[ab547e2] | 1 | /*****************************************************************************\ |
---|
| 2 | * Computer Algebra System SINGULAR |
---|
| 3 | \*****************************************************************************/ |
---|
| 4 | /** @file facFqFactorize.cc |
---|
| 5 | * |
---|
| 6 | * multivariate factorization over Q(a) |
---|
| 7 | * |
---|
| 8 | * @author Martin Lee |
---|
| 9 | * |
---|
| 10 | **/ |
---|
| 11 | /*****************************************************************************/ |
---|
| 12 | |
---|
[e4fe2b] | 13 | #include "config.h" |
---|
[ab547e2] | 14 | |
---|
| 15 | #include "assert.h" |
---|
| 16 | #include "debug.h" |
---|
| 17 | #include "timing.h" |
---|
| 18 | |
---|
[d990001] | 19 | #include "cf_algorithm.h" |
---|
[ab547e2] | 20 | #include "facFqFactorizeUtil.h" |
---|
| 21 | #include "facFactorize.h" |
---|
| 22 | #include "facFqFactorize.h" |
---|
| 23 | #include "cf_random.h" |
---|
| 24 | #include "facHensel.h" |
---|
| 25 | #include "cf_gcd_smallp.h" |
---|
| 26 | #include "cf_map_ext.h" |
---|
| 27 | #include "algext.h" |
---|
| 28 | #include "cf_reval.h" |
---|
[91788c0] | 29 | #include "facSparseHensel.h" |
---|
[ab547e2] | 30 | |
---|
[ec664a2] | 31 | TIMING_DEFINE_PRINT(fac_bi_factorize) |
---|
| 32 | TIMING_DEFINE_PRINT(fac_hensel_lift) |
---|
| 33 | TIMING_DEFINE_PRINT(fac_factor_recombination) |
---|
[0b618a7] | 34 | |
---|
[d990001] | 35 | #ifdef HAVE_NTL |
---|
[ab547e2] | 36 | CFList evalPoints (const CanonicalForm& F, CFList& eval, Evaluation& E) |
---|
| 37 | { |
---|
| 38 | CFList result; |
---|
| 39 | Variable x= Variable (1); |
---|
| 40 | |
---|
| 41 | bool found= false; |
---|
[c8fff0] | 42 | bool allZero= true; |
---|
| 43 | bool foundZero= false; |
---|
[ab547e2] | 44 | CanonicalForm deriv_x, gcd_deriv; |
---|
[38ffb7] | 45 | CFListIterator iter; |
---|
[ab547e2] | 46 | do |
---|
| 47 | { |
---|
| 48 | eval.insert (F); |
---|
| 49 | bool bad= false; |
---|
| 50 | for (int i= E.max(); i >= E.min(); i--) |
---|
| 51 | { |
---|
| 52 | eval.insert (eval.getFirst()( E [i], i)); |
---|
| 53 | result.append (E[i]); |
---|
[c8fff0] | 54 | if (!E[i].isZero()) |
---|
| 55 | allZero= false; |
---|
| 56 | else |
---|
| 57 | foundZero= true; |
---|
| 58 | if (!allZero && foundZero) |
---|
| 59 | { |
---|
| 60 | result= CFList(); |
---|
| 61 | eval= CFList(); |
---|
| 62 | bad= true; |
---|
| 63 | foundZero= false; |
---|
| 64 | break; |
---|
| 65 | } |
---|
[ab547e2] | 66 | if (degree (eval.getFirst(), i - 1) != degree (F, i - 1)) |
---|
| 67 | { |
---|
| 68 | result= CFList(); |
---|
| 69 | eval= CFList(); |
---|
| 70 | bad= true; |
---|
| 71 | break; |
---|
| 72 | } |
---|
| 73 | } |
---|
| 74 | |
---|
| 75 | if (bad) |
---|
| 76 | { |
---|
| 77 | E.nextpoint(); |
---|
| 78 | continue; |
---|
| 79 | } |
---|
| 80 | |
---|
| 81 | if (degree (eval.getFirst()) != degree (F, 1)) |
---|
| 82 | { |
---|
| 83 | result= CFList(); |
---|
| 84 | eval= CFList(); |
---|
| 85 | E.nextpoint(); |
---|
| 86 | continue; |
---|
| 87 | } |
---|
| 88 | |
---|
| 89 | deriv_x= deriv (eval.getFirst(), x); |
---|
| 90 | gcd_deriv= gcd (eval.getFirst(), deriv_x); |
---|
| 91 | if (degree (gcd_deriv) > 0) |
---|
| 92 | { |
---|
| 93 | result= CFList(); |
---|
| 94 | eval= CFList(); |
---|
| 95 | E.nextpoint(); |
---|
| 96 | continue; |
---|
| 97 | } |
---|
[38ffb7] | 98 | iter= eval; |
---|
| 99 | iter++; |
---|
| 100 | CanonicalForm contentx= content (iter.getItem(), x); |
---|
[ab547e2] | 101 | if (degree (contentx) > 0) |
---|
| 102 | { |
---|
| 103 | result= CFList(); |
---|
| 104 | eval= CFList(); |
---|
| 105 | E.nextpoint(); |
---|
| 106 | continue; |
---|
| 107 | } |
---|
| 108 | found= true; |
---|
| 109 | } |
---|
| 110 | while (!found); |
---|
| 111 | |
---|
| 112 | if (!eval.isEmpty()) |
---|
| 113 | eval.removeFirst(); |
---|
| 114 | return result; |
---|
| 115 | } |
---|
| 116 | |
---|
| 117 | void |
---|
| 118 | factorizationWRTDifferentSecondVars (const CanonicalForm& A, CFList*& Aeval, |
---|
| 119 | int& minFactorsLength, bool& irred, |
---|
| 120 | const Variable& w) |
---|
| 121 | { |
---|
| 122 | Variable x= Variable (1); |
---|
| 123 | minFactorsLength= 0; |
---|
| 124 | irred= false; |
---|
[38ffb7] | 125 | Variable v; |
---|
| 126 | CFList factors; |
---|
[afb6a6] | 127 | CanonicalForm LCA= LC (A,1); |
---|
| 128 | if (!LCA.inCoeffDomain()) |
---|
[ab547e2] | 129 | { |
---|
[afb6a6] | 130 | for (int j= 0; j < A.level() - 2; j++) |
---|
[ab547e2] | 131 | { |
---|
[afb6a6] | 132 | if (!Aeval[j].isEmpty() && (degree (LCA, j+3) > 0)) |
---|
| 133 | { |
---|
| 134 | v= Variable (Aeval[j].getFirst().level()); |
---|
[ab547e2] | 135 | |
---|
[afb6a6] | 136 | factors= ratBiSqrfFactorize (Aeval[j].getFirst(), w); |
---|
[ab547e2] | 137 | |
---|
[afb6a6] | 138 | if (factors.getFirst().inCoeffDomain()) |
---|
| 139 | factors.removeFirst(); |
---|
[ab547e2] | 140 | |
---|
[afb6a6] | 141 | if (minFactorsLength == 0) |
---|
| 142 | minFactorsLength= factors.length(); |
---|
| 143 | else |
---|
| 144 | minFactorsLength= tmin (minFactorsLength, factors.length()); |
---|
[ab547e2] | 145 | |
---|
[afb6a6] | 146 | if (factors.length() == 1) |
---|
| 147 | { |
---|
| 148 | irred= true; |
---|
| 149 | return; |
---|
| 150 | } |
---|
| 151 | sortList (factors, x); |
---|
| 152 | Aeval [j]= factors; |
---|
| 153 | } |
---|
| 154 | else if (!Aeval[j].isEmpty()) |
---|
[ab547e2] | 155 | { |
---|
[afb6a6] | 156 | Aeval[j]=CFList(); |
---|
[ab547e2] | 157 | } |
---|
| 158 | } |
---|
| 159 | } |
---|
[afb6a6] | 160 | else |
---|
| 161 | { |
---|
| 162 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 163 | Aeval[j]= CFList(); |
---|
| 164 | } |
---|
[ab547e2] | 165 | } |
---|
| 166 | |
---|
| 167 | int |
---|
| 168 | testFactors (const CanonicalForm& G, const CFList& uniFactors, |
---|
| 169 | CanonicalForm& sqrfPartF, CFList& factors, |
---|
[eefc3a] | 170 | CFFList*& bufSqrfFactors, CFList& evalSqrfPartF, |
---|
| 171 | const CFArray& evalPoint) |
---|
[ab547e2] | 172 | { |
---|
[38ffb7] | 173 | CanonicalForm tmp; |
---|
| 174 | CFListIterator j; |
---|
[ab547e2] | 175 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
---|
| 176 | { |
---|
[38ffb7] | 177 | tmp= i.getItem(); |
---|
[ab547e2] | 178 | if (i.hasItem()) |
---|
| 179 | i++; |
---|
| 180 | else |
---|
| 181 | break; |
---|
[38ffb7] | 182 | for (j= i; j.hasItem(); j++) |
---|
[ab547e2] | 183 | { |
---|
| 184 | if (tmp == j.getItem()) |
---|
| 185 | return 0; |
---|
| 186 | } |
---|
| 187 | } |
---|
| 188 | |
---|
| 189 | CanonicalForm F= G; |
---|
| 190 | CFFList sqrfFactorization= sqrFree (F); |
---|
| 191 | |
---|
| 192 | sqrfPartF= 1; |
---|
| 193 | for (CFFListIterator i= sqrfFactorization; i.hasItem(); i++) |
---|
| 194 | sqrfPartF *= i.getItem().factor(); |
---|
| 195 | |
---|
[eefc3a] | 196 | evalSqrfPartF= evaluateAtEval (sqrfPartF, evalPoint); |
---|
[ab547e2] | 197 | |
---|
[eefc3a] | 198 | CanonicalForm test= evalSqrfPartF.getFirst() (evalPoint[0], 2); |
---|
[ab547e2] | 199 | |
---|
[9dacf3f] | 200 | if (degree (test) != degree (sqrfPartF, 1) || test.inCoeffDomain()) |
---|
[ab547e2] | 201 | return 0; |
---|
| 202 | |
---|
| 203 | CFFList sqrfFactors; |
---|
| 204 | CFList tmp2; |
---|
| 205 | int k= 0; |
---|
| 206 | factors= uniFactors; |
---|
[38ffb7] | 207 | CFFListIterator iter; |
---|
[ab547e2] | 208 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
| 209 | { |
---|
[38ffb7] | 210 | tmp= 1; |
---|
[ab547e2] | 211 | sqrfFactors= sqrFree (i.getItem()); |
---|
| 212 | |
---|
[38ffb7] | 213 | for (iter= sqrfFactors; iter.hasItem(); iter++) |
---|
[ab547e2] | 214 | { |
---|
[38ffb7] | 215 | tmp2.append (iter.getItem().factor()); |
---|
| 216 | tmp *= iter.getItem().factor(); |
---|
[ab547e2] | 217 | } |
---|
| 218 | i.getItem()= tmp/Lc(tmp); |
---|
| 219 | bufSqrfFactors [k]= sqrfFactors; |
---|
| 220 | } |
---|
| 221 | |
---|
| 222 | for (int i= 0; i < factors.length() - 1; i++) |
---|
| 223 | { |
---|
| 224 | for (int k= i + 1; k < factors.length(); k++) |
---|
| 225 | { |
---|
| 226 | gcdFreeBasis (bufSqrfFactors [i], bufSqrfFactors[k]); |
---|
| 227 | } |
---|
| 228 | } |
---|
| 229 | |
---|
| 230 | factors= CFList(); |
---|
| 231 | for (int i= 0; i < uniFactors.length(); i++) |
---|
| 232 | { |
---|
| 233 | if (i == 0) |
---|
| 234 | { |
---|
[38ffb7] | 235 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
---|
[ab547e2] | 236 | { |
---|
[327efa2] | 237 | if (iter.getItem().factor().inCoeffDomain()) |
---|
| 238 | continue; |
---|
[38ffb7] | 239 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
---|
| 240 | Lc (iter.getItem().factor()), |
---|
| 241 | iter.getItem().exp()); |
---|
| 242 | factors.append (iter.getItem().factor()); |
---|
[ab547e2] | 243 | } |
---|
| 244 | } |
---|
| 245 | else |
---|
| 246 | { |
---|
[38ffb7] | 247 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
---|
[ab547e2] | 248 | { |
---|
[327efa2] | 249 | if (iter.getItem().factor().inCoeffDomain()) |
---|
| 250 | continue; |
---|
[38ffb7] | 251 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
---|
| 252 | Lc (iter.getItem().factor()), |
---|
| 253 | iter.getItem().exp()); |
---|
| 254 | if (!find (factors, iter.getItem().factor())) |
---|
| 255 | factors.append (iter.getItem().factor()); |
---|
[ab547e2] | 256 | } |
---|
| 257 | } |
---|
| 258 | } |
---|
| 259 | |
---|
| 260 | test= prod (factors); |
---|
[eefc3a] | 261 | tmp= evalSqrfPartF.getFirst() (evalPoint[0],2); |
---|
[ab547e2] | 262 | if (test/Lc (test) != tmp/Lc (tmp)) |
---|
| 263 | return 0; |
---|
| 264 | else |
---|
| 265 | return 1; |
---|
| 266 | } |
---|
| 267 | |
---|
| 268 | CFList |
---|
| 269 | precomputeLeadingCoeff (const CanonicalForm& LCF, const CFList& LCFFactors, |
---|
| 270 | const CFList& evaluation,CFList*& differentSecondVarLCs, |
---|
| 271 | int length, Variable& y |
---|
| 272 | ) |
---|
| 273 | { |
---|
| 274 | y= Variable (1); |
---|
| 275 | if (LCF.inCoeffDomain()) |
---|
| 276 | { |
---|
| 277 | CFList result; |
---|
| 278 | for (int i= 1; i <= LCFFactors.length() + 1; i++) |
---|
| 279 | result.append (1); |
---|
| 280 | return result; |
---|
| 281 | } |
---|
| 282 | |
---|
[8256fd] | 283 | CFMap N, M; |
---|
[8a30b1] | 284 | CFArray dummy= CFArray (2); |
---|
[8256fd] | 285 | dummy [0]= LCF; |
---|
[8a30b1] | 286 | dummy [1]= Variable (2); |
---|
[8256fd] | 287 | compress (dummy, M, N); |
---|
| 288 | CanonicalForm F= M (LCF); |
---|
[ab547e2] | 289 | if (LCF.isUnivariate()) |
---|
| 290 | { |
---|
| 291 | CFList result; |
---|
| 292 | int LCFLevel= LCF.level(); |
---|
| 293 | bool found= false; |
---|
| 294 | if (LCFLevel == 2) |
---|
| 295 | { |
---|
| 296 | //bivariate leading coefficients are already the true leading coefficients |
---|
| 297 | result= LCFFactors; |
---|
| 298 | found= true; |
---|
| 299 | } |
---|
| 300 | else |
---|
| 301 | { |
---|
[38ffb7] | 302 | CFListIterator j; |
---|
[ab547e2] | 303 | for (int i= 0; i < length; i++) |
---|
| 304 | { |
---|
[38ffb7] | 305 | for (j= differentSecondVarLCs[i]; j.hasItem(); j++) |
---|
[ab547e2] | 306 | { |
---|
| 307 | if (j.getItem().level() == LCFLevel) |
---|
| 308 | { |
---|
| 309 | found= true; |
---|
| 310 | break; |
---|
| 311 | } |
---|
| 312 | } |
---|
| 313 | if (found) |
---|
| 314 | { |
---|
| 315 | result= differentSecondVarLCs [i]; |
---|
| 316 | break; |
---|
| 317 | } |
---|
| 318 | } |
---|
| 319 | if (!found) |
---|
| 320 | result= LCFFactors; |
---|
| 321 | } |
---|
| 322 | if (found) |
---|
| 323 | result.insert (Lc (LCF)); |
---|
| 324 | else |
---|
| 325 | result.append (LCF); |
---|
| 326 | return result; |
---|
| 327 | } |
---|
| 328 | |
---|
| 329 | CFList factors= LCFFactors; |
---|
| 330 | |
---|
| 331 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[8256fd] | 332 | i.getItem()= M (i.getItem()); |
---|
[ab547e2] | 333 | |
---|
| 334 | CanonicalForm sqrfPartF; |
---|
| 335 | CFFList * bufSqrfFactors= new CFFList [factors.length()]; |
---|
[eefc3a] | 336 | CFList evalSqrfPartF, bufFactors; |
---|
| 337 | CFArray evalPoint= CFArray (evaluation.length() - 1); |
---|
[8a30b1] | 338 | CFArray buf= CFArray (evaluation.length()); |
---|
| 339 | CFArray swap= CFArray (evaluation.length()); |
---|
[eefc3a] | 340 | CFListIterator iter= evaluation; |
---|
[9dacf3f] | 341 | CanonicalForm vars=getVars (LCF)*Variable (2); |
---|
[8a30b1] | 342 | for (int i= evaluation.length() +1; i > 1; i--, iter++) |
---|
| 343 | { |
---|
| 344 | buf[i-2]=iter.getItem(); |
---|
| 345 | if (degree (vars, i) > 0) |
---|
| 346 | swap[M(Variable (i)).level()-1]=buf[i-2]; |
---|
| 347 | } |
---|
| 348 | buf= swap; |
---|
| 349 | for (int i= 0; i < evaluation.length() - 1; i++) |
---|
| 350 | evalPoint[i]= buf[i+1]; |
---|
| 351 | |
---|
[ab547e2] | 352 | //TODO sqrfPartF einmal berechnen nicht stÀndig |
---|
| 353 | int pass= testFactors (F, factors, sqrfPartF, |
---|
[eefc3a] | 354 | bufFactors, bufSqrfFactors, evalSqrfPartF, evalPoint); |
---|
[ab547e2] | 355 | |
---|
| 356 | bool foundDifferent= false; |
---|
| 357 | Variable z; |
---|
| 358 | Variable x= y; |
---|
| 359 | int j= 0; |
---|
| 360 | if (!pass) |
---|
| 361 | { |
---|
[7a1151] | 362 | int lev= 0; |
---|
[8a30b1] | 363 | CanonicalForm bufF; |
---|
| 364 | CFList bufBufFactors; |
---|
[ab547e2] | 365 | for (int i= 0; i < length; i++) |
---|
| 366 | { |
---|
| 367 | if (!differentSecondVarLCs [i].isEmpty()) |
---|
| 368 | { |
---|
| 369 | bool allConstant= true; |
---|
[38ffb7] | 370 | for (iter= differentSecondVarLCs[i]; iter.hasItem(); iter++) |
---|
[ab547e2] | 371 | { |
---|
| 372 | if (!iter.getItem().inCoeffDomain()) |
---|
| 373 | { |
---|
| 374 | allConstant= false; |
---|
| 375 | y= Variable (iter.getItem().level()); |
---|
[8256fd] | 376 | lev= M(y).level(); |
---|
[ab547e2] | 377 | } |
---|
| 378 | } |
---|
| 379 | if (allConstant) |
---|
| 380 | continue; |
---|
| 381 | |
---|
| 382 | bufFactors= differentSecondVarLCs [i]; |
---|
[38ffb7] | 383 | for (iter= bufFactors; iter.hasItem(); iter++) |
---|
[ab547e2] | 384 | iter.getItem()= swapvar (iter.getItem(), x, y); |
---|
[38ffb7] | 385 | bufF= F; |
---|
[8256fd] | 386 | z= Variable (lev); |
---|
[ab547e2] | 387 | bufF= swapvar (bufF, x, z); |
---|
[38ffb7] | 388 | bufBufFactors= bufFactors; |
---|
[eefc3a] | 389 | evalPoint= CFArray (evaluation.length() - 1); |
---|
[8a30b1] | 390 | for (int k= 0; k < evaluation.length()-1; k++) |
---|
[eefc3a] | 391 | { |
---|
[9dacf3f] | 392 | if (N (Variable (k+1)).level() != y.level()) |
---|
[8a30b1] | 393 | evalPoint[k]= buf[k+1]; |
---|
| 394 | else |
---|
| 395 | evalPoint[k]= buf[0]; |
---|
[eefc3a] | 396 | } |
---|
[ab547e2] | 397 | pass= testFactors (bufF, bufBufFactors, sqrfPartF, bufFactors, |
---|
[eefc3a] | 398 | bufSqrfFactors, evalSqrfPartF, evalPoint); |
---|
[ab547e2] | 399 | if (pass) |
---|
| 400 | { |
---|
| 401 | foundDifferent= true; |
---|
| 402 | F= bufF; |
---|
| 403 | CFList l= factors; |
---|
[38ffb7] | 404 | for (iter= l; iter.hasItem(); iter++) |
---|
[ab547e2] | 405 | iter.getItem()= swapvar (iter.getItem(), x, y); |
---|
| 406 | differentSecondVarLCs [i]= l; |
---|
| 407 | j= i; |
---|
| 408 | break; |
---|
| 409 | } |
---|
| 410 | if (!pass && i == length - 1) |
---|
| 411 | { |
---|
| 412 | CFList result; |
---|
| 413 | result.append (LCF); |
---|
| 414 | for (int j= 1; j <= factors.length(); j++) |
---|
| 415 | result.append (LCF); |
---|
| 416 | y= Variable (1); |
---|
[229530] | 417 | delete [] bufSqrfFactors; |
---|
[ab547e2] | 418 | return result; |
---|
| 419 | } |
---|
| 420 | } |
---|
| 421 | } |
---|
| 422 | } |
---|
| 423 | if (!pass) |
---|
| 424 | { |
---|
| 425 | CFList result; |
---|
| 426 | result.append (LCF); |
---|
| 427 | for (int j= 1; j <= factors.length(); j++) |
---|
| 428 | result.append (LCF); |
---|
| 429 | y= Variable (1); |
---|
[229530] | 430 | delete [] bufSqrfFactors; |
---|
[ab547e2] | 431 | return result; |
---|
| 432 | } |
---|
| 433 | else |
---|
| 434 | factors= bufFactors; |
---|
| 435 | |
---|
| 436 | |
---|
| 437 | bufFactors= factors; |
---|
[1a2d66] | 438 | |
---|
| 439 | CFMap MM, NN; |
---|
| 440 | dummy [0]= sqrfPartF; |
---|
| 441 | dummy [1]= 1; |
---|
| 442 | compress (dummy, MM, NN); |
---|
| 443 | sqrfPartF= MM (sqrfPartF); |
---|
| 444 | CanonicalForm varsSqrfPartF= getVars (sqrfPartF); |
---|
| 445 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
| 446 | iter.getItem()= MM (iter.getItem()); |
---|
| 447 | |
---|
[eefc3a] | 448 | CFList evaluation2; |
---|
[1a2d66] | 449 | for (int i= 2; i <= varsSqrfPartF.level(); i++) |
---|
| 450 | evaluation2.insert (evalPoint[NN (Variable (i)).level()-2]); |
---|
[327efa2] | 451 | |
---|
[ec16f0] | 452 | CFList interMedResult; |
---|
| 453 | CanonicalForm oldSqrfPartF= sqrfPartF; |
---|
[8a30b1] | 454 | sqrfPartF= shift2Zero (sqrfPartF, evalSqrfPartF, evaluation2); |
---|
[327efa2] | 455 | if (factors.length() > 1) |
---|
| 456 | { |
---|
[ec16f0] | 457 | CanonicalForm LC1= LC (oldSqrfPartF, 1); |
---|
| 458 | CFList leadingCoeffs; |
---|
[327efa2] | 459 | for (int i= 0; i < factors.length(); i++) |
---|
[ec16f0] | 460 | leadingCoeffs.append (LC1); |
---|
| 461 | |
---|
[8a30b1] | 462 | CFList LC1eval= evaluateAtEval (LC1, evaluation2,2); |
---|
[ec16f0] | 463 | CFList oldFactors= factors; |
---|
| 464 | for (CFListIterator i= oldFactors; i.hasItem(); i++) |
---|
| 465 | i.getItem() *= LC1eval.getFirst()/Lc (i.getItem()); |
---|
| 466 | |
---|
| 467 | bool success= false; |
---|
[64b824] | 468 | CanonicalForm oldSqrfPartFPowLC= oldSqrfPartF*power(LC1,factors.length()-1); |
---|
| 469 | if (size (oldSqrfPartFPowLC)/getNumVars (oldSqrfPartFPowLC) < 500 && |
---|
| 470 | LucksWangSparseHeuristic (oldSqrfPartFPowLC, |
---|
[8a30b1] | 471 | oldFactors, 2, leadingCoeffs, factors)) |
---|
[eefc3a] | 472 | { |
---|
[ec16f0] | 473 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
---|
| 474 | if (oldFactors.length() == interMedResult.length()) |
---|
| 475 | success= true; |
---|
[eefc3a] | 476 | } |
---|
[ec16f0] | 477 | if (!success) |
---|
| 478 | { |
---|
| 479 | LC1= LC (evalSqrfPartF.getFirst(), 1); |
---|
[327efa2] | 480 | |
---|
[ec16f0] | 481 | CFArray leadingCoeffs= CFArray (factors.length()); |
---|
| 482 | for (int i= 0; i < factors.length(); i++) |
---|
| 483 | leadingCoeffs[i]= LC1; |
---|
[327efa2] | 484 | |
---|
[ec16f0] | 485 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 486 | i.getItem() *= LC1 (0,2)/Lc (i.getItem()); |
---|
| 487 | factors.insert (1); |
---|
[327efa2] | 488 | |
---|
[ec16f0] | 489 | CanonicalForm |
---|
| 490 | newSqrfPartF= evalSqrfPartF.getFirst()*power (LC1, factors.length() - 2); |
---|
[327efa2] | 491 | |
---|
[ec16f0] | 492 | int liftBound= degree (newSqrfPartF,2) + 1; |
---|
| 493 | |
---|
| 494 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
| 495 | CFArray Pi; |
---|
| 496 | CFList diophant; |
---|
[81d96c] | 497 | nonMonicHenselLift12 (newSqrfPartF, factors, liftBound, Pi, diophant, M, |
---|
| 498 | leadingCoeffs, false); |
---|
[ec16f0] | 499 | |
---|
| 500 | if (sqrfPartF.level() > 2) |
---|
[327efa2] | 501 | { |
---|
[ec16f0] | 502 | int* liftBounds= new int [sqrfPartF.level() - 1]; |
---|
| 503 | liftBounds [0]= liftBound; |
---|
| 504 | bool noOneToOne= false; |
---|
| 505 | CFList *leadingCoeffs2= new CFList [sqrfPartF.level()-2]; |
---|
| 506 | LC1= LC (evalSqrfPartF.getLast(), 1); |
---|
| 507 | CFList LCs; |
---|
| 508 | for (int i= 0; i < factors.length(); i++) |
---|
| 509 | LCs.append (LC1); |
---|
| 510 | leadingCoeffs2 [sqrfPartF.level() - 3]= LCs; |
---|
| 511 | for (int i= sqrfPartF.level() - 1; i > 2; i--) |
---|
| 512 | { |
---|
| 513 | for (CFListIterator j= LCs; j.hasItem(); j++) |
---|
| 514 | j.getItem()= j.getItem() (0, i + 1); |
---|
| 515 | leadingCoeffs2 [i - 3]= LCs; |
---|
| 516 | } |
---|
| 517 | sqrfPartF *= power (LC1, factors.length()-1); |
---|
| 518 | |
---|
| 519 | int liftBoundsLength= sqrfPartF.level() - 1; |
---|
| 520 | for (int i= 1; i < liftBoundsLength; i++) |
---|
| 521 | liftBounds [i]= degree (sqrfPartF, i + 2) + 1; |
---|
| 522 | evalSqrfPartF= evaluateAtZero (sqrfPartF); |
---|
| 523 | evalSqrfPartF.removeFirst(); |
---|
| 524 | factors= nonMonicHenselLift (evalSqrfPartF, factors, leadingCoeffs2, |
---|
| 525 | diophant, Pi, liftBounds, sqrfPartF.level() - 1, noOneToOne); |
---|
| 526 | delete [] leadingCoeffs2; |
---|
| 527 | delete [] liftBounds; |
---|
[327efa2] | 528 | } |
---|
[ec16f0] | 529 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
[8a30b1] | 530 | iter.getItem()= reverseShift (iter.getItem(), evaluation2); |
---|
[ec16f0] | 531 | |
---|
| 532 | interMedResult= |
---|
[8a30b1] | 533 | recoverFactors (reverseShift(evalSqrfPartF.getLast(),evaluation2), |
---|
[ec16f0] | 534 | factors); |
---|
[327efa2] | 535 | } |
---|
| 536 | } |
---|
| 537 | else |
---|
[ec16f0] | 538 | { |
---|
[8256fd] | 539 | CanonicalForm contF=content (oldSqrfPartF,1); |
---|
| 540 | factors= CFList (oldSqrfPartF/contF); |
---|
[ec16f0] | 541 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
---|
| 542 | } |
---|
[ab547e2] | 543 | |
---|
[1a2d66] | 544 | for (CFListIterator iter= interMedResult; iter.hasItem(); iter++) |
---|
| 545 | iter.getItem()= NN (iter.getItem()); |
---|
| 546 | |
---|
[ab547e2] | 547 | CFList result; |
---|
[38ffb7] | 548 | CFFListIterator k; |
---|
| 549 | CanonicalForm tmp; |
---|
[ab547e2] | 550 | for (int i= 0; i < LCFFactors.length(); i++) |
---|
| 551 | { |
---|
[38ffb7] | 552 | tmp= 1; |
---|
| 553 | for (k= bufSqrfFactors[i]; k.hasItem(); k++) |
---|
[ab547e2] | 554 | { |
---|
| 555 | int pos= findItem (bufFactors, k.getItem().factor()); |
---|
| 556 | if (pos) |
---|
| 557 | tmp *= power (getItem (interMedResult, pos), k.getItem().exp()); |
---|
| 558 | } |
---|
| 559 | result.append (tmp); |
---|
| 560 | } |
---|
| 561 | |
---|
| 562 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
| 563 | { |
---|
| 564 | F /= i.getItem(); |
---|
| 565 | if (foundDifferent) |
---|
| 566 | i.getItem()= swapvar (i.getItem(), x, z); |
---|
| 567 | i.getItem()= N (i.getItem()); |
---|
| 568 | } |
---|
| 569 | |
---|
| 570 | if (foundDifferent) |
---|
| 571 | { |
---|
| 572 | CFList l= differentSecondVarLCs [j]; |
---|
| 573 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 574 | i.getItem()= swapvar (i.getItem(), y, z); |
---|
| 575 | differentSecondVarLCs [j]= l; |
---|
| 576 | F= swapvar (F, x, z); |
---|
| 577 | } |
---|
| 578 | |
---|
| 579 | result.insert (N (F)); |
---|
| 580 | |
---|
| 581 | result= distributeContent (result, differentSecondVarLCs, length); |
---|
| 582 | |
---|
| 583 | if (!result.getFirst().inCoeffDomain()) |
---|
| 584 | { |
---|
| 585 | CFListIterator i= result; |
---|
| 586 | CanonicalForm tmp; |
---|
| 587 | if (foundDifferent) |
---|
| 588 | i.getItem()= swapvar (i.getItem(), Variable (2), y); |
---|
| 589 | |
---|
| 590 | tmp= i.getItem(); |
---|
| 591 | |
---|
| 592 | i++; |
---|
| 593 | for (; i.hasItem(); i++) |
---|
| 594 | { |
---|
| 595 | if (foundDifferent) |
---|
| 596 | i.getItem()= swapvar (i.getItem(), Variable (2), y)*tmp; |
---|
| 597 | else |
---|
| 598 | i.getItem() *= tmp; |
---|
| 599 | } |
---|
| 600 | } |
---|
| 601 | else |
---|
| 602 | y= Variable (1); |
---|
| 603 | |
---|
[229530] | 604 | delete [] bufSqrfFactors; |
---|
| 605 | |
---|
[ab547e2] | 606 | return result; |
---|
| 607 | } |
---|
| 608 | |
---|
| 609 | |
---|
| 610 | CFList |
---|
| 611 | multiFactorize (const CanonicalForm& F, const Variable& v) |
---|
| 612 | { |
---|
| 613 | if (F.inCoeffDomain()) |
---|
| 614 | return CFList (F); |
---|
| 615 | |
---|
| 616 | // compress and find main Variable |
---|
| 617 | CFMap N; |
---|
| 618 | CanonicalForm A= myCompress (F, N); |
---|
| 619 | |
---|
| 620 | //univariate case |
---|
| 621 | if (F.isUnivariate()) |
---|
| 622 | { |
---|
[0e6668] | 623 | CFList result; |
---|
| 624 | if (v.level() != 1) |
---|
| 625 | result= conv (factorize (F, v)); |
---|
| 626 | else |
---|
| 627 | result= conv (factorize (F,true)); |
---|
[ab547e2] | 628 | if (result.getFirst().inCoeffDomain()) |
---|
| 629 | result.removeFirst(); |
---|
| 630 | return result; |
---|
| 631 | } |
---|
| 632 | |
---|
| 633 | //bivariate case |
---|
| 634 | if (A.level() == 2) |
---|
| 635 | { |
---|
| 636 | CFList buf= biFactorize (F, v); |
---|
| 637 | return buf; |
---|
| 638 | } |
---|
| 639 | |
---|
| 640 | Variable x= Variable (1); |
---|
| 641 | Variable y= Variable (2); |
---|
| 642 | |
---|
| 643 | // remove content |
---|
| 644 | CFList contentAi; |
---|
| 645 | CanonicalForm lcmCont= lcmContent (A, contentAi); |
---|
| 646 | A /= lcmCont; |
---|
| 647 | |
---|
| 648 | // trivial after content removal |
---|
| 649 | CFList contentAFactors; |
---|
| 650 | if (A.inCoeffDomain()) |
---|
| 651 | { |
---|
| 652 | for (CFListIterator i= contentAi; i.hasItem(); i++) |
---|
| 653 | { |
---|
| 654 | if (i.getItem().inCoeffDomain()) |
---|
| 655 | continue; |
---|
| 656 | else |
---|
| 657 | { |
---|
| 658 | lcmCont /= i.getItem(); |
---|
| 659 | contentAFactors= |
---|
| 660 | Union (multiFactorize (lcmCont, v), |
---|
| 661 | multiFactorize (i.getItem(), v)); |
---|
| 662 | break; |
---|
| 663 | } |
---|
| 664 | } |
---|
| 665 | decompress (contentAFactors, N); |
---|
| 666 | if (isOn (SW_RATIONAL)) |
---|
| 667 | normalize (contentAFactors); |
---|
| 668 | return contentAFactors; |
---|
| 669 | } |
---|
| 670 | |
---|
| 671 | // factorize content |
---|
| 672 | contentAFactors= multiFactorize (lcmCont, v); |
---|
| 673 | |
---|
| 674 | // univariate after content removal |
---|
| 675 | CFList factors; |
---|
| 676 | if (A.isUnivariate ()) |
---|
| 677 | { |
---|
[0e6668] | 678 | if (v.level() != 1) |
---|
| 679 | factors= conv (factorize (A, v)); |
---|
| 680 | else |
---|
| 681 | factors= conv (factorize (A,true)); |
---|
[ab547e2] | 682 | append (factors, contentAFactors); |
---|
| 683 | decompress (factors, N); |
---|
| 684 | return factors; |
---|
| 685 | } |
---|
| 686 | |
---|
[f55f39] | 687 | A *= bCommonDen (A); |
---|
[ab547e2] | 688 | // check main variable |
---|
| 689 | CFList Aeval, list, evaluation, bufEvaluation, bufAeval; |
---|
| 690 | int factorNums= 3; |
---|
| 691 | CanonicalForm bivarEval; |
---|
| 692 | CFList biFactors, bufBiFactors; |
---|
| 693 | CanonicalForm evalPoly; |
---|
| 694 | int lift, bufLift; |
---|
| 695 | CFList* bufAeval2= new CFList [A.level() - 2]; |
---|
| 696 | CFList* Aeval2= new CFList [A.level() - 2]; |
---|
| 697 | int counter; |
---|
| 698 | int differentSecondVar= 0; |
---|
| 699 | CanonicalForm bufA; |
---|
| 700 | // several bivariate factorizations |
---|
| 701 | REvaluation E (2, A.level(), IntRandom (25)); |
---|
| 702 | for (int i= 0; i < factorNums; i++) |
---|
| 703 | { |
---|
| 704 | counter= 0; |
---|
| 705 | bufA= A; |
---|
| 706 | bufAeval= CFList(); |
---|
| 707 | bufEvaluation= evalPoints (bufA, bufAeval, E); |
---|
| 708 | E.nextpoint(); |
---|
| 709 | evalPoly= 0; |
---|
| 710 | |
---|
| 711 | bivarEval= bufEvaluation.getLast(); |
---|
| 712 | |
---|
| 713 | evaluationWRTDifferentSecondVars (bufAeval2, bufEvaluation, A); |
---|
| 714 | |
---|
| 715 | for (int j= 0; j < A.level() - 1; j++) |
---|
| 716 | { |
---|
| 717 | if (!bufAeval2[j].isEmpty()) |
---|
| 718 | counter++; |
---|
| 719 | } |
---|
| 720 | |
---|
| 721 | bufLift= degree (A, y) + 1 + degree (LC(A, x), y); |
---|
| 722 | |
---|
[ec664a2] | 723 | TIMING_START (fac_bi_factorize); |
---|
[ab547e2] | 724 | bufBiFactors= ratBiSqrfFactorize (bufAeval.getFirst(), v); |
---|
[ec664a2] | 725 | TIMING_END_AND_PRINT (fac_bi_factorize, |
---|
[ab547e2] | 726 | "time for bivariate factorization: "); |
---|
| 727 | bufBiFactors.removeFirst(); |
---|
| 728 | |
---|
| 729 | if (bufBiFactors.length() == 1) |
---|
| 730 | { |
---|
| 731 | factors.append (A); |
---|
| 732 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 733 | if (isOn (SW_RATIONAL)) |
---|
| 734 | normalize (factors); |
---|
| 735 | delete [] bufAeval2; |
---|
| 736 | delete [] Aeval2; |
---|
| 737 | return factors; |
---|
| 738 | } |
---|
| 739 | |
---|
| 740 | if (i == 0) |
---|
| 741 | { |
---|
| 742 | Aeval= bufAeval; |
---|
| 743 | evaluation= bufEvaluation; |
---|
| 744 | biFactors= bufBiFactors; |
---|
| 745 | lift= bufLift; |
---|
| 746 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 747 | Aeval2 [j]= bufAeval2 [j]; |
---|
| 748 | differentSecondVar= counter; |
---|
| 749 | } |
---|
| 750 | else |
---|
| 751 | { |
---|
| 752 | if (bufBiFactors.length() < biFactors.length() || |
---|
| 753 | ((bufLift < lift) && (bufBiFactors.length() == biFactors.length())) || |
---|
| 754 | counter > differentSecondVar) |
---|
| 755 | { |
---|
| 756 | Aeval= bufAeval; |
---|
| 757 | evaluation= bufEvaluation; |
---|
| 758 | biFactors= bufBiFactors; |
---|
| 759 | lift= bufLift; |
---|
| 760 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 761 | Aeval2 [j]= bufAeval2 [j]; |
---|
| 762 | differentSecondVar= counter; |
---|
| 763 | } |
---|
| 764 | } |
---|
| 765 | int k= 0; |
---|
| 766 | for (CFListIterator j= bufEvaluation; j.hasItem(); j++, k++) |
---|
| 767 | evalPoly += j.getItem()*power (x, k); |
---|
| 768 | list.append (evalPoly); |
---|
| 769 | } |
---|
| 770 | |
---|
| 771 | delete [] bufAeval2; |
---|
| 772 | |
---|
| 773 | sortList (biFactors, x); |
---|
| 774 | |
---|
| 775 | int minFactorsLength; |
---|
| 776 | bool irred= false; |
---|
| 777 | factorizationWRTDifferentSecondVars (A, Aeval2, minFactorsLength, irred, v); |
---|
| 778 | |
---|
| 779 | if (irred) |
---|
| 780 | { |
---|
| 781 | factors.append (A); |
---|
| 782 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 783 | if (isOn (SW_RATIONAL)) |
---|
| 784 | normalize (factors); |
---|
| 785 | delete [] Aeval2; |
---|
| 786 | return factors; |
---|
| 787 | } |
---|
| 788 | |
---|
| 789 | if (minFactorsLength == 0) |
---|
| 790 | minFactorsLength= biFactors.length(); |
---|
| 791 | else if (biFactors.length() > minFactorsLength) |
---|
| 792 | refineBiFactors (A, biFactors, Aeval2, evaluation, minFactorsLength); |
---|
| 793 | |
---|
[8681bf] | 794 | if (differentSecondVar == A.level() - 2 && getNumVars(LC(A,1)) == A.level()-1) |
---|
[6036d90] | 795 | { |
---|
| 796 | bool zeroOccured= false; |
---|
| 797 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++) |
---|
| 798 | { |
---|
| 799 | if (iter.getItem().isZero()) |
---|
| 800 | { |
---|
| 801 | zeroOccured= true; |
---|
| 802 | break; |
---|
| 803 | } |
---|
| 804 | } |
---|
| 805 | if (!zeroOccured) |
---|
| 806 | { |
---|
[8256fd] | 807 | factors= sparseHeuristic (A, biFactors, Aeval2, evaluation, |
---|
| 808 | minFactorsLength); |
---|
[6036d90] | 809 | if (factors.length() == biFactors.length()) |
---|
| 810 | { |
---|
| 811 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 812 | normalize (factors); |
---|
| 813 | delete [] Aeval2; |
---|
| 814 | return factors; |
---|
| 815 | } |
---|
| 816 | else |
---|
| 817 | factors= CFList(); |
---|
| 818 | //TODO case where factors.length() > 0 |
---|
| 819 | } |
---|
| 820 | } |
---|
| 821 | |
---|
[ab547e2] | 822 | CFList uniFactors= buildUniFactors (biFactors, evaluation.getLast(), y); |
---|
| 823 | |
---|
[fce807] | 824 | sortByUniFactors (Aeval2, A.level() - 2, uniFactors, evaluation); |
---|
| 825 | |
---|
[ab547e2] | 826 | CFList * oldAeval= new CFList [A.level() - 2]; |
---|
| 827 | for (int i= 0; i < A.level() - 2; i++) |
---|
| 828 | oldAeval[i]= Aeval2[i]; |
---|
| 829 | |
---|
| 830 | getLeadingCoeffs (A, Aeval2, uniFactors, evaluation); |
---|
| 831 | |
---|
| 832 | CFList biFactorsLCs; |
---|
| 833 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 834 | biFactorsLCs.append (LC (i.getItem(), 1)); |
---|
| 835 | |
---|
| 836 | Variable w; |
---|
| 837 | CFList leadingCoeffs= precomputeLeadingCoeff (LC (A, 1), biFactorsLCs, |
---|
| 838 | evaluation, Aeval2, A.level() - 2, w); |
---|
| 839 | |
---|
| 840 | if (w.level() != 1) |
---|
| 841 | { |
---|
| 842 | A= swapvar (A, y, w); |
---|
| 843 | int i= A.level(); |
---|
| 844 | CanonicalForm evalPoint; |
---|
| 845 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++, i--) |
---|
| 846 | { |
---|
| 847 | if (i == w.level()) |
---|
| 848 | { |
---|
| 849 | evalPoint= iter.getItem(); |
---|
| 850 | iter.getItem()= evaluation.getLast(); |
---|
| 851 | evaluation.removeLast(); |
---|
| 852 | evaluation.append (evalPoint); |
---|
| 853 | break; |
---|
| 854 | } |
---|
| 855 | } |
---|
[8256fd] | 856 | for (i= 0; i < A.level() - 2; i++) |
---|
| 857 | { |
---|
| 858 | if (oldAeval[i].isEmpty()) |
---|
| 859 | continue; |
---|
| 860 | if (oldAeval[i].getFirst().level() == w.level()) |
---|
| 861 | { |
---|
| 862 | CFArray tmp= copy (oldAeval[i]); |
---|
[753fb61] | 863 | oldAeval[i]= biFactors; |
---|
| 864 | for (CFListIterator iter= oldAeval[i]; iter.hasItem(); iter++) |
---|
| 865 | iter.getItem()= swapvar (iter.getItem(), w, y); |
---|
[8256fd] | 866 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
| 867 | tmp[ii]= swapvar (tmp[ii], w, y); |
---|
| 868 | CFArray tmp2= CFArray (tmp.size()); |
---|
| 869 | CanonicalForm buf; |
---|
| 870 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
| 871 | { |
---|
| 872 | buf= tmp[ii] (evaluation.getLast(),y); |
---|
| 873 | buf /= Lc (buf); |
---|
| 874 | tmp2[findItem (uniFactors, buf)-1]=tmp[ii]; |
---|
| 875 | } |
---|
| 876 | biFactors= CFList(); |
---|
| 877 | for (int j= 0; j < tmp2.size(); j++) |
---|
| 878 | biFactors.append (tmp2[j]); |
---|
| 879 | } |
---|
| 880 | } |
---|
[ab547e2] | 881 | } |
---|
| 882 | |
---|
[eefc3a] | 883 | CFListIterator iter; |
---|
[ab547e2] | 884 | CanonicalForm oldA= A; |
---|
| 885 | CFList oldBiFactors= biFactors; |
---|
| 886 | if (!leadingCoeffs.getFirst().inCoeffDomain()) |
---|
| 887 | { |
---|
| 888 | CanonicalForm tmp= power (leadingCoeffs.getFirst(), biFactors.length() - 1); |
---|
| 889 | A *= tmp; |
---|
| 890 | tmp= leadingCoeffs.getFirst(); |
---|
[eefc3a] | 891 | iter= evaluation; |
---|
| 892 | for (int i= A.level(); i > 2; i--, iter++) |
---|
| 893 | tmp= tmp (iter.getItem(), i); |
---|
[ab547e2] | 894 | if (!tmp.inCoeffDomain()) |
---|
| 895 | { |
---|
| 896 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 897 | { |
---|
| 898 | i.getItem() *= tmp/LC (i.getItem(), 1); |
---|
| 899 | i.getItem() /= Lc (i.getItem()); |
---|
| 900 | } |
---|
| 901 | } |
---|
| 902 | } |
---|
| 903 | |
---|
[5295f9] | 904 | CanonicalForm LCmultiplier= leadingCoeffs.getFirst(); |
---|
[fcd296] | 905 | bool LCmultiplierIsConst= LCmultiplier.inCoeffDomain(); |
---|
[ab547e2] | 906 | leadingCoeffs.removeFirst(); |
---|
| 907 | |
---|
| 908 | //prepare leading coefficients |
---|
| 909 | CFList* leadingCoeffs2= new CFList [A.level() - 2]; |
---|
[eefc3a] | 910 | prepareLeadingCoeffs (leadingCoeffs2, A.level(), leadingCoeffs, biFactors, |
---|
| 911 | evaluation); |
---|
| 912 | |
---|
| 913 | |
---|
| 914 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
| 915 | |
---|
| 916 | CanonicalForm hh= Lc (Aeval.getFirst()); |
---|
| 917 | |
---|
[464b18] | 918 | for (iter= Aeval; iter.hasItem(); iter++) |
---|
| 919 | iter.getItem() /= hh; |
---|
[eefc3a] | 920 | |
---|
| 921 | A /= hh; |
---|
| 922 | |
---|
[6af78bb] | 923 | CFListIterator iter2; |
---|
[fcd296] | 924 | CFList bufLeadingCoeffs2= leadingCoeffs2[A.level()-3]; |
---|
| 925 | bufBiFactors= biFactors; |
---|
| 926 | bufA= A; |
---|
[5079887] | 927 | CFList bufFactors= CFList(); |
---|
[fcd296] | 928 | bool LCheuristic= false; |
---|
[5079887] | 929 | if (LucksWangSparseHeuristic (A, biFactors, 2, leadingCoeffs2 [A.level() - 3], |
---|
[64b824] | 930 | factors)) |
---|
[4fe8a3] | 931 | { |
---|
[5079887] | 932 | int check= biFactors.length(); |
---|
| 933 | int * index= new int [factors.length()]; |
---|
| 934 | CFList oldFactors= factors; |
---|
| 935 | factors= recoverFactors (A, factors, index); |
---|
[4fe8a3] | 936 | |
---|
| 937 | if (check == factors.length()) |
---|
| 938 | { |
---|
[8256fd] | 939 | if (w.level() != 1) |
---|
| 940 | { |
---|
[5079887] | 941 | for (iter= factors; iter.hasItem(); iter++) |
---|
[8256fd] | 942 | iter.getItem()= swapvar (iter.getItem(), w, y); |
---|
| 943 | } |
---|
| 944 | |
---|
[4fe8a3] | 945 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 946 | normalize (factors); |
---|
[5079887] | 947 | delete [] index; |
---|
[4fe8a3] | 948 | delete [] Aeval2; |
---|
| 949 | return factors; |
---|
| 950 | } |
---|
[5079887] | 951 | else if (factors.length() > 0) |
---|
| 952 | { |
---|
| 953 | int oneCount= 0; |
---|
| 954 | CFList l; |
---|
| 955 | for (int i= 0; i < check; i++) |
---|
| 956 | { |
---|
| 957 | if (index[i] == 1) |
---|
| 958 | { |
---|
| 959 | iter=biFactors; |
---|
| 960 | for (int j=1; j <= i-oneCount; j++) |
---|
| 961 | iter++; |
---|
| 962 | iter.remove (1); |
---|
| 963 | for (int j= 0; j < A.level() -2; j++) |
---|
| 964 | { |
---|
| 965 | l= leadingCoeffs2[j]; |
---|
| 966 | iter= l; |
---|
| 967 | for (int k=1; k <= i-oneCount; k++) |
---|
| 968 | iter++; |
---|
| 969 | iter.remove (1); |
---|
| 970 | leadingCoeffs2[j]=l; |
---|
| 971 | } |
---|
| 972 | oneCount++; |
---|
| 973 | } |
---|
| 974 | } |
---|
| 975 | bufFactors= factors; |
---|
| 976 | factors= CFList(); |
---|
| 977 | } |
---|
[5295f9] | 978 | else if (!LCmultiplier.inCoeffDomain() && factors.length() == 0) |
---|
| 979 | { |
---|
[fcd296] | 980 | LCheuristic= true; |
---|
[5295f9] | 981 | factors= oldFactors; |
---|
| 982 | CanonicalForm cont; |
---|
| 983 | CFList contents, LCs; |
---|
| 984 | int index=1; |
---|
| 985 | bool foundTrueMultiplier= false; |
---|
| 986 | for (iter= factors; iter.hasItem(); iter++, index++) |
---|
| 987 | { |
---|
| 988 | cont= content (iter.getItem(), 1); |
---|
| 989 | cont= gcd (cont , LCmultiplier); |
---|
| 990 | contents.append (cont); |
---|
| 991 | if (cont.inCoeffDomain()) // trivial content->LCmultiplier needs to go there |
---|
| 992 | { |
---|
| 993 | foundTrueMultiplier= true; |
---|
| 994 | int index2= 1; |
---|
| 995 | for (iter2= leadingCoeffs2[A.level()-3]; iter2.hasItem(); iter2++, |
---|
| 996 | index2++) |
---|
| 997 | { |
---|
| 998 | if (index2 == index) |
---|
| 999 | continue; |
---|
| 1000 | iter2.getItem() /= LCmultiplier; |
---|
| 1001 | } |
---|
| 1002 | A /= power (LCmultiplier, biFactors.length() -1); |
---|
| 1003 | leadingCoeffs= leadingCoeffs2[A.level()-3]; |
---|
| 1004 | for (int i= A.level()-3; i > -1; i--) |
---|
| 1005 | leadingCoeffs2[i]= CFList(); |
---|
| 1006 | prepareLeadingCoeffs (leadingCoeffs2, A.level(), leadingCoeffs, |
---|
| 1007 | biFactors, evaluation ); |
---|
| 1008 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
| 1009 | |
---|
| 1010 | hh= Lc (Aeval.getFirst()); |
---|
| 1011 | |
---|
| 1012 | for (iter2= Aeval; iter2.hasItem(); iter2++) |
---|
| 1013 | iter2.getItem() /= hh; |
---|
| 1014 | |
---|
| 1015 | A /= hh; |
---|
| 1016 | break; |
---|
| 1017 | } |
---|
| 1018 | else |
---|
| 1019 | LCs.append (LC (iter.getItem()/cont, 1)); |
---|
| 1020 | } |
---|
| 1021 | if (!foundTrueMultiplier) |
---|
| 1022 | { |
---|
| 1023 | index= 1; |
---|
| 1024 | iter2= factors; |
---|
| 1025 | bool foundMultiplier= false; |
---|
| 1026 | for (iter= contents; iter.hasItem(); iter++, iter2++, index++) |
---|
| 1027 | { |
---|
| 1028 | if (fdivides (iter.getItem(), LCmultiplier)) |
---|
| 1029 | { |
---|
| 1030 | if ((LCmultiplier/iter.getItem()).inCoeffDomain() && |
---|
| 1031 | !isOnlyLeadingCoeff(iter2.getItem())) //content divides LCmultiplier completely and factor consists of more terms than just the leading coeff |
---|
| 1032 | { |
---|
| 1033 | int index2= 1; |
---|
| 1034 | for (CFListIterator iter3= leadingCoeffs2[A.level()-3]; |
---|
| 1035 | iter3.hasItem(); iter3++, index2++) |
---|
| 1036 | { |
---|
| 1037 | if (index2 == index) |
---|
| 1038 | { |
---|
| 1039 | iter3.getItem() /= LCmultiplier; |
---|
| 1040 | break; |
---|
| 1041 | } |
---|
| 1042 | } |
---|
| 1043 | A /= LCmultiplier; |
---|
| 1044 | foundMultiplier= true; |
---|
| 1045 | iter.getItem()= 1; |
---|
| 1046 | break; |
---|
| 1047 | } |
---|
| 1048 | } |
---|
| 1049 | } |
---|
| 1050 | // coming from above: divide out more LCmultiplier if possible |
---|
| 1051 | if (foundMultiplier) |
---|
| 1052 | { |
---|
| 1053 | foundMultiplier= false; |
---|
| 1054 | index=1; |
---|
| 1055 | iter2= factors; |
---|
| 1056 | for (iter= contents; iter.hasItem(); iter++, iter2++, index++) |
---|
| 1057 | { |
---|
| 1058 | if (!(iter.getItem().isOne()) && |
---|
| 1059 | fdivides (iter.getItem(), LCmultiplier)) |
---|
| 1060 | { |
---|
| 1061 | if (!isOnlyLeadingCoeff (iter2.getItem())) // factor is more than just leading coeff |
---|
| 1062 | { |
---|
| 1063 | int index2= 1; |
---|
| 1064 | for (iter2= leadingCoeffs2[A.level()-3]; iter2.hasItem(); |
---|
| 1065 | iter2++, index2++) |
---|
| 1066 | { |
---|
| 1067 | if (index2 == index) |
---|
| 1068 | { |
---|
| 1069 | iter2.getItem() /= iter.getItem(); |
---|
| 1070 | foundMultiplier= true; |
---|
| 1071 | break; |
---|
| 1072 | } |
---|
| 1073 | } |
---|
| 1074 | A /= iter.getItem(); |
---|
| 1075 | LCmultiplier /= iter.getItem(); |
---|
| 1076 | iter.getItem()= 1; |
---|
| 1077 | break; |
---|
| 1078 | } |
---|
[fcd296] | 1079 | else //factor consists of just leading coeff |
---|
[5295f9] | 1080 | { |
---|
| 1081 | CanonicalForm vars=getVars (iter.getItem()); |
---|
| 1082 | CanonicalForm factor; |
---|
| 1083 | Variable xx; |
---|
| 1084 | bool oneVariableNotInCommon= false; |
---|
| 1085 | for (int i= 0; i < A.level()-2; i++) |
---|
| 1086 | { |
---|
| 1087 | if (oldAeval[i].isEmpty()) |
---|
| 1088 | continue; |
---|
| 1089 | xx= oldAeval[i].getFirst().mvar(); |
---|
| 1090 | factor= LC (getItem (oldAeval[i], index),1); |
---|
| 1091 | if ((factor.inCoeffDomain() && degree (vars,xx) > 0) || |
---|
[fcd296] | 1092 | (degree (factor,xx) > 0 && degree (vars,xx) <= 0)) //scan for bivariate factors with leading coeff that does not contain variables which occur in LCmultiplier |
---|
[5295f9] | 1093 | { |
---|
| 1094 | oneVariableNotInCommon= true; |
---|
| 1095 | break; |
---|
| 1096 | } |
---|
| 1097 | } |
---|
| 1098 | if (oneVariableNotInCommon) |
---|
| 1099 | { |
---|
| 1100 | int index2= 1; |
---|
| 1101 | for (iter2= leadingCoeffs2[A.level()-3]; iter2.hasItem(); |
---|
| 1102 | iter2++, index2++) |
---|
| 1103 | { |
---|
| 1104 | if (index2 == index) |
---|
| 1105 | { |
---|
| 1106 | iter2.getItem() /= iter.getItem(); |
---|
| 1107 | foundMultiplier= true; |
---|
| 1108 | break; |
---|
| 1109 | } |
---|
| 1110 | } |
---|
| 1111 | A /= iter.getItem(); |
---|
| 1112 | LCmultiplier /= iter.getItem(); |
---|
| 1113 | iter.getItem()= 1; |
---|
| 1114 | break; |
---|
| 1115 | } |
---|
| 1116 | } |
---|
| 1117 | } |
---|
| 1118 | } |
---|
| 1119 | // wipe out the last LCmultiplier |
---|
| 1120 | if (foundMultiplier) |
---|
| 1121 | { |
---|
| 1122 | index= 1; |
---|
| 1123 | for (iter= contents; iter.hasItem(); iter++, index++) |
---|
| 1124 | { |
---|
| 1125 | if (!iter.getItem().isOne() && |
---|
| 1126 | fdivides (LCmultiplier, iter.getItem())) |
---|
| 1127 | { |
---|
| 1128 | int index2= 1; |
---|
| 1129 | for (iter2= leadingCoeffs2[A.level()-3]; iter2.hasItem(); |
---|
| 1130 | iter2++, index2++) |
---|
| 1131 | { |
---|
| 1132 | if (index2 == index) |
---|
| 1133 | { |
---|
| 1134 | iter2.getItem() /= LCmultiplier; |
---|
| 1135 | A /= LCmultiplier; |
---|
| 1136 | iter.getItem() /= LCmultiplier; |
---|
| 1137 | } |
---|
| 1138 | } |
---|
| 1139 | } |
---|
| 1140 | } |
---|
| 1141 | } |
---|
| 1142 | } |
---|
| 1143 | else |
---|
| 1144 | { |
---|
| 1145 | CanonicalForm pLCs= prod (LCs); |
---|
| 1146 | if (fdivides (pLCs, LC (oldA,1)) && (LC(oldA,1)/pLCs).inCoeffDomain()) // check if the product of the lead coeffs of the primitive factors equals the lead coeff of the old A |
---|
| 1147 | { |
---|
| 1148 | A= oldA; |
---|
| 1149 | iter2= leadingCoeffs2[A.level()-3]; |
---|
| 1150 | for (iter= contents; iter.hasItem(); iter++, iter2++) |
---|
| 1151 | iter2.getItem() /= iter.getItem(); |
---|
| 1152 | } |
---|
| 1153 | } |
---|
| 1154 | |
---|
| 1155 | // patch everything together again |
---|
| 1156 | leadingCoeffs= leadingCoeffs2[A.level()-3]; |
---|
| 1157 | for (int i= A.level()-3; i > -1; i--) |
---|
| 1158 | leadingCoeffs2[i]= CFList(); |
---|
| 1159 | prepareLeadingCoeffs (leadingCoeffs2,A.level(),leadingCoeffs, biFactors, |
---|
| 1160 | evaluation); |
---|
| 1161 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
| 1162 | |
---|
| 1163 | hh= Lc (Aeval.getFirst()); |
---|
| 1164 | |
---|
| 1165 | for (CFListIterator i= Aeval; i.hasItem(); i++) |
---|
| 1166 | i.getItem() /= hh; |
---|
| 1167 | |
---|
| 1168 | A /= hh; |
---|
| 1169 | } |
---|
| 1170 | factors= CFList(); |
---|
| 1171 | } |
---|
[4fe8a3] | 1172 | else |
---|
| 1173 | factors= CFList(); |
---|
[5079887] | 1174 | delete [] index; |
---|
[64b824] | 1175 | } |
---|
[4fe8a3] | 1176 | |
---|
[fcd296] | 1177 | tryAgainWithoutHeu: |
---|
[eefc3a] | 1178 | //shifting to zero |
---|
| 1179 | A= shift2Zero (A, Aeval, evaluation); |
---|
| 1180 | |
---|
| 1181 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
| 1182 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
| 1183 | |
---|
[464b18] | 1184 | for (int i= 0; i < A.level() - 3; i++) |
---|
| 1185 | leadingCoeffs2[i]= CFList(); |
---|
[eefc3a] | 1186 | for (iter= leadingCoeffs2[A.level() - 3]; iter.hasItem(); iter++) |
---|
| 1187 | { |
---|
| 1188 | iter.getItem()= shift2Zero (iter.getItem(), list, evaluation); |
---|
| 1189 | for (int i= A.level() - 4; i > -1; i--) |
---|
| 1190 | { |
---|
| 1191 | if (i + 1 == A.level() - 3) |
---|
| 1192 | leadingCoeffs2[i].append (iter.getItem() (0, i + 4)); |
---|
| 1193 | else |
---|
| 1194 | leadingCoeffs2[i].append (leadingCoeffs2[i+1].getLast() (0, i + 4)); |
---|
| 1195 | } |
---|
| 1196 | } |
---|
[ab547e2] | 1197 | |
---|
| 1198 | CFArray Pi; |
---|
| 1199 | CFList diophant; |
---|
| 1200 | int* liftBounds= new int [A.level() - 1]; |
---|
| 1201 | int liftBoundsLength= A.level() - 1; |
---|
| 1202 | for (int i= 0; i < liftBoundsLength; i++) |
---|
| 1203 | liftBounds [i]= degree (A, i + 2) + 1; |
---|
| 1204 | |
---|
| 1205 | Aeval.removeFirst(); |
---|
| 1206 | bool noOneToOne= false; |
---|
| 1207 | |
---|
[f55f39] | 1208 | CFList commonDenominators; |
---|
[6af78bb] | 1209 | for (iter=biFactors; iter.hasItem(); iter++) |
---|
[f55f39] | 1210 | commonDenominators.append (bCommonDen (iter.getItem())); |
---|
| 1211 | CanonicalForm tmp1, tmp2, tmp3=1; |
---|
| 1212 | for (int i= 0; i < A.level() - 2; i++) |
---|
| 1213 | { |
---|
| 1214 | iter2= commonDenominators; |
---|
[6af78bb] | 1215 | for (iter= leadingCoeffs2[i]; iter.hasItem(); iter++, iter2++) |
---|
[f55f39] | 1216 | { |
---|
[6af78bb] | 1217 | tmp1= bCommonDen (iter.getItem()); |
---|
[f55f39] | 1218 | Off (SW_RATIONAL); |
---|
| 1219 | iter2.getItem()= lcm (iter2.getItem(), tmp1); |
---|
| 1220 | On (SW_RATIONAL); |
---|
| 1221 | } |
---|
| 1222 | } |
---|
| 1223 | tmp1= prod (commonDenominators); |
---|
[6af78bb] | 1224 | for (iter= Aeval; iter.hasItem(); iter++) |
---|
[f55f39] | 1225 | { |
---|
[6af78bb] | 1226 | tmp2= bCommonDen (iter.getItem()); |
---|
[f55f39] | 1227 | Off (SW_RATIONAL); |
---|
| 1228 | tmp3= lcm (tmp2,tmp3); |
---|
| 1229 | On (SW_RATIONAL); |
---|
| 1230 | } |
---|
| 1231 | CanonicalForm multiplier; |
---|
| 1232 | multiplier= tmp3/tmp1; |
---|
| 1233 | iter2= commonDenominators; |
---|
[6af78bb] | 1234 | for (iter=biFactors; iter.hasItem(); iter++, iter2++) |
---|
| 1235 | iter.getItem() *= iter2.getItem()*multiplier; |
---|
[f55f39] | 1236 | |
---|
[6af78bb] | 1237 | for (iter= Aeval; iter.hasItem(); iter++) |
---|
| 1238 | iter.getItem() *= tmp3*power (multiplier, biFactors.length() - 1); |
---|
[f55f39] | 1239 | |
---|
| 1240 | for (int i= 0; i < A.level() - 2; i++) |
---|
| 1241 | { |
---|
| 1242 | iter2= commonDenominators; |
---|
[6af78bb] | 1243 | for (iter= leadingCoeffs2[i]; iter.hasItem(); iter++, iter2++) |
---|
| 1244 | iter.getItem() *= iter2.getItem()*multiplier; |
---|
[f55f39] | 1245 | } |
---|
| 1246 | |
---|
| 1247 | |
---|
[ab547e2] | 1248 | factors= nonMonicHenselLift (Aeval, biFactors, leadingCoeffs2, diophant, |
---|
| 1249 | Pi, liftBounds, liftBoundsLength, noOneToOne); |
---|
| 1250 | |
---|
| 1251 | if (!noOneToOne) |
---|
| 1252 | { |
---|
| 1253 | int check= factors.length(); |
---|
[eefc3a] | 1254 | A= oldA; |
---|
| 1255 | factors= recoverFactors (A, factors, evaluation); |
---|
[ab547e2] | 1256 | if (check != factors.length()) |
---|
| 1257 | noOneToOne= true; |
---|
[5079887] | 1258 | else |
---|
| 1259 | factors= Union (factors, bufFactors); |
---|
[ab547e2] | 1260 | } |
---|
| 1261 | if (noOneToOne) |
---|
| 1262 | { |
---|
[fcd296] | 1263 | if (!LCmultiplierIsConst && LCheuristic) |
---|
| 1264 | { |
---|
| 1265 | A= bufA; |
---|
| 1266 | biFactors= bufBiFactors; |
---|
| 1267 | leadingCoeffs2[A.level()-3]= bufLeadingCoeffs2; |
---|
| 1268 | delete [] liftBounds; |
---|
| 1269 | LCheuristic= false; |
---|
| 1270 | goto tryAgainWithoutHeu; |
---|
| 1271 | //something probably went wrong in the heuristic |
---|
| 1272 | } |
---|
| 1273 | |
---|
[eefc3a] | 1274 | A= shift2Zero (oldA, Aeval, evaluation); |
---|
[ab547e2] | 1275 | biFactors= oldBiFactors; |
---|
[eefc3a] | 1276 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
| 1277 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
[ab547e2] | 1278 | CanonicalForm LCA= LC (Aeval.getFirst(), 1); |
---|
| 1279 | CanonicalForm yToLift= power (y, lift); |
---|
| 1280 | CFListIterator i= biFactors; |
---|
| 1281 | lift= degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1; |
---|
| 1282 | i++; |
---|
| 1283 | |
---|
| 1284 | for (; i.hasItem(); i++) |
---|
| 1285 | lift= tmax (lift, degree (i.getItem(), 2)+degree (LC (i.getItem(), 1))+1); |
---|
| 1286 | |
---|
| 1287 | lift= tmax (degree (Aeval.getFirst() , 2) + 1, lift); |
---|
| 1288 | |
---|
| 1289 | i= biFactors; |
---|
| 1290 | yToLift= power (y, lift); |
---|
| 1291 | CanonicalForm dummy; |
---|
| 1292 | for (; i.hasItem(); i++) |
---|
| 1293 | { |
---|
| 1294 | LCA= LC (i.getItem(), 1); |
---|
| 1295 | extgcd (LCA, yToLift, LCA, dummy); |
---|
| 1296 | i.getItem()= mod (i.getItem()*LCA, yToLift); |
---|
| 1297 | } |
---|
| 1298 | |
---|
| 1299 | liftBoundsLength= F.level() - 1; |
---|
| 1300 | liftBounds= liftingBounds (A, lift); |
---|
| 1301 | |
---|
| 1302 | CFList MOD; |
---|
| 1303 | bool earlySuccess; |
---|
| 1304 | CFList earlyFactors; |
---|
| 1305 | ExtensionInfo info= ExtensionInfo (false); |
---|
[0b618a7] | 1306 | CFList liftedFactors; |
---|
[ec664a2] | 1307 | TIMING_START (fac_hensel_lift); |
---|
[0b618a7] | 1308 | liftedFactors= henselLiftAndEarly |
---|
| 1309 | (A, MOD, liftBounds, earlySuccess, earlyFactors, |
---|
| 1310 | Aeval, biFactors, evaluation, info); |
---|
[ec664a2] | 1311 | TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: "); |
---|
[0b618a7] | 1312 | |
---|
[ec664a2] | 1313 | TIMING_START (fac_factor_recombination); |
---|
[ab547e2] | 1314 | factors= factorRecombination (A, liftedFactors, MOD); |
---|
[ec664a2] | 1315 | TIMING_END_AND_PRINT (fac_factor_recombination, |
---|
[ab547e2] | 1316 | "time for factor recombination: "); |
---|
| 1317 | |
---|
| 1318 | if (earlySuccess) |
---|
| 1319 | factors= Union (factors, earlyFactors); |
---|
| 1320 | |
---|
[c79a9d] | 1321 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[ab547e2] | 1322 | { |
---|
[c79a9d] | 1323 | int kk= Aeval.getLast().level(); |
---|
| 1324 | for (CFListIterator j= evaluation; j.hasItem(); j++, kk--) |
---|
| 1325 | { |
---|
| 1326 | if (i.getItem().level() < kk) |
---|
| 1327 | continue; |
---|
| 1328 | i.getItem()= i.getItem() (Variable (kk) - j.getItem(), kk); |
---|
| 1329 | } |
---|
[ab547e2] | 1330 | } |
---|
| 1331 | } |
---|
| 1332 | |
---|
| 1333 | if (w.level() != 1) |
---|
| 1334 | { |
---|
| 1335 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
| 1336 | iter.getItem()= swapvar (iter.getItem(), w, y); |
---|
| 1337 | } |
---|
| 1338 | |
---|
| 1339 | swap (factors, 0, 0, x); |
---|
| 1340 | append (factors, contentAFactors); |
---|
| 1341 | decompress (factors, N); |
---|
| 1342 | if (isOn (SW_RATIONAL)) |
---|
| 1343 | normalize (factors); |
---|
| 1344 | |
---|
[229530] | 1345 | delete [] leadingCoeffs2; |
---|
| 1346 | delete [] oldAeval; |
---|
| 1347 | delete [] Aeval2; |
---|
[ab547e2] | 1348 | delete[] liftBounds; |
---|
| 1349 | |
---|
| 1350 | return factors; |
---|
| 1351 | } |
---|
[d990001] | 1352 | |
---|
| 1353 | #endif |
---|