[35aab3] | 1 | /**************************************** |
---|
| 2 | * Computer Algebra System SINGULAR * |
---|
| 3 | ****************************************/ |
---|
| 4 | /*************************************************************** |
---|
| 5 | * File: p_polys.cc |
---|
[45d2332] | 6 | * Purpose: implementation of ring independent poly procedures? |
---|
[35aab3] | 7 | * Author: obachman (Olaf Bachmann) |
---|
| 8 | * Created: 8/00 |
---|
[341696] | 9 | * Version: $Id$ |
---|
[35aab3] | 10 | *******************************************************************/ |
---|
| 11 | |
---|
[8a8c9e] | 12 | #include <ctype.h> |
---|
[9982049] | 13 | |
---|
[45d2332] | 14 | |
---|
| 15 | #include <omalloc/omalloc.h> |
---|
[6bec87] | 16 | #include <misc/auxiliary.h> |
---|
[45d2332] | 17 | #include <misc/options.h> |
---|
| 18 | #include <misc/intvec.h> |
---|
| 19 | |
---|
| 20 | #include <coeffs/longrat.h> // ??? |
---|
| 21 | |
---|
[af598e] | 22 | #include "weight.h" |
---|
| 23 | #include "simpleideals.h" |
---|
[9982049] | 24 | |
---|
[af598e] | 25 | #include "monomials/ring.h" |
---|
| 26 | #include "monomials/p_polys.h" |
---|
[304ad9b] | 27 | #include <polys/templates/p_MemCmp.h> |
---|
| 28 | #include <polys/templates/p_MemAdd.h> |
---|
| 29 | #include <polys/templates/p_MemCopy.h> |
---|
| 30 | |
---|
[45d2332] | 31 | |
---|
[20b794] | 32 | // #include <???/ideals.h> |
---|
| 33 | // #include <???/int64vec.h> |
---|
[45d2332] | 34 | |
---|
[fc5095] | 35 | #ifndef NDEBUG |
---|
[20b794] | 36 | // #include <???/febase.h> |
---|
[fc5095] | 37 | #endif |
---|
[35aab3] | 38 | |
---|
[45d2332] | 39 | #ifdef HAVE_PLURAL |
---|
[af598e] | 40 | #include "nc/nc.h" |
---|
| 41 | #include "nc/sca.h" |
---|
[45d2332] | 42 | #endif |
---|
| 43 | |
---|
[af598e] | 44 | #include "coeffrings.h" |
---|
[0654122] | 45 | #ifdef HAVE_FACTORY |
---|
[af598e] | 46 | #include "clapsing.h" |
---|
[0654122] | 47 | #endif |
---|
[32d07a5] | 48 | |
---|
[35aab3] | 49 | /*************************************************************** |
---|
| 50 | * |
---|
| 51 | * Completing what needs to be set for the monomial |
---|
| 52 | * |
---|
| 53 | ***************************************************************/ |
---|
| 54 | // this is special for the syz stuff |
---|
[eb72ba1] | 55 | static int* _components = NULL; |
---|
| 56 | static long* _componentsShifted = NULL; |
---|
| 57 | static int _componentsExternal = 0; |
---|
[35aab3] | 58 | |
---|
[fc5095] | 59 | BOOLEAN pSetm_error=0; |
---|
| 60 | |
---|
[324710] | 61 | #ifndef NDEBUG |
---|
| 62 | # define MYTEST 0 |
---|
| 63 | #else /* ifndef NDEBUG */ |
---|
| 64 | # define MYTEST 0 |
---|
| 65 | #endif /* ifndef NDEBUG */ |
---|
| 66 | |
---|
[33c36d] | 67 | void p_Setm_General(poly p, const ring r) |
---|
[35aab3] | 68 | { |
---|
| 69 | p_LmCheckPolyRing(p, r); |
---|
| 70 | int pos=0; |
---|
| 71 | if (r->typ!=NULL) |
---|
| 72 | { |
---|
| 73 | loop |
---|
| 74 | { |
---|
| 75 | long ord=0; |
---|
| 76 | sro_ord* o=&(r->typ[pos]); |
---|
| 77 | switch(o->ord_typ) |
---|
| 78 | { |
---|
| 79 | case ro_dp: |
---|
| 80 | { |
---|
| 81 | int a,e; |
---|
| 82 | a=o->data.dp.start; |
---|
| 83 | e=o->data.dp.end; |
---|
| 84 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r); |
---|
| 85 | p->exp[o->data.dp.place]=ord; |
---|
| 86 | break; |
---|
| 87 | } |
---|
| 88 | case ro_wp_neg: |
---|
| 89 | ord=POLY_NEGWEIGHT_OFFSET; |
---|
| 90 | // no break; |
---|
| 91 | case ro_wp: |
---|
| 92 | { |
---|
| 93 | int a,e; |
---|
| 94 | a=o->data.wp.start; |
---|
| 95 | e=o->data.wp.end; |
---|
| 96 | int *w=o->data.wp.weights; |
---|
[fc5095] | 97 | #if 1 |
---|
[35aab3] | 98 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r)*w[i-a]; |
---|
[fc5095] | 99 | #else |
---|
| 100 | long ai; |
---|
| 101 | int ei,wi; |
---|
| 102 | for(int i=a;i<=e;i++) |
---|
| 103 | { |
---|
| 104 | ei=p_GetExp(p,i,r); |
---|
| 105 | wi=w[i-a]; |
---|
| 106 | ai=ei*wi; |
---|
| 107 | if (ai/ei!=wi) pSetm_error=TRUE; |
---|
| 108 | ord+=ai; |
---|
| 109 | if (ord<ai) pSetm_error=TRUE; |
---|
| 110 | } |
---|
[ab4778] | 111 | #endif |
---|
[35aab3] | 112 | p->exp[o->data.wp.place]=ord; |
---|
| 113 | break; |
---|
| 114 | } |
---|
[fc5095] | 115 | case ro_wp64: |
---|
| 116 | { |
---|
[ab4778] | 117 | int64 ord=0; |
---|
[fc5095] | 118 | int a,e; |
---|
| 119 | a=o->data.wp64.start; |
---|
| 120 | e=o->data.wp64.end; |
---|
| 121 | int64 *w=o->data.wp64.weights64; |
---|
| 122 | int64 ei,wi,ai; |
---|
[2132395] | 123 | for(int i=a;i<=e;i++) |
---|
[b5d4d1] | 124 | { |
---|
[fc5095] | 125 | //Print("exp %d w %d \n",p_GetExp(p,i,r),(int)w[i-a]); |
---|
| 126 | //ord+=((int64)p_GetExp(p,i,r))*w[i-a]; |
---|
| 127 | ei=(int64)p_GetExp(p,i,r); |
---|
| 128 | wi=w[i-a]; |
---|
| 129 | ai=ei*wi; |
---|
[2132395] | 130 | if(ei!=0 && ai/ei!=wi) |
---|
[b5d4d1] | 131 | { |
---|
[fc5095] | 132 | pSetm_error=TRUE; |
---|
[b5d4d1] | 133 | #if SIZEOF_LONG == 4 |
---|
[fc5095] | 134 | Print("ai %lld, wi %lld\n",ai,wi); |
---|
[b5d4d1] | 135 | #else |
---|
[2132395] | 136 | Print("ai %ld, wi %ld\n",ai,wi); |
---|
[b5d4d1] | 137 | #endif |
---|
[fc5095] | 138 | } |
---|
| 139 | ord+=ai; |
---|
[2132395] | 140 | if (ord<ai) |
---|
[b5d4d1] | 141 | { |
---|
[2132395] | 142 | pSetm_error=TRUE; |
---|
[b5d4d1] | 143 | #if SIZEOF_LONG == 4 |
---|
[2132395] | 144 | Print("ai %lld, ord %lld\n",ai,ord); |
---|
[b5d4d1] | 145 | #else |
---|
[2132395] | 146 | Print("ai %ld, ord %ld\n",ai,ord); |
---|
[b5d4d1] | 147 | #endif |
---|
[fc5095] | 148 | } |
---|
| 149 | } |
---|
| 150 | int64 mask=(int64)0x7fffffff; |
---|
| 151 | long a_0=(long)(ord&mask); //2^31 |
---|
| 152 | long a_1=(long)(ord >>31 ); /*(ord/(mask+1));*/ |
---|
| 153 | |
---|
[ab4778] | 154 | //Print("mask: %x, ord: %d, a_0: %d, a_1: %d\n" |
---|
| 155 | //,(int)mask,(int)ord,(int)a_0,(int)a_1); |
---|
| 156 | //Print("mask: %d",mask); |
---|
[fc5095] | 157 | |
---|
| 158 | p->exp[o->data.wp64.place]=a_1; |
---|
[ab4778] | 159 | p->exp[o->data.wp64.place+1]=a_0; |
---|
[fc5095] | 160 | // if(p_Setm_error) Print("***************************\n |
---|
| 161 | // ***************************\n |
---|
| 162 | // **WARNING: overflow error**\n |
---|
| 163 | // ***************************\n |
---|
| 164 | // ***************************\n"); |
---|
| 165 | break; |
---|
| 166 | } |
---|
[35aab3] | 167 | case ro_cp: |
---|
| 168 | { |
---|
| 169 | int a,e; |
---|
| 170 | a=o->data.cp.start; |
---|
| 171 | e=o->data.cp.end; |
---|
| 172 | int pl=o->data.cp.place; |
---|
| 173 | for(int i=a;i<=e;i++) { p->exp[pl]=p_GetExp(p,i,r); pl++; } |
---|
| 174 | break; |
---|
| 175 | } |
---|
| 176 | case ro_syzcomp: |
---|
| 177 | { |
---|
| 178 | int c=p_GetComp(p,r); |
---|
| 179 | long sc = c; |
---|
[eb72ba1] | 180 | int* Components = (_componentsExternal ? _components : |
---|
[35aab3] | 181 | o->data.syzcomp.Components); |
---|
[eb72ba1] | 182 | long* ShiftedComponents = (_componentsExternal ? _componentsShifted: |
---|
[35aab3] | 183 | o->data.syzcomp.ShiftedComponents); |
---|
| 184 | if (ShiftedComponents != NULL) |
---|
| 185 | { |
---|
| 186 | assume(Components != NULL); |
---|
| 187 | assume(c == 0 || Components[c] != 0); |
---|
| 188 | sc = ShiftedComponents[Components[c]]; |
---|
| 189 | assume(c == 0 || sc != 0); |
---|
| 190 | } |
---|
| 191 | p->exp[o->data.syzcomp.place]=sc; |
---|
| 192 | break; |
---|
| 193 | } |
---|
| 194 | case ro_syz: |
---|
| 195 | { |
---|
[273fed] | 196 | const unsigned long c = p_GetComp(p, r); |
---|
| 197 | const short place = o->data.syz.place; |
---|
| 198 | const int limit = o->data.syz.limit; |
---|
| 199 | |
---|
| 200 | if (c > limit) |
---|
| 201 | p->exp[place] = o->data.syz.curr_index; |
---|
[35aab3] | 202 | else if (c > 0) |
---|
[273fed] | 203 | { |
---|
| 204 | assume( (1 <= c) && (c <= limit) ); |
---|
| 205 | p->exp[place]= o->data.syz.syz_index[c]; |
---|
| 206 | } |
---|
[35aab3] | 207 | else |
---|
| 208 | { |
---|
| 209 | assume(c == 0); |
---|
[273fed] | 210 | p->exp[place]= 0; |
---|
[35aab3] | 211 | } |
---|
| 212 | break; |
---|
| 213 | } |
---|
[645a19] | 214 | // Prefix for Induced Schreyer ordering |
---|
| 215 | case ro_isTemp: // Do nothing?? (to be removed into suffix later on...?) |
---|
| 216 | { |
---|
| 217 | assume(p != NULL); |
---|
| 218 | |
---|
| 219 | #ifndef NDEBUG |
---|
| 220 | #if MYTEST |
---|
[273fed] | 221 | Print("p_Setm_General: isTemp ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
---|
[645a19] | 222 | #endif |
---|
| 223 | #endif |
---|
| 224 | int c = p_GetComp(p, r); |
---|
| 225 | |
---|
| 226 | assume( c >= 0 ); |
---|
| 227 | |
---|
| 228 | // Let's simulate case ro_syz above.... |
---|
| 229 | // Should accumulate (by Suffix) and be a level indicator |
---|
| 230 | const int* const pVarOffset = o->data.isTemp.pVarOffset; |
---|
| 231 | |
---|
| 232 | assume( pVarOffset != NULL ); |
---|
| 233 | |
---|
| 234 | // TODO: Can this be done in the suffix??? |
---|
| 235 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
---|
| 236 | { |
---|
| 237 | const int vo = pVarOffset[i]; |
---|
| 238 | if( vo != -1) // TODO: optimize: can be done once! |
---|
| 239 | { |
---|
[5cb9ec] | 240 | // Hans! Please don't break it again! p_SetExp(p, ..., r, vo) is correct: |
---|
| 241 | p_SetExp(p, p_GetExp(p, i, r), r, vo); // copy put them verbatim |
---|
| 242 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
---|
| 243 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
---|
[645a19] | 244 | } |
---|
| 245 | } |
---|
| 246 | #ifndef NDEBUG |
---|
| 247 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
---|
| 248 | { |
---|
| 249 | const int vo = pVarOffset[i]; |
---|
| 250 | if( vo != -1) // TODO: optimize: can be done once! |
---|
| 251 | { |
---|
[5cb9ec] | 252 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
---|
| 253 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
---|
[645a19] | 254 | } |
---|
| 255 | } |
---|
| 256 | #if MYTEST |
---|
[1b816a3] | 257 | // if( p->exp[o->data.isTemp.start] > 0 ) |
---|
| 258 | // { |
---|
| 259 | // PrintS("Initial Value: "); p_DebugPrint(p, r, r, 1); |
---|
| 260 | // } |
---|
[645a19] | 261 | #endif |
---|
| 262 | #endif |
---|
| 263 | break; |
---|
| 264 | } |
---|
| 265 | |
---|
| 266 | // Suffix for Induced Schreyer ordering |
---|
| 267 | case ro_is: |
---|
| 268 | { |
---|
[273fed] | 269 | #ifndef NDEBUG |
---|
| 270 | #if MYTEST |
---|
| 271 | Print("p_Setm_General: ro_is ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
---|
| 272 | #endif |
---|
| 273 | #endif |
---|
| 274 | |
---|
[645a19] | 275 | assume(p != NULL); |
---|
| 276 | |
---|
| 277 | int c = p_GetComp(p, r); |
---|
| 278 | |
---|
| 279 | assume( c >= 0 ); |
---|
| 280 | const ideal F = o->data.is.F; |
---|
| 281 | const int limit = o->data.is.limit; |
---|
| 282 | |
---|
| 283 | if( F != NULL && c > limit ) |
---|
| 284 | { |
---|
| 285 | #ifndef NDEBUG |
---|
| 286 | #if MYTEST |
---|
[6e66d2] | 287 | Print("p_Setm_General: ro_is : in rSetm: pos: %d, c: %d > limit: %d\n", c, pos, limit); // p_DebugPrint(p, r, r, 1); |
---|
[645a19] | 288 | #endif |
---|
| 289 | #endif |
---|
| 290 | |
---|
| 291 | c -= limit; |
---|
| 292 | assume( c > 0 ); |
---|
| 293 | c--; |
---|
| 294 | |
---|
| 295 | assume( c < IDELEMS(F) ); // What about others??? |
---|
| 296 | |
---|
| 297 | const poly pp = F->m[c]; // get reference monomial!!! |
---|
| 298 | |
---|
| 299 | #ifndef NDEBUG |
---|
| 300 | #if MYTEST |
---|
| 301 | Print("Respective F[c - %d: %d] pp: ", limit, c); |
---|
| 302 | p_DebugPrint(pp, r, r, 1); |
---|
| 303 | #endif |
---|
| 304 | #endif |
---|
| 305 | |
---|
| 306 | |
---|
[6e66d2] | 307 | assume(pp != NULL); |
---|
[645a19] | 308 | if(pp == NULL) break; |
---|
| 309 | |
---|
| 310 | const int start = o->data.is.start; |
---|
| 311 | const int end = o->data.is.end; |
---|
| 312 | |
---|
| 313 | assume(start <= end); |
---|
[6e66d2] | 314 | |
---|
| 315 | // const int limit = o->data.is.limit; |
---|
| 316 | assume( limit >= 0 ); |
---|
| 317 | |
---|
| 318 | // const int st = o->data.isTemp.start; |
---|
| 319 | |
---|
| 320 | if( c > limit ) |
---|
| 321 | p->exp[start] = 1; |
---|
| 322 | // else |
---|
| 323 | // p->exp[start] = 0; |
---|
| 324 | |
---|
| 325 | |
---|
| 326 | #ifndef NDEBUG |
---|
[a41623] | 327 | Print("p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]); |
---|
[6e66d2] | 328 | #endif |
---|
| 329 | |
---|
[645a19] | 330 | |
---|
| 331 | for( int i = start; i <= end; i++) // v[0] may be here... |
---|
| 332 | p->exp[i] += pp->exp[i]; // !!!!!!!! ADD corresponding LT(F) |
---|
| 333 | |
---|
[6e66d2] | 334 | |
---|
| 335 | |
---|
| 336 | |
---|
[645a19] | 337 | #ifndef NDEBUG |
---|
| 338 | const int* const pVarOffset = o->data.is.pVarOffset; |
---|
| 339 | |
---|
| 340 | assume( pVarOffset != NULL ); |
---|
| 341 | |
---|
| 342 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
---|
| 343 | { |
---|
| 344 | const int vo = pVarOffset[i]; |
---|
| 345 | if( vo != -1) // TODO: optimize: can be done once! |
---|
[5cb9ec] | 346 | // Hans! Please don't break it again! p_GetExp(p/pp, r, vo) is correct: |
---|
| 347 | assume( p_GetExp(p, r, vo) == (p_GetExp(p, i, r) + p_GetExp(pp, r, vo)) ); |
---|
[645a19] | 348 | } |
---|
| 349 | // TODO: how to check this for computed values??? |
---|
| 350 | #endif |
---|
| 351 | } else |
---|
| 352 | { |
---|
| 353 | const int* const pVarOffset = o->data.is.pVarOffset; |
---|
| 354 | |
---|
| 355 | // What about v[0] - component: it will be added later by |
---|
| 356 | // suffix!!! |
---|
| 357 | // TODO: Test it! |
---|
| 358 | const int vo = pVarOffset[0]; |
---|
| 359 | if( vo != -1 ) |
---|
| 360 | p->exp[vo] = c; // initial component v[0]! |
---|
[6e66d2] | 361 | |
---|
| 362 | #ifndef NDEBUG |
---|
| 363 | #if MYTEST |
---|
| 364 | Print("p_Setm_General: ro_is :: c: %d <= limit: %d, vo: %d, exp: %d\n", c, limit, vo, p->exp[vo]); |
---|
| 365 | p_DebugPrint(p, r, r, 1); |
---|
| 366 | #endif |
---|
| 367 | #endif |
---|
[645a19] | 368 | } |
---|
[6e66d2] | 369 | |
---|
[645a19] | 370 | |
---|
| 371 | break; |
---|
| 372 | } |
---|
[35aab3] | 373 | default: |
---|
| 374 | dReportError("wrong ord in rSetm:%d\n",o->ord_typ); |
---|
| 375 | return; |
---|
| 376 | } |
---|
| 377 | pos++; |
---|
| 378 | if (pos == r->OrdSize) return; |
---|
| 379 | } |
---|
| 380 | } |
---|
| 381 | } |
---|
| 382 | |
---|
| 383 | void p_Setm_Syz(poly p, ring r, int* Components, long* ShiftedComponents) |
---|
| 384 | { |
---|
[eb72ba1] | 385 | _components = Components; |
---|
| 386 | _componentsShifted = ShiftedComponents; |
---|
| 387 | _componentsExternal = 1; |
---|
[35aab3] | 388 | p_Setm_General(p, r); |
---|
[eb72ba1] | 389 | _componentsExternal = 0; |
---|
[35aab3] | 390 | } |
---|
| 391 | |
---|
| 392 | // dummy for lp, ls, etc |
---|
[33c36d] | 393 | void p_Setm_Dummy(poly p, const ring r) |
---|
[35aab3] | 394 | { |
---|
| 395 | p_LmCheckPolyRing(p, r); |
---|
| 396 | } |
---|
| 397 | |
---|
| 398 | // for dp, Dp, ds, etc |
---|
[33c36d] | 399 | void p_Setm_TotalDegree(poly p, const ring r) |
---|
[35aab3] | 400 | { |
---|
| 401 | p_LmCheckPolyRing(p, r); |
---|
[99bdcf] | 402 | p->exp[r->pOrdIndex] = p_Totaldegree(p, r); |
---|
[35aab3] | 403 | } |
---|
| 404 | |
---|
| 405 | // for wp, Wp, ws, etc |
---|
[33c36d] | 406 | void p_Setm_WFirstTotalDegree(poly p, const ring r) |
---|
[35aab3] | 407 | { |
---|
| 408 | p_LmCheckPolyRing(p, r); |
---|
[19ae652] | 409 | p->exp[r->pOrdIndex] = p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 410 | } |
---|
| 411 | |
---|
| 412 | p_SetmProc p_GetSetmProc(ring r) |
---|
| 413 | { |
---|
[ab4778] | 414 | // covers lp, rp, ls, |
---|
[35aab3] | 415 | if (r->typ == NULL) return p_Setm_Dummy; |
---|
| 416 | |
---|
| 417 | if (r->OrdSize == 1) |
---|
| 418 | { |
---|
[ab4778] | 419 | if (r->typ[0].ord_typ == ro_dp && |
---|
[35aab3] | 420 | r->typ[0].data.dp.start == 1 && |
---|
| 421 | r->typ[0].data.dp.end == r->N && |
---|
| 422 | r->typ[0].data.dp.place == r->pOrdIndex) |
---|
| 423 | return p_Setm_TotalDegree; |
---|
[ab4778] | 424 | if (r->typ[0].ord_typ == ro_wp && |
---|
[35aab3] | 425 | r->typ[0].data.wp.start == 1 && |
---|
| 426 | r->typ[0].data.wp.end == r->N && |
---|
| 427 | r->typ[0].data.wp.place == r->pOrdIndex && |
---|
| 428 | r->typ[0].data.wp.weights == r->firstwv) |
---|
| 429 | return p_Setm_WFirstTotalDegree; |
---|
| 430 | } |
---|
| 431 | return p_Setm_General; |
---|
| 432 | } |
---|
| 433 | |
---|
| 434 | |
---|
| 435 | /* -------------------------------------------------------------------*/ |
---|
| 436 | /* several possibilities for pFDeg: the degree of the head term */ |
---|
[b5d4d1] | 437 | |
---|
| 438 | /* comptible with ordering */ |
---|
[bf183f] | 439 | long p_Deg(poly a, const ring r) |
---|
[35aab3] | 440 | { |
---|
| 441 | p_LmCheckPolyRing(a, r); |
---|
[19ae652] | 442 | assume(p_GetOrder(a, r) == p_WTotaldegree(a, r)); |
---|
[35aab3] | 443 | return p_GetOrder(a, r); |
---|
| 444 | } |
---|
| 445 | |
---|
[19ae652] | 446 | // p_WTotalDegree for weighted orderings |
---|
[35aab3] | 447 | // whose first block covers all variables |
---|
[19ae652] | 448 | long p_WFirstTotalDegree(poly p, const ring r) |
---|
[35aab3] | 449 | { |
---|
| 450 | int i; |
---|
| 451 | long sum = 0; |
---|
[ab4778] | 452 | |
---|
[35aab3] | 453 | for (i=1; i<= r->firstBlockEnds; i++) |
---|
| 454 | { |
---|
| 455 | sum += p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
| 456 | } |
---|
| 457 | return sum; |
---|
| 458 | } |
---|
| 459 | |
---|
| 460 | /*2 |
---|
| 461 | * compute the degree of the leading monomial of p |
---|
| 462 | * with respect to weigths from the ordering |
---|
| 463 | * the ordering is not compatible with degree so do not use p->Order |
---|
| 464 | */ |
---|
[19ae652] | 465 | long p_WTotaldegree(poly p, const ring r) |
---|
[35aab3] | 466 | { |
---|
| 467 | p_LmCheckPolyRing(p, r); |
---|
| 468 | int i, k; |
---|
| 469 | long j =0; |
---|
| 470 | |
---|
| 471 | // iterate through each block: |
---|
| 472 | for (i=0;r->order[i]!=0;i++) |
---|
| 473 | { |
---|
[ab4778] | 474 | int b0=r->block0[i]; |
---|
| 475 | int b1=r->block1[i]; |
---|
[35aab3] | 476 | switch(r->order[i]) |
---|
| 477 | { |
---|
[3e0a7b] | 478 | case ringorder_M: |
---|
[ab4778] | 479 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
| 480 | { // in jedem block: |
---|
| 481 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]*r->OrdSgn; |
---|
| 482 | } |
---|
| 483 | break; |
---|
[35aab3] | 484 | case ringorder_wp: |
---|
| 485 | case ringorder_ws: |
---|
| 486 | case ringorder_Wp: |
---|
| 487 | case ringorder_Ws: |
---|
[ab4778] | 488 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 489 | { // in jedem block: |
---|
[ab4778] | 490 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]; |
---|
[35aab3] | 491 | } |
---|
| 492 | break; |
---|
| 493 | case ringorder_lp: |
---|
| 494 | case ringorder_ls: |
---|
[e519c5c] | 495 | case ringorder_rs: |
---|
[35aab3] | 496 | case ringorder_dp: |
---|
| 497 | case ringorder_ds: |
---|
| 498 | case ringorder_Dp: |
---|
| 499 | case ringorder_Ds: |
---|
| 500 | case ringorder_rp: |
---|
[ab4778] | 501 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 502 | { |
---|
| 503 | j+= p_GetExp(p,k,r); |
---|
| 504 | } |
---|
| 505 | break; |
---|
[fc5095] | 506 | case ringorder_a64: |
---|
| 507 | { |
---|
| 508 | int64* w=(int64*)r->wvhdl[i]; |
---|
[ab4778] | 509 | for (k=0;k<=(b1 /*r->block1[i]*/ - b0 /*r->block0[i]*/);k++) |
---|
| 510 | { |
---|
[fc5095] | 511 | //there should be added a line which checks if w[k]>2^31 |
---|
| 512 | j+= p_GetExp(p,k+1, r)*(long)w[k]; |
---|
| 513 | } |
---|
| 514 | //break; |
---|
| 515 | return j; |
---|
| 516 | } |
---|
[35aab3] | 517 | case ringorder_c: |
---|
| 518 | case ringorder_C: |
---|
| 519 | case ringorder_S: |
---|
| 520 | case ringorder_s: |
---|
[645a19] | 521 | case ringorder_IS: |
---|
[35aab3] | 522 | case ringorder_aa: |
---|
| 523 | break; |
---|
| 524 | case ringorder_a: |
---|
[ab4778] | 525 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
[35aab3] | 526 | { // only one line |
---|
[ab4778] | 527 | j+= p_GetExp(p,k, r)*r->wvhdl[i][ k- b0 /*r->block0[i]*/]; |
---|
[35aab3] | 528 | } |
---|
[fc5095] | 529 | //break; |
---|
[35aab3] | 530 | return j; |
---|
[fc5095] | 531 | |
---|
[35aab3] | 532 | #ifndef NDEBUG |
---|
| 533 | default: |
---|
[19ae652] | 534 | Print("missing order %d in p_WTotaldegree\n",r->order[i]); |
---|
[35aab3] | 535 | break; |
---|
| 536 | #endif |
---|
| 537 | } |
---|
| 538 | } |
---|
| 539 | return j; |
---|
| 540 | } |
---|
| 541 | |
---|
[ba0fc3] | 542 | long p_DegW(poly p, const short *w, const ring R) |
---|
| 543 | { |
---|
| 544 | long r=~0L; |
---|
| 545 | |
---|
| 546 | while (p!=NULL) |
---|
| 547 | { |
---|
| 548 | long t=totaldegreeWecart_IV(p,R,w); |
---|
| 549 | if (t>r) r=t; |
---|
| 550 | pIter(p); |
---|
| 551 | } |
---|
| 552 | return r; |
---|
| 553 | } |
---|
| 554 | |
---|
[bf183f] | 555 | int p_Weight(int i, const ring r) |
---|
[35aab3] | 556 | { |
---|
| 557 | if ((r->firstwv==NULL) || (i>r->firstBlockEnds)) |
---|
| 558 | { |
---|
| 559 | return 1; |
---|
| 560 | } |
---|
| 561 | return r->firstwv[i-1]; |
---|
| 562 | } |
---|
| 563 | |
---|
[bf183f] | 564 | long p_WDegree(poly p, const ring r) |
---|
[35aab3] | 565 | { |
---|
[99bdcf] | 566 | if (r->firstwv==NULL) return p_Totaldegree(p, r); |
---|
[35aab3] | 567 | p_LmCheckPolyRing(p, r); |
---|
[9f73e80] | 568 | int i; |
---|
[35aab3] | 569 | long j =0; |
---|
| 570 | |
---|
| 571 | for(i=1;i<=r->firstBlockEnds;i++) |
---|
| 572 | j+=p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
| 573 | |
---|
| 574 | for (;i<=r->N;i++) |
---|
[8a8c9e] | 575 | j+=p_GetExp(p,i, r)*p_Weight(i, r); |
---|
[35aab3] | 576 | |
---|
| 577 | return j; |
---|
| 578 | } |
---|
| 579 | |
---|
| 580 | |
---|
| 581 | /* ---------------------------------------------------------------------*/ |
---|
| 582 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
| 583 | /* compute in l also the pLength of p */ |
---|
| 584 | |
---|
| 585 | /*2 |
---|
| 586 | * compute the length of a polynomial (in l) |
---|
| 587 | * and the degree of the monomial with maximal degree: the last one |
---|
| 588 | */ |
---|
[107986] | 589 | long pLDeg0(poly p,int *l, const ring r) |
---|
[35aab3] | 590 | { |
---|
| 591 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 592 | long k= p_GetComp(p, r); |
---|
[35aab3] | 593 | int ll=1; |
---|
| 594 | |
---|
| 595 | if (k > 0) |
---|
| 596 | { |
---|
| 597 | while ((pNext(p)!=NULL) && (p_GetComp(pNext(p), r)==k)) |
---|
| 598 | { |
---|
| 599 | pIter(p); |
---|
| 600 | ll++; |
---|
| 601 | } |
---|
| 602 | } |
---|
| 603 | else |
---|
| 604 | { |
---|
| 605 | while (pNext(p)!=NULL) |
---|
| 606 | { |
---|
| 607 | pIter(p); |
---|
| 608 | ll++; |
---|
| 609 | } |
---|
| 610 | } |
---|
| 611 | *l=ll; |
---|
| 612 | return r->pFDeg(p, r); |
---|
| 613 | } |
---|
| 614 | |
---|
| 615 | /*2 |
---|
| 616 | * compute the length of a polynomial (in l) |
---|
| 617 | * and the degree of the monomial with maximal degree: the last one |
---|
| 618 | * but search in all components before syzcomp |
---|
| 619 | */ |
---|
[107986] | 620 | long pLDeg0c(poly p,int *l, const ring r) |
---|
[35aab3] | 621 | { |
---|
| 622 | assume(p!=NULL); |
---|
| 623 | #ifdef PDEBUG |
---|
| 624 | _p_Test(p,r,PDEBUG); |
---|
| 625 | #endif |
---|
| 626 | p_CheckPolyRing(p, r); |
---|
| 627 | long o; |
---|
| 628 | int ll=1; |
---|
| 629 | |
---|
| 630 | if (! rIsSyzIndexRing(r)) |
---|
| 631 | { |
---|
[ab4778] | 632 | while (pNext(p) != NULL) |
---|
[35aab3] | 633 | { |
---|
| 634 | pIter(p); |
---|
| 635 | ll++; |
---|
| 636 | } |
---|
| 637 | o = r->pFDeg(p, r); |
---|
| 638 | } |
---|
| 639 | else |
---|
| 640 | { |
---|
| 641 | int curr_limit = rGetCurrSyzLimit(r); |
---|
| 642 | poly pp = p; |
---|
| 643 | while ((p=pNext(p))!=NULL) |
---|
| 644 | { |
---|
| 645 | if (p_GetComp(p, r)<=curr_limit/*syzComp*/) |
---|
| 646 | ll++; |
---|
| 647 | else break; |
---|
| 648 | pp = p; |
---|
| 649 | } |
---|
| 650 | #ifdef PDEBUG |
---|
| 651 | _p_Test(pp,r,PDEBUG); |
---|
| 652 | #endif |
---|
| 653 | o = r->pFDeg(pp, r); |
---|
| 654 | } |
---|
| 655 | *l=ll; |
---|
| 656 | return o; |
---|
| 657 | } |
---|
| 658 | |
---|
| 659 | /*2 |
---|
| 660 | * compute the length of a polynomial (in l) |
---|
| 661 | * and the degree of the monomial with maximal degree: the first one |
---|
| 662 | * this works for the polynomial case with degree orderings |
---|
| 663 | * (both c,dp and dp,c) |
---|
| 664 | */ |
---|
[107986] | 665 | long pLDegb(poly p,int *l, const ring r) |
---|
[35aab3] | 666 | { |
---|
| 667 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 668 | long k= p_GetComp(p, r); |
---|
[35aab3] | 669 | long o = r->pFDeg(p, r); |
---|
| 670 | int ll=1; |
---|
| 671 | |
---|
| 672 | if (k != 0) |
---|
| 673 | { |
---|
| 674 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 675 | { |
---|
| 676 | ll++; |
---|
| 677 | } |
---|
| 678 | } |
---|
| 679 | else |
---|
| 680 | { |
---|
| 681 | while ((p=pNext(p)) !=NULL) |
---|
| 682 | { |
---|
| 683 | ll++; |
---|
| 684 | } |
---|
| 685 | } |
---|
| 686 | *l=ll; |
---|
| 687 | return o; |
---|
| 688 | } |
---|
| 689 | |
---|
| 690 | /*2 |
---|
| 691 | * compute the length of a polynomial (in l) |
---|
| 692 | * and the degree of the monomial with maximal degree: |
---|
| 693 | * this is NOT the last one, we have to look for it |
---|
| 694 | */ |
---|
[107986] | 695 | long pLDeg1(poly p,int *l, const ring r) |
---|
[35aab3] | 696 | { |
---|
| 697 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 698 | long k= p_GetComp(p, r); |
---|
[35aab3] | 699 | int ll=1; |
---|
| 700 | long t,max; |
---|
| 701 | |
---|
| 702 | max=r->pFDeg(p, r); |
---|
| 703 | if (k > 0) |
---|
| 704 | { |
---|
| 705 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 706 | { |
---|
| 707 | t=r->pFDeg(p, r); |
---|
| 708 | if (t>max) max=t; |
---|
| 709 | ll++; |
---|
| 710 | } |
---|
| 711 | } |
---|
| 712 | else |
---|
| 713 | { |
---|
| 714 | while ((p=pNext(p))!=NULL) |
---|
| 715 | { |
---|
| 716 | t=r->pFDeg(p, r); |
---|
| 717 | if (t>max) max=t; |
---|
| 718 | ll++; |
---|
| 719 | } |
---|
| 720 | } |
---|
| 721 | *l=ll; |
---|
| 722 | return max; |
---|
| 723 | } |
---|
| 724 | |
---|
| 725 | /*2 |
---|
| 726 | * compute the length of a polynomial (in l) |
---|
| 727 | * and the degree of the monomial with maximal degree: |
---|
| 728 | * this is NOT the last one, we have to look for it |
---|
| 729 | * in all components |
---|
| 730 | */ |
---|
[107986] | 731 | long pLDeg1c(poly p,int *l, const ring r) |
---|
[35aab3] | 732 | { |
---|
| 733 | p_CheckPolyRing(p, r); |
---|
| 734 | int ll=1; |
---|
| 735 | long t,max; |
---|
| 736 | |
---|
| 737 | max=r->pFDeg(p, r); |
---|
| 738 | if (rIsSyzIndexRing(r)) |
---|
| 739 | { |
---|
| 740 | long limit = rGetCurrSyzLimit(r); |
---|
| 741 | while ((p=pNext(p))!=NULL) |
---|
| 742 | { |
---|
| 743 | if (p_GetComp(p, r)<=limit) |
---|
| 744 | { |
---|
| 745 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
| 746 | ll++; |
---|
| 747 | } |
---|
| 748 | else break; |
---|
| 749 | } |
---|
| 750 | } |
---|
| 751 | else |
---|
| 752 | { |
---|
| 753 | while ((p=pNext(p))!=NULL) |
---|
| 754 | { |
---|
| 755 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
| 756 | ll++; |
---|
| 757 | } |
---|
| 758 | } |
---|
| 759 | *l=ll; |
---|
| 760 | return max; |
---|
| 761 | } |
---|
| 762 | |
---|
| 763 | // like pLDeg1, only pFDeg == pDeg |
---|
[107986] | 764 | long pLDeg1_Deg(poly p,int *l, const ring r) |
---|
[35aab3] | 765 | { |
---|
[45d2332] | 766 | assume(r->pFDeg == p_Deg); |
---|
[35aab3] | 767 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 768 | long k= p_GetComp(p, r); |
---|
[35aab3] | 769 | int ll=1; |
---|
| 770 | long t,max; |
---|
| 771 | |
---|
[b5d4d1] | 772 | max=p_GetOrder(p, r); |
---|
[35aab3] | 773 | if (k > 0) |
---|
| 774 | { |
---|
| 775 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 776 | { |
---|
[b5d4d1] | 777 | t=p_GetOrder(p, r); |
---|
[35aab3] | 778 | if (t>max) max=t; |
---|
| 779 | ll++; |
---|
| 780 | } |
---|
| 781 | } |
---|
| 782 | else |
---|
| 783 | { |
---|
| 784 | while ((p=pNext(p))!=NULL) |
---|
| 785 | { |
---|
[b5d4d1] | 786 | t=p_GetOrder(p, r); |
---|
[35aab3] | 787 | if (t>max) max=t; |
---|
| 788 | ll++; |
---|
| 789 | } |
---|
| 790 | } |
---|
| 791 | *l=ll; |
---|
| 792 | return max; |
---|
| 793 | } |
---|
| 794 | |
---|
[107986] | 795 | long pLDeg1c_Deg(poly p,int *l, const ring r) |
---|
[35aab3] | 796 | { |
---|
[45d2332] | 797 | assume(r->pFDeg == p_Deg); |
---|
[35aab3] | 798 | p_CheckPolyRing(p, r); |
---|
| 799 | int ll=1; |
---|
| 800 | long t,max; |
---|
| 801 | |
---|
[b5d4d1] | 802 | max=p_GetOrder(p, r); |
---|
[35aab3] | 803 | if (rIsSyzIndexRing(r)) |
---|
| 804 | { |
---|
| 805 | long limit = rGetCurrSyzLimit(r); |
---|
| 806 | while ((p=pNext(p))!=NULL) |
---|
| 807 | { |
---|
| 808 | if (p_GetComp(p, r)<=limit) |
---|
| 809 | { |
---|
[b5d4d1] | 810 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
[35aab3] | 811 | ll++; |
---|
| 812 | } |
---|
| 813 | else break; |
---|
| 814 | } |
---|
| 815 | } |
---|
| 816 | else |
---|
| 817 | { |
---|
| 818 | while ((p=pNext(p))!=NULL) |
---|
| 819 | { |
---|
[b5d4d1] | 820 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
[35aab3] | 821 | ll++; |
---|
| 822 | } |
---|
| 823 | } |
---|
| 824 | *l=ll; |
---|
| 825 | return max; |
---|
| 826 | } |
---|
| 827 | |
---|
| 828 | // like pLDeg1, only pFDeg == pTotoalDegree |
---|
[107986] | 829 | long pLDeg1_Totaldegree(poly p,int *l, const ring r) |
---|
[35aab3] | 830 | { |
---|
| 831 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 832 | long k= p_GetComp(p, r); |
---|
[35aab3] | 833 | int ll=1; |
---|
| 834 | long t,max; |
---|
| 835 | |
---|
[99bdcf] | 836 | max=p_Totaldegree(p, r); |
---|
[35aab3] | 837 | if (k > 0) |
---|
| 838 | { |
---|
| 839 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 840 | { |
---|
[99bdcf] | 841 | t=p_Totaldegree(p, r); |
---|
[35aab3] | 842 | if (t>max) max=t; |
---|
| 843 | ll++; |
---|
| 844 | } |
---|
| 845 | } |
---|
| 846 | else |
---|
| 847 | { |
---|
| 848 | while ((p=pNext(p))!=NULL) |
---|
| 849 | { |
---|
[99bdcf] | 850 | t=p_Totaldegree(p, r); |
---|
[35aab3] | 851 | if (t>max) max=t; |
---|
| 852 | ll++; |
---|
| 853 | } |
---|
| 854 | } |
---|
| 855 | *l=ll; |
---|
| 856 | return max; |
---|
| 857 | } |
---|
| 858 | |
---|
[107986] | 859 | long pLDeg1c_Totaldegree(poly p,int *l, const ring r) |
---|
[35aab3] | 860 | { |
---|
| 861 | p_CheckPolyRing(p, r); |
---|
| 862 | int ll=1; |
---|
| 863 | long t,max; |
---|
| 864 | |
---|
[99bdcf] | 865 | max=p_Totaldegree(p, r); |
---|
[35aab3] | 866 | if (rIsSyzIndexRing(r)) |
---|
| 867 | { |
---|
| 868 | long limit = rGetCurrSyzLimit(r); |
---|
| 869 | while ((p=pNext(p))!=NULL) |
---|
| 870 | { |
---|
| 871 | if (p_GetComp(p, r)<=limit) |
---|
| 872 | { |
---|
[99bdcf] | 873 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 874 | ll++; |
---|
| 875 | } |
---|
| 876 | else break; |
---|
| 877 | } |
---|
| 878 | } |
---|
| 879 | else |
---|
| 880 | { |
---|
| 881 | while ((p=pNext(p))!=NULL) |
---|
| 882 | { |
---|
[99bdcf] | 883 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 884 | ll++; |
---|
| 885 | } |
---|
| 886 | } |
---|
| 887 | *l=ll; |
---|
| 888 | return max; |
---|
| 889 | } |
---|
| 890 | |
---|
[19ae652] | 891 | // like pLDeg1, only pFDeg == p_WFirstTotalDegree |
---|
[107986] | 892 | long pLDeg1_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
[35aab3] | 893 | { |
---|
| 894 | p_CheckPolyRing(p, r); |
---|
[0b5e3d] | 895 | long k= p_GetComp(p, r); |
---|
[35aab3] | 896 | int ll=1; |
---|
| 897 | long t,max; |
---|
| 898 | |
---|
[19ae652] | 899 | max=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 900 | if (k > 0) |
---|
| 901 | { |
---|
| 902 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
| 903 | { |
---|
[19ae652] | 904 | t=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 905 | if (t>max) max=t; |
---|
| 906 | ll++; |
---|
| 907 | } |
---|
| 908 | } |
---|
| 909 | else |
---|
| 910 | { |
---|
| 911 | while ((p=pNext(p))!=NULL) |
---|
| 912 | { |
---|
[19ae652] | 913 | t=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 914 | if (t>max) max=t; |
---|
| 915 | ll++; |
---|
| 916 | } |
---|
| 917 | } |
---|
| 918 | *l=ll; |
---|
| 919 | return max; |
---|
| 920 | } |
---|
| 921 | |
---|
[107986] | 922 | long pLDeg1c_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
[35aab3] | 923 | { |
---|
| 924 | p_CheckPolyRing(p, r); |
---|
| 925 | int ll=1; |
---|
| 926 | long t,max; |
---|
| 927 | |
---|
[19ae652] | 928 | max=p_WFirstTotalDegree(p, r); |
---|
[35aab3] | 929 | if (rIsSyzIndexRing(r)) |
---|
| 930 | { |
---|
| 931 | long limit = rGetCurrSyzLimit(r); |
---|
| 932 | while ((p=pNext(p))!=NULL) |
---|
| 933 | { |
---|
| 934 | if (p_GetComp(p, r)<=limit) |
---|
| 935 | { |
---|
[99bdcf] | 936 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 937 | ll++; |
---|
| 938 | } |
---|
| 939 | else break; |
---|
| 940 | } |
---|
| 941 | } |
---|
| 942 | else |
---|
| 943 | { |
---|
| 944 | while ((p=pNext(p))!=NULL) |
---|
| 945 | { |
---|
[99bdcf] | 946 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
[35aab3] | 947 | ll++; |
---|
| 948 | } |
---|
| 949 | } |
---|
| 950 | *l=ll; |
---|
| 951 | return max; |
---|
| 952 | } |
---|
| 953 | |
---|
| 954 | /*************************************************************** |
---|
| 955 | * |
---|
| 956 | * Maximal Exponent business |
---|
| 957 | * |
---|
| 958 | ***************************************************************/ |
---|
| 959 | |
---|
[ab4778] | 960 | static inline unsigned long |
---|
[107986] | 961 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, |
---|
[35aab3] | 962 | unsigned long number_of_exp) |
---|
| 963 | { |
---|
| 964 | const unsigned long bitmask = r->bitmask; |
---|
| 965 | unsigned long ml1 = l1 & bitmask; |
---|
| 966 | unsigned long ml2 = l2 & bitmask; |
---|
| 967 | unsigned long max = (ml1 > ml2 ? ml1 : ml2); |
---|
| 968 | unsigned long j = number_of_exp - 1; |
---|
| 969 | |
---|
| 970 | if (j > 0) |
---|
| 971 | { |
---|
| 972 | unsigned long mask = bitmask << r->BitsPerExp; |
---|
| 973 | while (1) |
---|
| 974 | { |
---|
| 975 | ml1 = l1 & mask; |
---|
| 976 | ml2 = l2 & mask; |
---|
| 977 | max |= ((ml1 > ml2 ? ml1 : ml2) & mask); |
---|
| 978 | j--; |
---|
| 979 | if (j == 0) break; |
---|
| 980 | mask = mask << r->BitsPerExp; |
---|
| 981 | } |
---|
| 982 | } |
---|
| 983 | return max; |
---|
| 984 | } |
---|
| 985 | |
---|
| 986 | static inline unsigned long |
---|
[107986] | 987 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r) |
---|
[35aab3] | 988 | { |
---|
| 989 | return p_GetMaxExpL2(l1, l2, r, r->ExpPerLong); |
---|
| 990 | } |
---|
| 991 | |
---|
[107986] | 992 | poly p_GetMaxExpP(poly p, const ring r) |
---|
[35aab3] | 993 | { |
---|
| 994 | p_CheckPolyRing(p, r); |
---|
| 995 | if (p == NULL) return p_Init(r); |
---|
| 996 | poly max = p_LmInit(p, r); |
---|
| 997 | pIter(p); |
---|
| 998 | if (p == NULL) return max; |
---|
| 999 | int i, offset; |
---|
| 1000 | unsigned long l_p, l_max; |
---|
| 1001 | unsigned long divmask = r->divmask; |
---|
[ab4778] | 1002 | |
---|
[35aab3] | 1003 | do |
---|
| 1004 | { |
---|
| 1005 | offset = r->VarL_Offset[0]; |
---|
| 1006 | l_p = p->exp[offset]; |
---|
| 1007 | l_max = max->exp[offset]; |
---|
| 1008 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1009 | if (l_p > l_max || |
---|
[35aab3] | 1010 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1011 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1012 | |
---|
| 1013 | for (i=1; i<r->VarL_Size; i++) |
---|
| 1014 | { |
---|
| 1015 | offset = r->VarL_Offset[i]; |
---|
| 1016 | l_p = p->exp[offset]; |
---|
| 1017 | l_max = max->exp[offset]; |
---|
| 1018 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1019 | if (l_p > l_max || |
---|
[35aab3] | 1020 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1021 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1022 | } |
---|
| 1023 | pIter(p); |
---|
| 1024 | } |
---|
| 1025 | while (p != NULL); |
---|
| 1026 | return max; |
---|
| 1027 | } |
---|
| 1028 | |
---|
[107986] | 1029 | unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max) |
---|
[35aab3] | 1030 | { |
---|
| 1031 | unsigned long l_p, divmask = r->divmask; |
---|
| 1032 | int i; |
---|
[ab4778] | 1033 | |
---|
[35aab3] | 1034 | while (p != NULL) |
---|
| 1035 | { |
---|
| 1036 | l_p = p->exp[r->VarL_Offset[0]]; |
---|
| 1037 | if (l_p > l_max || |
---|
| 1038 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1039 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1040 | for (i=1; i<r->VarL_Size; i++) |
---|
| 1041 | { |
---|
| 1042 | l_p = p->exp[r->VarL_Offset[i]]; |
---|
| 1043 | // do the divisibility trick to find out whether l has an exponent |
---|
[ab4778] | 1044 | if (l_p > l_max || |
---|
[35aab3] | 1045 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
| 1046 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
| 1047 | } |
---|
| 1048 | pIter(p); |
---|
| 1049 | } |
---|
| 1050 | return l_max; |
---|
| 1051 | } |
---|
| 1052 | |
---|
[fc5095] | 1053 | |
---|
| 1054 | |
---|
[ab4778] | 1055 | |
---|
[35aab3] | 1056 | /*************************************************************** |
---|
| 1057 | * |
---|
| 1058 | * Misc things |
---|
| 1059 | * |
---|
| 1060 | ***************************************************************/ |
---|
| 1061 | // returns TRUE, if all monoms have the same component |
---|
[107986] | 1062 | BOOLEAN p_OneComp(poly p, const ring r) |
---|
[35aab3] | 1063 | { |
---|
| 1064 | if(p!=NULL) |
---|
| 1065 | { |
---|
| 1066 | long i = p_GetComp(p, r); |
---|
| 1067 | while (pNext(p)!=NULL) |
---|
| 1068 | { |
---|
| 1069 | pIter(p); |
---|
| 1070 | if(i != p_GetComp(p, r)) return FALSE; |
---|
| 1071 | } |
---|
| 1072 | } |
---|
| 1073 | return TRUE; |
---|
| 1074 | } |
---|
| 1075 | |
---|
| 1076 | /*2 |
---|
| 1077 | *test if a monomial /head term is a pure power |
---|
| 1078 | */ |
---|
| 1079 | int p_IsPurePower(const poly p, const ring r) |
---|
| 1080 | { |
---|
| 1081 | int i,k=0; |
---|
| 1082 | |
---|
| 1083 | for (i=r->N;i;i--) |
---|
| 1084 | { |
---|
| 1085 | if (p_GetExp(p,i, r)!=0) |
---|
| 1086 | { |
---|
| 1087 | if(k!=0) return 0; |
---|
| 1088 | k=i; |
---|
| 1089 | } |
---|
| 1090 | } |
---|
| 1091 | return k; |
---|
| 1092 | } |
---|
| 1093 | |
---|
[2f0d83f] | 1094 | /*2 |
---|
| 1095 | *test if a polynomial is univariate |
---|
| 1096 | * return -1 for constant, |
---|
| 1097 | * 0 for not univariate,s |
---|
| 1098 | * i if dep. on var(i) |
---|
| 1099 | */ |
---|
| 1100 | int p_IsUnivariate(poly p, const ring r) |
---|
| 1101 | { |
---|
| 1102 | int i,k=-1; |
---|
| 1103 | |
---|
| 1104 | while (p!=NULL) |
---|
| 1105 | { |
---|
| 1106 | for (i=r->N;i;i--) |
---|
| 1107 | { |
---|
| 1108 | if (p_GetExp(p,i, r)!=0) |
---|
| 1109 | { |
---|
| 1110 | if((k!=-1)&&(k!=i)) return 0; |
---|
| 1111 | k=i; |
---|
| 1112 | } |
---|
| 1113 | } |
---|
| 1114 | pIter(p); |
---|
| 1115 | } |
---|
| 1116 | return k; |
---|
| 1117 | } |
---|
| 1118 | |
---|
[3931bf] | 1119 | // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 |
---|
[f46646] | 1120 | int p_GetVariables(poly p, int * e, const ring r) |
---|
[3931bf] | 1121 | { |
---|
| 1122 | int i; |
---|
[f46646] | 1123 | int n=0; |
---|
[3931bf] | 1124 | while(p!=NULL) |
---|
| 1125 | { |
---|
[f46646] | 1126 | n=0; |
---|
[95450e] | 1127 | for(i=r->N; i>0; i--) |
---|
[3931bf] | 1128 | { |
---|
| 1129 | if(e[i]==0) |
---|
| 1130 | { |
---|
| 1131 | if (p_GetExp(p,i,r)>0) |
---|
[f46646] | 1132 | { |
---|
[3931bf] | 1133 | e[i]=1; |
---|
[f46646] | 1134 | n++; |
---|
| 1135 | } |
---|
[3931bf] | 1136 | } |
---|
[f46646] | 1137 | else |
---|
| 1138 | n++; |
---|
[3931bf] | 1139 | } |
---|
[f46646] | 1140 | if (n==r->N) break; |
---|
[3931bf] | 1141 | pIter(p); |
---|
| 1142 | } |
---|
[f46646] | 1143 | return n; |
---|
[3931bf] | 1144 | } |
---|
| 1145 | |
---|
| 1146 | |
---|
[35aab3] | 1147 | /*2 |
---|
| 1148 | * returns a polynomial representing the integer i |
---|
| 1149 | */ |
---|
[107986] | 1150 | poly p_ISet(int i, const ring r) |
---|
[35aab3] | 1151 | { |
---|
| 1152 | poly rc = NULL; |
---|
| 1153 | if (i!=0) |
---|
| 1154 | { |
---|
| 1155 | rc = p_Init(r); |
---|
[8a8c9e] | 1156 | pSetCoeff0(rc,n_Init(i,r->cf)); |
---|
| 1157 | if (n_IsZero(pGetCoeff(rc),r->cf)) |
---|
[fb82895] | 1158 | p_LmDelete(&rc,r); |
---|
[35aab3] | 1159 | } |
---|
| 1160 | return rc; |
---|
| 1161 | } |
---|
| 1162 | |
---|
[1c33e0d] | 1163 | /*2 |
---|
| 1164 | * an optimized version of p_ISet for the special case 1 |
---|
| 1165 | */ |
---|
[5bc4103] | 1166 | poly p_One(const ring r) |
---|
[1c33e0d] | 1167 | { |
---|
| 1168 | poly rc = p_Init(r); |
---|
[8a8c9e] | 1169 | pSetCoeff0(rc,n_Init(1,r->cf)); |
---|
[1c33e0d] | 1170 | return rc; |
---|
| 1171 | } |
---|
| 1172 | |
---|
[f34215] | 1173 | void p_Split(poly p, poly *h) |
---|
| 1174 | { |
---|
| 1175 | *h=pNext(p); |
---|
| 1176 | pNext(p)=NULL; |
---|
| 1177 | } |
---|
| 1178 | |
---|
| 1179 | /*2 |
---|
| 1180 | * pair has no common factor ? or is no polynomial |
---|
| 1181 | */ |
---|
| 1182 | BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r) |
---|
| 1183 | { |
---|
| 1184 | |
---|
| 1185 | if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0) |
---|
| 1186 | return FALSE; |
---|
| 1187 | int i = rVar(r); |
---|
| 1188 | loop |
---|
| 1189 | { |
---|
| 1190 | if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0)) |
---|
| 1191 | return FALSE; |
---|
| 1192 | i--; |
---|
| 1193 | if (i == 0) |
---|
| 1194 | return TRUE; |
---|
| 1195 | } |
---|
| 1196 | } |
---|
| 1197 | |
---|
| 1198 | /*2 |
---|
| 1199 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
| 1200 | */ |
---|
| 1201 | const char * p_Read(const char *st, poly &rc, const ring r) |
---|
| 1202 | { |
---|
| 1203 | if (r==NULL) { rc=NULL;return st;} |
---|
| 1204 | int i,j; |
---|
| 1205 | rc = p_Init(r); |
---|
[8a8c9e] | 1206 | const char *s = r->cf->cfRead(st,&(rc->coef),r->cf); |
---|
[f34215] | 1207 | if (s==st) |
---|
| 1208 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
| 1209 | { |
---|
| 1210 | j = r_IsRingVar(s,r); |
---|
| 1211 | if (j >= 0) |
---|
| 1212 | { |
---|
| 1213 | p_IncrExp(rc,1+j,r); |
---|
| 1214 | while (*s!='\0') s++; |
---|
| 1215 | goto done; |
---|
| 1216 | } |
---|
| 1217 | } |
---|
| 1218 | while (*s!='\0') |
---|
| 1219 | { |
---|
| 1220 | char ss[2]; |
---|
| 1221 | ss[0] = *s++; |
---|
| 1222 | ss[1] = '\0'; |
---|
| 1223 | j = r_IsRingVar(ss,r); |
---|
| 1224 | if (j >= 0) |
---|
| 1225 | { |
---|
| 1226 | const char *s_save=s; |
---|
| 1227 | s = eati(s,&i); |
---|
| 1228 | if (((unsigned long)i) > r->bitmask) |
---|
| 1229 | { |
---|
| 1230 | // exponent to large: it is not a monomial |
---|
| 1231 | p_LmDelete(&rc,r); |
---|
| 1232 | return s_save; |
---|
| 1233 | } |
---|
| 1234 | p_AddExp(rc,1+j, (long)i, r); |
---|
| 1235 | } |
---|
| 1236 | else |
---|
| 1237 | { |
---|
| 1238 | // 1st char of is not a varname |
---|
| 1239 | p_LmDelete(&rc,r); |
---|
| 1240 | s--; |
---|
| 1241 | return s; |
---|
| 1242 | } |
---|
| 1243 | } |
---|
| 1244 | done: |
---|
[8a8c9e] | 1245 | if (n_IsZero(pGetCoeff(rc),r->cf)) p_LmDelete(&rc,r); |
---|
[f34215] | 1246 | else |
---|
| 1247 | { |
---|
| 1248 | #ifdef HAVE_PLURAL |
---|
| 1249 | // in super-commutative ring |
---|
| 1250 | // squares of anti-commutative variables are zeroes! |
---|
| 1251 | if(rIsSCA(r)) |
---|
| 1252 | { |
---|
| 1253 | const unsigned int iFirstAltVar = scaFirstAltVar(r); |
---|
| 1254 | const unsigned int iLastAltVar = scaLastAltVar(r); |
---|
| 1255 | |
---|
| 1256 | assume(rc != NULL); |
---|
| 1257 | |
---|
| 1258 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
| 1259 | if( p_GetExp(rc, k, r) > 1 ) |
---|
| 1260 | { |
---|
| 1261 | p_LmDelete(&rc, r); |
---|
| 1262 | goto finish; |
---|
| 1263 | } |
---|
| 1264 | } |
---|
| 1265 | #endif |
---|
[71ba5b8] | 1266 | |
---|
[f34215] | 1267 | p_Setm(rc,r); |
---|
| 1268 | } |
---|
[71ba5b8] | 1269 | finish: |
---|
[f34215] | 1270 | return s; |
---|
| 1271 | } |
---|
| 1272 | poly p_mInit(const char *st, BOOLEAN &ok, const ring r) |
---|
| 1273 | { |
---|
| 1274 | poly p; |
---|
| 1275 | const char *s=p_Read(st,p,r); |
---|
| 1276 | if (*s!='\0') |
---|
| 1277 | { |
---|
| 1278 | if ((s!=st)&&isdigit(st[0])) |
---|
| 1279 | { |
---|
| 1280 | errorreported=TRUE; |
---|
| 1281 | } |
---|
| 1282 | ok=FALSE; |
---|
| 1283 | p_Delete(&p,r); |
---|
| 1284 | return NULL; |
---|
| 1285 | } |
---|
| 1286 | #ifdef PDEBUG |
---|
| 1287 | _p_Test(p,r,PDEBUG); |
---|
| 1288 | #endif |
---|
| 1289 | ok=!errorreported; |
---|
| 1290 | return p; |
---|
| 1291 | } |
---|
| 1292 | |
---|
[35aab3] | 1293 | /*2 |
---|
| 1294 | * returns a polynomial representing the number n |
---|
| 1295 | * destroys n |
---|
| 1296 | */ |
---|
[107986] | 1297 | poly p_NSet(number n, const ring r) |
---|
[35aab3] | 1298 | { |
---|
[8a8c9e] | 1299 | if (n_IsZero(n,r->cf)) |
---|
[35aab3] | 1300 | { |
---|
[8a8c9e] | 1301 | n_Delete(&n, r->cf); |
---|
[35aab3] | 1302 | return NULL; |
---|
| 1303 | } |
---|
| 1304 | else |
---|
| 1305 | { |
---|
| 1306 | poly rc = p_Init(r); |
---|
| 1307 | pSetCoeff0(rc,n); |
---|
| 1308 | return rc; |
---|
| 1309 | } |
---|
| 1310 | } |
---|
[fb4075b] | 1311 | /*2 |
---|
[e5d267] | 1312 | * assumes that LM(a) = LM(b)*m, for some monomial m, |
---|
| 1313 | * returns the multiplicant m, |
---|
| 1314 | * leaves a and b unmodified |
---|
[fb4075b] | 1315 | */ |
---|
| 1316 | poly p_Divide(poly a, poly b, const ring r) |
---|
| 1317 | { |
---|
| 1318 | assume((p_GetComp(a,r)==p_GetComp(b,r)) || (p_GetComp(b,r)==0)); |
---|
| 1319 | int i; |
---|
[8a8c9e] | 1320 | poly result = p_Init(r); |
---|
[fb4075b] | 1321 | |
---|
| 1322 | for(i=(int)r->N; i; i--) |
---|
| 1323 | p_SetExp(result,i, p_GetExp(a,i,r)- p_GetExp(b,i,r),r); |
---|
| 1324 | p_SetComp(result, p_GetComp(a,r) - p_GetComp(b,r),r); |
---|
| 1325 | p_Setm(result,r); |
---|
| 1326 | return result; |
---|
| 1327 | } |
---|
| 1328 | |
---|
[8a8c9e] | 1329 | poly p_Div_nn(poly p, const number n, const ring r) |
---|
| 1330 | { |
---|
[45d2332] | 1331 | pAssume(!n_IsZero(n,r->cf)); |
---|
[8a8c9e] | 1332 | p_Test(p, r); |
---|
| 1333 | |
---|
| 1334 | poly q = p; |
---|
| 1335 | while (p != NULL) |
---|
| 1336 | { |
---|
| 1337 | number nc = pGetCoeff(p); |
---|
| 1338 | pSetCoeff0(p, n_Div(nc, n, r->cf)); |
---|
| 1339 | n_Delete(&nc, r->cf); |
---|
| 1340 | pIter(p); |
---|
| 1341 | } |
---|
| 1342 | p_Test(q, r); |
---|
| 1343 | return q; |
---|
| 1344 | } |
---|
| 1345 | |
---|
[fb4075b] | 1346 | /*2 |
---|
| 1347 | * divides a by the monomial b, ignores monomials which are not divisible |
---|
[e432a0] | 1348 | * assumes that b is not NULL, destroyes b |
---|
[fb4075b] | 1349 | */ |
---|
| 1350 | poly p_DivideM(poly a, poly b, const ring r) |
---|
| 1351 | { |
---|
[e432a0] | 1352 | if (a==NULL) { p_Delete(&b,r); return NULL; } |
---|
[fb4075b] | 1353 | poly result=a; |
---|
| 1354 | poly prev=NULL; |
---|
| 1355 | int i; |
---|
| 1356 | #ifdef HAVE_RINGS |
---|
| 1357 | number inv=pGetCoeff(b); |
---|
| 1358 | #else |
---|
| 1359 | number inv=n_Invers(pGetCoeff(b),r->cf); |
---|
| 1360 | #endif |
---|
| 1361 | |
---|
| 1362 | while (a!=NULL) |
---|
| 1363 | { |
---|
| 1364 | if (p_DivisibleBy(b,a,r)) |
---|
| 1365 | { |
---|
| 1366 | for(i=(int)r->N; i; i--) |
---|
| 1367 | p_SubExp(a,i, p_GetExp(b,i,r),r); |
---|
| 1368 | p_SubComp(a, p_GetComp(b,r),r); |
---|
| 1369 | p_Setm(a,r); |
---|
| 1370 | prev=a; |
---|
| 1371 | pIter(a); |
---|
| 1372 | } |
---|
| 1373 | else |
---|
| 1374 | { |
---|
| 1375 | if (prev==NULL) |
---|
| 1376 | { |
---|
[8a8c9e] | 1377 | p_LmDelete(&result,r); |
---|
[fb4075b] | 1378 | a=result; |
---|
| 1379 | } |
---|
| 1380 | else |
---|
| 1381 | { |
---|
[8a8c9e] | 1382 | p_LmDelete(&pNext(prev),r); |
---|
[fb4075b] | 1383 | a=pNext(prev); |
---|
| 1384 | } |
---|
| 1385 | } |
---|
| 1386 | } |
---|
| 1387 | #ifdef HAVE_RINGS |
---|
| 1388 | if (n_IsUnit(inv,r->cf)) |
---|
| 1389 | { |
---|
| 1390 | inv = n_Invers(inv,r->cf); |
---|
| 1391 | p_Mult_nn(result,inv,r); |
---|
| 1392 | n_Delete(&inv, r->cf); |
---|
| 1393 | } |
---|
| 1394 | else |
---|
| 1395 | { |
---|
| 1396 | p_Div_nn(result,inv,r); |
---|
| 1397 | } |
---|
| 1398 | #else |
---|
| 1399 | p_Mult_nn(result,inv,r); |
---|
| 1400 | n_Delete(&inv, r->cf); |
---|
| 1401 | #endif |
---|
| 1402 | p_Delete(&b, r); |
---|
| 1403 | return result; |
---|
| 1404 | } |
---|
[35aab3] | 1405 | |
---|
[3d0808] | 1406 | #ifdef HAVE_RINGS |
---|
| 1407 | /* TRUE iff LT(f) | LT(g) */ |
---|
| 1408 | BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r) |
---|
| 1409 | { |
---|
| 1410 | int exponent; |
---|
| 1411 | for(int i = (int)rVar(r); i>0; i--) |
---|
| 1412 | { |
---|
| 1413 | exponent = p_GetExp(g, i, r) - p_GetExp(f, i, r); |
---|
| 1414 | if (exponent < 0) return FALSE; |
---|
| 1415 | } |
---|
| 1416 | return n_DivBy(pGetCoeff(g), pGetCoeff(f), r->cf); |
---|
| 1417 | } |
---|
| 1418 | #endif |
---|
| 1419 | |
---|
[a7ee69] | 1420 | /*2 |
---|
| 1421 | * returns the LCM of the head terms of a and b in *m |
---|
| 1422 | */ |
---|
| 1423 | void p_Lcm(poly a, poly b, poly m, const ring r) |
---|
| 1424 | { |
---|
| 1425 | int i; |
---|
| 1426 | for (i=rVar(r); i; i--) |
---|
| 1427 | { |
---|
| 1428 | p_SetExp(m,i, si_max( p_GetExp(a,i,r), p_GetExp(b,i,r)),r); |
---|
| 1429 | } |
---|
| 1430 | p_SetComp(m, si_max(p_GetComp(a,r), p_GetComp(b,r)),r); |
---|
| 1431 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
---|
| 1432 | } |
---|
| 1433 | |
---|
[f0b01f] | 1434 | /* assumes that p and divisor are univariate polynomials in r, |
---|
[ba2359] | 1435 | mentioning the same variable; |
---|
| 1436 | assumes divisor != NULL; |
---|
[f0b01f] | 1437 | p may be NULL; |
---|
[ba2359] | 1438 | assumes a global monomial ordering in r; |
---|
[f0b01f] | 1439 | performs polynomial division of p by divisor: |
---|
| 1440 | - afterwards p contains the remainder of the division, i.e., |
---|
| 1441 | p_before = result * divisor + p_afterwards; |
---|
[ba2359] | 1442 | - if needResult == TRUE, then the method computes and returns 'result', |
---|
| 1443 | otherwise NULL is returned (This parametrization can be used when |
---|
| 1444 | one is only interested in the remainder of the division. In this |
---|
[f0b01f] | 1445 | case, the method will be slightly faster.) |
---|
| 1446 | leaves divisor unmodified */ |
---|
| 1447 | poly p_PolyDiv(poly &p, poly divisor, BOOLEAN needResult, ring r) |
---|
[ba2359] | 1448 | { |
---|
| 1449 | assume(divisor != NULL); |
---|
[f0b01f] | 1450 | if (p == NULL) return NULL; |
---|
[ba2359] | 1451 | |
---|
[69fb9d0] | 1452 | poly result = NULL; |
---|
[f0b01f] | 1453 | number divisorLC = p_GetCoeff(divisor, r); |
---|
| 1454 | int divisorLE = p_GetExp(divisor, 1, r); |
---|
[c28ecf] | 1455 | while ((p != NULL) && (p_Deg(p, r) >= p_Deg(divisor, r))) |
---|
[69fb9d0] | 1456 | { |
---|
[f0b01f] | 1457 | /* determine t = LT(p) / LT(divisor) */ |
---|
[69fb9d0] | 1458 | poly t = p_ISet(1, r); |
---|
[f0b01f] | 1459 | number c = n_Div(p_GetCoeff(p, r), divisorLC, r->cf); |
---|
[69fb9d0] | 1460 | p_SetCoeff(t, c, r); |
---|
[f0b01f] | 1461 | int e = p_GetExp(p, 1, r) - divisorLE; |
---|
[69fb9d0] | 1462 | p_SetExp(t, 1, e, r); |
---|
| 1463 | p_Setm(t, r); |
---|
[f0b01f] | 1464 | if (needResult) result = p_Add_q(result, p_Copy(t, r), r); |
---|
| 1465 | p = p_Add_q(p, p_Neg(p_Mult_q(t, p_Copy(divisor, r), r), r), r); |
---|
[69fb9d0] | 1466 | } |
---|
| 1467 | return result; |
---|
| 1468 | } |
---|
| 1469 | |
---|
[c28ecf] | 1470 | /* returns NULL if p == NULL, otherwise makes p monic by dividing |
---|
| 1471 | by its leading coefficient (only done if this is not already 1); |
---|
| 1472 | this assumes that we are over a ground field so that division |
---|
| 1473 | is well-defined; |
---|
| 1474 | modifies p */ |
---|
| 1475 | void p_Monic(poly &p, ring r) |
---|
| 1476 | { |
---|
| 1477 | if (p == NULL) return; |
---|
| 1478 | poly pp = p; |
---|
| 1479 | number lc = p_GetCoeff(p, r); |
---|
| 1480 | if (n_IsOne(lc, r->cf)) return; |
---|
[cfb500] | 1481 | number lcInverse = n_Invers(lc, r->cf); |
---|
| 1482 | number n = n_Init(1, r->cf); |
---|
| 1483 | p_SetCoeff(p, n, r); // destroys old leading coefficient! |
---|
[c28ecf] | 1484 | p = pIter(p); |
---|
| 1485 | while (p != NULL) |
---|
| 1486 | { |
---|
[cfb500] | 1487 | number n = n_Mult(p_GetCoeff(p, r), lcInverse, r->cf); |
---|
| 1488 | p_SetCoeff(p, n, r); // destroys old leading coefficient! |
---|
[c28ecf] | 1489 | p = pIter(p); |
---|
| 1490 | } |
---|
[cfb500] | 1491 | n_Delete(&lcInverse, r->cf); |
---|
[c28ecf] | 1492 | p = pp; |
---|
| 1493 | } |
---|
| 1494 | |
---|
[69fb9d0] | 1495 | /* see p_Gcd; |
---|
[f0b01f] | 1496 | additional assumption: deg(p) >= deg(q); |
---|
| 1497 | must destroy p and q (unless one of them is returned) */ |
---|
| 1498 | poly p_GcdHelper(poly &p, poly &q, ring r) |
---|
[69fb9d0] | 1499 | { |
---|
[c28ecf] | 1500 | if (q == NULL) |
---|
| 1501 | { |
---|
| 1502 | /* We have to make p monic before we return it, so that if the |
---|
| 1503 | gcd is a unit in the ground field, we will actually return 1. */ |
---|
| 1504 | p_Monic(p, r); |
---|
| 1505 | return p; |
---|
| 1506 | } |
---|
[69fb9d0] | 1507 | else |
---|
| 1508 | { |
---|
[f0b01f] | 1509 | p_PolyDiv(p, q, FALSE, r); |
---|
[69fb9d0] | 1510 | return p_GcdHelper(q, p, r); |
---|
| 1511 | } |
---|
[ba2359] | 1512 | } |
---|
| 1513 | |
---|
| 1514 | /* assumes that p and q are univariate polynomials in r, |
---|
| 1515 | mentioning the same variable; |
---|
| 1516 | assumes a global monomial ordering in r; |
---|
| 1517 | assumes that not both p and q are NULL; |
---|
[69fb9d0] | 1518 | returns the gcd of p and q; |
---|
| 1519 | leaves p and q unmodified */ |
---|
[ba2359] | 1520 | poly p_Gcd(poly p, poly q, ring r) |
---|
| 1521 | { |
---|
| 1522 | assume((p != NULL) || (q != NULL)); |
---|
| 1523 | |
---|
[69fb9d0] | 1524 | poly a = p; poly b = q; |
---|
| 1525 | if (p_Deg(a, r) < p_Deg(b, r)) { a = q; b = p; } |
---|
| 1526 | a = p_Copy(a, r); b = p_Copy(b, r); |
---|
[f0b01f] | 1527 | return p_GcdHelper(a, b, r); |
---|
[69fb9d0] | 1528 | } |
---|
| 1529 | |
---|
| 1530 | /* see p_ExtGcd; |
---|
[f0b01f] | 1531 | additional assumption: deg(p) >= deg(q); |
---|
| 1532 | must destroy p and q (unless one of them is returned) */ |
---|
| 1533 | poly p_ExtGcdHelper(poly &p, poly &pFactor, poly &q, poly &qFactor, |
---|
[69fb9d0] | 1534 | ring r) |
---|
| 1535 | { |
---|
| 1536 | if (q == NULL) |
---|
| 1537 | { |
---|
[c28ecf] | 1538 | qFactor = NULL; |
---|
| 1539 | pFactor = p_ISet(1, r); |
---|
| 1540 | p_SetCoeff(pFactor, n_Invers(p_GetCoeff(p, r), r->cf), r); |
---|
| 1541 | p_Monic(p, r); |
---|
| 1542 | return p; |
---|
[69fb9d0] | 1543 | } |
---|
| 1544 | else |
---|
| 1545 | { |
---|
[f0b01f] | 1546 | poly pDivQ = p_PolyDiv(p, q, TRUE, r); |
---|
[c28ecf] | 1547 | poly ppFactor = NULL; poly qqFactor = NULL; |
---|
| 1548 | poly theGcd = p_ExtGcdHelper(q, qqFactor, p, ppFactor, r); |
---|
| 1549 | pFactor = ppFactor; |
---|
| 1550 | qFactor = p_Add_q(qqFactor, |
---|
| 1551 | p_Neg(p_Mult_q(pDivQ, p_Copy(ppFactor, r), r), r), |
---|
[f0b01f] | 1552 | r); |
---|
[69fb9d0] | 1553 | return theGcd; |
---|
| 1554 | } |
---|
[ba2359] | 1555 | } |
---|
| 1556 | |
---|
| 1557 | /* assumes that p and q are univariate polynomials in r, |
---|
| 1558 | mentioning the same variable; |
---|
| 1559 | assumes a global monomial ordering in r; |
---|
| 1560 | assumes that not both p and q are NULL; |
---|
| 1561 | returns the gcd of p and q; |
---|
[f0b01f] | 1562 | moreover, afterwards pFactor and qFactor contain appropriate |
---|
| 1563 | factors such that gcd(p, q) = p * pFactor + q * qFactor; |
---|
[69fb9d0] | 1564 | leaves p and q unmodified */ |
---|
[f0b01f] | 1565 | poly p_ExtGcd(poly p, poly &pFactor, poly q, poly &qFactor, ring r) |
---|
[ba2359] | 1566 | { |
---|
[f0b01f] | 1567 | assume((p != NULL) || (q != NULL)); |
---|
[c28ecf] | 1568 | poly a = p; poly b = q; BOOLEAN aCorrespondsToP = TRUE; |
---|
[69fb9d0] | 1569 | if (p_Deg(a, r) < p_Deg(b, r)) |
---|
[c28ecf] | 1570 | { a = q; b = p; aCorrespondsToP = FALSE; } |
---|
[69fb9d0] | 1571 | a = p_Copy(a, r); b = p_Copy(b, r); |
---|
[c28ecf] | 1572 | poly aFactor = NULL; poly bFactor = NULL; |
---|
| 1573 | poly theGcd = p_ExtGcdHelper(a, aFactor, b, bFactor, r); |
---|
| 1574 | if (aCorrespondsToP) { pFactor = aFactor; qFactor = bFactor; } |
---|
| 1575 | else { pFactor = bFactor; qFactor = aFactor; } |
---|
| 1576 | return theGcd; |
---|
[ba2359] | 1577 | } |
---|
| 1578 | |
---|
[ac0bd6] | 1579 | /*2 |
---|
| 1580 | * returns the partial differentiate of a by the k-th variable |
---|
| 1581 | * does not destroy the input |
---|
| 1582 | */ |
---|
| 1583 | poly p_Diff(poly a, int k, const ring r) |
---|
| 1584 | { |
---|
| 1585 | poly res, f, last; |
---|
| 1586 | number t; |
---|
| 1587 | |
---|
| 1588 | last = res = NULL; |
---|
| 1589 | while (a!=NULL) |
---|
| 1590 | { |
---|
| 1591 | if (p_GetExp(a,k,r)!=0) |
---|
| 1592 | { |
---|
| 1593 | f = p_LmInit(a,r); |
---|
| 1594 | t = n_Init(p_GetExp(a,k,r),r->cf); |
---|
| 1595 | pSetCoeff0(f,n_Mult(t,pGetCoeff(a),r->cf)); |
---|
| 1596 | n_Delete(&t,r->cf); |
---|
| 1597 | if (n_IsZero(pGetCoeff(f),r->cf)) |
---|
| 1598 | p_LmDelete(&f,r); |
---|
| 1599 | else |
---|
| 1600 | { |
---|
| 1601 | p_DecrExp(f,k,r); |
---|
| 1602 | p_Setm(f,r); |
---|
| 1603 | if (res==NULL) |
---|
| 1604 | { |
---|
| 1605 | res=last=f; |
---|
| 1606 | } |
---|
| 1607 | else |
---|
| 1608 | { |
---|
| 1609 | pNext(last)=f; |
---|
| 1610 | last=f; |
---|
| 1611 | } |
---|
| 1612 | } |
---|
| 1613 | } |
---|
| 1614 | pIter(a); |
---|
| 1615 | } |
---|
| 1616 | return res; |
---|
| 1617 | } |
---|
[5162db] | 1618 | |
---|
[8a8c9e] | 1619 | static poly p_DiffOpM(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
[5162db] | 1620 | { |
---|
| 1621 | int i,j,s; |
---|
| 1622 | number n,h,hh; |
---|
| 1623 | poly p=p_One(r); |
---|
| 1624 | n=n_Mult(pGetCoeff(a),pGetCoeff(b),r->cf); |
---|
| 1625 | for(i=rVar(r);i>0;i--) |
---|
| 1626 | { |
---|
| 1627 | s=p_GetExp(b,i,r); |
---|
| 1628 | if (s<p_GetExp(a,i,r)) |
---|
| 1629 | { |
---|
| 1630 | n_Delete(&n,r->cf); |
---|
| 1631 | p_LmDelete(&p,r); |
---|
| 1632 | return NULL; |
---|
| 1633 | } |
---|
| 1634 | if (multiply) |
---|
| 1635 | { |
---|
| 1636 | for(j=p_GetExp(a,i,r); j>0;j--) |
---|
| 1637 | { |
---|
| 1638 | h = n_Init(s,r->cf); |
---|
| 1639 | hh=n_Mult(n,h,r->cf); |
---|
| 1640 | n_Delete(&h,r->cf); |
---|
| 1641 | n_Delete(&n,r->cf); |
---|
| 1642 | n=hh; |
---|
| 1643 | s--; |
---|
| 1644 | } |
---|
| 1645 | p_SetExp(p,i,s,r); |
---|
| 1646 | } |
---|
| 1647 | else |
---|
| 1648 | { |
---|
| 1649 | p_SetExp(p,i,s-p_GetExp(a,i,r),r); |
---|
| 1650 | } |
---|
| 1651 | } |
---|
| 1652 | p_Setm(p,r); |
---|
| 1653 | /*if (multiply)*/ p_SetCoeff(p,n,r); |
---|
| 1654 | if (n_IsZero(n,r->cf)) p=p_LmDeleteAndNext(p,r); // return NULL as p is a monomial |
---|
| 1655 | return p; |
---|
| 1656 | } |
---|
| 1657 | |
---|
| 1658 | poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
| 1659 | { |
---|
| 1660 | poly result=NULL; |
---|
| 1661 | poly h; |
---|
| 1662 | for(;a!=NULL;pIter(a)) |
---|
| 1663 | { |
---|
| 1664 | for(h=b;h!=NULL;pIter(h)) |
---|
| 1665 | { |
---|
| 1666 | result=p_Add_q(result,p_DiffOpM(a,h,multiply,r),r); |
---|
| 1667 | } |
---|
| 1668 | } |
---|
| 1669 | return result; |
---|
| 1670 | } |
---|
[bf183f] | 1671 | /*2 |
---|
| 1672 | * subtract p2 from p1, p1 and p2 are destroyed |
---|
| 1673 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
| 1674 | */ |
---|
| 1675 | poly p_Sub(poly p1, poly p2, const ring r) |
---|
| 1676 | { |
---|
| 1677 | return p_Add_q(p1, p_Neg(p2,r),r); |
---|
| 1678 | } |
---|
| 1679 | |
---|
| 1680 | /*3 |
---|
| 1681 | * compute for a monomial m |
---|
| 1682 | * the power m^exp, exp > 1 |
---|
| 1683 | * destroys p |
---|
| 1684 | */ |
---|
| 1685 | static poly p_MonPower(poly p, int exp, const ring r) |
---|
| 1686 | { |
---|
| 1687 | int i; |
---|
| 1688 | |
---|
[8a8c9e] | 1689 | if(!n_IsOne(pGetCoeff(p),r->cf)) |
---|
[bf183f] | 1690 | { |
---|
| 1691 | number x, y; |
---|
| 1692 | y = pGetCoeff(p); |
---|
[8a8c9e] | 1693 | n_Power(y,exp,&x,r->cf); |
---|
| 1694 | n_Delete(&y,r->cf); |
---|
[bf183f] | 1695 | pSetCoeff0(p,x); |
---|
| 1696 | } |
---|
| 1697 | for (i=rVar(r); i!=0; i--) |
---|
| 1698 | { |
---|
| 1699 | p_MultExp(p,i, exp,r); |
---|
| 1700 | } |
---|
| 1701 | p_Setm(p,r); |
---|
| 1702 | return p; |
---|
| 1703 | } |
---|
| 1704 | |
---|
| 1705 | /*3 |
---|
| 1706 | * compute for monomials p*q |
---|
| 1707 | * destroys p, keeps q |
---|
| 1708 | */ |
---|
| 1709 | static void p_MonMult(poly p, poly q, const ring r) |
---|
| 1710 | { |
---|
| 1711 | number x, y; |
---|
| 1712 | |
---|
| 1713 | y = pGetCoeff(p); |
---|
[8a8c9e] | 1714 | x = n_Mult(y,pGetCoeff(q),r->cf); |
---|
| 1715 | n_Delete(&y,r->cf); |
---|
[bf183f] | 1716 | pSetCoeff0(p,x); |
---|
[abb4787] | 1717 | //for (int i=pVariables; i!=0; i--) |
---|
[bf183f] | 1718 | //{ |
---|
| 1719 | // pAddExp(p,i, pGetExp(q,i)); |
---|
| 1720 | //} |
---|
| 1721 | //p->Order += q->Order; |
---|
| 1722 | p_ExpVectorAdd(p,q,r); |
---|
| 1723 | } |
---|
| 1724 | |
---|
| 1725 | /*3 |
---|
| 1726 | * compute for monomials p*q |
---|
| 1727 | * keeps p, q |
---|
| 1728 | */ |
---|
| 1729 | static poly p_MonMultC(poly p, poly q, const ring rr) |
---|
| 1730 | { |
---|
| 1731 | number x; |
---|
| 1732 | poly r = p_Init(rr); |
---|
| 1733 | |
---|
[8a8c9e] | 1734 | x = n_Mult(pGetCoeff(p),pGetCoeff(q),rr->cf); |
---|
[bf183f] | 1735 | pSetCoeff0(r,x); |
---|
| 1736 | p_ExpVectorSum(r,p, q, rr); |
---|
| 1737 | return r; |
---|
| 1738 | } |
---|
| 1739 | |
---|
[5679049] | 1740 | /*3 |
---|
| 1741 | * create binomial coef. |
---|
| 1742 | */ |
---|
| 1743 | static number* pnBin(int exp, const ring r) |
---|
| 1744 | { |
---|
| 1745 | int e, i, h; |
---|
| 1746 | number x, y, *bin=NULL; |
---|
| 1747 | |
---|
| 1748 | x = n_Init(exp,r->cf); |
---|
| 1749 | if (n_IsZero(x,r->cf)) |
---|
| 1750 | { |
---|
| 1751 | n_Delete(&x,r->cf); |
---|
| 1752 | return bin; |
---|
| 1753 | } |
---|
| 1754 | h = (exp >> 1) + 1; |
---|
| 1755 | bin = (number *)omAlloc0(h*sizeof(number)); |
---|
| 1756 | bin[1] = x; |
---|
| 1757 | if (exp < 4) |
---|
| 1758 | return bin; |
---|
| 1759 | i = exp - 1; |
---|
| 1760 | for (e=2; e<h; e++) |
---|
| 1761 | { |
---|
| 1762 | x = n_Init(i,r->cf); |
---|
| 1763 | i--; |
---|
| 1764 | y = n_Mult(x,bin[e-1],r->cf); |
---|
| 1765 | n_Delete(&x,r->cf); |
---|
| 1766 | x = n_Init(e,r->cf); |
---|
| 1767 | bin[e] = n_IntDiv(y,x,r->cf); |
---|
| 1768 | n_Delete(&x,r->cf); |
---|
| 1769 | n_Delete(&y,r->cf); |
---|
| 1770 | } |
---|
| 1771 | return bin; |
---|
| 1772 | } |
---|
| 1773 | |
---|
[1389a4] | 1774 | static void pnFreeBin(number *bin, int exp,const coeffs r) |
---|
| 1775 | { |
---|
| 1776 | int e, h = (exp >> 1) + 1; |
---|
| 1777 | |
---|
| 1778 | if (bin[1] != NULL) |
---|
| 1779 | { |
---|
| 1780 | for (e=1; e<h; e++) |
---|
| 1781 | n_Delete(&(bin[e]),r); |
---|
| 1782 | } |
---|
| 1783 | omFreeSize((ADDRESS)bin, h*sizeof(number)); |
---|
| 1784 | } |
---|
| 1785 | |
---|
[bf183f] | 1786 | /* |
---|
| 1787 | * compute for a poly p = head+tail, tail is monomial |
---|
| 1788 | * (head + tail)^exp, exp > 1 |
---|
| 1789 | * with binomial coef. |
---|
| 1790 | */ |
---|
| 1791 | static poly p_TwoMonPower(poly p, int exp, const ring r) |
---|
| 1792 | { |
---|
| 1793 | int eh, e; |
---|
| 1794 | long al; |
---|
| 1795 | poly *a; |
---|
| 1796 | poly tail, b, res, h; |
---|
| 1797 | number x; |
---|
[7eb7b5] | 1798 | number *bin = pnBin(exp,r); |
---|
[bf183f] | 1799 | |
---|
| 1800 | tail = pNext(p); |
---|
| 1801 | if (bin == NULL) |
---|
| 1802 | { |
---|
| 1803 | p_MonPower(p,exp,r); |
---|
| 1804 | p_MonPower(tail,exp,r); |
---|
| 1805 | #ifdef PDEBUG |
---|
| 1806 | p_Test(p,r); |
---|
| 1807 | #endif |
---|
| 1808 | return p; |
---|
| 1809 | } |
---|
| 1810 | eh = exp >> 1; |
---|
| 1811 | al = (exp + 1) * sizeof(poly); |
---|
| 1812 | a = (poly *)omAlloc(al); |
---|
| 1813 | a[1] = p; |
---|
| 1814 | for (e=1; e<exp; e++) |
---|
| 1815 | { |
---|
| 1816 | a[e+1] = p_MonMultC(a[e],p,r); |
---|
| 1817 | } |
---|
| 1818 | res = a[exp]; |
---|
| 1819 | b = p_Head(tail,r); |
---|
| 1820 | for (e=exp-1; e>eh; e--) |
---|
| 1821 | { |
---|
| 1822 | h = a[e]; |
---|
[8a8c9e] | 1823 | x = n_Mult(bin[exp-e],pGetCoeff(h),r->cf); |
---|
[bf183f] | 1824 | p_SetCoeff(h,x,r); |
---|
| 1825 | p_MonMult(h,b,r); |
---|
| 1826 | res = pNext(res) = h; |
---|
| 1827 | p_MonMult(b,tail,r); |
---|
| 1828 | } |
---|
| 1829 | for (e=eh; e!=0; e--) |
---|
| 1830 | { |
---|
| 1831 | h = a[e]; |
---|
[8a8c9e] | 1832 | x = n_Mult(bin[e],pGetCoeff(h),r->cf); |
---|
[bf183f] | 1833 | p_SetCoeff(h,x,r); |
---|
| 1834 | p_MonMult(h,b,r); |
---|
| 1835 | res = pNext(res) = h; |
---|
| 1836 | p_MonMult(b,tail,r); |
---|
| 1837 | } |
---|
| 1838 | p_LmDelete(&tail,r); |
---|
| 1839 | pNext(res) = b; |
---|
| 1840 | pNext(b) = NULL; |
---|
| 1841 | res = a[exp]; |
---|
| 1842 | omFreeSize((ADDRESS)a, al); |
---|
[1389a4] | 1843 | pnFreeBin(bin, exp, r->cf); |
---|
[bf183f] | 1844 | // tail=res; |
---|
| 1845 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
---|
| 1846 | // { |
---|
| 1847 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
---|
| 1848 | // { |
---|
| 1849 | // pLmDelete(&pNext(tail)); |
---|
| 1850 | // } |
---|
| 1851 | // else |
---|
| 1852 | // pIter(tail); |
---|
| 1853 | // } |
---|
| 1854 | #ifdef PDEBUG |
---|
| 1855 | p_Test(res,r); |
---|
| 1856 | #endif |
---|
| 1857 | return res; |
---|
| 1858 | } |
---|
| 1859 | |
---|
| 1860 | static poly p_Pow(poly p, int i, const ring r) |
---|
| 1861 | { |
---|
| 1862 | poly rc = p_Copy(p,r); |
---|
| 1863 | i -= 2; |
---|
| 1864 | do |
---|
| 1865 | { |
---|
| 1866 | rc = p_Mult_q(rc,p_Copy(p,r),r); |
---|
| 1867 | p_Normalize(rc,r); |
---|
| 1868 | i--; |
---|
| 1869 | } |
---|
| 1870 | while (i != 0); |
---|
| 1871 | return p_Mult_q(rc,p,r); |
---|
| 1872 | } |
---|
| 1873 | |
---|
| 1874 | /*2 |
---|
| 1875 | * returns the i-th power of p |
---|
| 1876 | * p will be destroyed |
---|
| 1877 | */ |
---|
| 1878 | poly p_Power(poly p, int i, const ring r) |
---|
| 1879 | { |
---|
| 1880 | poly rc=NULL; |
---|
| 1881 | |
---|
| 1882 | if (i==0) |
---|
| 1883 | { |
---|
| 1884 | p_Delete(&p,r); |
---|
| 1885 | return p_One(r); |
---|
| 1886 | } |
---|
| 1887 | |
---|
| 1888 | if(p!=NULL) |
---|
| 1889 | { |
---|
| 1890 | if ( (i > 0) && ((unsigned long ) i > (r->bitmask))) |
---|
| 1891 | { |
---|
| 1892 | Werror("exponent %d is too large, max. is %ld",i,r->bitmask); |
---|
| 1893 | return NULL; |
---|
| 1894 | } |
---|
| 1895 | switch (i) |
---|
| 1896 | { |
---|
| 1897 | // cannot happen, see above |
---|
| 1898 | // case 0: |
---|
| 1899 | // { |
---|
| 1900 | // rc=pOne(); |
---|
| 1901 | // pDelete(&p); |
---|
| 1902 | // break; |
---|
| 1903 | // } |
---|
| 1904 | case 1: |
---|
| 1905 | rc=p; |
---|
| 1906 | break; |
---|
| 1907 | case 2: |
---|
| 1908 | rc=p_Mult_q(p_Copy(p,r),p,r); |
---|
| 1909 | break; |
---|
| 1910 | default: |
---|
| 1911 | if (i < 0) |
---|
| 1912 | { |
---|
| 1913 | p_Delete(&p,r); |
---|
| 1914 | return NULL; |
---|
| 1915 | } |
---|
| 1916 | else |
---|
| 1917 | { |
---|
| 1918 | #ifdef HAVE_PLURAL |
---|
| 1919 | if (rIsPluralRing(r)) /* in the NC case nothing helps :-( */ |
---|
| 1920 | { |
---|
| 1921 | int j=i; |
---|
| 1922 | rc = p_Copy(p,r); |
---|
| 1923 | while (j>1) |
---|
| 1924 | { |
---|
| 1925 | rc = p_Mult_q(p_Copy(p,r),rc,r); |
---|
| 1926 | j--; |
---|
| 1927 | } |
---|
| 1928 | p_Delete(&p,r); |
---|
| 1929 | return rc; |
---|
| 1930 | } |
---|
| 1931 | #endif |
---|
| 1932 | rc = pNext(p); |
---|
| 1933 | if (rc == NULL) |
---|
| 1934 | return p_MonPower(p,i,r); |
---|
| 1935 | /* else: binom ?*/ |
---|
| 1936 | int char_p=rChar(r); |
---|
| 1937 | if ((pNext(rc) != NULL) |
---|
| 1938 | #ifdef HAVE_RINGS |
---|
| 1939 | || rField_is_Ring(r) |
---|
| 1940 | #endif |
---|
| 1941 | ) |
---|
| 1942 | return p_Pow(p,i,r); |
---|
| 1943 | if ((char_p==0) || (i<=char_p)) |
---|
| 1944 | return p_TwoMonPower(p,i,r); |
---|
| 1945 | poly p_p=p_TwoMonPower(p_Copy(p,r),char_p,r); |
---|
| 1946 | return p_Mult_q(p_Power(p,i-char_p,r),p_p,r); |
---|
| 1947 | } |
---|
| 1948 | /*end default:*/ |
---|
| 1949 | } |
---|
| 1950 | } |
---|
| 1951 | return rc; |
---|
| 1952 | } |
---|
[8d1d30c] | 1953 | |
---|
| 1954 | /* --------------------------------------------------------------------------------*/ |
---|
| 1955 | /* content suff */ |
---|
| 1956 | |
---|
| 1957 | static number p_InitContent(poly ph, const ring r); |
---|
| 1958 | static number p_InitContent_a(poly ph, const ring r); |
---|
| 1959 | |
---|
| 1960 | void p_Content(poly ph, const ring r) |
---|
| 1961 | { |
---|
| 1962 | #ifdef HAVE_RINGS |
---|
| 1963 | if (rField_is_Ring(r)) |
---|
| 1964 | { |
---|
| 1965 | if ((ph!=NULL) && rField_has_Units(r)) |
---|
| 1966 | { |
---|
[8a8c9e] | 1967 | number k = n_GetUnit(pGetCoeff(ph),r->cf); |
---|
[8d1d30c] | 1968 | if (!n_IsOne(k,r->cf)) |
---|
| 1969 | { |
---|
| 1970 | number tmpGMP = k; |
---|
| 1971 | k = n_Invers(k,r->cf); |
---|
| 1972 | n_Delete(&tmpGMP,r->cf); |
---|
| 1973 | poly h = pNext(ph); |
---|
| 1974 | p_SetCoeff(ph, n_Mult(pGetCoeff(ph), k,r->cf),r); |
---|
| 1975 | while (h != NULL) |
---|
| 1976 | { |
---|
| 1977 | p_SetCoeff(h, n_Mult(pGetCoeff(h), k,r->cf),r); |
---|
| 1978 | pIter(h); |
---|
| 1979 | } |
---|
| 1980 | } |
---|
| 1981 | n_Delete(&k,r->cf); |
---|
| 1982 | } |
---|
| 1983 | return; |
---|
| 1984 | } |
---|
| 1985 | #endif |
---|
| 1986 | number h,d; |
---|
| 1987 | poly p; |
---|
| 1988 | |
---|
| 1989 | if(TEST_OPT_CONTENTSB) return; |
---|
| 1990 | if(pNext(ph)==NULL) |
---|
| 1991 | { |
---|
[8a8c9e] | 1992 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
[8d1d30c] | 1993 | } |
---|
| 1994 | else |
---|
| 1995 | { |
---|
| 1996 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
| 1997 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
[8a8c9e] | 1998 | if (rField_is_Q(r)) |
---|
[8d1d30c] | 1999 | { |
---|
| 2000 | h=p_InitContent(ph,r); |
---|
| 2001 | p=ph; |
---|
| 2002 | } |
---|
[4c6e420] | 2003 | else if (rField_is_Extension(r) |
---|
| 2004 | && |
---|
| 2005 | ( |
---|
| 2006 | (rPar(r)>1) || rMinpolyIsNULL(r) |
---|
| 2007 | ) |
---|
| 2008 | ) |
---|
[8d1d30c] | 2009 | { |
---|
| 2010 | h=p_InitContent_a(ph,r); |
---|
| 2011 | p=ph; |
---|
| 2012 | } |
---|
| 2013 | else |
---|
| 2014 | { |
---|
| 2015 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
| 2016 | p = pNext(ph); |
---|
| 2017 | } |
---|
| 2018 | while (p!=NULL) |
---|
| 2019 | { |
---|
| 2020 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2021 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
| 2022 | n_Delete(&h,r->cf); |
---|
| 2023 | h = d; |
---|
| 2024 | if(n_IsOne(h,r->cf)) |
---|
| 2025 | { |
---|
| 2026 | break; |
---|
| 2027 | } |
---|
| 2028 | pIter(p); |
---|
| 2029 | } |
---|
| 2030 | p = ph; |
---|
| 2031 | //number tmp; |
---|
| 2032 | if(!n_IsOne(h,r->cf)) |
---|
| 2033 | { |
---|
| 2034 | while (p!=NULL) |
---|
| 2035 | { |
---|
| 2036 | //d = nDiv(pGetCoeff(p),h); |
---|
| 2037 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
| 2038 | //if (!nEqual(d,tmp)) |
---|
| 2039 | //{ |
---|
| 2040 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
| 2041 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
| 2042 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
| 2043 | //} |
---|
| 2044 | //nDelete(&tmp); |
---|
| 2045 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2046 | p_SetCoeff(p,d,r); |
---|
| 2047 | pIter(p); |
---|
| 2048 | } |
---|
| 2049 | } |
---|
| 2050 | n_Delete(&h,r->cf); |
---|
| 2051 | #ifdef HAVE_FACTORY |
---|
[02c42d] | 2052 | if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
[8d1d30c] | 2053 | { |
---|
[ce3f53c] | 2054 | singclap_divide_content(ph, r); |
---|
[8d1d30c] | 2055 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
| 2056 | } |
---|
| 2057 | #endif |
---|
| 2058 | if (rField_is_Q_a(r)) |
---|
| 2059 | { |
---|
[abb4787] | 2060 | //number hzz = nlInit(1, r->cf); |
---|
[8d1d30c] | 2061 | h = nlInit(1, r->cf); |
---|
| 2062 | p=ph; |
---|
[fd01a8] | 2063 | Werror("longalg missing 1"); |
---|
[9c83f2] | 2064 | #if 0 |
---|
[8d1d30c] | 2065 | while (p!=NULL) |
---|
| 2066 | { // each monom: coeff in Q_a |
---|
| 2067 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
[8a8c9e] | 2068 | poly c_n=c_n_n->z; |
---|
[8d1d30c] | 2069 | while (c_n!=NULL) |
---|
| 2070 | { // each monom: coeff in Q |
---|
[6ccdd3a] | 2071 | d=nlLcm(hzz,pGetCoeff(c_n),r->extRing->cf); |
---|
| 2072 | n_Delete(&hzz,r->extRing->cf); |
---|
[8d1d30c] | 2073 | hzz=d; |
---|
| 2074 | pIter(c_n); |
---|
| 2075 | } |
---|
| 2076 | c_n=c_n_n->n; |
---|
| 2077 | while (c_n!=NULL) |
---|
| 2078 | { // each monom: coeff in Q |
---|
[6ccdd3a] | 2079 | d=nlLcm(h,pGetCoeff(c_n),r->extRing->cf); |
---|
| 2080 | n_Delete(&h,r->extRing->cf); |
---|
[8d1d30c] | 2081 | h=d; |
---|
| 2082 | pIter(c_n); |
---|
| 2083 | } |
---|
| 2084 | pIter(p); |
---|
| 2085 | } |
---|
| 2086 | /* hzz contains the 1/lcm of all denominators in c_n_n->z*/ |
---|
| 2087 | /* h contains the 1/lcm of all denominators in c_n_n->n*/ |
---|
[6ccdd3a] | 2088 | number htmp=nlInvers(h,r->extRing->cf); |
---|
| 2089 | number hzztmp=nlInvers(hzz,r->extRing->cf); |
---|
| 2090 | number hh=nlMult(hzz,h,r->extRing->cf); |
---|
| 2091 | nlDelete(&hzz,r->extRing->cf); |
---|
| 2092 | nlDelete(&h,r->extRing->cf); |
---|
| 2093 | number hg=nlGcd(hzztmp,htmp,r->extRing->cf); |
---|
| 2094 | nlDelete(&hzztmp,r->extRing->cf); |
---|
| 2095 | nlDelete(&htmp,r->extRing->cf); |
---|
| 2096 | h=nlMult(hh,hg,r->extRing->cf); |
---|
| 2097 | nlDelete(&hg,r->extRing->cf); |
---|
| 2098 | nlDelete(&hh,r->extRing->cf); |
---|
| 2099 | nlNormalize(h,r->extRing->cf); |
---|
| 2100 | if(!nlIsOne(h,r->extRing->cf)) |
---|
[8d1d30c] | 2101 | { |
---|
| 2102 | p=ph; |
---|
| 2103 | while (p!=NULL) |
---|
| 2104 | { // each monom: coeff in Q_a |
---|
| 2105 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
[8a8c9e] | 2106 | poly c_n=c_n_n->z; |
---|
[8d1d30c] | 2107 | while (c_n!=NULL) |
---|
| 2108 | { // each monom: coeff in Q |
---|
[6ccdd3a] | 2109 | d=nlMult(h,pGetCoeff(c_n),r->extRing->cf); |
---|
| 2110 | nlNormalize(d,r->extRing->cf); |
---|
| 2111 | nlDelete(&pGetCoeff(c_n),r->extRing->cf); |
---|
[8d1d30c] | 2112 | pGetCoeff(c_n)=d; |
---|
| 2113 | pIter(c_n); |
---|
| 2114 | } |
---|
| 2115 | c_n=c_n_n->n; |
---|
| 2116 | while (c_n!=NULL) |
---|
| 2117 | { // each monom: coeff in Q |
---|
[6ccdd3a] | 2118 | d=nlMult(h,pGetCoeff(c_n),r->extRing->cf); |
---|
| 2119 | nlNormalize(d,r->extRing->cf); |
---|
| 2120 | nlDelete(&pGetCoeff(c_n),r->extRing->cf); |
---|
[8d1d30c] | 2121 | pGetCoeff(c_n)=d; |
---|
| 2122 | pIter(c_n); |
---|
| 2123 | } |
---|
| 2124 | pIter(p); |
---|
| 2125 | } |
---|
| 2126 | } |
---|
[6ccdd3a] | 2127 | nlDelete(&h,r->extRing->cf); |
---|
[9c83f2] | 2128 | #endif |
---|
[8d1d30c] | 2129 | } |
---|
| 2130 | } |
---|
| 2131 | } |
---|
[5698bb] | 2132 | #if 0 // currently not used |
---|
[8d1d30c] | 2133 | void p_SimpleContent(poly ph,int smax, const ring r) |
---|
| 2134 | { |
---|
| 2135 | if(TEST_OPT_CONTENTSB) return; |
---|
| 2136 | if (ph==NULL) return; |
---|
| 2137 | if (pNext(ph)==NULL) |
---|
| 2138 | { |
---|
| 2139 | p_SetCoeff(ph,n_Init(1,r_cf),r); |
---|
| 2140 | return; |
---|
| 2141 | } |
---|
| 2142 | if ((pNext(pNext(ph))==NULL)||(!rField_is_Q(r))) |
---|
| 2143 | { |
---|
| 2144 | return; |
---|
| 2145 | } |
---|
| 2146 | number d=p_InitContent(ph,r); |
---|
| 2147 | if (nlSize(d,r->cf)<=smax) |
---|
| 2148 | { |
---|
| 2149 | //if (TEST_OPT_PROT) PrintS("G"); |
---|
| 2150 | return; |
---|
| 2151 | } |
---|
| 2152 | poly p=ph; |
---|
| 2153 | number h=d; |
---|
| 2154 | if (smax==1) smax=2; |
---|
| 2155 | while (p!=NULL) |
---|
| 2156 | { |
---|
| 2157 | #if 0 |
---|
| 2158 | d=nlGcd(h,pGetCoeff(p),r->cf); |
---|
| 2159 | nlDelete(&h,r->cf); |
---|
| 2160 | h = d; |
---|
| 2161 | #else |
---|
| 2162 | nlInpGcd(h,pGetCoeff(p),r->cf); |
---|
| 2163 | #endif |
---|
| 2164 | if(nlSize(h,r->cf)<smax) |
---|
| 2165 | { |
---|
| 2166 | //if (TEST_OPT_PROT) PrintS("g"); |
---|
| 2167 | return; |
---|
| 2168 | } |
---|
| 2169 | pIter(p); |
---|
| 2170 | } |
---|
| 2171 | p = ph; |
---|
| 2172 | if (!nlGreaterZero(pGetCoeff(p),r->cf)) h=nlNeg(h,r->cf); |
---|
| 2173 | if(nlIsOne(h,r->cf)) return; |
---|
| 2174 | //if (TEST_OPT_PROT) PrintS("c"); |
---|
| 2175 | while (p!=NULL) |
---|
| 2176 | { |
---|
| 2177 | #if 1 |
---|
| 2178 | d = nlIntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2179 | p_SetCoeff(p,d,r); |
---|
| 2180 | #else |
---|
| 2181 | nlInpIntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2182 | #endif |
---|
| 2183 | pIter(p); |
---|
| 2184 | } |
---|
| 2185 | nlDelete(&h,r->cf); |
---|
| 2186 | } |
---|
[5698bb] | 2187 | #endif |
---|
[8d1d30c] | 2188 | |
---|
| 2189 | static number p_InitContent(poly ph, const ring r) |
---|
| 2190 | // only for coefficients in Q |
---|
| 2191 | #if 0 |
---|
| 2192 | { |
---|
| 2193 | assume(!TEST_OPT_CONTENTSB); |
---|
| 2194 | assume(ph!=NULL); |
---|
| 2195 | assume(pNext(ph)!=NULL); |
---|
| 2196 | assume(rField_is_Q(r)); |
---|
| 2197 | if (pNext(pNext(ph))==NULL) |
---|
| 2198 | { |
---|
| 2199 | return nlGetNom(pGetCoeff(pNext(ph)),r->cf); |
---|
| 2200 | } |
---|
| 2201 | poly p=ph; |
---|
| 2202 | number n1=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2203 | pIter(p); |
---|
| 2204 | number n2=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2205 | pIter(p); |
---|
| 2206 | number d; |
---|
| 2207 | number t; |
---|
| 2208 | loop |
---|
| 2209 | { |
---|
| 2210 | nlNormalize(pGetCoeff(p),r->cf); |
---|
| 2211 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2212 | if (nlGreaterZero(t,r->cf)) |
---|
| 2213 | d=nlAdd(n1,t,r->cf); |
---|
| 2214 | else |
---|
| 2215 | d=nlSub(n1,t,r->cf); |
---|
| 2216 | nlDelete(&t,r->cf); |
---|
| 2217 | nlDelete(&n1,r->cf); |
---|
| 2218 | n1=d; |
---|
| 2219 | pIter(p); |
---|
| 2220 | if (p==NULL) break; |
---|
| 2221 | nlNormalize(pGetCoeff(p),r->cf); |
---|
| 2222 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
| 2223 | if (nlGreaterZero(t,r->cf)) |
---|
| 2224 | d=nlAdd(n2,t,r->cf); |
---|
| 2225 | else |
---|
| 2226 | d=nlSub(n2,t,r->cf); |
---|
| 2227 | nlDelete(&t,r->cf); |
---|
| 2228 | nlDelete(&n2,r->cf); |
---|
| 2229 | n2=d; |
---|
| 2230 | pIter(p); |
---|
| 2231 | if (p==NULL) break; |
---|
| 2232 | } |
---|
| 2233 | d=nlGcd(n1,n2,r->cf); |
---|
| 2234 | nlDelete(&n1,r->cf); |
---|
| 2235 | nlDelete(&n2,r->cf); |
---|
| 2236 | return d; |
---|
| 2237 | } |
---|
| 2238 | #else |
---|
| 2239 | { |
---|
| 2240 | number d=pGetCoeff(ph); |
---|
| 2241 | if(SR_HDL(d)&SR_INT) return d; |
---|
| 2242 | int s=mpz_size1(d->z); |
---|
| 2243 | int s2=-1; |
---|
| 2244 | number d2; |
---|
| 2245 | loop |
---|
| 2246 | { |
---|
| 2247 | pIter(ph); |
---|
| 2248 | if(ph==NULL) |
---|
| 2249 | { |
---|
| 2250 | if (s2==-1) return nlCopy(d,r->cf); |
---|
| 2251 | break; |
---|
| 2252 | } |
---|
| 2253 | if (SR_HDL(pGetCoeff(ph))&SR_INT) |
---|
| 2254 | { |
---|
| 2255 | s2=s; |
---|
| 2256 | d2=d; |
---|
| 2257 | s=0; |
---|
| 2258 | d=pGetCoeff(ph); |
---|
| 2259 | if (s2==0) break; |
---|
| 2260 | } |
---|
| 2261 | else |
---|
| 2262 | if (mpz_size1((pGetCoeff(ph)->z))<=s) |
---|
| 2263 | { |
---|
| 2264 | s2=s; |
---|
| 2265 | d2=d; |
---|
| 2266 | d=pGetCoeff(ph); |
---|
| 2267 | s=mpz_size1(d->z); |
---|
| 2268 | } |
---|
| 2269 | } |
---|
| 2270 | return nlGcd(d,d2,r->cf); |
---|
| 2271 | } |
---|
| 2272 | #endif |
---|
| 2273 | |
---|
| 2274 | number p_InitContent_a(poly ph, const ring r) |
---|
[0afa07] | 2275 | // only for coefficients in K(a)/<minpoly(a)> and K(t_1, t_2, ..., t_n) |
---|
[8d1d30c] | 2276 | { |
---|
| 2277 | number d=pGetCoeff(ph); |
---|
[0afa07] | 2278 | /* old: int s=n_ParDeg(d,r->cf); new: */ |
---|
| 2279 | int s = p_Totaldegree((poly)d, r->cf->extRing); |
---|
| 2280 | if (s <=1) return n_Copy(d,r->cf); |
---|
[8d1d30c] | 2281 | int s2=-1; |
---|
| 2282 | number d2; |
---|
| 2283 | int ss; |
---|
| 2284 | loop |
---|
| 2285 | { |
---|
| 2286 | pIter(ph); |
---|
| 2287 | if(ph==NULL) |
---|
| 2288 | { |
---|
[1389a4] | 2289 | if (s2==-1) return n_Copy(d,r->cf); |
---|
[8d1d30c] | 2290 | break; |
---|
| 2291 | } |
---|
[0afa07] | 2292 | /* old: if ((ss=n_ParDeg(pGetCoeff(ph),r->cf))<s) new: */ |
---|
| 2293 | if ((ss = p_Totaldegree((poly)pGetCoeff(ph), r->cf->extRing)) < s) |
---|
[8d1d30c] | 2294 | { |
---|
| 2295 | s2=s; |
---|
| 2296 | d2=d; |
---|
| 2297 | s=ss; |
---|
| 2298 | d=pGetCoeff(ph); |
---|
| 2299 | if (s2<=1) break; |
---|
| 2300 | } |
---|
| 2301 | } |
---|
[1389a4] | 2302 | return n_Gcd(d,d2,r->cf); |
---|
[8d1d30c] | 2303 | } |
---|
| 2304 | |
---|
| 2305 | |
---|
| 2306 | //void pContent(poly ph) |
---|
| 2307 | //{ |
---|
| 2308 | // number h,d; |
---|
| 2309 | // poly p; |
---|
| 2310 | // |
---|
| 2311 | // p = ph; |
---|
| 2312 | // if(pNext(p)==NULL) |
---|
| 2313 | // { |
---|
| 2314 | // pSetCoeff(p,nInit(1)); |
---|
| 2315 | // } |
---|
| 2316 | // else |
---|
| 2317 | // { |
---|
| 2318 | //#ifdef PDEBUG |
---|
| 2319 | // if (!pTest(p)) return; |
---|
| 2320 | //#endif |
---|
| 2321 | // nNormalize(pGetCoeff(p)); |
---|
| 2322 | // if(!nGreaterZero(pGetCoeff(ph))) |
---|
| 2323 | // { |
---|
| 2324 | // ph = pNeg(ph); |
---|
| 2325 | // nNormalize(pGetCoeff(p)); |
---|
| 2326 | // } |
---|
| 2327 | // h=pGetCoeff(p); |
---|
| 2328 | // pIter(p); |
---|
| 2329 | // while (p!=NULL) |
---|
| 2330 | // { |
---|
| 2331 | // nNormalize(pGetCoeff(p)); |
---|
| 2332 | // if (nGreater(h,pGetCoeff(p))) h=pGetCoeff(p); |
---|
| 2333 | // pIter(p); |
---|
| 2334 | // } |
---|
| 2335 | // h=nCopy(h); |
---|
| 2336 | // p=ph; |
---|
| 2337 | // while (p!=NULL) |
---|
| 2338 | // { |
---|
[32d07a5] | 2339 | // d=n_Gcd(h,pGetCoeff(p)); |
---|
[8d1d30c] | 2340 | // nDelete(&h); |
---|
| 2341 | // h = d; |
---|
| 2342 | // if(nIsOne(h)) |
---|
| 2343 | // { |
---|
| 2344 | // break; |
---|
| 2345 | // } |
---|
| 2346 | // pIter(p); |
---|
| 2347 | // } |
---|
| 2348 | // p = ph; |
---|
| 2349 | // //number tmp; |
---|
| 2350 | // if(!nIsOne(h)) |
---|
| 2351 | // { |
---|
| 2352 | // while (p!=NULL) |
---|
| 2353 | // { |
---|
| 2354 | // d = nIntDiv(pGetCoeff(p),h); |
---|
| 2355 | // pSetCoeff(p,d); |
---|
| 2356 | // pIter(p); |
---|
| 2357 | // } |
---|
| 2358 | // } |
---|
| 2359 | // nDelete(&h); |
---|
| 2360 | //#ifdef HAVE_FACTORY |
---|
| 2361 | // if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2362 | // { |
---|
| 2363 | // pTest(ph); |
---|
| 2364 | // singclap_divide_content(ph); |
---|
| 2365 | // pTest(ph); |
---|
| 2366 | // } |
---|
| 2367 | //#endif |
---|
| 2368 | // } |
---|
| 2369 | //} |
---|
| 2370 | #if 0 |
---|
| 2371 | void p_Content(poly ph, const ring r) |
---|
| 2372 | { |
---|
| 2373 | number h,d; |
---|
| 2374 | poly p; |
---|
| 2375 | |
---|
| 2376 | if(pNext(ph)==NULL) |
---|
| 2377 | { |
---|
| 2378 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
| 2379 | } |
---|
| 2380 | else |
---|
| 2381 | { |
---|
| 2382 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
| 2383 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
| 2384 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
| 2385 | p = pNext(ph); |
---|
| 2386 | while (p!=NULL) |
---|
| 2387 | { |
---|
| 2388 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2389 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
| 2390 | n_Delete(&h,r->cf); |
---|
| 2391 | h = d; |
---|
| 2392 | if(n_IsOne(h,r->cf)) |
---|
| 2393 | { |
---|
| 2394 | break; |
---|
| 2395 | } |
---|
| 2396 | pIter(p); |
---|
| 2397 | } |
---|
| 2398 | p = ph; |
---|
| 2399 | //number tmp; |
---|
| 2400 | if(!n_IsOne(h,r->cf)) |
---|
| 2401 | { |
---|
| 2402 | while (p!=NULL) |
---|
| 2403 | { |
---|
| 2404 | //d = nDiv(pGetCoeff(p),h); |
---|
| 2405 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
| 2406 | //if (!nEqual(d,tmp)) |
---|
| 2407 | //{ |
---|
| 2408 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
| 2409 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
| 2410 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
| 2411 | //} |
---|
| 2412 | //nDelete(&tmp); |
---|
| 2413 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
| 2414 | p_SetCoeff(p,d,r->cf); |
---|
| 2415 | pIter(p); |
---|
| 2416 | } |
---|
| 2417 | } |
---|
| 2418 | n_Delete(&h,r->cf); |
---|
| 2419 | #ifdef HAVE_FACTORY |
---|
| 2420 | //if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
| 2421 | //{ |
---|
| 2422 | // singclap_divide_content(ph); |
---|
| 2423 | // if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
| 2424 | //} |
---|
| 2425 | #endif |
---|
| 2426 | } |
---|
| 2427 | } |
---|
| 2428 | #endif |
---|
[fbf8a6] | 2429 | /* ---------------------------------------------------------------------------*/ |
---|
| 2430 | /* cleardenom suff */ |
---|
[8d1d30c] | 2431 | poly p_Cleardenom(poly ph, const ring r) |
---|
| 2432 | { |
---|
| 2433 | poly start=ph; |
---|
| 2434 | number d, h; |
---|
| 2435 | poly p; |
---|
| 2436 | |
---|
| 2437 | #ifdef HAVE_RINGS |
---|
| 2438 | if (rField_is_Ring(r)) |
---|
| 2439 | { |
---|
| 2440 | p_Content(ph,r); |
---|
| 2441 | return start; |
---|
| 2442 | } |
---|
| 2443 | #endif |
---|
| 2444 | if (rField_is_Zp(r) && TEST_OPT_INTSTRATEGY) return start; |
---|
| 2445 | p = ph; |
---|
| 2446 | if(pNext(p)==NULL) |
---|
| 2447 | { |
---|
| 2448 | if (TEST_OPT_CONTENTSB) |
---|
| 2449 | { |
---|
| 2450 | number n=n_GetDenom(pGetCoeff(p),r->cf); |
---|
| 2451 | if (!n_IsOne(n,r->cf)) |
---|
| 2452 | { |
---|
| 2453 | number nn=n_Mult(pGetCoeff(p),n,r->cf); |
---|
| 2454 | n_Normalize(nn,r->cf); |
---|
| 2455 | p_SetCoeff(p,nn,r); |
---|
| 2456 | } |
---|
| 2457 | n_Delete(&n,r->cf); |
---|
| 2458 | } |
---|
| 2459 | else |
---|
| 2460 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
| 2461 | } |
---|
| 2462 | else |
---|
| 2463 | { |
---|
| 2464 | h = n_Init(1,r->cf); |
---|
| 2465 | while (p!=NULL) |
---|
| 2466 | { |
---|
[8a8c9e] | 2467 | n_Normalize(pGetCoeff(p),r->cf); |
---|
[8d1d30c] | 2468 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2469 | n_Delete(&h,r->cf); |
---|
| 2470 | h=d; |
---|
| 2471 | pIter(p); |
---|
| 2472 | } |
---|
| 2473 | /* contains the 1/lcm of all denominators */ |
---|
| 2474 | if(!n_IsOne(h,r->cf)) |
---|
| 2475 | { |
---|
| 2476 | p = ph; |
---|
| 2477 | while (p!=NULL) |
---|
| 2478 | { |
---|
| 2479 | /* should be: |
---|
| 2480 | * number hh; |
---|
| 2481 | * nGetDenom(p->coef,&hh); |
---|
| 2482 | * nMult(&h,&hh,&d); |
---|
| 2483 | * nNormalize(d); |
---|
| 2484 | * nDelete(&hh); |
---|
| 2485 | * nMult(d,p->coef,&hh); |
---|
| 2486 | * nDelete(&d); |
---|
| 2487 | * nDelete(&(p->coef)); |
---|
| 2488 | * p->coef =hh; |
---|
| 2489 | */ |
---|
| 2490 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2491 | n_Normalize(d,r->cf); |
---|
| 2492 | p_SetCoeff(p,d,r); |
---|
| 2493 | pIter(p); |
---|
| 2494 | } |
---|
| 2495 | n_Delete(&h,r->cf); |
---|
[5679049] | 2496 | if (n_GetChar(r->cf)==1) |
---|
[8d1d30c] | 2497 | { |
---|
| 2498 | loop |
---|
| 2499 | { |
---|
| 2500 | h = n_Init(1,r->cf); |
---|
| 2501 | p=ph; |
---|
| 2502 | while (p!=NULL) |
---|
| 2503 | { |
---|
| 2504 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2505 | n_Delete(&h,r->cf); |
---|
| 2506 | h=d; |
---|
| 2507 | pIter(p); |
---|
| 2508 | } |
---|
| 2509 | /* contains the 1/lcm of all denominators */ |
---|
| 2510 | if(!n_IsOne(h,r->cf)) |
---|
| 2511 | { |
---|
| 2512 | p = ph; |
---|
| 2513 | while (p!=NULL) |
---|
| 2514 | { |
---|
| 2515 | /* should be: |
---|
| 2516 | * number hh; |
---|
| 2517 | * nGetDenom(p->coef,&hh); |
---|
| 2518 | * nMult(&h,&hh,&d); |
---|
| 2519 | * nNormalize(d); |
---|
| 2520 | * nDelete(&hh); |
---|
| 2521 | * nMult(d,p->coef,&hh); |
---|
| 2522 | * nDelete(&d); |
---|
| 2523 | * nDelete(&(p->coef)); |
---|
| 2524 | * p->coef =hh; |
---|
| 2525 | */ |
---|
| 2526 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2527 | n_Normalize(d,r->cf); |
---|
| 2528 | p_SetCoeff(p,d,r); |
---|
| 2529 | pIter(p); |
---|
| 2530 | } |
---|
| 2531 | n_Delete(&h,r->cf); |
---|
| 2532 | } |
---|
| 2533 | else |
---|
| 2534 | { |
---|
| 2535 | n_Delete(&h,r->cf); |
---|
| 2536 | break; |
---|
| 2537 | } |
---|
| 2538 | } |
---|
| 2539 | } |
---|
| 2540 | } |
---|
| 2541 | if (h!=NULL) n_Delete(&h,r->cf); |
---|
[71ba5b8] | 2542 | |
---|
[8d1d30c] | 2543 | p_Content(ph,r); |
---|
| 2544 | #ifdef HAVE_RATGRING |
---|
| 2545 | if (rIsRatGRing(r)) |
---|
| 2546 | { |
---|
| 2547 | /* quick unit detection in the rational case is done in gr_nc_bba */ |
---|
| 2548 | pContentRat(ph); |
---|
| 2549 | start=ph; |
---|
| 2550 | } |
---|
| 2551 | #endif |
---|
| 2552 | } |
---|
| 2553 | return start; |
---|
| 2554 | } |
---|
| 2555 | |
---|
| 2556 | void p_Cleardenom_n(poly ph,const ring r,number &c) |
---|
| 2557 | { |
---|
| 2558 | number d, h; |
---|
| 2559 | poly p; |
---|
| 2560 | |
---|
| 2561 | p = ph; |
---|
| 2562 | if(pNext(p)==NULL) |
---|
| 2563 | { |
---|
| 2564 | c=n_Invers(pGetCoeff(p),r->cf); |
---|
| 2565 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
| 2566 | } |
---|
| 2567 | else |
---|
| 2568 | { |
---|
| 2569 | h = n_Init(1,r->cf); |
---|
| 2570 | while (p!=NULL) |
---|
| 2571 | { |
---|
| 2572 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 2573 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2574 | n_Delete(&h,r->cf); |
---|
| 2575 | h=d; |
---|
| 2576 | pIter(p); |
---|
| 2577 | } |
---|
| 2578 | c=h; |
---|
| 2579 | /* contains the 1/lcm of all denominators */ |
---|
| 2580 | if(!n_IsOne(h,r->cf)) |
---|
| 2581 | { |
---|
| 2582 | p = ph; |
---|
| 2583 | while (p!=NULL) |
---|
| 2584 | { |
---|
| 2585 | /* should be: |
---|
| 2586 | * number hh; |
---|
| 2587 | * nGetDenom(p->coef,&hh); |
---|
| 2588 | * nMult(&h,&hh,&d); |
---|
| 2589 | * nNormalize(d); |
---|
| 2590 | * nDelete(&hh); |
---|
| 2591 | * nMult(d,p->coef,&hh); |
---|
| 2592 | * nDelete(&d); |
---|
| 2593 | * nDelete(&(p->coef)); |
---|
| 2594 | * p->coef =hh; |
---|
| 2595 | */ |
---|
| 2596 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2597 | n_Normalize(d,r->cf); |
---|
| 2598 | p_SetCoeff(p,d,r); |
---|
| 2599 | pIter(p); |
---|
| 2600 | } |
---|
| 2601 | if (rField_is_Q_a(r)) |
---|
| 2602 | { |
---|
| 2603 | loop |
---|
| 2604 | { |
---|
| 2605 | h = n_Init(1,r->cf); |
---|
| 2606 | p=ph; |
---|
| 2607 | while (p!=NULL) |
---|
| 2608 | { |
---|
| 2609 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
| 2610 | n_Delete(&h,r->cf); |
---|
| 2611 | h=d; |
---|
| 2612 | pIter(p); |
---|
| 2613 | } |
---|
| 2614 | /* contains the 1/lcm of all denominators */ |
---|
| 2615 | if(!n_IsOne(h,r->cf)) |
---|
| 2616 | { |
---|
| 2617 | p = ph; |
---|
| 2618 | while (p!=NULL) |
---|
| 2619 | { |
---|
| 2620 | /* should be: |
---|
| 2621 | * number hh; |
---|
| 2622 | * nGetDenom(p->coef,&hh); |
---|
| 2623 | * nMult(&h,&hh,&d); |
---|
| 2624 | * nNormalize(d); |
---|
| 2625 | * nDelete(&hh); |
---|
| 2626 | * nMult(d,p->coef,&hh); |
---|
| 2627 | * nDelete(&d); |
---|
| 2628 | * nDelete(&(p->coef)); |
---|
| 2629 | * p->coef =hh; |
---|
| 2630 | */ |
---|
| 2631 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
| 2632 | n_Normalize(d,r->cf); |
---|
| 2633 | p_SetCoeff(p,d,r); |
---|
| 2634 | pIter(p); |
---|
| 2635 | } |
---|
| 2636 | number t=n_Mult(c,h,r->cf); |
---|
| 2637 | n_Delete(&c,r->cf); |
---|
| 2638 | c=t; |
---|
| 2639 | } |
---|
| 2640 | else |
---|
| 2641 | { |
---|
| 2642 | break; |
---|
| 2643 | } |
---|
| 2644 | n_Delete(&h,r->cf); |
---|
| 2645 | } |
---|
| 2646 | } |
---|
| 2647 | } |
---|
| 2648 | } |
---|
| 2649 | } |
---|
| 2650 | |
---|
| 2651 | number p_GetAllDenom(poly ph, const ring r) |
---|
| 2652 | { |
---|
| 2653 | number d=n_Init(1,r->cf); |
---|
| 2654 | poly p = ph; |
---|
| 2655 | |
---|
| 2656 | while (p!=NULL) |
---|
| 2657 | { |
---|
| 2658 | number h=n_GetDenom(pGetCoeff(p),r->cf); |
---|
| 2659 | if (!n_IsOne(h,r->cf)) |
---|
| 2660 | { |
---|
| 2661 | number dd=n_Mult(d,h,r->cf); |
---|
| 2662 | n_Delete(&d,r->cf); |
---|
| 2663 | d=dd; |
---|
| 2664 | } |
---|
| 2665 | n_Delete(&h,r->cf); |
---|
| 2666 | pIter(p); |
---|
| 2667 | } |
---|
| 2668 | return d; |
---|
| 2669 | } |
---|
| 2670 | |
---|
[fbf8a6] | 2671 | int p_Size(poly p, const ring r) |
---|
| 2672 | { |
---|
| 2673 | int count = 0; |
---|
| 2674 | while ( p != NULL ) |
---|
| 2675 | { |
---|
| 2676 | count+= n_Size( pGetCoeff( p ), r->cf ); |
---|
| 2677 | pIter( p ); |
---|
| 2678 | } |
---|
| 2679 | return count; |
---|
| 2680 | } |
---|
| 2681 | |
---|
[4e8ef90] | 2682 | /*2 |
---|
| 2683 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
---|
| 2684 | *assume: deg(var(varnum))==1 |
---|
| 2685 | */ |
---|
| 2686 | poly p_Homogen (poly p, int varnum, const ring r) |
---|
| 2687 | { |
---|
| 2688 | pFDegProc deg; |
---|
[5679049] | 2689 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
[4e8ef90] | 2690 | deg=p_Totaldegree; |
---|
| 2691 | else |
---|
[9765f3] | 2692 | deg=r->pFDeg; |
---|
[4e8ef90] | 2693 | |
---|
| 2694 | poly q=NULL, qn; |
---|
| 2695 | int o,ii; |
---|
| 2696 | sBucket_pt bp; |
---|
| 2697 | |
---|
| 2698 | if (p!=NULL) |
---|
| 2699 | { |
---|
| 2700 | if ((varnum < 1) || (varnum > rVar(r))) |
---|
| 2701 | { |
---|
| 2702 | return NULL; |
---|
| 2703 | } |
---|
| 2704 | o=deg(p,r); |
---|
| 2705 | q=pNext(p); |
---|
| 2706 | while (q != NULL) |
---|
| 2707 | { |
---|
| 2708 | ii=deg(q,r); |
---|
| 2709 | if (ii>o) o=ii; |
---|
| 2710 | pIter(q); |
---|
| 2711 | } |
---|
| 2712 | q = p_Copy(p,r); |
---|
| 2713 | bp = sBucketCreate(r); |
---|
| 2714 | while (q != NULL) |
---|
| 2715 | { |
---|
| 2716 | ii = o-deg(q,r); |
---|
| 2717 | if (ii!=0) |
---|
| 2718 | { |
---|
| 2719 | p_AddExp(q,varnum, (long)ii,r); |
---|
| 2720 | p_Setm(q,r); |
---|
| 2721 | } |
---|
| 2722 | qn = pNext(q); |
---|
| 2723 | pNext(q) = NULL; |
---|
| 2724 | sBucket_Add_p(bp, q, 1); |
---|
| 2725 | q = qn; |
---|
| 2726 | } |
---|
| 2727 | sBucketDestroyAdd(bp, &q, &ii); |
---|
| 2728 | } |
---|
| 2729 | return q; |
---|
| 2730 | } |
---|
| 2731 | |
---|
| 2732 | /*2 |
---|
| 2733 | *tests if p is homogeneous with respect to the actual weigths |
---|
| 2734 | */ |
---|
| 2735 | BOOLEAN p_IsHomogeneous (poly p, const ring r) |
---|
| 2736 | { |
---|
| 2737 | poly qp=p; |
---|
| 2738 | int o; |
---|
| 2739 | |
---|
| 2740 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
| 2741 | pFDegProc d; |
---|
[5679049] | 2742 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
[4e8ef90] | 2743 | d=p_Totaldegree; |
---|
[71ba5b8] | 2744 | else |
---|
[9765f3] | 2745 | d=r->pFDeg; |
---|
[8a8c9e] | 2746 | o = d(p,r); |
---|
[4e8ef90] | 2747 | do |
---|
| 2748 | { |
---|
| 2749 | if (d(qp,r) != o) return FALSE; |
---|
| 2750 | pIter(qp); |
---|
| 2751 | } |
---|
| 2752 | while (qp != NULL); |
---|
| 2753 | return TRUE; |
---|
| 2754 | } |
---|
| 2755 | |
---|
[cd246b] | 2756 | /*----------utilities for syzygies--------------*/ |
---|
| 2757 | BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r) |
---|
| 2758 | { |
---|
| 2759 | poly q=p,qq; |
---|
| 2760 | int i; |
---|
| 2761 | |
---|
| 2762 | while (q!=NULL) |
---|
| 2763 | { |
---|
| 2764 | if (p_LmIsConstantComp(q,r)) |
---|
| 2765 | { |
---|
| 2766 | i = p_GetComp(q,r); |
---|
| 2767 | qq = p; |
---|
| 2768 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
| 2769 | if (qq == q) |
---|
| 2770 | { |
---|
| 2771 | *k = i; |
---|
| 2772 | return TRUE; |
---|
| 2773 | } |
---|
| 2774 | else |
---|
| 2775 | pIter(q); |
---|
| 2776 | } |
---|
| 2777 | else pIter(q); |
---|
| 2778 | } |
---|
| 2779 | return FALSE; |
---|
| 2780 | } |
---|
| 2781 | |
---|
| 2782 | void p_VectorHasUnit(poly p, int * k, int * len, const ring r) |
---|
| 2783 | { |
---|
| 2784 | poly q=p,qq; |
---|
| 2785 | int i,j=0; |
---|
| 2786 | |
---|
| 2787 | *len = 0; |
---|
| 2788 | while (q!=NULL) |
---|
| 2789 | { |
---|
| 2790 | if (p_LmIsConstantComp(q,r)) |
---|
| 2791 | { |
---|
| 2792 | i = p_GetComp(q,r); |
---|
| 2793 | qq = p; |
---|
| 2794 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
| 2795 | if (qq == q) |
---|
| 2796 | { |
---|
| 2797 | j = 0; |
---|
| 2798 | while (qq!=NULL) |
---|
| 2799 | { |
---|
| 2800 | if (p_GetComp(qq,r)==i) j++; |
---|
| 2801 | pIter(qq); |
---|
| 2802 | } |
---|
| 2803 | if ((*len == 0) || (j<*len)) |
---|
| 2804 | { |
---|
| 2805 | *len = j; |
---|
| 2806 | *k = i; |
---|
| 2807 | } |
---|
| 2808 | } |
---|
| 2809 | } |
---|
| 2810 | pIter(q); |
---|
| 2811 | } |
---|
| 2812 | } |
---|
| 2813 | |
---|
| 2814 | poly p_TakeOutComp1(poly * p, int k, const ring r) |
---|
| 2815 | { |
---|
| 2816 | poly q = *p; |
---|
| 2817 | |
---|
| 2818 | if (q==NULL) return NULL; |
---|
| 2819 | |
---|
| 2820 | poly qq=NULL,result = NULL; |
---|
| 2821 | |
---|
| 2822 | if (p_GetComp(q,r)==k) |
---|
| 2823 | { |
---|
| 2824 | result = q; /* *p */ |
---|
| 2825 | while ((q!=NULL) && (p_GetComp(q,r)==k)) |
---|
| 2826 | { |
---|
| 2827 | p_SetComp(q,0,r); |
---|
| 2828 | p_SetmComp(q,r); |
---|
| 2829 | qq = q; |
---|
| 2830 | pIter(q); |
---|
| 2831 | } |
---|
| 2832 | *p = q; |
---|
| 2833 | pNext(qq) = NULL; |
---|
| 2834 | } |
---|
| 2835 | if (q==NULL) return result; |
---|
| 2836 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 2837 | while (pNext(q)!=NULL) |
---|
| 2838 | { |
---|
| 2839 | if (p_GetComp(pNext(q),r)==k) |
---|
| 2840 | { |
---|
| 2841 | if (result==NULL) |
---|
| 2842 | { |
---|
| 2843 | result = pNext(q); |
---|
| 2844 | qq = result; |
---|
| 2845 | } |
---|
| 2846 | else |
---|
| 2847 | { |
---|
| 2848 | pNext(qq) = pNext(q); |
---|
| 2849 | pIter(qq); |
---|
| 2850 | } |
---|
| 2851 | pNext(q) = pNext(pNext(q)); |
---|
| 2852 | pNext(qq) =NULL; |
---|
| 2853 | p_SetComp(qq,0,r); |
---|
| 2854 | p_SetmComp(qq,r); |
---|
| 2855 | } |
---|
| 2856 | else |
---|
| 2857 | { |
---|
| 2858 | pIter(q); |
---|
| 2859 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 2860 | } |
---|
| 2861 | } |
---|
| 2862 | return result; |
---|
| 2863 | } |
---|
[74021a] | 2864 | |
---|
| 2865 | poly p_TakeOutComp(poly * p, int k, const ring r) |
---|
| 2866 | { |
---|
| 2867 | poly q = *p,qq=NULL,result = NULL; |
---|
| 2868 | |
---|
| 2869 | if (q==NULL) return NULL; |
---|
| 2870 | BOOLEAN use_setmcomp=rOrd_SetCompRequiresSetm(r); |
---|
| 2871 | if (p_GetComp(q,r)==k) |
---|
| 2872 | { |
---|
| 2873 | result = q; |
---|
| 2874 | do |
---|
| 2875 | { |
---|
| 2876 | p_SetComp(q,0,r); |
---|
| 2877 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2878 | qq = q; |
---|
| 2879 | pIter(q); |
---|
| 2880 | } |
---|
| 2881 | while ((q!=NULL) && (p_GetComp(q,r)==k)); |
---|
| 2882 | *p = q; |
---|
| 2883 | pNext(qq) = NULL; |
---|
| 2884 | } |
---|
| 2885 | if (q==NULL) return result; |
---|
| 2886 | if (p_GetComp(q,r) > k) |
---|
| 2887 | { |
---|
| 2888 | p_SubComp(q,1,r); |
---|
| 2889 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2890 | } |
---|
| 2891 | poly pNext_q; |
---|
| 2892 | while ((pNext_q=pNext(q))!=NULL) |
---|
| 2893 | { |
---|
| 2894 | if (p_GetComp(pNext_q,r)==k) |
---|
| 2895 | { |
---|
| 2896 | if (result==NULL) |
---|
| 2897 | { |
---|
| 2898 | result = pNext_q; |
---|
| 2899 | qq = result; |
---|
| 2900 | } |
---|
| 2901 | else |
---|
| 2902 | { |
---|
| 2903 | pNext(qq) = pNext_q; |
---|
| 2904 | pIter(qq); |
---|
| 2905 | } |
---|
| 2906 | pNext(q) = pNext(pNext_q); |
---|
| 2907 | pNext(qq) =NULL; |
---|
| 2908 | p_SetComp(qq,0,r); |
---|
| 2909 | if (use_setmcomp) p_SetmComp(qq,r); |
---|
| 2910 | } |
---|
| 2911 | else |
---|
| 2912 | { |
---|
| 2913 | /*pIter(q);*/ q=pNext_q; |
---|
| 2914 | if (p_GetComp(q,r) > k) |
---|
| 2915 | { |
---|
| 2916 | p_SubComp(q,1,r); |
---|
| 2917 | if (use_setmcomp) p_SetmComp(q,r); |
---|
| 2918 | } |
---|
| 2919 | } |
---|
| 2920 | } |
---|
| 2921 | return result; |
---|
| 2922 | } |
---|
| 2923 | |
---|
| 2924 | // Splits *p into two polys: *q which consists of all monoms with |
---|
| 2925 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
| 2926 | void p_TakeOutComp(poly *r_p, long comp, poly *r_q, int *lq, const ring r) |
---|
| 2927 | { |
---|
| 2928 | spolyrec pp, qq; |
---|
| 2929 | poly p, q, p_prev; |
---|
| 2930 | int l = 0; |
---|
| 2931 | |
---|
| 2932 | #ifdef HAVE_ASSUME |
---|
| 2933 | int lp = pLength(*r_p); |
---|
| 2934 | #endif |
---|
| 2935 | |
---|
| 2936 | pNext(&pp) = *r_p; |
---|
| 2937 | p = *r_p; |
---|
| 2938 | p_prev = &pp; |
---|
| 2939 | q = &qq; |
---|
| 2940 | |
---|
| 2941 | while(p != NULL) |
---|
| 2942 | { |
---|
| 2943 | while (p_GetComp(p,r) == comp) |
---|
| 2944 | { |
---|
| 2945 | pNext(q) = p; |
---|
| 2946 | pIter(q); |
---|
| 2947 | p_SetComp(p, 0,r); |
---|
| 2948 | p_SetmComp(p,r); |
---|
| 2949 | pIter(p); |
---|
| 2950 | l++; |
---|
| 2951 | if (p == NULL) |
---|
| 2952 | { |
---|
| 2953 | pNext(p_prev) = NULL; |
---|
| 2954 | goto Finish; |
---|
| 2955 | } |
---|
| 2956 | } |
---|
| 2957 | pNext(p_prev) = p; |
---|
| 2958 | p_prev = p; |
---|
| 2959 | pIter(p); |
---|
| 2960 | } |
---|
| 2961 | |
---|
| 2962 | Finish: |
---|
| 2963 | pNext(q) = NULL; |
---|
| 2964 | *r_p = pNext(&pp); |
---|
| 2965 | *r_q = pNext(&qq); |
---|
| 2966 | *lq = l; |
---|
| 2967 | #ifdef HAVE_ASSUME |
---|
| 2968 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
| 2969 | #endif |
---|
| 2970 | p_Test(*r_p,r); |
---|
| 2971 | p_Test(*r_q,r); |
---|
| 2972 | } |
---|
| 2973 | |
---|
| 2974 | void p_DeleteComp(poly * p,int k, const ring r) |
---|
| 2975 | { |
---|
| 2976 | poly q; |
---|
| 2977 | |
---|
| 2978 | while ((*p!=NULL) && (p_GetComp(*p,r)==k)) p_LmDelete(p,r); |
---|
| 2979 | if (*p==NULL) return; |
---|
| 2980 | q = *p; |
---|
| 2981 | if (p_GetComp(q,r)>k) |
---|
| 2982 | { |
---|
| 2983 | p_SubComp(q,1,r); |
---|
| 2984 | p_SetmComp(q,r); |
---|
| 2985 | } |
---|
| 2986 | while (pNext(q)!=NULL) |
---|
| 2987 | { |
---|
| 2988 | if (p_GetComp(pNext(q),r)==k) |
---|
| 2989 | p_LmDelete(&(pNext(q)),r); |
---|
| 2990 | else |
---|
| 2991 | { |
---|
| 2992 | pIter(q); |
---|
| 2993 | if (p_GetComp(q,r)>k) |
---|
| 2994 | { |
---|
| 2995 | p_SubComp(q,1,r); |
---|
| 2996 | p_SetmComp(q,r); |
---|
| 2997 | } |
---|
| 2998 | } |
---|
| 2999 | } |
---|
| 3000 | } |
---|
[dd693a] | 3001 | |
---|
| 3002 | /*2 |
---|
| 3003 | * convert a vector to a set of polys, |
---|
| 3004 | * allocates the polyset, (entries 0..(*len)-1) |
---|
| 3005 | * the vector will not be changed |
---|
| 3006 | */ |
---|
| 3007 | void p_Vec2Polys(poly v, poly* *p, int *len, const ring r) |
---|
| 3008 | { |
---|
| 3009 | poly h; |
---|
| 3010 | int k; |
---|
| 3011 | |
---|
| 3012 | *len=p_MaxComp(v,r); |
---|
| 3013 | if (*len==0) *len=1; |
---|
| 3014 | *p=(poly*)omAlloc0((*len)*sizeof(poly)); |
---|
| 3015 | while (v!=NULL) |
---|
| 3016 | { |
---|
| 3017 | h=p_Head(v,r); |
---|
| 3018 | k=p_GetComp(h,r); |
---|
| 3019 | p_SetComp(h,0,r); |
---|
| 3020 | (*p)[k-1]=p_Add_q((*p)[k-1],h,r); |
---|
| 3021 | pIter(v); |
---|
| 3022 | } |
---|
| 3023 | } |
---|
| 3024 | |
---|
[5c39a9] | 3025 | /* -------------------------------------------------------- */ |
---|
| 3026 | /*2 |
---|
| 3027 | * change all global variables to fit the description of the new ring |
---|
| 3028 | */ |
---|
| 3029 | |
---|
| 3030 | void p_SetGlobals(const ring r, BOOLEAN complete) |
---|
| 3031 | { |
---|
[5679049] | 3032 | if (r->ppNoether!=NULL) p_Delete(&r->ppNoether,r); |
---|
[5c39a9] | 3033 | |
---|
| 3034 | if (complete) |
---|
| 3035 | { |
---|
| 3036 | test &= ~ TEST_RINGDEP_OPTS; |
---|
| 3037 | test |= r->options; |
---|
| 3038 | } |
---|
| 3039 | } |
---|
[949e57] | 3040 | // |
---|
| 3041 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
---|
| 3042 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
---|
[45d2332] | 3043 | // only uses pFDeg (and not p_Deg, or pTotalDegree, etc) |
---|
[949e57] | 3044 | void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg) |
---|
| 3045 | { |
---|
| 3046 | assume(new_FDeg != NULL); |
---|
| 3047 | r->pFDeg = new_FDeg; |
---|
| 3048 | |
---|
| 3049 | if (new_lDeg == NULL) |
---|
| 3050 | new_lDeg = r->pLDegOrig; |
---|
| 3051 | |
---|
| 3052 | r->pLDeg = new_lDeg; |
---|
| 3053 | } |
---|
| 3054 | |
---|
| 3055 | // restores pFDeg and pLDeg: |
---|
| 3056 | void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
---|
| 3057 | { |
---|
| 3058 | assume(old_FDeg != NULL && old_lDeg != NULL); |
---|
| 3059 | r->pFDeg = old_FDeg; |
---|
| 3060 | r->pLDeg = old_lDeg; |
---|
| 3061 | } |
---|
| 3062 | |
---|
[5bc2461] | 3063 | /*-------- several access procedures to monomials -------------------- */ |
---|
| 3064 | /* |
---|
| 3065 | * the module weights for std |
---|
| 3066 | */ |
---|
| 3067 | static pFDegProc pOldFDeg; |
---|
| 3068 | static pLDegProc pOldLDeg; |
---|
| 3069 | static intvec * pModW; |
---|
| 3070 | static BOOLEAN pOldLexOrder; |
---|
| 3071 | |
---|
[8a8c9e] | 3072 | static long pModDeg(poly p, ring r) |
---|
[5bc2461] | 3073 | { |
---|
| 3074 | long d=pOldFDeg(p, r); |
---|
| 3075 | int c=p_GetComp(p, r); |
---|
| 3076 | if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1]; |
---|
| 3077 | return d; |
---|
| 3078 | //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1]; |
---|
| 3079 | } |
---|
| 3080 | |
---|
| 3081 | void p_SetModDeg(intvec *w, ring r) |
---|
| 3082 | { |
---|
| 3083 | if (w!=NULL) |
---|
| 3084 | { |
---|
| 3085 | r->pModW = w; |
---|
| 3086 | pOldFDeg = r->pFDeg; |
---|
| 3087 | pOldLDeg = r->pLDeg; |
---|
| 3088 | pOldLexOrder = r->pLexOrder; |
---|
| 3089 | pSetDegProcs(r,pModDeg); |
---|
| 3090 | r->pLexOrder = TRUE; |
---|
| 3091 | } |
---|
| 3092 | else |
---|
| 3093 | { |
---|
| 3094 | r->pModW = NULL; |
---|
[5679049] | 3095 | pRestoreDegProcs(r,pOldFDeg, pOldLDeg); |
---|
[5bc2461] | 3096 | r->pLexOrder = pOldLexOrder; |
---|
| 3097 | } |
---|
| 3098 | } |
---|
| 3099 | |
---|
[c6a3eb2] | 3100 | /*2 |
---|
| 3101 | * handle memory request for sets of polynomials (ideals) |
---|
| 3102 | * l is the length of *p, increment is the difference (may be negative) |
---|
| 3103 | */ |
---|
| 3104 | void pEnlargeSet(poly* *p, int l, int increment) |
---|
| 3105 | { |
---|
| 3106 | poly* h; |
---|
| 3107 | |
---|
| 3108 | h=(poly*)omReallocSize((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly)); |
---|
| 3109 | if (increment>0) |
---|
| 3110 | { |
---|
| 3111 | //for (i=l; i<l+increment; i++) |
---|
| 3112 | // h[i]=NULL; |
---|
| 3113 | memset(&(h[l]),0,increment*sizeof(poly)); |
---|
| 3114 | } |
---|
| 3115 | *p=h; |
---|
| 3116 | } |
---|
| 3117 | |
---|
[71ba5b8] | 3118 | /*2 |
---|
| 3119 | *divides p1 by its leading coefficient |
---|
| 3120 | */ |
---|
| 3121 | void p_Norm(poly p1, const ring r) |
---|
| 3122 | { |
---|
| 3123 | #ifdef HAVE_RINGS |
---|
| 3124 | if (rField_is_Ring(r)) |
---|
| 3125 | { |
---|
[45d2332] | 3126 | if (!n_IsUnit(pGetCoeff(p1), r->cf)) return; |
---|
[71ba5b8] | 3127 | // Werror("p_Norm not possible in the case of coefficient rings."); |
---|
| 3128 | } |
---|
| 3129 | else |
---|
| 3130 | #endif |
---|
| 3131 | if (p1!=NULL) |
---|
| 3132 | { |
---|
| 3133 | if (pNext(p1)==NULL) |
---|
| 3134 | { |
---|
| 3135 | p_SetCoeff(p1,n_Init(1,r->cf),r); |
---|
| 3136 | return; |
---|
| 3137 | } |
---|
| 3138 | poly h; |
---|
| 3139 | if (!n_IsOne(pGetCoeff(p1),r->cf)) |
---|
| 3140 | { |
---|
| 3141 | number k, c; |
---|
| 3142 | n_Normalize(pGetCoeff(p1),r->cf); |
---|
| 3143 | k = pGetCoeff(p1); |
---|
| 3144 | c = n_Init(1,r->cf); |
---|
| 3145 | pSetCoeff0(p1,c); |
---|
| 3146 | h = pNext(p1); |
---|
| 3147 | while (h!=NULL) |
---|
| 3148 | { |
---|
| 3149 | c=n_Div(pGetCoeff(h),k,r->cf); |
---|
| 3150 | // no need to normalize: Z/p, R |
---|
| 3151 | // normalize already in nDiv: Q_a, Z/p_a |
---|
| 3152 | // remains: Q |
---|
| 3153 | if (rField_is_Q(r) && (!n_IsOne(c,r->cf))) n_Normalize(c,r->cf); |
---|
| 3154 | p_SetCoeff(h,c,r); |
---|
| 3155 | pIter(h); |
---|
| 3156 | } |
---|
| 3157 | n_Delete(&k,r->cf); |
---|
| 3158 | } |
---|
| 3159 | else |
---|
| 3160 | { |
---|
| 3161 | //if (r->cf->cfNormalize != nDummy2) //TODO: OPTIMIZE |
---|
| 3162 | { |
---|
| 3163 | h = pNext(p1); |
---|
| 3164 | while (h!=NULL) |
---|
| 3165 | { |
---|
| 3166 | n_Normalize(pGetCoeff(h),r->cf); |
---|
| 3167 | pIter(h); |
---|
| 3168 | } |
---|
| 3169 | } |
---|
| 3170 | } |
---|
| 3171 | } |
---|
| 3172 | } |
---|
| 3173 | |
---|
| 3174 | /*2 |
---|
| 3175 | *normalize all coefficients |
---|
| 3176 | */ |
---|
| 3177 | void p_Normalize(poly p,const ring r) |
---|
| 3178 | { |
---|
| 3179 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
| 3180 | while (p!=NULL) |
---|
| 3181 | { |
---|
| 3182 | #ifdef LDEBUG |
---|
[45d2332] | 3183 | n_Test(pGetCoeff(p), r->cf); |
---|
[71ba5b8] | 3184 | #endif |
---|
| 3185 | n_Normalize(pGetCoeff(p),r->cf); |
---|
| 3186 | pIter(p); |
---|
| 3187 | } |
---|
| 3188 | } |
---|
| 3189 | |
---|
| 3190 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
| 3191 | // Poly with Exp(n) != 0 is reversed |
---|
| 3192 | static void p_SplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero, const ring r) |
---|
| 3193 | { |
---|
| 3194 | if (p == NULL) |
---|
| 3195 | { |
---|
| 3196 | *non_zero = NULL; |
---|
| 3197 | *zero = NULL; |
---|
| 3198 | return; |
---|
| 3199 | } |
---|
| 3200 | spolyrec sz; |
---|
| 3201 | poly z, n_z, next; |
---|
| 3202 | z = &sz; |
---|
| 3203 | n_z = NULL; |
---|
| 3204 | |
---|
| 3205 | while(p != NULL) |
---|
| 3206 | { |
---|
| 3207 | next = pNext(p); |
---|
| 3208 | if (p_GetExp(p, n,r) == 0) |
---|
| 3209 | { |
---|
| 3210 | pNext(z) = p; |
---|
| 3211 | pIter(z); |
---|
| 3212 | } |
---|
| 3213 | else |
---|
| 3214 | { |
---|
| 3215 | pNext(p) = n_z; |
---|
| 3216 | n_z = p; |
---|
| 3217 | } |
---|
| 3218 | p = next; |
---|
| 3219 | } |
---|
| 3220 | pNext(z) = NULL; |
---|
| 3221 | *zero = pNext(&sz); |
---|
| 3222 | *non_zero = n_z; |
---|
| 3223 | } |
---|
| 3224 | /*3 |
---|
| 3225 | * substitute the n-th variable by 1 in p |
---|
| 3226 | * destroy p |
---|
| 3227 | */ |
---|
| 3228 | static poly p_Subst1 (poly p,int n, const ring r) |
---|
| 3229 | { |
---|
| 3230 | poly qq=NULL, result = NULL; |
---|
| 3231 | poly zero=NULL, non_zero=NULL; |
---|
| 3232 | |
---|
| 3233 | // reverse, so that add is likely to be linear |
---|
| 3234 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
| 3235 | |
---|
| 3236 | while (non_zero != NULL) |
---|
| 3237 | { |
---|
| 3238 | assume(p_GetExp(non_zero, n,r) != 0); |
---|
| 3239 | qq = non_zero; |
---|
| 3240 | pIter(non_zero); |
---|
| 3241 | qq->next = NULL; |
---|
| 3242 | p_SetExp(qq,n,0,r); |
---|
| 3243 | p_Setm(qq,r); |
---|
| 3244 | result = p_Add_q(result,qq,r); |
---|
| 3245 | } |
---|
| 3246 | p = p_Add_q(result, zero,r); |
---|
| 3247 | p_Test(p,r); |
---|
| 3248 | return p; |
---|
| 3249 | } |
---|
| 3250 | |
---|
| 3251 | /*3 |
---|
| 3252 | * substitute the n-th variable by number e in p |
---|
| 3253 | * destroy p |
---|
| 3254 | */ |
---|
| 3255 | static poly p_Subst2 (poly p,int n, number e, const ring r) |
---|
| 3256 | { |
---|
| 3257 | assume( ! n_IsZero(e,r->cf) ); |
---|
| 3258 | poly qq,result = NULL; |
---|
| 3259 | number nn, nm; |
---|
| 3260 | poly zero, non_zero; |
---|
| 3261 | |
---|
| 3262 | // reverse, so that add is likely to be linear |
---|
| 3263 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
| 3264 | |
---|
| 3265 | while (non_zero != NULL) |
---|
| 3266 | { |
---|
[45d2332] | 3267 | assume(p_GetExp(non_zero, n, r) != 0); |
---|
[71ba5b8] | 3268 | qq = non_zero; |
---|
| 3269 | pIter(non_zero); |
---|
| 3270 | qq->next = NULL; |
---|
| 3271 | n_Power(e, p_GetExp(qq, n, r), &nn,r->cf); |
---|
| 3272 | nm = n_Mult(nn, pGetCoeff(qq),r->cf); |
---|
| 3273 | #ifdef HAVE_RINGS |
---|
| 3274 | if (n_IsZero(nm,r->cf)) |
---|
| 3275 | { |
---|
| 3276 | p_LmFree(&qq,r); |
---|
| 3277 | n_Delete(&nm,r->cf); |
---|
| 3278 | } |
---|
| 3279 | else |
---|
| 3280 | #endif |
---|
| 3281 | { |
---|
| 3282 | p_SetCoeff(qq, nm,r); |
---|
| 3283 | p_SetExp(qq, n, 0,r); |
---|
| 3284 | p_Setm(qq,r); |
---|
| 3285 | result = p_Add_q(result,qq,r); |
---|
| 3286 | } |
---|
| 3287 | n_Delete(&nn,r->cf); |
---|
| 3288 | } |
---|
| 3289 | p = p_Add_q(result, zero,r); |
---|
| 3290 | p_Test(p,r); |
---|
| 3291 | return p; |
---|
| 3292 | } |
---|
| 3293 | |
---|
| 3294 | |
---|
| 3295 | /* delete monoms whose n-th exponent is different from zero */ |
---|
| 3296 | static poly p_Subst0(poly p, int n, const ring r) |
---|
| 3297 | { |
---|
| 3298 | spolyrec res; |
---|
| 3299 | poly h = &res; |
---|
| 3300 | pNext(h) = p; |
---|
| 3301 | |
---|
| 3302 | while (pNext(h)!=NULL) |
---|
| 3303 | { |
---|
| 3304 | if (p_GetExp(pNext(h),n,r)!=0) |
---|
| 3305 | { |
---|
| 3306 | p_LmDelete(&pNext(h),r); |
---|
| 3307 | } |
---|
| 3308 | else |
---|
| 3309 | { |
---|
| 3310 | pIter(h); |
---|
| 3311 | } |
---|
| 3312 | } |
---|
| 3313 | p_Test(pNext(&res),r); |
---|
| 3314 | return pNext(&res); |
---|
| 3315 | } |
---|
| 3316 | |
---|
| 3317 | /*2 |
---|
| 3318 | * substitute the n-th variable by e in p |
---|
| 3319 | * destroy p |
---|
| 3320 | */ |
---|
| 3321 | poly p_Subst(poly p, int n, poly e, const ring r) |
---|
| 3322 | { |
---|
| 3323 | if (e == NULL) return p_Subst0(p, n,r); |
---|
| 3324 | |
---|
| 3325 | if (p_IsConstant(e,r)) |
---|
| 3326 | { |
---|
| 3327 | if (n_IsOne(pGetCoeff(e),r->cf)) return p_Subst1(p,n,r); |
---|
| 3328 | else return p_Subst2(p, n, pGetCoeff(e),r); |
---|
| 3329 | } |
---|
| 3330 | |
---|
| 3331 | #ifdef HAVE_PLURAL |
---|
| 3332 | if (rIsPluralRing(r)) |
---|
| 3333 | { |
---|
| 3334 | return nc_pSubst(p,n,e,r); |
---|
| 3335 | } |
---|
| 3336 | #endif |
---|
| 3337 | |
---|
| 3338 | int exponent,i; |
---|
| 3339 | poly h, res, m; |
---|
| 3340 | int *me,*ee; |
---|
| 3341 | number nu,nu1; |
---|
| 3342 | |
---|
| 3343 | me=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
| 3344 | ee=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
| 3345 | if (e!=NULL) p_GetExpV(e,ee,r); |
---|
| 3346 | res=NULL; |
---|
| 3347 | h=p; |
---|
| 3348 | while (h!=NULL) |
---|
| 3349 | { |
---|
| 3350 | if ((e!=NULL) || (p_GetExp(h,n,r)==0)) |
---|
| 3351 | { |
---|
| 3352 | m=p_Head(h,r); |
---|
| 3353 | p_GetExpV(m,me,r); |
---|
| 3354 | exponent=me[n]; |
---|
| 3355 | me[n]=0; |
---|
| 3356 | for(i=rVar(r);i>0;i--) |
---|
| 3357 | me[i]+=exponent*ee[i]; |
---|
| 3358 | p_SetExpV(m,me,r); |
---|
| 3359 | if (e!=NULL) |
---|
| 3360 | { |
---|
| 3361 | n_Power(pGetCoeff(e),exponent,&nu,r->cf); |
---|
| 3362 | nu1=n_Mult(pGetCoeff(m),nu,r->cf); |
---|
| 3363 | n_Delete(&nu,r->cf); |
---|
| 3364 | p_SetCoeff(m,nu1,r); |
---|
| 3365 | } |
---|
| 3366 | res=p_Add_q(res,m,r); |
---|
| 3367 | } |
---|
| 3368 | p_LmDelete(&h,r); |
---|
| 3369 | } |
---|
| 3370 | omFreeSize((ADDRESS)me,(rVar(r)+1)*sizeof(int)); |
---|
| 3371 | omFreeSize((ADDRESS)ee,(rVar(r)+1)*sizeof(int)); |
---|
| 3372 | return res; |
---|
| 3373 | } |
---|
[deca086] | 3374 | /*2 |
---|
| 3375 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
| 3376 | */ |
---|
| 3377 | poly p_PermPoly (poly p, int * perm, const ring oldRing, const ring dst, |
---|
| 3378 | nMapFunc nMap, int *par_perm, int OldPar) |
---|
| 3379 | { |
---|
| 3380 | int OldpVariables = oldRing->N; |
---|
| 3381 | poly result = NULL; |
---|
| 3382 | poly result_last = NULL; |
---|
| 3383 | poly aq=NULL; /* the map coefficient */ |
---|
| 3384 | poly qq; /* the mapped monomial */ |
---|
| 3385 | |
---|
| 3386 | while (p != NULL) |
---|
| 3387 | { |
---|
| 3388 | if ((OldPar==0)||(rField_is_GF(oldRing))) |
---|
| 3389 | { |
---|
| 3390 | qq = p_Init(dst); |
---|
[4581a96] | 3391 | number n=nMap(pGetCoeff(p),oldRing->cf,dst->cf); |
---|
[4c6e420] | 3392 | if ((!rMinpolyIsNULL(dst)) |
---|
[deca086] | 3393 | && ((rField_is_Zp_a(dst)) || (rField_is_Q_a(dst)))) |
---|
| 3394 | { |
---|
| 3395 | n_Normalize(n,dst->cf); |
---|
| 3396 | } |
---|
| 3397 | pGetCoeff(qq)=n; |
---|
| 3398 | // coef may be zero: pTest(qq); |
---|
| 3399 | } |
---|
| 3400 | else |
---|
| 3401 | { |
---|
| 3402 | qq=p_One(dst); |
---|
[fd01a8] | 3403 | WerrorS("longalg missing 2"); |
---|
[4581a96] | 3404 | #if 0 |
---|
[deca086] | 3405 | aq=naPermNumber(pGetCoeff(p),par_perm,OldPar, oldRing); |
---|
[4c6e420] | 3406 | if ((!rMinpolyIsNULL(dst)) |
---|
[deca086] | 3407 | && ((rField_is_Zp_a(dst)) || (rField_is_Q_a(dst)))) |
---|
| 3408 | { |
---|
[df43d9] | 3409 | p_Normalize(aq,dst); |
---|
| 3410 | if (aq==NULL) |
---|
| 3411 | p_SetCoeff(qq,n_Init(0,dst->cf),dst); |
---|
[deca086] | 3412 | } |
---|
[7eb7b5] | 3413 | p_Test(aq,dst); |
---|
[4581a96] | 3414 | #endif |
---|
[deca086] | 3415 | } |
---|
| 3416 | if (rRing_has_Comp(dst)) p_SetComp(qq, p_GetComp(p,oldRing),dst); |
---|
| 3417 | if (n_IsZero(pGetCoeff(qq),dst->cf)) |
---|
| 3418 | { |
---|
| 3419 | p_LmDelete(&qq,dst); |
---|
| 3420 | } |
---|
| 3421 | else |
---|
| 3422 | { |
---|
| 3423 | int i; |
---|
| 3424 | int mapped_to_par=0; |
---|
| 3425 | for(i=1; i<=OldpVariables; i++) |
---|
| 3426 | { |
---|
| 3427 | int e=p_GetExp(p,i,oldRing); |
---|
| 3428 | if (e!=0) |
---|
| 3429 | { |
---|
| 3430 | if (perm==NULL) |
---|
| 3431 | { |
---|
| 3432 | p_SetExp(qq,i, e, dst); |
---|
| 3433 | } |
---|
| 3434 | else if (perm[i]>0) |
---|
| 3435 | p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, dst); |
---|
| 3436 | else if (perm[i]<0) |
---|
| 3437 | { |
---|
| 3438 | if (rField_is_GF(dst)) |
---|
| 3439 | { |
---|
| 3440 | number c=pGetCoeff(qq); |
---|
[0afa07] | 3441 | number ee=(number)rGetVar(1, dst->cf->extRing); |
---|
[1389a4] | 3442 | number eee;n_Power(ee,e,&eee,dst->cf); //nfDelete(ee,dst); |
---|
| 3443 | ee=n_Mult(c,eee,dst->cf); |
---|
[8a8c9e] | 3444 | //nfDelete(c,dst);nfDelete(eee,dst); |
---|
[deca086] | 3445 | pSetCoeff0(qq,ee); |
---|
| 3446 | } |
---|
| 3447 | else |
---|
| 3448 | { |
---|
[fd01a8] | 3449 | WerrorS("longalg missing 3"); |
---|
[71ba5b8] | 3450 | #if 0 |
---|
[deca086] | 3451 | lnumber c=(lnumber)pGetCoeff(qq); |
---|
| 3452 | if (c->z->next==NULL) |
---|
[6ccdd3a] | 3453 | p_AddExp(c->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/,dst->extRing); |
---|
[deca086] | 3454 | else /* more difficult: we have really to multiply: */ |
---|
| 3455 | { |
---|
[8a8c9e] | 3456 | lnumber mmc=(lnumber)naInit(1,dst); |
---|
[6ccdd3a] | 3457 | p_SetExp(mmc->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/,dst->extRing); |
---|
| 3458 | p_Setm(mmc->z,dst->extRing->cf); |
---|
[1389a4] | 3459 | pGetCoeff(qq)=n_Mult((number)c,(number)mmc,dst->cf); |
---|
[deca086] | 3460 | n_Delete((number *)&c,dst->cf); |
---|
[71ba5b8] | 3461 | n_Delete((number *)&mmc,dst->cf); |
---|
[deca086] | 3462 | } |
---|
| 3463 | mapped_to_par=1; |
---|
[71ba5b8] | 3464 | #endif |
---|
[deca086] | 3465 | } |
---|
| 3466 | } |
---|
| 3467 | else |
---|
| 3468 | { |
---|
| 3469 | /* this variable maps to 0 !*/ |
---|
| 3470 | p_LmDelete(&qq,dst); |
---|
| 3471 | break; |
---|
| 3472 | } |
---|
| 3473 | } |
---|
| 3474 | } |
---|
| 3475 | if (mapped_to_par |
---|
[4c6e420] | 3476 | && (!rMinpolyIsNULL(dst))) |
---|
[deca086] | 3477 | { |
---|
| 3478 | number n=pGetCoeff(qq); |
---|
| 3479 | n_Normalize(n,dst->cf); |
---|
| 3480 | pGetCoeff(qq)=n; |
---|
| 3481 | } |
---|
| 3482 | } |
---|
| 3483 | pIter(p); |
---|
| 3484 | #if 1 |
---|
| 3485 | if (qq!=NULL) |
---|
| 3486 | { |
---|
| 3487 | p_Setm(qq,dst); |
---|
| 3488 | p_Test(aq,dst); |
---|
| 3489 | p_Test(qq,dst); |
---|
[5679049] | 3490 | if (aq!=NULL) qq=p_Mult_q(aq,qq,dst); |
---|
[deca086] | 3491 | aq = qq; |
---|
| 3492 | while (pNext(aq) != NULL) pIter(aq); |
---|
| 3493 | if (result_last==NULL) |
---|
| 3494 | { |
---|
| 3495 | result=qq; |
---|
| 3496 | } |
---|
| 3497 | else |
---|
| 3498 | { |
---|
| 3499 | pNext(result_last)=qq; |
---|
| 3500 | } |
---|
| 3501 | result_last=aq; |
---|
| 3502 | aq = NULL; |
---|
| 3503 | } |
---|
| 3504 | else if (aq!=NULL) |
---|
| 3505 | { |
---|
| 3506 | p_Delete(&aq,dst); |
---|
| 3507 | } |
---|
| 3508 | } |
---|
| 3509 | result=p_SortAdd(result,dst); |
---|
| 3510 | #else |
---|
| 3511 | // if (qq!=NULL) |
---|
| 3512 | // { |
---|
| 3513 | // pSetm(qq); |
---|
| 3514 | // pTest(qq); |
---|
| 3515 | // pTest(aq); |
---|
| 3516 | // if (aq!=NULL) qq=pMult(aq,qq); |
---|
| 3517 | // aq = qq; |
---|
| 3518 | // while (pNext(aq) != NULL) pIter(aq); |
---|
| 3519 | // pNext(aq) = result; |
---|
| 3520 | // aq = NULL; |
---|
| 3521 | // result = qq; |
---|
| 3522 | // } |
---|
| 3523 | // else if (aq!=NULL) |
---|
| 3524 | // { |
---|
| 3525 | // pDelete(&aq); |
---|
| 3526 | // } |
---|
| 3527 | //} |
---|
| 3528 | //p = result; |
---|
| 3529 | //result = NULL; |
---|
| 3530 | //while (p != NULL) |
---|
| 3531 | //{ |
---|
| 3532 | // qq = p; |
---|
| 3533 | // pIter(p); |
---|
| 3534 | // qq->next = NULL; |
---|
| 3535 | // result = pAdd(result, qq); |
---|
| 3536 | //} |
---|
| 3537 | #endif |
---|
| 3538 | p_Test(result,dst); |
---|
| 3539 | return result; |
---|
| 3540 | } |
---|
[f550e86] | 3541 | /************************************************************** |
---|
| 3542 | * |
---|
| 3543 | * Jet |
---|
| 3544 | * |
---|
| 3545 | **************************************************************/ |
---|
| 3546 | |
---|
| 3547 | poly pp_Jet(poly p, int m, const ring R) |
---|
| 3548 | { |
---|
| 3549 | poly r=NULL; |
---|
| 3550 | poly t=NULL; |
---|
| 3551 | |
---|
| 3552 | while (p!=NULL) |
---|
| 3553 | { |
---|
| 3554 | if (p_Totaldegree(p,R)<=m) |
---|
| 3555 | { |
---|
| 3556 | if (r==NULL) |
---|
| 3557 | r=p_Head(p,R); |
---|
| 3558 | else |
---|
| 3559 | if (t==NULL) |
---|
| 3560 | { |
---|
| 3561 | pNext(r)=p_Head(p,R); |
---|
| 3562 | t=pNext(r); |
---|
| 3563 | } |
---|
| 3564 | else |
---|
| 3565 | { |
---|
| 3566 | pNext(t)=p_Head(p,R); |
---|
| 3567 | pIter(t); |
---|
| 3568 | } |
---|
| 3569 | } |
---|
| 3570 | pIter(p); |
---|
| 3571 | } |
---|
| 3572 | return r; |
---|
| 3573 | } |
---|
| 3574 | |
---|
| 3575 | poly p_Jet(poly p, int m,const ring R) |
---|
| 3576 | { |
---|
| 3577 | poly t=NULL; |
---|
| 3578 | |
---|
| 3579 | while((p!=NULL) && (p_Totaldegree(p,R)>m)) p_LmDelete(&p,R); |
---|
| 3580 | if (p==NULL) return NULL; |
---|
| 3581 | poly r=p; |
---|
| 3582 | while (pNext(p)!=NULL) |
---|
| 3583 | { |
---|
| 3584 | if (p_Totaldegree(pNext(p),R)>m) |
---|
| 3585 | { |
---|
| 3586 | p_LmDelete(&pNext(p),R); |
---|
| 3587 | } |
---|
| 3588 | else |
---|
| 3589 | pIter(p); |
---|
| 3590 | } |
---|
| 3591 | return r; |
---|
| 3592 | } |
---|
| 3593 | |
---|
| 3594 | poly pp_JetW(poly p, int m, short *w, const ring R) |
---|
| 3595 | { |
---|
| 3596 | poly r=NULL; |
---|
| 3597 | poly t=NULL; |
---|
| 3598 | while (p!=NULL) |
---|
| 3599 | { |
---|
| 3600 | if (totaldegreeWecart_IV(p,R,w)<=m) |
---|
| 3601 | { |
---|
| 3602 | if (r==NULL) |
---|
| 3603 | r=p_Head(p,R); |
---|
| 3604 | else |
---|
| 3605 | if (t==NULL) |
---|
| 3606 | { |
---|
| 3607 | pNext(r)=p_Head(p,R); |
---|
| 3608 | t=pNext(r); |
---|
| 3609 | } |
---|
| 3610 | else |
---|
| 3611 | { |
---|
| 3612 | pNext(t)=p_Head(p,R); |
---|
| 3613 | pIter(t); |
---|
| 3614 | } |
---|
| 3615 | } |
---|
| 3616 | pIter(p); |
---|
| 3617 | } |
---|
| 3618 | return r; |
---|
| 3619 | } |
---|
| 3620 | |
---|
| 3621 | poly p_JetW(poly p, int m, short *w, const ring R) |
---|
| 3622 | { |
---|
| 3623 | while((p!=NULL) && (totaldegreeWecart_IV(p,R,w)>m)) p_LmDelete(&p,R); |
---|
| 3624 | if (p==NULL) return NULL; |
---|
| 3625 | poly r=p; |
---|
| 3626 | while (pNext(p)!=NULL) |
---|
| 3627 | { |
---|
| 3628 | if (totaldegreeWecart_IV(pNext(p),R,w)>m) |
---|
| 3629 | { |
---|
| 3630 | p_LmDelete(&pNext(p),R); |
---|
| 3631 | } |
---|
| 3632 | else |
---|
| 3633 | pIter(p); |
---|
| 3634 | } |
---|
| 3635 | return r; |
---|
| 3636 | } |
---|
[5c39a9] | 3637 | |
---|
[ba0fc3] | 3638 | /*************************************************************/ |
---|
| 3639 | int p_MinDeg(poly p,intvec *w, const ring R) |
---|
| 3640 | { |
---|
| 3641 | if(p==NULL) |
---|
| 3642 | return -1; |
---|
| 3643 | int d=-1; |
---|
| 3644 | while(p!=NULL) |
---|
| 3645 | { |
---|
| 3646 | int d0=0; |
---|
| 3647 | for(int j=0;j<rVar(R);j++) |
---|
| 3648 | if(w==NULL||j>=w->length()) |
---|
| 3649 | d0+=p_GetExp(p,j+1,R); |
---|
| 3650 | else |
---|
| 3651 | d0+=(*w)[j]*p_GetExp(p,j+1,R); |
---|
| 3652 | if(d0<d||d==-1) |
---|
| 3653 | d=d0; |
---|
| 3654 | pIter(p); |
---|
| 3655 | } |
---|
| 3656 | return d; |
---|
| 3657 | } |
---|
| 3658 | |
---|
[a4081e5] | 3659 | /***************************************************************/ |
---|
| 3660 | |
---|
| 3661 | poly p_Series(int n,poly p,poly u, intvec *w, const ring R) |
---|
| 3662 | { |
---|
| 3663 | short *ww=iv2array(w,R); |
---|
| 3664 | if(p!=NULL) |
---|
| 3665 | { |
---|
| 3666 | if(u==NULL) |
---|
| 3667 | p=p_JetW(p,n,ww,R); |
---|
| 3668 | else |
---|
| 3669 | p=p_JetW(p_Mult_q(p,p_Invers(n-p_MinDeg(p,w,R),u,w,R),R),n,ww,R); |
---|
| 3670 | } |
---|
| 3671 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3672 | return p; |
---|
| 3673 | } |
---|
| 3674 | |
---|
| 3675 | poly p_Invers(int n,poly u,intvec *w, const ring R) |
---|
| 3676 | { |
---|
| 3677 | if(n<0) |
---|
| 3678 | return NULL; |
---|
| 3679 | number u0=n_Invers(pGetCoeff(u),R->cf); |
---|
| 3680 | poly v=p_NSet(u0,R); |
---|
| 3681 | if(n==0) |
---|
| 3682 | return v; |
---|
| 3683 | short *ww=iv2array(w,R); |
---|
| 3684 | poly u1=p_JetW(p_Sub(p_One(R),p_Mult_nn(u,u0,R),R),n,ww,R); |
---|
| 3685 | if(u1==NULL) |
---|
| 3686 | { |
---|
| 3687 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3688 | return v; |
---|
| 3689 | } |
---|
| 3690 | poly v1=p_Mult_nn(p_Copy(u1,R),u0,R); |
---|
| 3691 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
| 3692 | for(int i=n/p_MinDeg(u1,w,R);i>1;i--) |
---|
| 3693 | { |
---|
| 3694 | v1=p_JetW(p_Mult_q(v1,p_Copy(u1,R),R),n,ww,R); |
---|
| 3695 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
| 3696 | } |
---|
| 3697 | p_Delete(&u1,R); |
---|
| 3698 | p_Delete(&v1,R); |
---|
| 3699 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
| 3700 | return v; |
---|
| 3701 | } |
---|
| 3702 | |
---|
[7dce2d7] | 3703 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r) |
---|
| 3704 | { |
---|
| 3705 | while ((p1 != NULL) && (p2 != NULL)) |
---|
| 3706 | { |
---|
| 3707 | if (! p_LmEqual(p1, p2,r)) |
---|
| 3708 | return FALSE; |
---|
| 3709 | if (! n_Equal(p_GetCoeff(p1,r), p_GetCoeff(p2,r),r )) |
---|
| 3710 | return FALSE; |
---|
| 3711 | pIter(p1); |
---|
| 3712 | pIter(p2); |
---|
| 3713 | } |
---|
| 3714 | return (p1==p2); |
---|
| 3715 | } |
---|
[32d07a5] | 3716 | |
---|
| 3717 | /*2 |
---|
| 3718 | *returns TRUE if p1 is a skalar multiple of p2 |
---|
| 3719 | *assume p1 != NULL and p2 != NULL |
---|
| 3720 | */ |
---|
| 3721 | BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r) |
---|
| 3722 | { |
---|
| 3723 | number n,nn; |
---|
| 3724 | pAssume(p1 != NULL && p2 != NULL); |
---|
| 3725 | |
---|
| 3726 | if (!p_LmEqual(p1,p2,r)) //compare leading mons |
---|
| 3727 | return FALSE; |
---|
| 3728 | if ((pNext(p1)==NULL) && (pNext(p2)!=NULL)) |
---|
| 3729 | return FALSE; |
---|
| 3730 | if ((pNext(p2)==NULL) && (pNext(p1)!=NULL)) |
---|
| 3731 | return FALSE; |
---|
| 3732 | if (pLength(p1) != pLength(p2)) |
---|
| 3733 | return FALSE; |
---|
| 3734 | #ifdef HAVE_RINGS |
---|
| 3735 | if (rField_is_Ring(r)) |
---|
| 3736 | { |
---|
| 3737 | if (!n_DivBy(p_GetCoeff(p1, r), p_GetCoeff(p2, r), r)) return FALSE; |
---|
| 3738 | } |
---|
| 3739 | #endif |
---|
| 3740 | n=n_Div(p_GetCoeff(p1,r),p_GetCoeff(p2,r),r); |
---|
| 3741 | while ((p1 != NULL) /*&& (p2 != NULL)*/) |
---|
| 3742 | { |
---|
| 3743 | if ( ! p_LmEqual(p1, p2,r)) |
---|
| 3744 | { |
---|
| 3745 | n_Delete(&n, r); |
---|
| 3746 | return FALSE; |
---|
| 3747 | } |
---|
| 3748 | if (!n_Equal(p_GetCoeff(p1, r), nn = n_Mult(p_GetCoeff(p2, r),n, r), r)) |
---|
| 3749 | { |
---|
| 3750 | n_Delete(&n, r); |
---|
| 3751 | n_Delete(&nn, r); |
---|
| 3752 | return FALSE; |
---|
| 3753 | } |
---|
| 3754 | n_Delete(&nn, r); |
---|
| 3755 | pIter(p1); |
---|
| 3756 | pIter(p2); |
---|
| 3757 | } |
---|
| 3758 | n_Delete(&n, r); |
---|
| 3759 | return TRUE; |
---|
| 3760 | } |
---|
| 3761 | |
---|
| 3762 | |
---|
[50c414] | 3763 | /*************************************************************** |
---|
| 3764 | * |
---|
| 3765 | * p_ShallowDelete |
---|
| 3766 | * |
---|
| 3767 | ***************************************************************/ |
---|
| 3768 | #undef LINKAGE |
---|
| 3769 | #define LINKAGE |
---|
[38500a] | 3770 | #undef p_Delete__T |
---|
| 3771 | #define p_Delete__T p_ShallowDelete |
---|
[35eaf8] | 3772 | #undef n_Delete__T |
---|
| 3773 | #define n_Delete__T(n, r) ((void)0) |
---|
[50c414] | 3774 | |
---|
[20b794] | 3775 | #include <polys/templates/p_Delete__T.cc> |
---|
[50c414] | 3776 | |
---|
[71ba5b8] | 3777 | #ifdef HAVE_RINGS |
---|
| 3778 | /* TRUE iff LT(f) | LT(g) */ |
---|
| 3779 | BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r) |
---|
| 3780 | { |
---|
| 3781 | int exponent; |
---|
| 3782 | for(int i = (int)r->N; i; i--) |
---|
| 3783 | { |
---|
| 3784 | exponent = p_GetExp(g, i, r) - p_GetExp(f, i, r); |
---|
| 3785 | if (exponent < 0) return FALSE; |
---|
| 3786 | } |
---|
| 3787 | return n_DivBy(p_GetCoeff(g,r), p_GetCoeff(f,r),r->cf); |
---|
| 3788 | } |
---|
| 3789 | #endif |
---|