1843 | int c = gen; |
---|
| 1844 | int v = 1; |
---|
| 1845 | while(c > m) |
---|
| 1846 | { |
---|
| 1847 | c -= m; |
---|
| 1848 | v++; |
---|
| 1849 | } |
---|
| 1850 | */ |
---|
| 1851 | |
---|
[592906] | 1852 | int cc = gen % m; |
---|
[90a60f] | 1853 | if( cc == 0) cc = m; |
---|
| 1854 | int vv = 1 + (gen - cc) / m; |
---|
| 1855 | |
---|
| 1856 | // assume( cc == c ); |
---|
| 1857 | // assume( vv == v ); |
---|
| 1858 | |
---|
| 1859 | // 1<= c <= m |
---|
| 1860 | assume( cc > 0 ); |
---|
| 1861 | assume( cc <= m ); |
---|
| 1862 | |
---|
| 1863 | assume( vv > 0 ); |
---|
| 1864 | assume( vv <= n ); |
---|
| 1865 | |
---|
| 1866 | assume( (cc + (vv-1)*m) == gen ); |
---|
| 1867 | |
---|
[9c1b63] | 1868 | p_IncrExp(h, vv, rRing); // h *= var(j) && // p_AddExp(h, vv, 1, rRing); |
---|
[592906] | 1869 | p_SetComp(h, cc, rRing); |
---|
[90a60f] | 1870 | |
---|
| 1871 | p_Setm(h, rRing); // addjust degree after the previous steps! |
---|
| 1872 | |
---|
| 1873 | pTempSum = p_Add_q(pTempSum, h, rRing); // it is slow since h will be usually put to the back of pTempSum!!! |
---|
| 1874 | |
---|
| 1875 | pIter(w); |
---|
| 1876 | } |
---|
| 1877 | |
---|
| 1878 | idTemp->m[i] = pTempSum; |
---|
| 1879 | } |
---|
| 1880 | |
---|
| 1881 | // simplify idTemp??? |
---|
| 1882 | |
---|
| 1883 | ideal idResult = id_Transp(idTemp, rRing); |
---|
| 1884 | |
---|
| 1885 | id_Delete(&idTemp, rRing); |
---|
| 1886 | |
---|
| 1887 | return(idResult); |
---|
| 1888 | } |
---|