1 | /***************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | *****************************************/ |
---|
4 | /* $Id$ */ |
---|
5 | /* |
---|
6 | * ABSTRACT: Implementation of the Groebner walk |
---|
7 | */ |
---|
8 | |
---|
9 | // define if the Buchberger alg should be used |
---|
10 | // to compute a reduced GB of a omega-homogenoues ideal |
---|
11 | // default: we use the hilbert driven algorithm. |
---|
12 | #define BUCHBERGER_ALG //we use the improved Buchberger alg. |
---|
13 | |
---|
14 | //#define UPPER_BOUND //for the original "Tran" algorithm |
---|
15 | //#define REPRESENTATION_OF_SIGMA //if one perturbs sigma in Tran |
---|
16 | |
---|
17 | //#define TEST_OVERFLOW |
---|
18 | //#define CHECK_IDEAL |
---|
19 | //#define CHECK_IDEAL_MWALK |
---|
20 | |
---|
21 | //#define NEXT_VECTORS_CC |
---|
22 | //#define PRINT_VECTORS //to print vectors (sigma, tau, omega) |
---|
23 | |
---|
24 | #define INVEPS_SMALL_IN_FRACTAL //to choose the small invers of epsilon |
---|
25 | #define INVEPS_SMALL_IN_MPERTVECTOR //to choose the small invers of epsilon |
---|
26 | #define INVEPS_SMALL_IN_TRAN //to choose the small invers of epsilon |
---|
27 | |
---|
28 | #define FIRST_STEP_FRACTAL // to define the first step of the fractal |
---|
29 | //#define MSTDCC_FRACTAL // apply Buchberger alg to compute a red GB, if |
---|
30 | // tau doesn't stay in the correct cone |
---|
31 | |
---|
32 | //#define TIME_TEST // print the used time of each subroutine |
---|
33 | //#define ENDWALKS //print the size of the last omega-homogenoues Groebner basis |
---|
34 | |
---|
35 | /* includes */ |
---|
36 | |
---|
37 | #include <kernel/mod2.h> |
---|
38 | #include <misc/intvec.h> |
---|
39 | #include <Singular/cntrlc.h> |
---|
40 | #include <misc/options.h> |
---|
41 | #include <omalloc/omalloc.h> |
---|
42 | #include <kernel/febase.h> |
---|
43 | #include <Singular/ipshell.h> |
---|
44 | #include <Singular/ipconv.h> |
---|
45 | #include <coeffs/ffields.h> |
---|
46 | #include <coeffs/coeffs.h> |
---|
47 | #include <Singular/subexpr.h> |
---|
48 | #include <polys/templates/p_Procs.h> |
---|
49 | |
---|
50 | #include <polys/monomials/maps.h> |
---|
51 | |
---|
52 | /* include Hilbert-function */ |
---|
53 | #include <kernel/GBEngine/stairc.h> |
---|
54 | |
---|
55 | /** kstd2.cc */ |
---|
56 | #include <kernel/GBEngine/kutil.h> |
---|
57 | #include <kernel/GBEngine/khstd.h> |
---|
58 | |
---|
59 | #include <Singular/walk.h> |
---|
60 | #include <kernel/polys.h> |
---|
61 | #include <kernel/ideals.h> |
---|
62 | #include <Singular/ipid.h> |
---|
63 | #include <Singular/tok.h> |
---|
64 | #include <kernel/febase.h> |
---|
65 | #include <coeffs/numbers.h> |
---|
66 | #include <Singular/ipid.h> |
---|
67 | #include <polys/monomials/ring.h> |
---|
68 | #include <kernel/GBEngine/kstd1.h> |
---|
69 | #include <polys/matpol.h> |
---|
70 | #include <polys/weight.h> |
---|
71 | #include <misc/intvec.h> |
---|
72 | #include <kernel/GBEngine/syz.h> |
---|
73 | #include <Singular/lists.h> |
---|
74 | #include <polys/prCopy.h> |
---|
75 | #include <polys/monomials/ring.h> |
---|
76 | //#include <polys/ext_fields/longalg.h> |
---|
77 | #include <polys/clapsing.h> |
---|
78 | |
---|
79 | #include <coeffs/mpr_complex.h> |
---|
80 | |
---|
81 | #include <stdio.h> |
---|
82 | // === Zeit & System (Holger Croeni === |
---|
83 | #include <time.h> |
---|
84 | #include <sys/time.h> |
---|
85 | #include <math.h> |
---|
86 | #include <sys/stat.h> |
---|
87 | #include <unistd.h> |
---|
88 | #include <float.h> |
---|
89 | #include <misc/mylimits.h> |
---|
90 | #include <sys/types.h> |
---|
91 | |
---|
92 | int nstep; |
---|
93 | |
---|
94 | extern BOOLEAN ErrorCheck(); |
---|
95 | |
---|
96 | extern BOOLEAN pSetm_error; |
---|
97 | |
---|
98 | void Set_Error( BOOLEAN f) { pSetm_error=f; } |
---|
99 | |
---|
100 | BOOLEAN Overflow_Error = FALSE; |
---|
101 | |
---|
102 | clock_t xtif, xtstd, xtlift, xtred, xtnw; |
---|
103 | clock_t xftostd, xtextra, xftinput, to; |
---|
104 | |
---|
105 | /**************************** |
---|
106 | * utilities for TSet, LSet * |
---|
107 | ****************************/ |
---|
108 | inline static intset initec (int maxnr) |
---|
109 | { |
---|
110 | return (intset)omAlloc(maxnr*sizeof(int)); |
---|
111 | } |
---|
112 | |
---|
113 | inline static unsigned long* initsevS (int maxnr) |
---|
114 | { |
---|
115 | return (unsigned long*)omAlloc0(maxnr*sizeof(unsigned long)); |
---|
116 | } |
---|
117 | inline static int* initS_2_R (int maxnr) |
---|
118 | { |
---|
119 | return (int*)omAlloc0(maxnr*sizeof(int)); |
---|
120 | } |
---|
121 | |
---|
122 | /************************************ |
---|
123 | * construct the set s from F u {P} * |
---|
124 | ************************************/ |
---|
125 | // unused |
---|
126 | #if 0 |
---|
127 | static void initSSpecialCC (ideal F, ideal Q, ideal P,kStrategy strat) |
---|
128 | { |
---|
129 | int i,pos; |
---|
130 | |
---|
131 | if (Q!=NULL) i=((IDELEMS(Q)+(setmaxTinc-1))/setmaxTinc)*setmaxTinc; |
---|
132 | else i=setmaxT; |
---|
133 | |
---|
134 | strat->ecartS=initec(i); |
---|
135 | strat->sevS=initsevS(i); |
---|
136 | strat->S_2_R=initS_2_R(i); |
---|
137 | strat->fromQ=NULL; |
---|
138 | strat->Shdl=idInit(i,F->rank); |
---|
139 | strat->S=strat->Shdl->m; |
---|
140 | |
---|
141 | // - put polys into S - |
---|
142 | if (Q!=NULL) |
---|
143 | { |
---|
144 | strat->fromQ=initec(i); |
---|
145 | memset(strat->fromQ,0,i*sizeof(int)); |
---|
146 | for (i=0; i<IDELEMS(Q); i++) |
---|
147 | { |
---|
148 | if (Q->m[i]!=NULL) |
---|
149 | { |
---|
150 | LObject h; |
---|
151 | h.p = pCopy(Q->m[i]); |
---|
152 | //if (TEST_OPT_INTSTRATEGY) |
---|
153 | //{ |
---|
154 | // //pContent(h.p); |
---|
155 | // h.pCleardenom(); // also does a pContent |
---|
156 | //} |
---|
157 | //else |
---|
158 | //{ |
---|
159 | // h.pNorm(); |
---|
160 | //} |
---|
161 | strat->initEcart(&h); |
---|
162 | if (rHasLocalOrMixedOrdering_currRing()) |
---|
163 | { |
---|
164 | deleteHC(&h,strat); |
---|
165 | } |
---|
166 | if (h.p!=NULL) |
---|
167 | { |
---|
168 | if (strat->sl==-1) |
---|
169 | pos =0; |
---|
170 | else |
---|
171 | { |
---|
172 | pos = posInS(strat,strat->sl,h.p,h.ecart); |
---|
173 | } |
---|
174 | h.sev = pGetShortExpVector(h.p); |
---|
175 | h.SetpFDeg(); |
---|
176 | strat->enterS(h,pos,strat, strat->tl+1); |
---|
177 | enterT(h, strat); |
---|
178 | strat->fromQ[pos]=1; |
---|
179 | } |
---|
180 | } |
---|
181 | } |
---|
182 | } |
---|
183 | //- put polys into S - |
---|
184 | for (i=0; i<IDELEMS(F); i++) |
---|
185 | { |
---|
186 | if (F->m[i]!=NULL) |
---|
187 | { |
---|
188 | LObject h; |
---|
189 | h.p = pCopy(F->m[i]); |
---|
190 | if (rHasGlobalOrdering(currRing)) |
---|
191 | { |
---|
192 | //h.p=redtailBba(h.p,strat->sl,strat); |
---|
193 | h.p=redtailBba(h.p,strat->sl,strat); |
---|
194 | } |
---|
195 | else |
---|
196 | { |
---|
197 | deleteHC(&h,strat); |
---|
198 | } |
---|
199 | strat->initEcart(&h); |
---|
200 | if (h.p!=NULL) |
---|
201 | { |
---|
202 | if (strat->sl==-1) |
---|
203 | pos =0; |
---|
204 | else |
---|
205 | pos = posInS(strat,strat->sl,h.p,h.ecart); |
---|
206 | h.sev = pGetShortExpVector(h.p); |
---|
207 | strat->enterS(h,pos,strat, strat->tl+1); |
---|
208 | h.length = pLength(h.p); |
---|
209 | h.SetpFDeg(); |
---|
210 | enterT(h,strat); |
---|
211 | } |
---|
212 | } |
---|
213 | } |
---|
214 | #ifdef INITSSPECIAL |
---|
215 | for (i=0; i<IDELEMS(P); i++) |
---|
216 | { |
---|
217 | if (P->m[i]!=NULL) |
---|
218 | { |
---|
219 | LObject h; |
---|
220 | h.p=pCopy(P->m[i]); |
---|
221 | strat->initEcart(&h); |
---|
222 | h.length = pLength(h.p); |
---|
223 | if (TEST_OPT_INTSTRATEGY) |
---|
224 | { |
---|
225 | h.pCleardenom(); |
---|
226 | } |
---|
227 | else |
---|
228 | { |
---|
229 | h.pNorm(); |
---|
230 | } |
---|
231 | if(strat->sl>=0) |
---|
232 | { |
---|
233 | if (rHasGlobalOrdering(currRing)) |
---|
234 | { |
---|
235 | h.p=redBba(h.p,strat->sl,strat); |
---|
236 | if (h.p!=NULL) |
---|
237 | h.p=redtailBba(h.p,strat->sl,strat); |
---|
238 | } |
---|
239 | else |
---|
240 | { |
---|
241 | h.p=redMora(h.p,strat->sl,strat); |
---|
242 | strat->initEcart(&h); |
---|
243 | } |
---|
244 | if(h.p!=NULL) |
---|
245 | { |
---|
246 | if (TEST_OPT_INTSTRATEGY) |
---|
247 | { |
---|
248 | h.pCleardenom(); |
---|
249 | } |
---|
250 | else |
---|
251 | { |
---|
252 | h.is_normalized = 0; |
---|
253 | h.pNorm(); |
---|
254 | } |
---|
255 | h.sev = pGetShortExpVector(h.p); |
---|
256 | h.SetpFDeg(); |
---|
257 | pos = posInS(strat->S,strat->sl,h.p,h.ecart); |
---|
258 | enterpairsSpecial(h.p,strat->sl,h.ecart,pos,strat,strat->tl+1); |
---|
259 | strat->enterS(h,pos,strat, strat->tl+1); |
---|
260 | enterT(h,strat); |
---|
261 | } |
---|
262 | } |
---|
263 | else |
---|
264 | { |
---|
265 | h.sev = pGetShortExpVector(h.p); |
---|
266 | h.SetpFDeg(); |
---|
267 | strat->enterS(h,0,strat, strat->tl+1); |
---|
268 | enterT(h,strat); |
---|
269 | } |
---|
270 | } |
---|
271 | } |
---|
272 | #endif |
---|
273 | } |
---|
274 | #endif |
---|
275 | |
---|
276 | /***************** |
---|
277 | *interreduce F * |
---|
278 | *****************/ |
---|
279 | static ideal kInterRedCC(ideal F, ideal Q) |
---|
280 | { |
---|
281 | int j; |
---|
282 | kStrategy strat = new skStrategy; |
---|
283 | |
---|
284 | // if (TEST_OPT_PROT) |
---|
285 | // { |
---|
286 | // writeTime("start InterRed:"); |
---|
287 | // mflush(); |
---|
288 | // } |
---|
289 | //strat->syzComp = 0; |
---|
290 | strat->kHEdgeFound = (currRing->ppNoether) != NULL; |
---|
291 | strat->kNoether=pCopy((currRing->ppNoether)); |
---|
292 | strat->ak = id_RankFreeModule(F, currRing); |
---|
293 | initBuchMoraCrit(strat); |
---|
294 | strat->NotUsedAxis = (BOOLEAN *)omAlloc((currRing->N+1)*sizeof(BOOLEAN)); |
---|
295 | for(j=currRing->N; j>0; j--) |
---|
296 | { |
---|
297 | strat->NotUsedAxis[j] = TRUE; |
---|
298 | } |
---|
299 | strat->enterS = enterSBba; |
---|
300 | strat->posInT = posInT0; |
---|
301 | strat->initEcart = initEcartNormal; |
---|
302 | strat->sl = -1; |
---|
303 | strat->tl = -1; |
---|
304 | strat->tmax = setmaxT; |
---|
305 | strat->T = initT(); |
---|
306 | strat->R = initR(); |
---|
307 | strat->sevT = initsevT(); |
---|
308 | if(rHasLocalOrMixedOrdering_currRing()) |
---|
309 | { |
---|
310 | strat->honey = TRUE; |
---|
311 | } |
---|
312 | |
---|
313 | //initSCC(F,Q,strat); |
---|
314 | initS(F,Q,strat); |
---|
315 | |
---|
316 | /* |
---|
317 | timetmp=clock();//22.01.02 |
---|
318 | initSSpecialCC(F,Q,NULL,strat); |
---|
319 | tininitS=tininitS+clock()-timetmp;//22.01.02 |
---|
320 | */ |
---|
321 | if(TEST_OPT_REDSB) |
---|
322 | { |
---|
323 | strat->noTailReduction=FALSE; |
---|
324 | } |
---|
325 | updateS(TRUE,strat); |
---|
326 | |
---|
327 | if(TEST_OPT_REDSB && TEST_OPT_INTSTRATEGY) |
---|
328 | { |
---|
329 | completeReduce(strat); |
---|
330 | } |
---|
331 | pDelete(&strat->kHEdge); |
---|
332 | omFreeSize((ADDRESS)strat->T,strat->tmax*sizeof(TObject)); |
---|
333 | omFreeSize((ADDRESS)strat->ecartS,IDELEMS(strat->Shdl)*sizeof(int)); |
---|
334 | omFreeSize((ADDRESS)strat->sevS,IDELEMS(strat->Shdl)*sizeof(unsigned long)); |
---|
335 | omFreeSize((ADDRESS)strat->NotUsedAxis,(currRing->N+1)*sizeof(BOOLEAN)); |
---|
336 | omfree(strat->sevT); |
---|
337 | omfree(strat->S_2_R); |
---|
338 | omfree(strat->R); |
---|
339 | |
---|
340 | if(strat->fromQ) |
---|
341 | { |
---|
342 | for(j=0; j<IDELEMS(strat->Shdl); j++) |
---|
343 | { |
---|
344 | if(strat->fromQ[j]) |
---|
345 | { |
---|
346 | pDelete(&strat->Shdl->m[j]); |
---|
347 | } |
---|
348 | } |
---|
349 | omFreeSize((ADDRESS)strat->fromQ,IDELEMS(strat->Shdl)*sizeof(int)); |
---|
350 | strat->fromQ = NULL; |
---|
351 | } |
---|
352 | // if (TEST_OPT_PROT) |
---|
353 | // { |
---|
354 | // writeTime("end Interred:"); |
---|
355 | // mflush(); |
---|
356 | // } |
---|
357 | ideal shdl=strat->Shdl; |
---|
358 | idSkipZeroes(shdl); |
---|
359 | delete(strat); |
---|
360 | |
---|
361 | return shdl; |
---|
362 | } |
---|
363 | |
---|
364 | //unused |
---|
365 | #if 0 |
---|
366 | static void TimeString(clock_t tinput, clock_t tostd, clock_t tif,clock_t tstd, |
---|
367 | clock_t tlf,clock_t tred, clock_t tnw, int step) |
---|
368 | { |
---|
369 | double totm = ((double) (clock() - tinput))/1000000; |
---|
370 | double ostd,mostd, mif, mstd, mlf, mred, mnw, mxif,mxstd,mxlf,mxred,mxnw,tot; |
---|
371 | // double mextra |
---|
372 | Print("\n// total time = %.2f sec", totm); |
---|
373 | Print("\n// tostd = %.2f sec = %.2f", ostd=((double) tostd)/1000000, |
---|
374 | mostd=((((double) tostd)/1000000)/totm)*100); |
---|
375 | Print("\n// tif = %.2f sec = %.2f", ((double) tif)/1000000, |
---|
376 | mif=((((double) tif)/1000000)/totm)*100); |
---|
377 | Print("\n// std = %.2f sec = %.2f", ((double) tstd)/1000000, |
---|
378 | mstd=((((double) tstd)/1000000)/totm)*100); |
---|
379 | Print("\n// lift = %.2f sec = %.2f", ((double) tlf)/1000000, |
---|
380 | mlf=((((double) tlf)/1000000)/totm)*100); |
---|
381 | Print("\n// ired = %.2f sec = %.2f", ((double) tred)/1000000, |
---|
382 | mred=((((double) tred)/1000000)/totm)*100); |
---|
383 | Print("\n// nextw = %.2f sec = %.2f", ((double) tnw)/1000000, |
---|
384 | mnw=((((double) tnw)/1000000)/totm)*100); |
---|
385 | PrintS("\n Time for the last step:"); |
---|
386 | Print("\n// xinfo = %.2f sec = %.2f", ((double) xtif)/1000000, |
---|
387 | mxif=((((double) xtif)/1000000)/totm)*100); |
---|
388 | Print("\n// xstd = %.2f sec = %.2f", ((double) xtstd)/1000000, |
---|
389 | mxstd=((((double) xtstd)/1000000)/totm)*100); |
---|
390 | Print("\n// xlift = %.2f sec = %.2f", ((double) xtlift)/1000000, |
---|
391 | mxlf=((((double) xtlift)/1000000)/totm)*100); |
---|
392 | Print("\n// xired = %.2f sec = %.2f", ((double) xtred)/1000000, |
---|
393 | mxred=((((double) xtred)/1000000)/totm)*100); |
---|
394 | Print("\n// xnextw= %.2f sec = %.2f", ((double) xtnw)/1000000, |
---|
395 | mxnw=((((double) xtnw)/1000000)/totm)*100); |
---|
396 | |
---|
397 | tot=mostd+mif+mstd+mlf+mred+mnw+mxif+mxstd+mxlf+mxred+mxnw; |
---|
398 | double res = (double) 100 - tot; |
---|
399 | Print("\n// &%d&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f(%.2f)\\ \\", |
---|
400 | step, ostd, totm, mostd,mif,mstd,mlf,mred,mnw,mxif,mxstd,mxlf,mxred,mxnw,tot,res, |
---|
401 | ((((double) xtextra)/1000000)/totm)*100); |
---|
402 | } |
---|
403 | #endif |
---|
404 | |
---|
405 | //unused |
---|
406 | #if 0 |
---|
407 | static void TimeStringFractal(clock_t tinput, clock_t tostd, clock_t tif,clock_t tstd, |
---|
408 | clock_t textra, clock_t tlf,clock_t tred, clock_t tnw) |
---|
409 | { |
---|
410 | |
---|
411 | double totm = ((double) (clock() - tinput))/1000000; |
---|
412 | double ostd, mostd, mif, mstd, mextra, mlf, mred, mnw, tot, res; |
---|
413 | Print("\n// total time = %.2f sec", totm); |
---|
414 | Print("\n// tostd = %.2f sec = %.2f", ostd=((double) tostd)/1000000, |
---|
415 | mostd=((((double) tostd)/1000000)/totm)*100); |
---|
416 | Print("\n// tif = %.2f sec = %.2f", ((double) tif)/1000000, |
---|
417 | mif=((((double) tif)/1000000)/totm)*100); |
---|
418 | Print("\n// std = %.2f sec = %.2f", ((double) tstd)/1000000, |
---|
419 | mstd=((((double) tstd)/1000000)/totm)*100); |
---|
420 | Print("\n// xstd = %.2f sec = %.2f", ((double) textra)/1000000, |
---|
421 | mextra=((((double) textra)/1000000)/totm)*100); |
---|
422 | Print("\n// lift = %.2f sec = %.2f", ((double) tlf)/1000000, |
---|
423 | mlf=((((double) tlf)/1000000)/totm)*100); |
---|
424 | Print("\n// ired = %.2f sec = %.2f", ((double) tred)/1000000, |
---|
425 | mred=((((double) tred)/1000000)/totm)*100); |
---|
426 | Print("\n// nextw = %.2f sec = %.2f", ((double) tnw)/1000000, |
---|
427 | mnw=((((double) tnw)/1000000)/totm)*100); |
---|
428 | tot = mostd+mif+mstd+mextra+mlf+mred+mnw; |
---|
429 | res = (double) 100.00-tot; |
---|
430 | Print("\n// &%.2f &%.2f&%.2f &%.2f &%.2f &%.2f &%.2f &%.2f &%.2f&%.2f&%.2f\\ \\ ", |
---|
431 | ostd,totm,mostd,mif,mstd,mextra,mlf,mred,mnw,tot,res); |
---|
432 | } |
---|
433 | #endif |
---|
434 | |
---|
435 | #ifdef CHECK_IDEAL_MWALK |
---|
436 | static void idString(ideal L, const char* st) |
---|
437 | { |
---|
438 | int i, nL = IDELEMS(L); |
---|
439 | |
---|
440 | Print("\n// ideal %s = ", st); |
---|
441 | for(i=0; i<nL-1; i++) |
---|
442 | { |
---|
443 | Print(" %s, ", pString(L->m[i])); |
---|
444 | } |
---|
445 | Print(" %s;", pString(L->m[nL-1])); |
---|
446 | } |
---|
447 | #endif |
---|
448 | |
---|
449 | #if defined(CHECK_IDEAL_MWALK) || defined(ENDWALKS) |
---|
450 | static void headidString(ideal L, char* st) |
---|
451 | { |
---|
452 | int i, nL = IDELEMS(L); |
---|
453 | |
---|
454 | Print("\n// ideal %s = ", st); |
---|
455 | for(i=0; i<nL-1; i++) |
---|
456 | { |
---|
457 | Print(" %s, ", pString(pHead(L->m[i]))); |
---|
458 | } |
---|
459 | Print(" %s;", pString(pHead(L->m[nL-1]))); |
---|
460 | } |
---|
461 | #endif |
---|
462 | |
---|
463 | #if defined(CHECK_IDEAL_MWALK) || defined(ENDWALKS) |
---|
464 | static void idElements(ideal L, char* st) |
---|
465 | { |
---|
466 | int i, nL = IDELEMS(L); |
---|
467 | int *K=(int *)omAlloc(nL*sizeof(int)); |
---|
468 | |
---|
469 | Print("\n// #monoms of %s = ", st); |
---|
470 | for(i=0; i<nL; i++) |
---|
471 | { |
---|
472 | K[i] = pLength(L->m[i]); |
---|
473 | } |
---|
474 | int j, nsame; |
---|
475 | // int nk=0; |
---|
476 | for(i=0; i<nL; i++) |
---|
477 | { |
---|
478 | if(K[i]!=0) |
---|
479 | { |
---|
480 | nsame = 1; |
---|
481 | for(j=i+1; j<nL; j++) |
---|
482 | { |
---|
483 | if(K[j]==K[i]) |
---|
484 | { |
---|
485 | nsame ++; |
---|
486 | K[j]=0; |
---|
487 | } |
---|
488 | } |
---|
489 | if(nsame == 1) |
---|
490 | { |
---|
491 | Print("%d, ",K[i]); |
---|
492 | } |
---|
493 | else |
---|
494 | { |
---|
495 | Print("%d[%d], ", K[i], nsame); |
---|
496 | } |
---|
497 | } |
---|
498 | } |
---|
499 | omFree(K); |
---|
500 | } |
---|
501 | #endif |
---|
502 | |
---|
503 | |
---|
504 | static void ivString(intvec* iv, const char* ch) |
---|
505 | { |
---|
506 | int nV = iv->length()-1; |
---|
507 | Print("\n// intvec %s = ", ch); |
---|
508 | |
---|
509 | for(int i=0; i<nV; i++) |
---|
510 | { |
---|
511 | Print("%d, ", (*iv)[i]); |
---|
512 | } |
---|
513 | Print("%d;", (*iv)[nV]); |
---|
514 | } |
---|
515 | |
---|
516 | //unused |
---|
517 | //#if 0 |
---|
518 | static void MivString(intvec* iva, intvec* ivb, intvec* ivc) |
---|
519 | { |
---|
520 | int nV = iva->length()-1; |
---|
521 | int i; |
---|
522 | PrintS("\n// ("); |
---|
523 | for(i=0; i<nV; i++) |
---|
524 | { |
---|
525 | Print("%d, ", (*iva)[i]); |
---|
526 | } |
---|
527 | Print("%d) ==> (", (*iva)[nV]); |
---|
528 | for(i=0; i<nV; i++) |
---|
529 | { |
---|
530 | Print("%d, ", (*ivb)[i]); |
---|
531 | } |
---|
532 | Print("%d) := (", (*ivb)[nV]); |
---|
533 | |
---|
534 | for(i=0; i<nV; i++) |
---|
535 | { |
---|
536 | Print("%d, ", (*ivc)[i]); |
---|
537 | } |
---|
538 | Print("%d)", (*ivc)[nV]); |
---|
539 | } |
---|
540 | //#endif |
---|
541 | |
---|
542 | /******************************************************************** |
---|
543 | * returns gcd of integers a and b * |
---|
544 | ********************************************************************/ |
---|
545 | static inline long gcd(const long a, const long b) |
---|
546 | { |
---|
547 | long r, p0 = a, p1 = b; |
---|
548 | //assume(p0 >= 0 && p1 >= 0); |
---|
549 | if(p0 < 0) |
---|
550 | { |
---|
551 | p0 = -p0; |
---|
552 | } |
---|
553 | if(p1 < 0) |
---|
554 | { |
---|
555 | p1 = -p1; |
---|
556 | } |
---|
557 | while(p1 != 0) |
---|
558 | { |
---|
559 | r = p0 % p1; |
---|
560 | p0 = p1; |
---|
561 | p1 = r; |
---|
562 | } |
---|
563 | return p0; |
---|
564 | } |
---|
565 | |
---|
566 | /********************************************* |
---|
567 | * cancel gcd of integers zaehler and nenner * |
---|
568 | *********************************************/ |
---|
569 | static void cancel(mpz_t zaehler, mpz_t nenner) |
---|
570 | { |
---|
571 | // assume(zaehler >= 0 && nenner > 0); |
---|
572 | mpz_t g; |
---|
573 | mpz_init(g); |
---|
574 | mpz_gcd(g, zaehler, nenner); |
---|
575 | |
---|
576 | mpz_div(zaehler , zaehler, g); |
---|
577 | mpz_div(nenner , nenner, g); |
---|
578 | |
---|
579 | mpz_clear(g); |
---|
580 | } |
---|
581 | |
---|
582 | //unused |
---|
583 | #if 0 |
---|
584 | static int isVectorNeg(intvec* omega) |
---|
585 | { |
---|
586 | int i; |
---|
587 | |
---|
588 | for(i=omega->length(); i>=0; i--) |
---|
589 | { |
---|
590 | if((*omega)[i]<0) |
---|
591 | { |
---|
592 | return 1; |
---|
593 | } |
---|
594 | } |
---|
595 | return 0; |
---|
596 | } |
---|
597 | #endif |
---|
598 | |
---|
599 | /******************************************************************** |
---|
600 | * compute a weight degree of a monomial p w.r.t. a weight_vector * |
---|
601 | ********************************************************************/ |
---|
602 | static inline int MLmWeightedDegree(const poly p, intvec* weight) |
---|
603 | { |
---|
604 | /* 2147483647 is max. integer representation in SINGULAR */ |
---|
605 | mpz_t sing_int; |
---|
606 | mpz_init_set_ui(sing_int, 2147483647); |
---|
607 | |
---|
608 | int i, wgrad; |
---|
609 | |
---|
610 | mpz_t zmul; |
---|
611 | mpz_init(zmul); |
---|
612 | mpz_t zvec; |
---|
613 | mpz_init(zvec); |
---|
614 | mpz_t zsum; |
---|
615 | mpz_init(zsum); |
---|
616 | |
---|
617 | for (i=currRing->N; i>0; i--) |
---|
618 | { |
---|
619 | mpz_set_si(zvec, (*weight)[i-1]); |
---|
620 | mpz_mul_ui(zmul, zvec, pGetExp(p, i)); |
---|
621 | mpz_add(zsum, zsum, zmul); |
---|
622 | } |
---|
623 | |
---|
624 | wgrad = mpz_get_ui(zsum); |
---|
625 | |
---|
626 | if(mpz_cmp(zsum, sing_int)>0) |
---|
627 | { |
---|
628 | if(Overflow_Error == FALSE) |
---|
629 | { |
---|
630 | PrintLn(); |
---|
631 | PrintS("\n// ** OVERFLOW in \"MwalkInitialForm\": "); |
---|
632 | mpz_out_str( stdout, 10, zsum); |
---|
633 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
634 | Overflow_Error = TRUE; |
---|
635 | } |
---|
636 | } |
---|
637 | |
---|
638 | mpz_clear(zmul); |
---|
639 | mpz_clear(zvec); |
---|
640 | mpz_clear(zsum); |
---|
641 | mpz_clear(sing_int); |
---|
642 | |
---|
643 | return wgrad; |
---|
644 | } |
---|
645 | |
---|
646 | /******************************************************************** |
---|
647 | * compute a weight degree of a polynomial p w.r.t. a weight_vector * |
---|
648 | ********************************************************************/ |
---|
649 | static inline int MwalkWeightDegree(poly p, intvec* weight_vector) |
---|
650 | { |
---|
651 | assume(weight_vector->length() >= currRing->N); |
---|
652 | int max = 0, maxtemp; |
---|
653 | |
---|
654 | while(p != NULL) |
---|
655 | { |
---|
656 | maxtemp = MLmWeightedDegree(p, weight_vector); |
---|
657 | pIter(p); |
---|
658 | |
---|
659 | if (maxtemp > max) |
---|
660 | { |
---|
661 | max = maxtemp; |
---|
662 | } |
---|
663 | } |
---|
664 | return max; |
---|
665 | } |
---|
666 | |
---|
667 | |
---|
668 | /******************************************************************** |
---|
669 | * compute a weight degree of a monomial p w.r.t. a weight_vector * |
---|
670 | ********************************************************************/ |
---|
671 | static void MLmWeightedDegree_gmp(mpz_t result, const poly p, intvec* weight) |
---|
672 | { |
---|
673 | /* 2147483647 is max. integer representation in SINGULAR */ |
---|
674 | mpz_t sing_int; |
---|
675 | mpz_init_set_ui(sing_int, 2147483647); |
---|
676 | |
---|
677 | int i; |
---|
678 | |
---|
679 | mpz_t zmul; |
---|
680 | mpz_init(zmul); |
---|
681 | mpz_t zvec; |
---|
682 | mpz_init(zvec); |
---|
683 | mpz_t ztmp; |
---|
684 | mpz_init(ztmp); |
---|
685 | |
---|
686 | for (i=currRing->N; i>0; i--) |
---|
687 | { |
---|
688 | mpz_set_si(zvec, (*weight)[i-1]); |
---|
689 | mpz_mul_ui(zmul, zvec, pGetExp(p, i)); |
---|
690 | mpz_add(ztmp, ztmp, zmul); |
---|
691 | } |
---|
692 | mpz_init_set(result, ztmp); |
---|
693 | mpz_clear(ztmp); |
---|
694 | mpz_clear(sing_int); |
---|
695 | mpz_clear(zvec); |
---|
696 | mpz_clear(zmul); |
---|
697 | } |
---|
698 | |
---|
699 | |
---|
700 | /***************************************************************************** |
---|
701 | * return an initial form of the polynom g w.r.t. a weight vector curr_weight * |
---|
702 | *****************************************************************************/ |
---|
703 | static poly MpolyInitialForm(poly g, intvec* curr_weight) |
---|
704 | { |
---|
705 | if(g == NULL) |
---|
706 | { |
---|
707 | return NULL; |
---|
708 | } |
---|
709 | mpz_t max; mpz_init(max); |
---|
710 | mpz_t maxtmp; mpz_init(maxtmp); |
---|
711 | |
---|
712 | poly hg, in_w_g = NULL; |
---|
713 | |
---|
714 | while(g != NULL) |
---|
715 | { |
---|
716 | hg = g; |
---|
717 | pIter(g); |
---|
718 | MLmWeightedDegree_gmp(maxtmp, hg, curr_weight); |
---|
719 | |
---|
720 | if(mpz_cmp(maxtmp, max)>0) |
---|
721 | { |
---|
722 | mpz_init_set(max, maxtmp); |
---|
723 | pDelete(&in_w_g); |
---|
724 | in_w_g = pHead(hg); |
---|
725 | } |
---|
726 | else |
---|
727 | { |
---|
728 | if(mpz_cmp(maxtmp, max)==0) |
---|
729 | { |
---|
730 | in_w_g = pAdd(in_w_g, pHead(hg)); |
---|
731 | } |
---|
732 | } |
---|
733 | } |
---|
734 | return in_w_g; |
---|
735 | } |
---|
736 | |
---|
737 | /************************************************************************ |
---|
738 | * compute the initial form of an ideal <G> w.r.t. a weight vector iva * |
---|
739 | ************************************************************************/ |
---|
740 | ideal MwalkInitialForm(ideal G, intvec* ivw) |
---|
741 | { |
---|
742 | BOOLEAN nError = Overflow_Error; |
---|
743 | Overflow_Error = FALSE; |
---|
744 | |
---|
745 | int i, nG = IDELEMS(G); |
---|
746 | ideal Gomega = idInit(nG, 1); |
---|
747 | |
---|
748 | for(i=nG-1; i>=0; i--) |
---|
749 | { |
---|
750 | Gomega->m[i] = MpolyInitialForm(G->m[i], ivw); |
---|
751 | } |
---|
752 | if(Overflow_Error == FALSE) |
---|
753 | { |
---|
754 | Overflow_Error = nError; |
---|
755 | } |
---|
756 | return Gomega; |
---|
757 | } |
---|
758 | |
---|
759 | /************************************************************************ |
---|
760 | * test whether the weight vector iv is in the cone of the ideal G * |
---|
761 | * i.e. test whether in(in_w(g)) = in(g) for all g in G * |
---|
762 | ************************************************************************/ |
---|
763 | |
---|
764 | static int test_w_in_ConeCC(ideal G, intvec* iv) |
---|
765 | { |
---|
766 | if(G->m[0] == NULL) |
---|
767 | { |
---|
768 | PrintS("//** the result may be WRONG, i.e. 0!!\n"); |
---|
769 | return 0; |
---|
770 | } |
---|
771 | |
---|
772 | BOOLEAN nError = Overflow_Error; |
---|
773 | Overflow_Error = FALSE; |
---|
774 | |
---|
775 | int i, nG = IDELEMS(G); |
---|
776 | poly mi, gi; |
---|
777 | |
---|
778 | for(i=nG-1; i>=0; i--) |
---|
779 | { |
---|
780 | mi = MpolyInitialForm(G->m[i], iv); |
---|
781 | gi = G->m[i]; |
---|
782 | |
---|
783 | if(mi == NULL) |
---|
784 | { |
---|
785 | pDelete(&mi); |
---|
786 | if(Overflow_Error == FALSE) |
---|
787 | { |
---|
788 | Overflow_Error = nError; |
---|
789 | } |
---|
790 | return 0; |
---|
791 | } |
---|
792 | if(!pLmEqual(mi, gi)) |
---|
793 | { |
---|
794 | pDelete(&mi); |
---|
795 | if(Overflow_Error == FALSE) |
---|
796 | { |
---|
797 | Overflow_Error = nError; |
---|
798 | } |
---|
799 | return 0; |
---|
800 | } |
---|
801 | pDelete(&mi); |
---|
802 | } |
---|
803 | |
---|
804 | if(Overflow_Error == FALSE) |
---|
805 | { |
---|
806 | Overflow_Error = nError; |
---|
807 | } |
---|
808 | return 1; |
---|
809 | } |
---|
810 | |
---|
811 | /*************************************************** |
---|
812 | * compute a least common multiple of two integers * |
---|
813 | ***************************************************/ |
---|
814 | static inline long Mlcm(long &i1, long &i2) |
---|
815 | { |
---|
816 | long temp = gcd(i1, i2); |
---|
817 | return ((i1 / temp)* i2); |
---|
818 | } |
---|
819 | |
---|
820 | |
---|
821 | /*************************************************** |
---|
822 | * return the dot product of two intvecs a and b * |
---|
823 | ***************************************************/ |
---|
824 | static inline long MivDotProduct(intvec* a, intvec* b) |
---|
825 | { |
---|
826 | assume( a->length() == b->length()); |
---|
827 | int i, n = a->length(); |
---|
828 | long result = 0; |
---|
829 | |
---|
830 | for(i=n-1; i>=0; i--) |
---|
831 | { |
---|
832 | result += (*a)[i] * (*b)[i]; |
---|
833 | } |
---|
834 | return result; |
---|
835 | } |
---|
836 | |
---|
837 | /***************************************************** |
---|
838 | * Substract two given intvecs componentwise * |
---|
839 | *****************************************************/ |
---|
840 | static intvec* MivSub(intvec* a, intvec* b) |
---|
841 | { |
---|
842 | assume( a->length() == b->length()); |
---|
843 | int i, n = a->length(); |
---|
844 | intvec* result = new intvec(n); |
---|
845 | |
---|
846 | for(i=n-1; i>=0; i--) |
---|
847 | { |
---|
848 | (*result)[i] = (*a)[i] - (*b)[i]; |
---|
849 | } |
---|
850 | return result; |
---|
851 | } |
---|
852 | |
---|
853 | /***************************************************** |
---|
854 | * return the "intvec" lead exponent of a polynomial * |
---|
855 | *****************************************************/ |
---|
856 | static intvec* MExpPol(poly f) |
---|
857 | { |
---|
858 | int i, nR = currRing->N; |
---|
859 | intvec* result = new intvec(nR); |
---|
860 | |
---|
861 | for(i=nR-1; i>=0; i--) |
---|
862 | { |
---|
863 | (*result)[i] = pGetExp(f,i+1); |
---|
864 | } |
---|
865 | return result; |
---|
866 | } |
---|
867 | |
---|
868 | /***************************************************** |
---|
869 | * Compare two given intvecs and return 1, if they * |
---|
870 | * are the same, otherwise 0 * |
---|
871 | *****************************************************/ |
---|
872 | int MivSame(intvec* u , intvec* v) |
---|
873 | { |
---|
874 | assume(u->length() == v->length()); |
---|
875 | |
---|
876 | int i, niv = u->length(); |
---|
877 | |
---|
878 | for (i=0; i<niv; i++) |
---|
879 | { |
---|
880 | if ((*u)[i] != (*v)[i]) |
---|
881 | { |
---|
882 | return 0; |
---|
883 | } |
---|
884 | } |
---|
885 | return 1; |
---|
886 | } |
---|
887 | |
---|
888 | /****************************************************** |
---|
889 | * Compare 3 given intvecs and return 0, if the first * |
---|
890 | * and the second are the same. Return 1, if the * |
---|
891 | * the second and the third are the same, otherwise 2 * |
---|
892 | ******************************************************/ |
---|
893 | int M3ivSame(intvec* temp, intvec* u , intvec* v) |
---|
894 | { |
---|
895 | assume(temp->length() == u->length() && u->length() == v->length()); |
---|
896 | |
---|
897 | if((MivSame(temp, u)) == 1) |
---|
898 | { |
---|
899 | return 0; |
---|
900 | } |
---|
901 | if((MivSame(temp, v)) == 1) |
---|
902 | { |
---|
903 | return 1; |
---|
904 | } |
---|
905 | return 2; |
---|
906 | } |
---|
907 | |
---|
908 | /***************************************************** |
---|
909 | * compute a Groebner basis of an ideal * |
---|
910 | *****************************************************/ |
---|
911 | static ideal MstdCC(ideal G) |
---|
912 | { |
---|
913 | BITSET save1,save2; |
---|
914 | SI_SAVE_OPT(save1,save2); |
---|
915 | si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB)); |
---|
916 | ideal G1 = kStd(G, NULL, testHomog, NULL); |
---|
917 | SI_RESTORE_OPT(save1,save2); |
---|
918 | |
---|
919 | idSkipZeroes(G1); |
---|
920 | return G1; |
---|
921 | } |
---|
922 | |
---|
923 | /***************************************************** |
---|
924 | * compute a Groebner basis of an homogeneous ideal * |
---|
925 | *****************************************************/ |
---|
926 | static ideal MstdhomCC(ideal G) |
---|
927 | { |
---|
928 | BITSET save1,save2; |
---|
929 | SI_SAVE_OPT(save1,save2); |
---|
930 | si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB)); |
---|
931 | ideal G1 = kStd(G, NULL, isHomog, NULL); |
---|
932 | SI_RESTORE_OPT(save1,save2); |
---|
933 | |
---|
934 | idSkipZeroes(G1); |
---|
935 | return G1; |
---|
936 | } |
---|
937 | |
---|
938 | |
---|
939 | /***************************************************************************** |
---|
940 | * create a weight matrix order as intvec of an extra weight vector (a(iv),lp)* |
---|
941 | ******************************************************************************/ |
---|
942 | intvec* MivMatrixOrder(intvec* iv) |
---|
943 | { |
---|
944 | int i, nR = iv->length(); |
---|
945 | |
---|
946 | intvec* ivm = new intvec(nR*nR); |
---|
947 | |
---|
948 | for(i=0; i<nR; i++) |
---|
949 | { |
---|
950 | (*ivm)[i] = (*iv)[i]; |
---|
951 | } |
---|
952 | for(i=1; i<nR; i++) |
---|
953 | { |
---|
954 | (*ivm)[i*nR+i-1] = 1; |
---|
955 | } |
---|
956 | return ivm; |
---|
957 | } |
---|
958 | |
---|
959 | /******************************* |
---|
960 | * return intvec = (1, ..., 1) * |
---|
961 | *******************************/ |
---|
962 | intvec* Mivdp(int nR) |
---|
963 | { |
---|
964 | int i; |
---|
965 | intvec* ivm = new intvec(nR); |
---|
966 | |
---|
967 | for(i=nR-1; i>=0; i--) |
---|
968 | { |
---|
969 | (*ivm)[i] = 1; |
---|
970 | } |
---|
971 | return ivm; |
---|
972 | } |
---|
973 | |
---|
974 | /********************************** |
---|
975 | * return intvvec = (1,0, ..., 0) * |
---|
976 | **********************************/ |
---|
977 | intvec* Mivlp(int nR) |
---|
978 | { |
---|
979 | intvec* ivm = new intvec(nR); |
---|
980 | (*ivm)[0] = 1; |
---|
981 | |
---|
982 | return ivm; |
---|
983 | } |
---|
984 | |
---|
985 | //unused |
---|
986 | /***************************************************************************** |
---|
987 | * print the max total degree and the max coefficient of G * |
---|
988 | *****************************************************************************/ |
---|
989 | #if 0 |
---|
990 | static void checkComplexity(ideal G, char* cG) |
---|
991 | { |
---|
992 | int nV = currRing->N; |
---|
993 | int nG = IDELEMS(G); |
---|
994 | intvec* ivUnit = Mivdp(nV); |
---|
995 | int i, tmpdeg, maxdeg=0; |
---|
996 | number tmpcoeff , maxcoeff=currRing->cf->nNULL; |
---|
997 | poly p; |
---|
998 | for(i=nG-1; i>=0; i--) |
---|
999 | { |
---|
1000 | tmpdeg = MwalkWeightDegree(G->m[i], ivUnit); |
---|
1001 | if(tmpdeg > maxdeg ) |
---|
1002 | { |
---|
1003 | maxdeg = tmpdeg; |
---|
1004 | } |
---|
1005 | } |
---|
1006 | |
---|
1007 | for(i=nG-1; i>=0; i--) |
---|
1008 | { |
---|
1009 | p = pCopy(G->m[i]); |
---|
1010 | while(p != NULL) |
---|
1011 | { |
---|
1012 | //tmpcoeff = pGetCoeff(pHead(p)); |
---|
1013 | tmpcoeff = pGetCoeff(p); |
---|
1014 | if(nGreater(tmpcoeff,maxcoeff)) |
---|
1015 | { |
---|
1016 | maxcoeff = nCopy(tmpcoeff); |
---|
1017 | } |
---|
1018 | pIter(p); |
---|
1019 | } |
---|
1020 | pDelete(&p); |
---|
1021 | } |
---|
1022 | p = pNSet(maxcoeff); |
---|
1023 | char* pStr = pString(p); |
---|
1024 | delete ivUnit; |
---|
1025 | Print("// max total degree of %s = %d\n",cG, maxdeg); |
---|
1026 | Print("// max coefficient of %s = %s", cG, pStr);//ing(p)); |
---|
1027 | Print(" which consists of %d digits", (int)strlen(pStr)); |
---|
1028 | PrintLn(); |
---|
1029 | } |
---|
1030 | #endif |
---|
1031 | |
---|
1032 | /***************************************************************************** |
---|
1033 | * If target_ord = intmat(A1, ..., An) then calculate the perturbation * |
---|
1034 | * vectors * |
---|
1035 | * tau_p_dep = inveps^(p_deg-1)*A1 + inveps^(p_deg-2)*A2 +... + A_p_deg * |
---|
1036 | * where * |
---|
1037 | * inveps > totaldegree(G)*(max(A2)+...+max(A_p_deg)) * |
---|
1038 | * intmat target_ord is an integer order matrix of the monomial ordering of * |
---|
1039 | * basering. * |
---|
1040 | * This programm computes a perturbated vector with a p_deg perturbation * |
---|
1041 | * degree which smaller than the numbers of variables * |
---|
1042 | ******************************************************************************/ |
---|
1043 | intvec* MPertVectors(ideal G, intvec* ivtarget, int pdeg) |
---|
1044 | { |
---|
1045 | // ivtarget is a matrix order of a degree reverse lex. order |
---|
1046 | int nV = currRing->N; |
---|
1047 | //assume(pdeg <= nV && pdeg >= 0); |
---|
1048 | |
---|
1049 | int i, j, nG = IDELEMS(G); |
---|
1050 | intvec* v_null = new intvec(nV); |
---|
1051 | |
---|
1052 | |
---|
1053 | // Check that the perturbed degree is valid |
---|
1054 | if(pdeg > nV || pdeg <= 0) |
---|
1055 | { |
---|
1056 | WerrorS("//** The perturbed degree is wrong!!"); |
---|
1057 | return v_null; |
---|
1058 | } |
---|
1059 | delete v_null; |
---|
1060 | |
---|
1061 | if(pdeg == 1) |
---|
1062 | { |
---|
1063 | return ivtarget; |
---|
1064 | } |
---|
1065 | mpz_t *pert_vector = (mpz_t*)omAlloc(nV*sizeof(mpz_t)); |
---|
1066 | //mpz_t *pert_vector1 = (mpz_t*)omAlloc(nV*sizeof(mpz_t)); |
---|
1067 | |
---|
1068 | for(i=0; i<nV; i++) |
---|
1069 | { |
---|
1070 | mpz_init_set_si(pert_vector[i], (*ivtarget)[i]); |
---|
1071 | // mpz_init_set_si(pert_vector1[i], (*ivtarget)[i]); |
---|
1072 | } |
---|
1073 | // Calculate max1 = Max(A2)+Max(A3)+...+Max(Apdeg), |
---|
1074 | // where the Ai are the i-te rows of the matrix target_ord. |
---|
1075 | int ntemp, maxAi, maxA=0; |
---|
1076 | for(i=1; i<pdeg; i++) |
---|
1077 | { |
---|
1078 | maxAi = (*ivtarget)[i*nV]; |
---|
1079 | if(maxAi<0) |
---|
1080 | { |
---|
1081 | maxAi = -maxAi; |
---|
1082 | } |
---|
1083 | for(j=i*nV+1; j<(i+1)*nV; j++) |
---|
1084 | { |
---|
1085 | ntemp = (*ivtarget)[j]; |
---|
1086 | if(ntemp < 0) |
---|
1087 | { |
---|
1088 | ntemp = -ntemp; |
---|
1089 | } |
---|
1090 | if(ntemp > maxAi) |
---|
1091 | { |
---|
1092 | maxAi = ntemp; |
---|
1093 | } |
---|
1094 | } |
---|
1095 | maxA += maxAi; |
---|
1096 | } |
---|
1097 | |
---|
1098 | // Calculate inveps = 1/eps, where 1/eps > totaldeg(p)*max1 for all p in G. |
---|
1099 | |
---|
1100 | intvec* ivUnit = Mivdp(nV); |
---|
1101 | |
---|
1102 | mpz_t tot_deg; mpz_init(tot_deg); |
---|
1103 | mpz_t maxdeg; mpz_init(maxdeg); |
---|
1104 | mpz_t inveps; mpz_init(inveps); |
---|
1105 | |
---|
1106 | |
---|
1107 | for(i=nG-1; i>=0; i--) |
---|
1108 | { |
---|
1109 | mpz_set_ui(maxdeg, MwalkWeightDegree(G->m[i], ivUnit)); |
---|
1110 | if (mpz_cmp(maxdeg, tot_deg) > 0 ) |
---|
1111 | { |
---|
1112 | mpz_set(tot_deg, maxdeg); |
---|
1113 | } |
---|
1114 | } |
---|
1115 | |
---|
1116 | delete ivUnit; |
---|
1117 | mpz_mul_ui(inveps, tot_deg, maxA); |
---|
1118 | mpz_add_ui(inveps, inveps, 1); |
---|
1119 | |
---|
1120 | |
---|
1121 | // takes "small" inveps |
---|
1122 | #ifdef INVEPS_SMALL_IN_MPERTVECTOR |
---|
1123 | if(mpz_cmp_ui(inveps, pdeg)>0 && pdeg > 3) |
---|
1124 | { |
---|
1125 | // Print("\n// choose the\"small\" inverse epsilon := %d / %d = ", mpz_get_si(inveps), pdeg); |
---|
1126 | mpz_fdiv_q_ui(inveps, inveps, pdeg); |
---|
1127 | // mpz_out_str(stdout, 10, inveps); |
---|
1128 | } |
---|
1129 | #else |
---|
1130 | // PrintS("\n// the \"big\" inverse epsilon: "); |
---|
1131 | mpz_out_str(stdout, 10, inveps); |
---|
1132 | #endif |
---|
1133 | |
---|
1134 | // pert(A1) = inveps^(pdeg-1)*A1 + inveps^(pdeg-2)*A2+...+A_pdeg, |
---|
1135 | // pert_vector := A1 |
---|
1136 | for( i=1; i < pdeg; i++ ) |
---|
1137 | { |
---|
1138 | for(j=0; j<nV; j++) |
---|
1139 | { |
---|
1140 | mpz_mul(pert_vector[j], pert_vector[j], inveps); |
---|
1141 | if((*ivtarget)[i*nV+j]<0) |
---|
1142 | { |
---|
1143 | mpz_sub_ui(pert_vector[j], pert_vector[j],-(*ivtarget)[i*nV+j]); |
---|
1144 | } |
---|
1145 | else |
---|
1146 | { |
---|
1147 | mpz_add_ui(pert_vector[j], pert_vector[j],(*ivtarget)[i*nV+j]); |
---|
1148 | } |
---|
1149 | } |
---|
1150 | } |
---|
1151 | mpz_t ztemp; |
---|
1152 | mpz_init(ztemp); |
---|
1153 | mpz_set(ztemp, pert_vector[0]); |
---|
1154 | for(i=1; i<nV; i++) |
---|
1155 | { |
---|
1156 | mpz_gcd(ztemp, ztemp, pert_vector[i]); |
---|
1157 | if(mpz_cmp_si(ztemp, 1) == 0) |
---|
1158 | { |
---|
1159 | break; |
---|
1160 | } |
---|
1161 | } |
---|
1162 | if(mpz_cmp_si(ztemp, 1) != 0) |
---|
1163 | { |
---|
1164 | for(i=0; i<nV; i++) |
---|
1165 | { |
---|
1166 | mpz_divexact(pert_vector[i], pert_vector[i], ztemp); |
---|
1167 | } |
---|
1168 | } |
---|
1169 | |
---|
1170 | intvec *pert_vector1= new intvec(nV); |
---|
1171 | j = 0; |
---|
1172 | for(i=0; i<nV; i++) |
---|
1173 | { |
---|
1174 | (* pert_vector1)[i] = mpz_get_si(pert_vector[i]); |
---|
1175 | (* pert_vector1)[i] = 0.1*(* pert_vector1)[i]; |
---|
1176 | (* pert_vector1)[i] = floor((* pert_vector1)[i] + 0.5); |
---|
1177 | if((* pert_vector1)[i] == 0) |
---|
1178 | { |
---|
1179 | j++; |
---|
1180 | } |
---|
1181 | } |
---|
1182 | if(j > nV - 1) |
---|
1183 | { |
---|
1184 | // Print("\n// MPertVectors: geaenderter vector gleich Null! \n"); |
---|
1185 | delete pert_vector1; |
---|
1186 | goto CHECK_OVERFLOW; |
---|
1187 | } |
---|
1188 | |
---|
1189 | // check that the perturbed weight vector lies in the Groebner cone |
---|
1190 | if(test_w_in_ConeCC(G,pert_vector1) != 0) |
---|
1191 | { |
---|
1192 | // Print("\n// MPertVectors: geaenderter vector liegt in Groebnerkegel! \n"); |
---|
1193 | for(i=0; i<nV; i++) |
---|
1194 | { |
---|
1195 | mpz_set_si(pert_vector[i], (*pert_vector1)[i]); |
---|
1196 | } |
---|
1197 | } |
---|
1198 | else |
---|
1199 | { |
---|
1200 | //Print("\n// MpertVectors: geaenderter vector liegt nicht in Groebnerkegel! \n"); |
---|
1201 | } |
---|
1202 | delete pert_vector1; |
---|
1203 | |
---|
1204 | CHECK_OVERFLOW: |
---|
1205 | intvec* result = new intvec(nV); |
---|
1206 | |
---|
1207 | /* 2147483647 is max. integer representation in SINGULAR */ |
---|
1208 | mpz_t sing_int; |
---|
1209 | mpz_init_set_ui(sing_int, 2147483647); |
---|
1210 | |
---|
1211 | int ntrue=0; |
---|
1212 | for(i=0; i<nV; i++) |
---|
1213 | { |
---|
1214 | (*result)[i] = mpz_get_si(pert_vector[i]); |
---|
1215 | if(mpz_cmp(pert_vector[i], sing_int)>=0) |
---|
1216 | { |
---|
1217 | ntrue++; |
---|
1218 | if(Overflow_Error == FALSE) |
---|
1219 | { |
---|
1220 | Overflow_Error = TRUE; |
---|
1221 | PrintS("\n// ** OVERFLOW in \"MPertvectors\": "); |
---|
1222 | mpz_out_str( stdout, 10, pert_vector[i]); |
---|
1223 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
1224 | Print("\n// So vector[%d] := %d is wrong!!", i+1, (*result)[i]); |
---|
1225 | } |
---|
1226 | } |
---|
1227 | } |
---|
1228 | |
---|
1229 | if(Overflow_Error == TRUE) |
---|
1230 | { |
---|
1231 | ivString(result, "pert_vector"); |
---|
1232 | Print("\n// %d element(s) of it is overflow!!", ntrue); |
---|
1233 | } |
---|
1234 | |
---|
1235 | mpz_clear(ztemp); |
---|
1236 | mpz_clear(sing_int); |
---|
1237 | omFree(pert_vector); |
---|
1238 | //omFree(pert_vector1); |
---|
1239 | mpz_clear(tot_deg); |
---|
1240 | mpz_clear(maxdeg); |
---|
1241 | mpz_clear(inveps); |
---|
1242 | |
---|
1243 | rComplete(currRing); |
---|
1244 | for(j=0; j<IDELEMS(G); j++) |
---|
1245 | { |
---|
1246 | poly p=G->m[j]; |
---|
1247 | while(p!=NULL) |
---|
1248 | { |
---|
1249 | p_Setm(p,currRing); pIter(p); |
---|
1250 | } |
---|
1251 | } |
---|
1252 | return result; |
---|
1253 | } |
---|
1254 | |
---|
1255 | /***************************************************************************** |
---|
1256 | * The following procedure returns * |
---|
1257 | * Pert(A1) = 1/eps^(pdeg-1)*A_1 + 1/eps^(pdeg-2)*A_2+...+A_pdeg, * |
---|
1258 | * where the A_i are the i-th rows of the matrix target_ord and * |
---|
1259 | * 1/eps > deg(p)*(max(A_2) + max(A_3)+...+max(A_pdeg)) * |
---|
1260 | *****************************************************************************/ |
---|
1261 | intvec* MPertVectorslp(ideal G, intvec* ivtarget, int pdeg) |
---|
1262 | { |
---|
1263 | // ivtarget is a matrix order of the lex. order |
---|
1264 | int nV = currRing->N; |
---|
1265 | //assume(pdeg <= nV && pdeg >= 0); |
---|
1266 | |
---|
1267 | int i, j, nG = IDELEMS(G); |
---|
1268 | intvec* pert_vector = new intvec(nV); |
---|
1269 | |
---|
1270 | //Checking that the perturbated degree is valid |
---|
1271 | if(pdeg > nV || pdeg <= 0) |
---|
1272 | { |
---|
1273 | WerrorS("//** The perturbed degree is wrong!!"); |
---|
1274 | return pert_vector; |
---|
1275 | } |
---|
1276 | for(i=0; i<nV; i++) |
---|
1277 | { |
---|
1278 | (*pert_vector)[i]=(*ivtarget)[i]; |
---|
1279 | } |
---|
1280 | if(pdeg == 1) |
---|
1281 | { |
---|
1282 | return pert_vector; |
---|
1283 | } |
---|
1284 | // Calculate max1 = Max(A2)+Max(A3)+...+Max(Apdeg), |
---|
1285 | // where the Ai are the i-te rows of the matrix target_ord. |
---|
1286 | int ntemp, maxAi, maxA=0; |
---|
1287 | for(i=1; i<pdeg; i++) |
---|
1288 | { |
---|
1289 | maxAi = (*ivtarget)[i*nV]; |
---|
1290 | for(j=i*nV+1; j<(i+1)*nV; j++) |
---|
1291 | { |
---|
1292 | ntemp = (*ivtarget)[j]; |
---|
1293 | if(ntemp > maxAi) |
---|
1294 | { |
---|
1295 | maxAi = ntemp; |
---|
1296 | } |
---|
1297 | } |
---|
1298 | maxA += maxAi; |
---|
1299 | } |
---|
1300 | |
---|
1301 | // Calculate inveps := 1/eps, where 1/eps > deg(p)*max1 for all p in G. |
---|
1302 | int inveps, tot_deg = 0, maxdeg; |
---|
1303 | |
---|
1304 | intvec* ivUnit = Mivdp(nV);//19.02 |
---|
1305 | for(i=nG-1; i>=0; i--) |
---|
1306 | { |
---|
1307 | // maxdeg = pTotaldegree(G->m[i], currRing); //it's wrong for ex1,2,rose |
---|
1308 | maxdeg = MwalkWeightDegree(G->m[i], ivUnit); |
---|
1309 | if (maxdeg > tot_deg ) |
---|
1310 | { |
---|
1311 | tot_deg = maxdeg; |
---|
1312 | } |
---|
1313 | } |
---|
1314 | delete ivUnit; |
---|
1315 | |
---|
1316 | inveps = (tot_deg * maxA) + 1; |
---|
1317 | |
---|
1318 | #ifdef INVEPS_SMALL_IN_FRACTAL |
---|
1319 | // Print("\n// choose the\"small\" inverse epsilon := %d / %d = ", inveps, pdeg); |
---|
1320 | if(inveps > pdeg && pdeg > 3) |
---|
1321 | { |
---|
1322 | inveps = inveps / pdeg; |
---|
1323 | } |
---|
1324 | // Print(" %d", inveps); |
---|
1325 | #else |
---|
1326 | PrintS("\n// the \"big\" inverse epsilon %d", inveps); |
---|
1327 | #endif |
---|
1328 | |
---|
1329 | // Pert(A1) = inveps^(pdeg-1)*A1 + inveps^(pdeg-2)*A2+...+A_pdeg |
---|
1330 | for ( i=1; i < pdeg; i++ ) |
---|
1331 | { |
---|
1332 | for(j=0; j<nV; j++) |
---|
1333 | { |
---|
1334 | (*pert_vector)[j] = inveps*((*pert_vector)[j]) + (*ivtarget)[i*nV+j]; |
---|
1335 | } |
---|
1336 | } |
---|
1337 | |
---|
1338 | int temp = (*pert_vector)[0]; |
---|
1339 | for(i=1; i<nV; i++) |
---|
1340 | { |
---|
1341 | temp = gcd(temp, (*pert_vector)[i]); |
---|
1342 | if(temp == 1) |
---|
1343 | { |
---|
1344 | break; |
---|
1345 | } |
---|
1346 | } |
---|
1347 | if(temp != 1) |
---|
1348 | { |
---|
1349 | for(i=0; i<nV; i++) |
---|
1350 | { |
---|
1351 | (*pert_vector)[i] = (*pert_vector)[i] / temp; |
---|
1352 | } |
---|
1353 | } |
---|
1354 | |
---|
1355 | intvec* result = pert_vector; |
---|
1356 | delete pert_vector; |
---|
1357 | return result; |
---|
1358 | } |
---|
1359 | |
---|
1360 | /***************************************************************************** |
---|
1361 | * define a lexicographic order matrix as intvec * |
---|
1362 | *****************************************************************************/ |
---|
1363 | intvec* MivMatrixOrderlp(int nV) |
---|
1364 | { |
---|
1365 | int i; |
---|
1366 | intvec* ivM = new intvec(nV*nV); |
---|
1367 | |
---|
1368 | for(i=0; i<nV; i++) |
---|
1369 | { |
---|
1370 | (*ivM)[i*nV + i] = 1; |
---|
1371 | } |
---|
1372 | return(ivM); |
---|
1373 | } |
---|
1374 | |
---|
1375 | |
---|
1376 | /***************************************************************************** |
---|
1377 | * define a reverse lexicographic order (dp) matrix as intvec * |
---|
1378 | *****************************************************************************/ |
---|
1379 | intvec* MivMatrixOrderdp(int nV) |
---|
1380 | { |
---|
1381 | int i; |
---|
1382 | intvec* ivM = new intvec(nV*nV); |
---|
1383 | |
---|
1384 | for(i=0; i<nV; i++) |
---|
1385 | { |
---|
1386 | (*ivM)[i] = 1; |
---|
1387 | } |
---|
1388 | for(i=1; i<nV; i++) |
---|
1389 | { |
---|
1390 | (*ivM)[(i+1)*nV - i] = -1; |
---|
1391 | } |
---|
1392 | return(ivM); |
---|
1393 | } |
---|
1394 | |
---|
1395 | /***************************************************************************** |
---|
1396 | * creates an intvec of the monomial order Wp(ivstart) * |
---|
1397 | *****************************************************************************/ |
---|
1398 | intvec* MivWeightOrderlp(intvec* ivstart) |
---|
1399 | { |
---|
1400 | int i; |
---|
1401 | int nV = ivstart->length(); |
---|
1402 | intvec* ivM = new intvec(nV*nV); |
---|
1403 | |
---|
1404 | for(i=0; i<nV; i++) |
---|
1405 | { |
---|
1406 | (*ivM)[i] = (*ivstart)[i]; |
---|
1407 | } |
---|
1408 | for(i=1; i<nV; i++) |
---|
1409 | { |
---|
1410 | (*ivM)[i*nV + i-1] = 1; |
---|
1411 | } |
---|
1412 | return(ivM); |
---|
1413 | } |
---|
1414 | |
---|
1415 | /***************************************************************************** |
---|
1416 | * creates an intvec of the monomial order dp(ivstart) * |
---|
1417 | *****************************************************************************/ |
---|
1418 | intvec* MivWeightOrderdp(intvec* ivstart) |
---|
1419 | { |
---|
1420 | int i; |
---|
1421 | int nV = ivstart->length(); |
---|
1422 | intvec* ivM = new intvec(nV*nV); |
---|
1423 | |
---|
1424 | for(i=0; i<nV; i++) |
---|
1425 | { |
---|
1426 | (*ivM)[i] = (*ivstart)[i]; |
---|
1427 | } |
---|
1428 | for(i=0; i<nV; i++) |
---|
1429 | { |
---|
1430 | (*ivM)[nV+i] = 1; |
---|
1431 | } |
---|
1432 | for(i=2; i<nV; i++) |
---|
1433 | { |
---|
1434 | (*ivM)[(i+1)*nV - i] = -1; |
---|
1435 | } |
---|
1436 | return(ivM); |
---|
1437 | } |
---|
1438 | |
---|
1439 | //unused |
---|
1440 | #if 0 |
---|
1441 | static intvec* MatrixOrderdp(int nV) |
---|
1442 | { |
---|
1443 | int i; |
---|
1444 | intvec* ivM = new intvec(nV*nV); |
---|
1445 | |
---|
1446 | for(i=0; i<nV; i++) |
---|
1447 | { |
---|
1448 | (*ivM)[i] = 1; |
---|
1449 | } |
---|
1450 | for(i=1; i<nV; i++) |
---|
1451 | { |
---|
1452 | (*ivM)[(i+1)*nV - i] = -1; |
---|
1453 | } |
---|
1454 | return(ivM); |
---|
1455 | } |
---|
1456 | #endif |
---|
1457 | |
---|
1458 | intvec* MivUnit(int nV) |
---|
1459 | { |
---|
1460 | int i; |
---|
1461 | intvec* ivM = new intvec(nV); |
---|
1462 | for(i=nV-1; i>=0; i--) |
---|
1463 | { |
---|
1464 | (*ivM)[i] = 1; |
---|
1465 | } |
---|
1466 | return(ivM); |
---|
1467 | } |
---|
1468 | |
---|
1469 | |
---|
1470 | /************************************************************************ |
---|
1471 | * compute a perturbed weight vector of a matrix order w.r.t. an ideal * |
---|
1472 | *************************************************************************/ |
---|
1473 | int Xnlev; |
---|
1474 | intvec* Mfpertvector(ideal G, intvec* ivtarget) |
---|
1475 | { |
---|
1476 | int i, j, nG = IDELEMS(G); |
---|
1477 | int nV = currRing->N; |
---|
1478 | int niv = nV*nV; |
---|
1479 | |
---|
1480 | |
---|
1481 | // Calculate maxA = Max(A2) + Max(A3) + ... + Max(AnV), |
---|
1482 | // where the Ai are the i-te rows of the matrix 'targer_ord'. |
---|
1483 | int ntemp, maxAi, maxA=0; |
---|
1484 | for(i=1; i<nV; i++) |
---|
1485 | { |
---|
1486 | maxAi = (*ivtarget)[i*nV]; |
---|
1487 | if(maxAi<0) |
---|
1488 | { |
---|
1489 | maxAi = -maxAi; |
---|
1490 | } |
---|
1491 | for(j=i*nV+1; j<(i+1)*nV; j++) |
---|
1492 | { |
---|
1493 | ntemp = (*ivtarget)[j]; |
---|
1494 | if(ntemp < 0) |
---|
1495 | { |
---|
1496 | ntemp = -ntemp; |
---|
1497 | } |
---|
1498 | if(ntemp > maxAi) |
---|
1499 | { |
---|
1500 | maxAi = ntemp; |
---|
1501 | } |
---|
1502 | } |
---|
1503 | maxA = maxA + maxAi; |
---|
1504 | } |
---|
1505 | intvec* ivUnit = Mivdp(nV); |
---|
1506 | |
---|
1507 | // Calculate inveps = 1/eps, where 1/eps > deg(p)*maxA for all p in G. |
---|
1508 | mpz_t tot_deg; mpz_init(tot_deg); |
---|
1509 | mpz_t maxdeg; mpz_init(maxdeg); |
---|
1510 | mpz_t inveps; mpz_init(inveps); |
---|
1511 | |
---|
1512 | |
---|
1513 | for(i=nG-1; i>=0; i--) |
---|
1514 | { |
---|
1515 | mpz_set_ui(maxdeg, MwalkWeightDegree(G->m[i], ivUnit)); |
---|
1516 | if (mpz_cmp(maxdeg, tot_deg) > 0 ) |
---|
1517 | { |
---|
1518 | mpz_set(tot_deg, maxdeg); |
---|
1519 | } |
---|
1520 | } |
---|
1521 | |
---|
1522 | delete ivUnit; |
---|
1523 | //inveps = (tot_deg * maxA) + 1; |
---|
1524 | mpz_mul_ui(inveps, tot_deg, maxA); |
---|
1525 | mpz_add_ui(inveps, inveps, 1); |
---|
1526 | |
---|
1527 | // takes "small" inveps |
---|
1528 | #ifdef INVEPS_SMALL_IN_FRACTAL |
---|
1529 | if(mpz_cmp_ui(inveps, nV)>0 && nV > 3) |
---|
1530 | { |
---|
1531 | mpz_cdiv_q_ui(inveps, inveps, nV); |
---|
1532 | } |
---|
1533 | //PrintS("\n// choose the \"small\" inverse epsilon!"); |
---|
1534 | #endif |
---|
1535 | |
---|
1536 | // PrintLn(); mpz_out_str(stdout, 10, inveps); |
---|
1537 | |
---|
1538 | // Calculate the perturbed target orders: |
---|
1539 | mpz_t *ivtemp=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
1540 | mpz_t *pert_vector=(mpz_t *)omAlloc(niv*sizeof(mpz_t)); |
---|
1541 | |
---|
1542 | for(i=0; i < nV; i++) |
---|
1543 | { |
---|
1544 | mpz_init_set_si(ivtemp[i], (*ivtarget)[i]); |
---|
1545 | mpz_init_set_si(pert_vector[i], (*ivtarget)[i]); |
---|
1546 | } |
---|
1547 | |
---|
1548 | mpz_t ztmp; mpz_init(ztmp); |
---|
1549 | // BOOLEAN isneg = FALSE; |
---|
1550 | |
---|
1551 | for(i=1; i<nV; i++) |
---|
1552 | { |
---|
1553 | for(j=0; j<nV; j++) |
---|
1554 | { |
---|
1555 | mpz_mul(ztmp, inveps, ivtemp[j]); |
---|
1556 | if((*ivtarget)[i*nV+j]<0) |
---|
1557 | { |
---|
1558 | mpz_sub_ui(ivtemp[j], ztmp, -(*ivtarget)[i*nV+j]); |
---|
1559 | } |
---|
1560 | else |
---|
1561 | { |
---|
1562 | mpz_add_ui(ivtemp[j], ztmp,(*ivtarget)[i*nV+j]); |
---|
1563 | } |
---|
1564 | } |
---|
1565 | |
---|
1566 | for(j=0; j<nV; j++) |
---|
1567 | { |
---|
1568 | mpz_init_set(pert_vector[i*nV+j],ivtemp[j]); |
---|
1569 | } |
---|
1570 | } |
---|
1571 | |
---|
1572 | /* 2147483647 is max. integer representation in SINGULAR */ |
---|
1573 | mpz_t sing_int; |
---|
1574 | mpz_init_set_ui(sing_int, 2147483647); |
---|
1575 | |
---|
1576 | intvec* result = new intvec(niv); |
---|
1577 | intvec* result1 = new intvec(niv); |
---|
1578 | BOOLEAN nflow = FALSE; |
---|
1579 | |
---|
1580 | // computes gcd |
---|
1581 | mpz_set(ztmp, pert_vector[0]); |
---|
1582 | for(i=0; i<niv; i++) |
---|
1583 | { |
---|
1584 | mpz_gcd(ztmp, ztmp, pert_vector[i]); |
---|
1585 | if(mpz_cmp_si(ztmp, 1)==0) |
---|
1586 | { |
---|
1587 | break; |
---|
1588 | } |
---|
1589 | } |
---|
1590 | |
---|
1591 | for(i=0; i<niv; i++) |
---|
1592 | { |
---|
1593 | mpz_divexact(pert_vector[i], pert_vector[i], ztmp); |
---|
1594 | (* result)[i] = mpz_get_si(pert_vector[i]); |
---|
1595 | } |
---|
1596 | |
---|
1597 | j = 0; |
---|
1598 | for(i=0; i<nV; i++) |
---|
1599 | { |
---|
1600 | (* result1)[i] = mpz_get_si(pert_vector[i]); |
---|
1601 | (* result1)[i] = 0.1*(* result1)[i]; |
---|
1602 | (* result1)[i] = floor((* result1)[i] + 0.5); |
---|
1603 | if((* result1)[i] == 0) |
---|
1604 | { |
---|
1605 | j++; |
---|
1606 | } |
---|
1607 | } |
---|
1608 | if(j > nV - 1) |
---|
1609 | { |
---|
1610 | // Print("\n// MfPertwalk: geaenderter vector gleich Null! \n"); |
---|
1611 | delete result1; |
---|
1612 | goto CHECK_OVERFLOW; |
---|
1613 | } |
---|
1614 | |
---|
1615 | // check that the perturbed weight vector lies in the Groebner cone |
---|
1616 | if(test_w_in_ConeCC(G,result1) != 0) |
---|
1617 | { |
---|
1618 | // Print("\n// MfPertwalk: geaenderter vector liegt in Groebnerkegel! \n"); |
---|
1619 | delete result; |
---|
1620 | result = result1; |
---|
1621 | for(i=0; i<nV; i++) |
---|
1622 | { |
---|
1623 | mpz_set_si(pert_vector[i], (*result1)[i]); |
---|
1624 | } |
---|
1625 | } |
---|
1626 | else |
---|
1627 | { |
---|
1628 | delete result1; |
---|
1629 | // Print("\n// Mfpertwalk: geaenderter vector liegt nicht in Groebnerkegel! \n"); |
---|
1630 | } |
---|
1631 | |
---|
1632 | CHECK_OVERFLOW: |
---|
1633 | |
---|
1634 | for(i=0; i<niv; i++) |
---|
1635 | { |
---|
1636 | if(mpz_cmp(pert_vector[i], sing_int)>0) |
---|
1637 | { |
---|
1638 | if(nflow == FALSE) |
---|
1639 | { |
---|
1640 | Xnlev = i / nV; |
---|
1641 | nflow = TRUE; |
---|
1642 | Overflow_Error = TRUE; |
---|
1643 | Print("\n// Xlev = %d and the %d-th element is", Xnlev, i+1); |
---|
1644 | PrintS("\n// ** OVERFLOW in \"Mfpertvector\": "); |
---|
1645 | mpz_out_str( stdout, 10, pert_vector[i]); |
---|
1646 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
1647 | Print("\n// So vector[%d] := %d is wrong!!", i+1, (*result)[i]); |
---|
1648 | } |
---|
1649 | } |
---|
1650 | } |
---|
1651 | if(Overflow_Error == TRUE) |
---|
1652 | { |
---|
1653 | ivString(result, "new_vector"); |
---|
1654 | } |
---|
1655 | omFree(pert_vector); |
---|
1656 | omFree(ivtemp); |
---|
1657 | mpz_clear(ztmp); |
---|
1658 | mpz_clear(tot_deg); |
---|
1659 | mpz_clear(maxdeg); |
---|
1660 | mpz_clear(inveps); |
---|
1661 | mpz_clear(sing_int); |
---|
1662 | |
---|
1663 | rComplete(currRing); |
---|
1664 | for(j=0; j<IDELEMS(G); j++) |
---|
1665 | { |
---|
1666 | poly p=G->m[j]; |
---|
1667 | while(p!=NULL) |
---|
1668 | { |
---|
1669 | p_Setm(p,currRing); pIter(p); |
---|
1670 | } |
---|
1671 | } |
---|
1672 | return result; |
---|
1673 | } |
---|
1674 | |
---|
1675 | /**************************************************************** |
---|
1676 | * Multiplication of two ideals element by element * |
---|
1677 | * i.e. Let be A := (a_i) and B := (b_i), return C := (a_i*b_i) * |
---|
1678 | * destroy A, keeps B * |
---|
1679 | ****************************************************************/ |
---|
1680 | static ideal MidMult(ideal A, ideal B) |
---|
1681 | { |
---|
1682 | int mA = IDELEMS(A), mB = IDELEMS(B); |
---|
1683 | |
---|
1684 | if(A==NULL || B==NULL) |
---|
1685 | { |
---|
1686 | return NULL; |
---|
1687 | } |
---|
1688 | if(mB < mA) |
---|
1689 | { |
---|
1690 | mA = mB; |
---|
1691 | } |
---|
1692 | ideal result = idInit(mA, 1); |
---|
1693 | |
---|
1694 | int i, k=0; |
---|
1695 | for(i=0; i<mA; i++) |
---|
1696 | { |
---|
1697 | result->m[k] = pMult(A->m[i], pCopy(B->m[i])); |
---|
1698 | A->m[i]=NULL; |
---|
1699 | if (result->m[k]!=NULL) |
---|
1700 | { |
---|
1701 | k++; |
---|
1702 | } |
---|
1703 | } |
---|
1704 | |
---|
1705 | idDelete(&A); |
---|
1706 | idSkipZeroes(result); |
---|
1707 | return result; |
---|
1708 | } |
---|
1709 | |
---|
1710 | /********************************************************************* |
---|
1711 | * G is a red. Groebner basis w.r.t. <_1 * |
---|
1712 | * Gomega is an initial form ideal of <G> w.r.t. a weight vector w * |
---|
1713 | * M is a subideal of <Gomega> and M selft is a red. Groebner basis * |
---|
1714 | * of the ideal <Gomega> w.r.t. <_w * |
---|
1715 | * Let m_i = h1.gw1 + ... + hs.gws for each m_i in M; gwi in Gomega * |
---|
1716 | * return F with n(F) = n(M) and f_i = h1.g1 + ... + hs.gs for each i* |
---|
1717 | ********************************************************************/ |
---|
1718 | static ideal MLifttwoIdeal(ideal Gw, ideal M, ideal G) |
---|
1719 | { |
---|
1720 | ideal Mtmp = idLift(Gw, M, NULL, FALSE, TRUE, TRUE, NULL); |
---|
1721 | |
---|
1722 | // If Gw is a GB, then isSB = TRUE, otherwise FALSE |
---|
1723 | // So, it is better, if one tests whether Gw is a GB |
---|
1724 | // in ideals.cc: |
---|
1725 | // idLift (ideal mod, ideal submod,ideal * rest, BOOLEAN goodShape, |
---|
1726 | // BOOLEAN isSB,BOOLEAN divide,matrix * unit) |
---|
1727 | |
---|
1728 | // Let be Mtmp = {m1,...,ms}, where mi=sum hij.in_gj, for all i=1,...,s |
---|
1729 | // We compute F = {f1,...,fs}, where fi=sum hij.gj |
---|
1730 | int i, j, nM = IDELEMS(Mtmp); |
---|
1731 | ideal idpol, idLG; |
---|
1732 | ideal F = idInit(nM, 1); |
---|
1733 | |
---|
1734 | for(i=0; i<nM; i++) |
---|
1735 | { |
---|
1736 | idpol = idVec2Ideal(Mtmp->m[i]); |
---|
1737 | idLG = MidMult(idpol, G); |
---|
1738 | idpol = NULL; |
---|
1739 | F->m[i] = NULL; |
---|
1740 | for(j=IDELEMS(idLG)-1; j>=0; j--) |
---|
1741 | { |
---|
1742 | F->m[i] = pAdd(F->m[i], idLG->m[j]); |
---|
1743 | idLG->m[j]=NULL; |
---|
1744 | } |
---|
1745 | idDelete(&idLG); |
---|
1746 | } |
---|
1747 | idDelete(&Mtmp); |
---|
1748 | return F; |
---|
1749 | } |
---|
1750 | |
---|
1751 | //unused |
---|
1752 | #if 0 |
---|
1753 | static void checkidealCC(ideal G, char* Ch) |
---|
1754 | { |
---|
1755 | int i,nmon=0,ntmp; |
---|
1756 | int nG = IDELEMS(G); |
---|
1757 | int n = nG-1; |
---|
1758 | Print("\n//** Ideal %s besteht aus %d Polynomen mit ", Ch, nG); |
---|
1759 | |
---|
1760 | for(i=0; i<nG; i++) |
---|
1761 | { |
---|
1762 | ntmp = pLength(G->m[i]); |
---|
1763 | nmon += ntmp; |
---|
1764 | |
---|
1765 | if(i != n) |
---|
1766 | { |
---|
1767 | Print("%d, ", ntmp); |
---|
1768 | } |
---|
1769 | else |
---|
1770 | { |
---|
1771 | Print(" bzw. %d ", ntmp); |
---|
1772 | } |
---|
1773 | } |
---|
1774 | PrintS(" Monomen.\n"); |
---|
1775 | Print("//** %s besitzt %d Monome.", Ch, nmon); |
---|
1776 | PrintLn(); |
---|
1777 | } |
---|
1778 | #endif |
---|
1779 | |
---|
1780 | //unused |
---|
1781 | #if 0 |
---|
1782 | static void HeadidString(ideal L, char* st) |
---|
1783 | { |
---|
1784 | int i, nL = IDELEMS(L)-1; |
---|
1785 | |
---|
1786 | Print("// The head terms of the ideal %s = ", st); |
---|
1787 | for(i=0; i<nL; i++) |
---|
1788 | { |
---|
1789 | Print(" %s, ", pString(pHead(L->m[i]))); |
---|
1790 | } |
---|
1791 | Print(" %s;\n", pString(pHead(L->m[nL]))); |
---|
1792 | } |
---|
1793 | #endif |
---|
1794 | |
---|
1795 | static inline int MivComp(intvec* iva, intvec* ivb) |
---|
1796 | { |
---|
1797 | assume(iva->length() == ivb->length()); |
---|
1798 | int i; |
---|
1799 | for(i=iva->length()-1; i>=0; i--) |
---|
1800 | { |
---|
1801 | if((*iva)[i] - (*ivb)[i] != 0) |
---|
1802 | { |
---|
1803 | return 0; |
---|
1804 | } |
---|
1805 | } |
---|
1806 | return 1; |
---|
1807 | } |
---|
1808 | |
---|
1809 | /********************************************** |
---|
1810 | * Look for the smallest absolut value in vec * |
---|
1811 | **********************************************/ |
---|
1812 | static int MivAbsMax(intvec* vec) |
---|
1813 | { |
---|
1814 | int i,k; |
---|
1815 | if((*vec)[0] < 0) |
---|
1816 | { |
---|
1817 | k = -(*vec)[0]; |
---|
1818 | } |
---|
1819 | else |
---|
1820 | { |
---|
1821 | k = (*vec)[0]; |
---|
1822 | } |
---|
1823 | for(i=1; i < (vec->length()); i++) |
---|
1824 | { |
---|
1825 | if((*vec)[i] < 0) |
---|
1826 | { |
---|
1827 | if(-(*vec)[i] > k) |
---|
1828 | { |
---|
1829 | k = -(*vec)[i]; |
---|
1830 | } |
---|
1831 | } |
---|
1832 | else |
---|
1833 | { |
---|
1834 | if((*vec)[i] > k) |
---|
1835 | { |
---|
1836 | k = (*vec)[i]; |
---|
1837 | } |
---|
1838 | } |
---|
1839 | } |
---|
1840 | return k; |
---|
1841 | } |
---|
1842 | |
---|
1843 | /********************************************************************** |
---|
1844 | * Compute a next weight vector between curr_weight and target_weight * |
---|
1845 | * with respect to an ideal <G>. * |
---|
1846 | **********************************************************************/ |
---|
1847 | static intvec* MwalkNextWeightCC(intvec* curr_weight, intvec* target_weight, |
---|
1848 | ideal G) |
---|
1849 | { |
---|
1850 | BOOLEAN nError = Overflow_Error; |
---|
1851 | Overflow_Error = FALSE; |
---|
1852 | |
---|
1853 | assume(currRing != NULL && curr_weight != NULL && |
---|
1854 | target_weight != NULL && G != NULL); |
---|
1855 | |
---|
1856 | int nRing = currRing->N; |
---|
1857 | int checkRed, j, kkk, nG = IDELEMS(G); |
---|
1858 | intvec* ivtemp; |
---|
1859 | |
---|
1860 | mpz_t t_zaehler, t_nenner; |
---|
1861 | mpz_init(t_zaehler); |
---|
1862 | mpz_init(t_nenner); |
---|
1863 | |
---|
1864 | mpz_t s_zaehler, s_nenner, temp, MwWd; |
---|
1865 | mpz_init(s_zaehler); |
---|
1866 | mpz_init(s_nenner); |
---|
1867 | mpz_init(temp); |
---|
1868 | mpz_init(MwWd); |
---|
1869 | |
---|
1870 | mpz_t sing_int; |
---|
1871 | mpz_init(sing_int); |
---|
1872 | mpz_set_si(sing_int, 2147483647); |
---|
1873 | |
---|
1874 | mpz_t sing_int_half; |
---|
1875 | mpz_init(sing_int_half); |
---|
1876 | mpz_set_si(sing_int_half, 3*(1073741824/2)); |
---|
1877 | |
---|
1878 | mpz_t deg_w0_p1, deg_d0_p1; |
---|
1879 | mpz_init(deg_w0_p1); |
---|
1880 | mpz_init(deg_d0_p1); |
---|
1881 | |
---|
1882 | mpz_t sztn, sntz; |
---|
1883 | mpz_init(sztn); |
---|
1884 | mpz_init(sntz); |
---|
1885 | |
---|
1886 | mpz_t t_null; |
---|
1887 | mpz_init(t_null); |
---|
1888 | |
---|
1889 | mpz_t ggt; |
---|
1890 | mpz_init(ggt); |
---|
1891 | |
---|
1892 | mpz_t dcw; |
---|
1893 | mpz_init(dcw); |
---|
1894 | |
---|
1895 | //int tn0, tn1, tz1, ncmp, gcd_tmp, ntmp; |
---|
1896 | int gcd_tmp; |
---|
1897 | intvec* diff_weight = MivSub(target_weight, curr_weight); |
---|
1898 | |
---|
1899 | intvec* diff_weight1 = MivSub(target_weight, curr_weight); |
---|
1900 | poly g; |
---|
1901 | //poly g, gw; |
---|
1902 | for (j=0; j<nG; j++) |
---|
1903 | { |
---|
1904 | g = G->m[j]; |
---|
1905 | if (g != NULL) |
---|
1906 | { |
---|
1907 | ivtemp = MExpPol(g); |
---|
1908 | mpz_set_si(deg_w0_p1, MivDotProduct(ivtemp, curr_weight)); |
---|
1909 | mpz_set_si(deg_d0_p1, MivDotProduct(ivtemp, diff_weight)); |
---|
1910 | delete ivtemp; |
---|
1911 | |
---|
1912 | pIter(g); |
---|
1913 | while (g != NULL) |
---|
1914 | { |
---|
1915 | ivtemp = MExpPol(g); |
---|
1916 | mpz_set_si(MwWd, MivDotProduct(ivtemp, curr_weight)); |
---|
1917 | mpz_sub(s_zaehler, deg_w0_p1, MwWd); |
---|
1918 | |
---|
1919 | if(mpz_cmp(s_zaehler, t_null) != 0) |
---|
1920 | { |
---|
1921 | mpz_set_si(MwWd, MivDotProduct(ivtemp, diff_weight)); |
---|
1922 | mpz_sub(s_nenner, MwWd, deg_d0_p1); |
---|
1923 | |
---|
1924 | // check for 0 < s <= 1 |
---|
1925 | if( (mpz_cmp(s_zaehler,t_null) > 0 && |
---|
1926 | mpz_cmp(s_nenner, s_zaehler)>=0) || |
---|
1927 | (mpz_cmp(s_zaehler, t_null) < 0 && |
---|
1928 | mpz_cmp(s_nenner, s_zaehler)<=0)) |
---|
1929 | { |
---|
1930 | // make both positive |
---|
1931 | if (mpz_cmp(s_zaehler, t_null) < 0) |
---|
1932 | { |
---|
1933 | mpz_neg(s_zaehler, s_zaehler); |
---|
1934 | mpz_neg(s_nenner, s_nenner); |
---|
1935 | } |
---|
1936 | |
---|
1937 | //compute a simple fraction of s |
---|
1938 | cancel(s_zaehler, s_nenner); |
---|
1939 | |
---|
1940 | if(mpz_cmp(t_nenner, t_null) != 0) |
---|
1941 | { |
---|
1942 | mpz_mul(sztn, s_zaehler, t_nenner); |
---|
1943 | mpz_mul(sntz, s_nenner, t_zaehler); |
---|
1944 | |
---|
1945 | if(mpz_cmp(sztn,sntz) < 0) |
---|
1946 | { |
---|
1947 | mpz_add(t_nenner, t_null, s_nenner); |
---|
1948 | mpz_add(t_zaehler,t_null, s_zaehler); |
---|
1949 | } |
---|
1950 | } |
---|
1951 | else |
---|
1952 | { |
---|
1953 | mpz_add(t_nenner, t_null, s_nenner); |
---|
1954 | mpz_add(t_zaehler,t_null, s_zaehler); |
---|
1955 | } |
---|
1956 | } |
---|
1957 | } |
---|
1958 | pIter(g); |
---|
1959 | delete ivtemp; |
---|
1960 | } |
---|
1961 | } |
---|
1962 | } |
---|
1963 | //Print("\n// Alloc Size = %d \n", nRing*sizeof(mpz_t)); |
---|
1964 | mpz_t *vec=(mpz_t*)omAlloc(nRing*sizeof(mpz_t)); |
---|
1965 | |
---|
1966 | |
---|
1967 | // there is no 0<t<1 and define the next weight vector that is equal to the current weight vector |
---|
1968 | if(mpz_cmp(t_nenner, t_null) == 0) |
---|
1969 | { |
---|
1970 | #ifndef SING_NDEBUG |
---|
1971 | Print("\n//MwalkNextWeightCC: t_nenner ist Null!"); |
---|
1972 | #endif |
---|
1973 | delete diff_weight; |
---|
1974 | diff_weight = ivCopy(curr_weight);//take memory |
---|
1975 | goto FINISH; |
---|
1976 | } |
---|
1977 | |
---|
1978 | // define the target vector as the next weight vector, if t = 1 |
---|
1979 | if(mpz_cmp_si(t_nenner, 1)==0 && mpz_cmp_si(t_zaehler,1)==0) |
---|
1980 | { |
---|
1981 | delete diff_weight; |
---|
1982 | diff_weight = ivCopy(target_weight); //this takes memory |
---|
1983 | goto FINISH; |
---|
1984 | } |
---|
1985 | |
---|
1986 | checkRed = 0; |
---|
1987 | |
---|
1988 | SIMPLIFY_GCD: |
---|
1989 | |
---|
1990 | // simplify the vectors curr_weight and diff_weight (C-int) |
---|
1991 | gcd_tmp = (*curr_weight)[0]; |
---|
1992 | |
---|
1993 | for (j=1; j<nRing; j++) |
---|
1994 | { |
---|
1995 | gcd_tmp = gcd(gcd_tmp, (*curr_weight)[j]); |
---|
1996 | if(gcd_tmp == 1) |
---|
1997 | { |
---|
1998 | break; |
---|
1999 | } |
---|
2000 | } |
---|
2001 | if(gcd_tmp != 1) |
---|
2002 | { |
---|
2003 | for (j=0; j<nRing; j++) |
---|
2004 | { |
---|
2005 | gcd_tmp = gcd(gcd_tmp, (*diff_weight)[j]); |
---|
2006 | if(gcd_tmp == 1) |
---|
2007 | { |
---|
2008 | break; |
---|
2009 | } |
---|
2010 | } |
---|
2011 | } |
---|
2012 | if(gcd_tmp != 1) |
---|
2013 | { |
---|
2014 | for (j=0; j<nRing; j++) |
---|
2015 | { |
---|
2016 | (*curr_weight)[j] = (*curr_weight)[j]/gcd_tmp; |
---|
2017 | (*diff_weight)[j] = (*diff_weight)[j]/gcd_tmp; |
---|
2018 | } |
---|
2019 | } |
---|
2020 | if(checkRed > 0) |
---|
2021 | { |
---|
2022 | for (j=0; j<nRing; j++) |
---|
2023 | { |
---|
2024 | mpz_set_si(vec[j], (*diff_weight)[j]); |
---|
2025 | } |
---|
2026 | goto TEST_OVERFLOW; |
---|
2027 | } |
---|
2028 | |
---|
2029 | #ifdef NEXT_VECTORS_CC |
---|
2030 | Print("\n// gcd of the weight vectors (current and target) = %d", gcd_tmp); |
---|
2031 | ivString(curr_weight, "new cw"); |
---|
2032 | ivString(diff_weight, "new dw"); |
---|
2033 | |
---|
2034 | PrintS("\n// t_zaehler: "); mpz_out_str( stdout, 10, t_zaehler); |
---|
2035 | PrintS(", t_nenner: "); mpz_out_str( stdout, 10, t_nenner); |
---|
2036 | #endif |
---|
2037 | |
---|
2038 | // BOOLEAN isdwpos; |
---|
2039 | |
---|
2040 | // construct a new weight vector |
---|
2041 | for (j=0; j<nRing; j++) |
---|
2042 | { |
---|
2043 | mpz_set_si(dcw, (*curr_weight)[j]); |
---|
2044 | mpz_mul(s_nenner, t_nenner, dcw); |
---|
2045 | |
---|
2046 | if( (*diff_weight)[j]>0) |
---|
2047 | { |
---|
2048 | mpz_mul_ui(s_zaehler, t_zaehler, (*diff_weight)[j]); |
---|
2049 | } |
---|
2050 | else |
---|
2051 | { |
---|
2052 | mpz_mul_ui(s_zaehler, t_zaehler, -(*diff_weight)[j]); |
---|
2053 | mpz_neg(s_zaehler, s_zaehler); |
---|
2054 | } |
---|
2055 | mpz_add(sntz, s_nenner, s_zaehler); |
---|
2056 | mpz_init_set(vec[j], sntz); |
---|
2057 | |
---|
2058 | #ifdef NEXT_VECTORS_CC |
---|
2059 | Print("\n// j = %d ==> ", j); |
---|
2060 | PrintS("("); |
---|
2061 | mpz_out_str( stdout, 10, t_nenner); |
---|
2062 | Print(" * %d)", (*curr_weight)[j]); |
---|
2063 | Print(" + ("); mpz_out_str( stdout, 10, t_zaehler); |
---|
2064 | Print(" * %d) = ", (*diff_weight)[j]); |
---|
2065 | mpz_out_str( stdout, 10, s_nenner); |
---|
2066 | PrintS(" + "); |
---|
2067 | mpz_out_str( stdout, 10, s_zaehler); |
---|
2068 | PrintS(" = "); mpz_out_str( stdout, 10, sntz); |
---|
2069 | Print(" ==> vector[%d]: ", j); mpz_out_str(stdout, 10, vec[j]); |
---|
2070 | #endif |
---|
2071 | |
---|
2072 | if(j==0) |
---|
2073 | { |
---|
2074 | mpz_set(ggt, sntz); |
---|
2075 | } |
---|
2076 | else |
---|
2077 | { |
---|
2078 | if(mpz_cmp_si(ggt,1) != 0) |
---|
2079 | { |
---|
2080 | mpz_gcd(ggt, ggt, sntz); |
---|
2081 | } |
---|
2082 | } |
---|
2083 | } |
---|
2084 | |
---|
2085 | #ifdef NEXT_VECTORS_CC |
---|
2086 | PrintS("\n// gcd of elements of the vector: "); |
---|
2087 | mpz_out_str( stdout, 10, ggt); |
---|
2088 | #endif |
---|
2089 | |
---|
2090 | /********************************************************************** |
---|
2091 | * construct a new weight vector and check whether vec[j] is overflow, * |
---|
2092 | * i.e. vec[j] > 2^31. * |
---|
2093 | * If vec[j] doesn't overflow, define a weight vector. Otherwise, * |
---|
2094 | * report that overflow appears. In the second case, test whether the * |
---|
2095 | * the correctness of the new vector plays an important role * |
---|
2096 | **********************************************************************/ |
---|
2097 | kkk=0; |
---|
2098 | for(j=0; j<nRing; j++) |
---|
2099 | { |
---|
2100 | if(mpz_cmp(vec[j], sing_int_half) >= 0) |
---|
2101 | { |
---|
2102 | goto REDUCTION; |
---|
2103 | } |
---|
2104 | } |
---|
2105 | checkRed = 1; |
---|
2106 | for (j=0; j<nRing; j++) |
---|
2107 | { |
---|
2108 | (*diff_weight)[j] = mpz_get_si(vec[j]); |
---|
2109 | } |
---|
2110 | goto SIMPLIFY_GCD; |
---|
2111 | |
---|
2112 | REDUCTION: |
---|
2113 | for (j=0; j<nRing; j++) |
---|
2114 | { |
---|
2115 | (*diff_weight)[j] = mpz_get_si(vec[j]); |
---|
2116 | } |
---|
2117 | while(MivAbsMax(diff_weight) >= 5) |
---|
2118 | { |
---|
2119 | for (j=0; j<nRing; j++) |
---|
2120 | { |
---|
2121 | if(mpz_cmp_si(ggt,1)==0) |
---|
2122 | { |
---|
2123 | (*diff_weight1)[j] = floor(0.1*(*diff_weight)[j] + 0.5); |
---|
2124 | // Print("\n// vector[%d] = %d \n",j+1, (*diff_weight1)[j]); |
---|
2125 | } |
---|
2126 | else |
---|
2127 | { |
---|
2128 | mpz_divexact(vec[j], vec[j], ggt); |
---|
2129 | (*diff_weight1)[j] = floor(0.1*(*diff_weight)[j] + 0.5); |
---|
2130 | // Print("\n// vector[%d] = %d \n",j+1, (*diff_weight1)[j]); |
---|
2131 | } |
---|
2132 | /* |
---|
2133 | if((*diff_weight1)[j] == 0) |
---|
2134 | { |
---|
2135 | kkk = kkk + 1; |
---|
2136 | } |
---|
2137 | */ |
---|
2138 | } |
---|
2139 | |
---|
2140 | |
---|
2141 | /* |
---|
2142 | if(kkk > nRing - 1) |
---|
2143 | { |
---|
2144 | // diff_weight was reduced to zero |
---|
2145 | // Print("\n // MwalkNextWeightCC: geaenderter Vector gleich Null! \n"); |
---|
2146 | goto TEST_OVERFLOW; |
---|
2147 | } |
---|
2148 | */ |
---|
2149 | |
---|
2150 | if(test_w_in_ConeCC(G,diff_weight1) != 0) |
---|
2151 | { |
---|
2152 | Print("\n// MwalkNextWeightCC: geaenderter vector liegt in Groebnerkegel! \n"); |
---|
2153 | for (j=0; j<nRing; j++) |
---|
2154 | { |
---|
2155 | (*diff_weight)[j] = (*diff_weight1)[j]; |
---|
2156 | } |
---|
2157 | if(MivAbsMax(diff_weight) < 5) |
---|
2158 | { |
---|
2159 | checkRed = 1; |
---|
2160 | goto SIMPLIFY_GCD; |
---|
2161 | } |
---|
2162 | } |
---|
2163 | else |
---|
2164 | { |
---|
2165 | // Print("\n// MwalkNextWeightCC: geaenderter vector liegt nicht in Groebnerkegel! \n"); |
---|
2166 | break; |
---|
2167 | } |
---|
2168 | } |
---|
2169 | |
---|
2170 | TEST_OVERFLOW: |
---|
2171 | |
---|
2172 | for (j=0; j<nRing; j++) |
---|
2173 | { |
---|
2174 | if(mpz_cmp(vec[j], sing_int)>=0) |
---|
2175 | { |
---|
2176 | if(Overflow_Error == FALSE) |
---|
2177 | { |
---|
2178 | Overflow_Error = TRUE; |
---|
2179 | PrintS("\n// ** OVERFLOW in \"MwalkNextWeightCC\": "); |
---|
2180 | mpz_out_str( stdout, 10, vec[j]); |
---|
2181 | PrintS(" is greater than 2147483647 (max. integer representation)\n"); |
---|
2182 | //Print("// So vector[%d] := %d is wrong!!\n",j+1, vec[j]);// vec[j] is mpz_t |
---|
2183 | } |
---|
2184 | } |
---|
2185 | } |
---|
2186 | |
---|
2187 | FINISH: |
---|
2188 | delete diff_weight1; |
---|
2189 | mpz_clear(t_zaehler); |
---|
2190 | mpz_clear(t_nenner); |
---|
2191 | mpz_clear(s_zaehler); |
---|
2192 | mpz_clear(s_nenner); |
---|
2193 | mpz_clear(sntz); |
---|
2194 | mpz_clear(sztn); |
---|
2195 | mpz_clear(temp); |
---|
2196 | mpz_clear(MwWd); |
---|
2197 | mpz_clear(deg_w0_p1); |
---|
2198 | mpz_clear(deg_d0_p1); |
---|
2199 | mpz_clear(ggt); |
---|
2200 | omFree(vec); |
---|
2201 | mpz_clear(sing_int_half); |
---|
2202 | mpz_clear(sing_int); |
---|
2203 | mpz_clear(dcw); |
---|
2204 | mpz_clear(t_null); |
---|
2205 | |
---|
2206 | |
---|
2207 | |
---|
2208 | if(Overflow_Error == FALSE) |
---|
2209 | { |
---|
2210 | Overflow_Error = nError; |
---|
2211 | } |
---|
2212 | rComplete(currRing); |
---|
2213 | for(kkk=0; kkk<IDELEMS(G);kkk++) |
---|
2214 | { |
---|
2215 | poly p=G->m[kkk]; |
---|
2216 | while(p!=NULL) |
---|
2217 | { |
---|
2218 | p_Setm(p,currRing); |
---|
2219 | pIter(p); |
---|
2220 | } |
---|
2221 | } |
---|
2222 | return diff_weight; |
---|
2223 | } |
---|
2224 | |
---|
2225 | /********************************************************************** |
---|
2226 | * Compute an intermediate weight vector from iva to ivb w.r.t. * |
---|
2227 | * the reduced Groebner basis G. * |
---|
2228 | * Return NULL, if it is equal to iva or iva = avb. * |
---|
2229 | **********************************************************************/ |
---|
2230 | intvec* MkInterRedNextWeight(intvec* iva, intvec* ivb, ideal G) |
---|
2231 | { |
---|
2232 | intvec* tmp = new intvec(iva->length()); |
---|
2233 | intvec* result; |
---|
2234 | |
---|
2235 | if(G == NULL) |
---|
2236 | { |
---|
2237 | return tmp; |
---|
2238 | } |
---|
2239 | if(MivComp(iva, ivb) == 1) |
---|
2240 | { |
---|
2241 | return tmp; |
---|
2242 | } |
---|
2243 | result = MwalkNextWeightCC(iva, ivb, G); |
---|
2244 | |
---|
2245 | if(MivComp(result, iva) == 1) |
---|
2246 | { |
---|
2247 | delete result; |
---|
2248 | return tmp; |
---|
2249 | } |
---|
2250 | |
---|
2251 | delete tmp; |
---|
2252 | return result; |
---|
2253 | } |
---|
2254 | |
---|
2255 | /************************************************************** |
---|
2256 | * define and execute a new ring which order is (a(vb),a(va),lp,C) * |
---|
2257 | * ************************************************************/ |
---|
2258 | static void VMrHomogeneous(intvec* va, intvec* vb) |
---|
2259 | { |
---|
2260 | |
---|
2261 | if ((currRing->ppNoether)!=NULL) |
---|
2262 | { |
---|
2263 | pDelete(&(currRing->ppNoether)); |
---|
2264 | } |
---|
2265 | if (((sLastPrinted.rtyp>BEGIN_RING) && (sLastPrinted.rtyp<END_RING)) || |
---|
2266 | ((sLastPrinted.rtyp==LIST_CMD)&&(lRingDependend((lists)sLastPrinted.data)))) |
---|
2267 | { |
---|
2268 | sLastPrinted.CleanUp(); |
---|
2269 | } |
---|
2270 | |
---|
2271 | ring r = (ring) omAlloc0Bin(sip_sring_bin); |
---|
2272 | int i, nv = currRing->N; |
---|
2273 | |
---|
2274 | r->cf = currRing->cf; |
---|
2275 | r->N = currRing->N; |
---|
2276 | int nb = 4; |
---|
2277 | |
---|
2278 | |
---|
2279 | //names |
---|
2280 | char* Q; // In order to avoid the corrupted memory, do not change. |
---|
2281 | r->names = (char **) omAlloc0(nv * sizeof(char_ptr)); |
---|
2282 | for(i=0; i<nv; i++) |
---|
2283 | { |
---|
2284 | Q = currRing->names[i]; |
---|
2285 | r->names[i] = omStrDup(Q); |
---|
2286 | } |
---|
2287 | |
---|
2288 | //weights: entries for 3 blocks: NULL Made:??? |
---|
2289 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2290 | r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int)); |
---|
2291 | r->wvhdl[1] = (int*) omAlloc((nv-1)*sizeof(int)); |
---|
2292 | |
---|
2293 | for(i=0; i<nv-1; i++) |
---|
2294 | { |
---|
2295 | r->wvhdl[1][i] = (*vb)[i]; |
---|
2296 | r->wvhdl[0][i] = (*va)[i]; |
---|
2297 | } |
---|
2298 | r->wvhdl[0][nv] = (*va)[nv]; |
---|
2299 | |
---|
2300 | // order: (1..1),a,lp,C |
---|
2301 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2302 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2303 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2304 | |
---|
2305 | // ringorder a for the first block: var 1..nv |
---|
2306 | r->order[0] = ringorder_a; |
---|
2307 | r->block0[0] = 1; |
---|
2308 | r->block1[0] = nv; |
---|
2309 | |
---|
2310 | // ringorder a for the second block: var 2..nv |
---|
2311 | r->order[1] = ringorder_a; |
---|
2312 | r->block0[1] = 2; |
---|
2313 | r->block1[1] = nv; |
---|
2314 | |
---|
2315 | // ringorder lp for the third block: var 2..nv |
---|
2316 | r->order[2] = ringorder_lp; |
---|
2317 | r->block0[2] = 2; |
---|
2318 | r->block1[2] = nv; |
---|
2319 | |
---|
2320 | // ringorder C for the 4th block |
---|
2321 | // it is very important within "idLift", |
---|
2322 | // especially, by ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
2323 | // therefore, nb must be (nBlocks(currRing) + 1) |
---|
2324 | r->order[3] = ringorder_C; |
---|
2325 | |
---|
2326 | // polynomial ring |
---|
2327 | r->OrdSgn = 1; |
---|
2328 | |
---|
2329 | // complete ring intializations |
---|
2330 | |
---|
2331 | rComplete(r); |
---|
2332 | |
---|
2333 | rChangeCurrRing(r); |
---|
2334 | } |
---|
2335 | |
---|
2336 | |
---|
2337 | /************************************************************** |
---|
2338 | * define and execute a new ring which order is (a(va),lp,C) * |
---|
2339 | * ************************************************************/ |
---|
2340 | static void VMrDefault(intvec* va) |
---|
2341 | { |
---|
2342 | |
---|
2343 | if ((currRing->ppNoether)!=NULL) |
---|
2344 | { |
---|
2345 | pDelete(&(currRing->ppNoether)); |
---|
2346 | } |
---|
2347 | if (((sLastPrinted.rtyp>BEGIN_RING) && (sLastPrinted.rtyp<END_RING)) || |
---|
2348 | ((sLastPrinted.rtyp==LIST_CMD)&&(lRingDependend((lists)sLastPrinted.data)))) |
---|
2349 | { |
---|
2350 | sLastPrinted.CleanUp(); |
---|
2351 | } |
---|
2352 | |
---|
2353 | ring r = (ring) omAlloc0Bin(sip_sring_bin); |
---|
2354 | int i, nv = currRing->N; |
---|
2355 | |
---|
2356 | r->cf = currRing->cf; |
---|
2357 | r->N = currRing->N; |
---|
2358 | |
---|
2359 | int nb = 4; |
---|
2360 | |
---|
2361 | //names |
---|
2362 | char* Q; // In order to avoid the corrupted memory, do not change. |
---|
2363 | r->names = (char **) omAlloc0(nv * sizeof(char_ptr)); |
---|
2364 | for(i=0; i<nv; i++) |
---|
2365 | { |
---|
2366 | Q = currRing->names[i]; |
---|
2367 | r->names[i] = omStrDup(Q); |
---|
2368 | } |
---|
2369 | |
---|
2370 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
2371 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2372 | r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int)); |
---|
2373 | for(i=0; i<nv; i++) |
---|
2374 | r->wvhdl[0][i] = (*va)[i]; |
---|
2375 | |
---|
2376 | /* order: a,lp,C,0 */ |
---|
2377 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2378 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2379 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2380 | |
---|
2381 | // ringorder a for the first block: var 1..nv |
---|
2382 | r->order[0] = ringorder_a; |
---|
2383 | r->block0[0] = 1; |
---|
2384 | r->block1[0] = nv; |
---|
2385 | |
---|
2386 | // ringorder lp for the second block: var 1..nv |
---|
2387 | r->order[1] = ringorder_lp; |
---|
2388 | r->block0[1] = 1; |
---|
2389 | r->block1[1] = nv; |
---|
2390 | |
---|
2391 | // ringorder C for the third block |
---|
2392 | // it is very important within "idLift", |
---|
2393 | // especially, by ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
2394 | // therefore, nb must be (nBlocks(currRing) + 1) |
---|
2395 | r->order[2] = ringorder_C; |
---|
2396 | |
---|
2397 | // the last block: everything is 0 |
---|
2398 | r->order[3] = 0; |
---|
2399 | |
---|
2400 | // polynomial ring |
---|
2401 | r->OrdSgn = 1; |
---|
2402 | |
---|
2403 | // complete ring intializations |
---|
2404 | |
---|
2405 | rComplete(r); |
---|
2406 | |
---|
2407 | rChangeCurrRing(r); |
---|
2408 | } |
---|
2409 | |
---|
2410 | /********************************************************************** |
---|
2411 | * define and execute a new ring which order is a lexicographic order * |
---|
2412 | ***********************************************************************/ |
---|
2413 | static void VMrDefaultlp(void) |
---|
2414 | { |
---|
2415 | |
---|
2416 | if ((currRing->ppNoether)!=NULL) |
---|
2417 | { |
---|
2418 | pDelete(&(currRing->ppNoether)); |
---|
2419 | } |
---|
2420 | if (((sLastPrinted.rtyp>BEGIN_RING) && (sLastPrinted.rtyp<END_RING)) || |
---|
2421 | ((sLastPrinted.rtyp==LIST_CMD)&&(lRingDependend((lists)sLastPrinted.data)))) |
---|
2422 | |
---|
2423 | { |
---|
2424 | sLastPrinted.CleanUp(); |
---|
2425 | } |
---|
2426 | |
---|
2427 | ring r = (ring) omAlloc0Bin(sip_sring_bin); |
---|
2428 | int i, nv = currRing->N; |
---|
2429 | |
---|
2430 | r->cf = currRing->cf; |
---|
2431 | r->N = currRing->N; |
---|
2432 | int nb = rBlocks(currRing) + 1; |
---|
2433 | |
---|
2434 | // names |
---|
2435 | char* Q; // to avoid the corrupted memory, do not change!! |
---|
2436 | r->names = (char **) omAlloc0(nv * sizeof(char_ptr)); |
---|
2437 | for(i=0; i<nv; i++) |
---|
2438 | { |
---|
2439 | Q = currRing->names[i]; |
---|
2440 | r->names[i] = omStrDup(Q); |
---|
2441 | } |
---|
2442 | |
---|
2443 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
2444 | |
---|
2445 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2446 | |
---|
2447 | /* order: lp,C,0 */ |
---|
2448 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2449 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2450 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2451 | |
---|
2452 | /* ringorder lp for the first block: var 1..nv */ |
---|
2453 | r->order[0] = ringorder_lp; |
---|
2454 | r->block0[0] = 1; |
---|
2455 | r->block1[0] = nv; |
---|
2456 | |
---|
2457 | /* ringorder C for the second block */ |
---|
2458 | r->order[1] = ringorder_C; |
---|
2459 | |
---|
2460 | /* the last block: everything is 0 */ |
---|
2461 | r->order[2] = 0; |
---|
2462 | |
---|
2463 | /*polynomial ring*/ |
---|
2464 | r->OrdSgn = 1; |
---|
2465 | |
---|
2466 | /* complete ring intializations */ |
---|
2467 | |
---|
2468 | rComplete(r); |
---|
2469 | |
---|
2470 | rChangeCurrRing(r); |
---|
2471 | } |
---|
2472 | |
---|
2473 | |
---|
2474 | /* define a ring with parameters und change to it */ |
---|
2475 | /* DefRingPar and DefRingParlp corrupt still memory */ |
---|
2476 | static void DefRingPar(intvec* va) |
---|
2477 | { |
---|
2478 | int i, nv = currRing->N; |
---|
2479 | int nb = rBlocks(currRing) + 1; |
---|
2480 | |
---|
2481 | ring res=(ring)omAllocBin(sip_sring_bin); |
---|
2482 | |
---|
2483 | memcpy(res,currRing,sizeof(ip_sring)); |
---|
2484 | |
---|
2485 | res->VarOffset = NULL; |
---|
2486 | res->ref=0; |
---|
2487 | |
---|
2488 | res->cf = currRing->cf; currRing->cf->ref++; |
---|
2489 | |
---|
2490 | |
---|
2491 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
2492 | res->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2493 | res->wvhdl[0] = (int*) omAlloc(nv*sizeof(int)); |
---|
2494 | for(i=0; i<nv; i++) |
---|
2495 | res->wvhdl[0][i] = (*va)[i]; |
---|
2496 | |
---|
2497 | /* order: a,lp,C,0 */ |
---|
2498 | |
---|
2499 | res->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2500 | res->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2501 | res->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2502 | |
---|
2503 | // ringorder a for the first block: var 1..nv |
---|
2504 | res->order[0] = ringorder_a; |
---|
2505 | res->block0[0] = 1; |
---|
2506 | res->block1[0] = nv; |
---|
2507 | |
---|
2508 | // ringorder lp for the second block: var 1..nv |
---|
2509 | res->order[1] = ringorder_lp; |
---|
2510 | res->block0[1] = 1; |
---|
2511 | res->block1[1] = nv; |
---|
2512 | |
---|
2513 | // ringorder C for the third block |
---|
2514 | // it is very important within "idLift", |
---|
2515 | // especially, by ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
2516 | // therefore, nb must be (nBlocks(currRing) + 1) |
---|
2517 | res->order[2] = ringorder_C; |
---|
2518 | |
---|
2519 | // the last block: everything is 0 |
---|
2520 | res->order[3] = 0; |
---|
2521 | |
---|
2522 | // polynomial ring |
---|
2523 | res->OrdSgn = 1; |
---|
2524 | |
---|
2525 | |
---|
2526 | res->names = (char **)omAlloc0(nv * sizeof(char_ptr)); |
---|
2527 | for (i=nv-1; i>=0; i--) |
---|
2528 | { |
---|
2529 | res->names[i] = omStrDup(currRing->names[i]); |
---|
2530 | } |
---|
2531 | // complete ring intializations |
---|
2532 | rComplete(res); |
---|
2533 | |
---|
2534 | // clean up history |
---|
2535 | if (sLastPrinted.RingDependend()) |
---|
2536 | { |
---|
2537 | sLastPrinted.CleanUp(); |
---|
2538 | } |
---|
2539 | |
---|
2540 | |
---|
2541 | // execute the created ring |
---|
2542 | rChangeCurrRing(res); |
---|
2543 | } |
---|
2544 | |
---|
2545 | |
---|
2546 | static void DefRingParlp(void) |
---|
2547 | { |
---|
2548 | int i, nv = currRing->N; |
---|
2549 | |
---|
2550 | ring r=(ring)omAllocBin(sip_sring_bin); |
---|
2551 | |
---|
2552 | memcpy(r,currRing,sizeof(ip_sring)); |
---|
2553 | |
---|
2554 | r->VarOffset = NULL; |
---|
2555 | r->ref=0; |
---|
2556 | |
---|
2557 | r->cf = currRing->cf; currRing->cf->ref++; |
---|
2558 | |
---|
2559 | |
---|
2560 | r->cf = currRing->cf; |
---|
2561 | r->N = currRing->N; |
---|
2562 | int nb = rBlocks(currRing) + 1; |
---|
2563 | |
---|
2564 | // names |
---|
2565 | char* Q; |
---|
2566 | r->names = (char **) omAlloc0(nv * sizeof(char_ptr)); |
---|
2567 | for(i=nv-1; i>=0; i--) |
---|
2568 | { |
---|
2569 | Q = currRing->names[i]; |
---|
2570 | r->names[i] = omStrDup(Q); |
---|
2571 | } |
---|
2572 | |
---|
2573 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
2574 | |
---|
2575 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2576 | |
---|
2577 | /* order: lp,C,0 */ |
---|
2578 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2579 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2580 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2581 | |
---|
2582 | /* ringorder lp for the first block: var 1..nv */ |
---|
2583 | r->order[0] = ringorder_lp; |
---|
2584 | r->block0[0] = 1; |
---|
2585 | r->block1[0] = nv; |
---|
2586 | |
---|
2587 | /* ringorder C for the second block */ |
---|
2588 | r->order[1] = ringorder_C; |
---|
2589 | |
---|
2590 | /* the last block: everything is 0 */ |
---|
2591 | r->order[2] = 0; |
---|
2592 | |
---|
2593 | /*polynomial ring*/ |
---|
2594 | r->OrdSgn = 1; |
---|
2595 | |
---|
2596 | |
---|
2597 | // if (rParameter(currRing)!=NULL) |
---|
2598 | // { |
---|
2599 | // r->cf->extRing->qideal->m[0]=p_Copy(currRing->cf->extRing->qideal->m[0], currRing->cf->extRing); |
---|
2600 | // int l=rPar(currRing); |
---|
2601 | // r->cf->extRing->names=(char **)omAlloc(l*sizeof(char_ptr)); |
---|
2602 | // |
---|
2603 | // for(i=l-1;i>=0;i--) |
---|
2604 | // { |
---|
2605 | // rParameter(r)[i]=omStrDup(rParameter(currRing)[i]); |
---|
2606 | // } |
---|
2607 | // } |
---|
2608 | |
---|
2609 | // complete ring intializations |
---|
2610 | |
---|
2611 | rComplete(r); |
---|
2612 | |
---|
2613 | // clean up history |
---|
2614 | if (sLastPrinted.RingDependend()) |
---|
2615 | { |
---|
2616 | sLastPrinted.CleanUp(); |
---|
2617 | } |
---|
2618 | |
---|
2619 | // execute the created ring |
---|
2620 | rChangeCurrRing(r); |
---|
2621 | } |
---|
2622 | |
---|
2623 | //unused |
---|
2624 | /************************************************************** |
---|
2625 | * check wheather one or more components of a vector are zero * |
---|
2626 | **************************************************************/ |
---|
2627 | //#if 0 |
---|
2628 | static int isNolVector(intvec* hilb) |
---|
2629 | { |
---|
2630 | int i; |
---|
2631 | for(i=hilb->length()-1; i>=0; i--) |
---|
2632 | { |
---|
2633 | if((* hilb)[i]==0) |
---|
2634 | { |
---|
2635 | return 1; |
---|
2636 | } |
---|
2637 | } |
---|
2638 | return 0; |
---|
2639 | } |
---|
2640 | //#endif |
---|
2641 | |
---|
2642 | /****************************** Februar 2002 **************************** |
---|
2643 | * G is a Groebner basis w.r.t. (a(curr_weight),lp) and * |
---|
2644 | * we compute a GB of <G> w.r.t. the lex. order by the perturbation walk * |
---|
2645 | * its perturbation degree is tp_deg * |
---|
2646 | * We call the following subfunction LastGB, if * |
---|
2647 | * the computed intermediate weight vector or * |
---|
2648 | * if the perturbed target weight vector does NOT lie n the correct cone * |
---|
2649 | **************************************************************************/ |
---|
2650 | |
---|
2651 | static ideal LastGB(ideal G, intvec* curr_weight,int tp_deg) |
---|
2652 | { |
---|
2653 | BOOLEAN nError = Overflow_Error; |
---|
2654 | Overflow_Error = FALSE; |
---|
2655 | |
---|
2656 | int i, nV = currRing->N; |
---|
2657 | int nwalk=0, endwalks=0, nnwinC=1; |
---|
2658 | int nlast = 0; |
---|
2659 | ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG; |
---|
2660 | ring newRing, oldRing, TargetRing; |
---|
2661 | intvec* iv_M_lp; |
---|
2662 | intvec* target_weight; |
---|
2663 | intvec* iv_lp = Mivlp(nV); //define (1,0,...,0) |
---|
2664 | intvec* pert_target_vector; |
---|
2665 | intvec* ivNull = new intvec(nV); |
---|
2666 | intvec* extra_curr_weight = new intvec(nV); |
---|
2667 | intvec* next_weight; |
---|
2668 | |
---|
2669 | #ifndef BUCHBERGER_ALG |
---|
2670 | intvec* hilb_func; |
---|
2671 | #endif |
---|
2672 | |
---|
2673 | // to avoid (1,0,...,0) as the target vector |
---|
2674 | intvec* last_omega = new intvec(nV); |
---|
2675 | for(i=nV-1; i>0; i--) |
---|
2676 | { |
---|
2677 | (*last_omega)[i] = 1; |
---|
2678 | } |
---|
2679 | (*last_omega)[0] = 10000; |
---|
2680 | |
---|
2681 | ring EXXRing = currRing; |
---|
2682 | |
---|
2683 | // compute a pertubed weight vector of the target weight vector |
---|
2684 | if(tp_deg > 1 && tp_deg <= nV) |
---|
2685 | { |
---|
2686 | //..25.03.03 VMrDefaultlp();// VMrDefault(target_weight); |
---|
2687 | if (rParameter (currRing) != NULL) |
---|
2688 | { |
---|
2689 | DefRingParlp(); |
---|
2690 | } |
---|
2691 | else |
---|
2692 | { |
---|
2693 | VMrDefaultlp(); |
---|
2694 | } |
---|
2695 | TargetRing = currRing; |
---|
2696 | ssG = idrMoveR(G,EXXRing,currRing); |
---|
2697 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
2698 | //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg); |
---|
2699 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
2700 | delete iv_M_lp; |
---|
2701 | pert_target_vector = target_weight; |
---|
2702 | |
---|
2703 | rChangeCurrRing(EXXRing); |
---|
2704 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
2705 | } |
---|
2706 | else |
---|
2707 | { |
---|
2708 | target_weight = Mivlp(nV); |
---|
2709 | } |
---|
2710 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2711 | |
---|
2712 | while(1) |
---|
2713 | { |
---|
2714 | nwalk++; |
---|
2715 | nstep++; |
---|
2716 | to=clock(); |
---|
2717 | // compute a next weight vector |
---|
2718 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
2719 | xtnw=xtnw+clock()-to; |
---|
2720 | |
---|
2721 | #ifdef PRINT_VECTORS |
---|
2722 | MivString(curr_weight, target_weight, next_weight); |
---|
2723 | #endif |
---|
2724 | |
---|
2725 | if(Overflow_Error == TRUE) |
---|
2726 | { |
---|
2727 | newRing = currRing; |
---|
2728 | nnwinC = 0; |
---|
2729 | if(tp_deg == 1) |
---|
2730 | { |
---|
2731 | nlast = 1; |
---|
2732 | } |
---|
2733 | delete next_weight; |
---|
2734 | |
---|
2735 | //idElements(G, "G"); |
---|
2736 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2737 | |
---|
2738 | break; |
---|
2739 | } |
---|
2740 | |
---|
2741 | if(MivComp(next_weight, ivNull) == 1) |
---|
2742 | { |
---|
2743 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2744 | newRing = currRing; |
---|
2745 | delete next_weight; |
---|
2746 | break; |
---|
2747 | } |
---|
2748 | |
---|
2749 | if(MivComp(next_weight, target_weight) == 1) |
---|
2750 | endwalks = 1; |
---|
2751 | |
---|
2752 | for(i=nV-1; i>=0; i--) |
---|
2753 | { |
---|
2754 | (*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
2755 | } |
---|
2756 | /* 06.11.01 NOT Changed */ |
---|
2757 | for(i=nV-1; i>=0; i--) |
---|
2758 | { |
---|
2759 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
2760 | } |
---|
2761 | oldRing = currRing; |
---|
2762 | to=clock(); |
---|
2763 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
2764 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
2765 | xtif=xtif+clock()-to; |
---|
2766 | |
---|
2767 | #ifdef ENDWALKS |
---|
2768 | if(endwalks == 1) |
---|
2769 | { |
---|
2770 | Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2771 | idElements(Gomega, "Gw"); |
---|
2772 | headidString(Gomega, "Gw"); |
---|
2773 | } |
---|
2774 | #endif |
---|
2775 | |
---|
2776 | #ifndef BUCHBERGER_ALG |
---|
2777 | if(isNolVector(curr_weight) == 0) |
---|
2778 | { |
---|
2779 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
2780 | } |
---|
2781 | else |
---|
2782 | { |
---|
2783 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
2784 | } |
---|
2785 | #endif // BUCHBERGER_ALG |
---|
2786 | |
---|
2787 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
2788 | //..25.03.03 VMrDefault(curr_weight); |
---|
2789 | if (rParameter (currRing) != NULL) |
---|
2790 | { |
---|
2791 | DefRingPar(curr_weight); |
---|
2792 | } |
---|
2793 | else |
---|
2794 | { |
---|
2795 | VMrDefault(curr_weight); |
---|
2796 | } |
---|
2797 | newRing = currRing; |
---|
2798 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
2799 | |
---|
2800 | to=clock(); |
---|
2801 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
2802 | #ifdef BUCHBERGER_ALG |
---|
2803 | M = MstdhomCC(Gomega1); |
---|
2804 | #else |
---|
2805 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
2806 | delete hilb_func; |
---|
2807 | #endif // BUCHBERGER_ALG |
---|
2808 | xtstd=xtstd+clock()-to; |
---|
2809 | /* change the ring to oldRing */ |
---|
2810 | rChangeCurrRing(oldRing); |
---|
2811 | M1 = idrMoveR(M, newRing,currRing); |
---|
2812 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
2813 | |
---|
2814 | to=clock(); |
---|
2815 | /* compute a reduced Groebner basis of <G> w.r.t. "newRing" */ |
---|
2816 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
2817 | xtlift=xtlift+clock()-to; |
---|
2818 | |
---|
2819 | idDelete(&M1); |
---|
2820 | idDelete(&G); |
---|
2821 | |
---|
2822 | /* change the ring to newRing */ |
---|
2823 | rChangeCurrRing(newRing); |
---|
2824 | F1 = idrMoveR(F, oldRing,currRing); |
---|
2825 | |
---|
2826 | to=clock(); |
---|
2827 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
2828 | G = kInterRedCC(F1, NULL); |
---|
2829 | xtred=xtred+clock()-to; |
---|
2830 | idDelete(&F1); |
---|
2831 | |
---|
2832 | if(endwalks == 1) |
---|
2833 | { |
---|
2834 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2835 | break; |
---|
2836 | } |
---|
2837 | |
---|
2838 | delete next_weight; |
---|
2839 | }//while |
---|
2840 | |
---|
2841 | delete ivNull; |
---|
2842 | |
---|
2843 | if(tp_deg != 1) |
---|
2844 | { |
---|
2845 | //..25.03.03 VMrDefaultlp();//define and execute the ring "lp" |
---|
2846 | if (rParameter (currRing) != NULL) |
---|
2847 | { |
---|
2848 | DefRingParlp(); |
---|
2849 | } |
---|
2850 | else |
---|
2851 | { |
---|
2852 | VMrDefaultlp(); |
---|
2853 | } |
---|
2854 | F1 = idrMoveR(G, newRing,currRing); |
---|
2855 | |
---|
2856 | if(nnwinC == 0 || test_w_in_ConeCC(F1, pert_target_vector) != 1) |
---|
2857 | { |
---|
2858 | oldRing = currRing; |
---|
2859 | rChangeCurrRing(newRing); |
---|
2860 | G = idrMoveR(F1, oldRing,currRing); |
---|
2861 | Print("\n// takes %d steps and calls the recursion of level %d:", |
---|
2862 | nwalk, tp_deg-1); |
---|
2863 | |
---|
2864 | F1 = LastGB(G,curr_weight, tp_deg-1); |
---|
2865 | } |
---|
2866 | |
---|
2867 | TargetRing = currRing; |
---|
2868 | rChangeCurrRing(EXXRing); |
---|
2869 | result = idrMoveR(F1, TargetRing,currRing); |
---|
2870 | } |
---|
2871 | else |
---|
2872 | { |
---|
2873 | if(nlast == 1) |
---|
2874 | { |
---|
2875 | //OMEGA_OVERFLOW_LASTGB: |
---|
2876 | /* |
---|
2877 | if(MivSame(curr_weight, iv_lp) == 1) |
---|
2878 | if (rParameter(currRing) != NULL) |
---|
2879 | DefRingParlp(); |
---|
2880 | else |
---|
2881 | VMrDefaultlp(); |
---|
2882 | else |
---|
2883 | if (rParameter(currRing) != NULL) |
---|
2884 | DefRingPar(curr_weight); |
---|
2885 | else |
---|
2886 | VMrDefault(curr_weight); |
---|
2887 | */ |
---|
2888 | |
---|
2889 | //..25.03.03 VMrDefaultlp();//define and execute the ring "lp" |
---|
2890 | if (rParameter (currRing) != NULL) |
---|
2891 | { |
---|
2892 | DefRingParlp(); |
---|
2893 | } |
---|
2894 | else |
---|
2895 | { |
---|
2896 | VMrDefaultlp(); |
---|
2897 | } |
---|
2898 | |
---|
2899 | F1 = idrMoveR(G, newRing,currRing); |
---|
2900 | //Print("\n// Apply \"std\" in ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2901 | |
---|
2902 | G = MstdCC(F1); |
---|
2903 | idDelete(&F1); |
---|
2904 | newRing = currRing; |
---|
2905 | } |
---|
2906 | |
---|
2907 | rChangeCurrRing(EXXRing); |
---|
2908 | result = idrMoveR(G, newRing,currRing); |
---|
2909 | } |
---|
2910 | delete target_weight; |
---|
2911 | delete last_omega; |
---|
2912 | delete iv_lp; |
---|
2913 | |
---|
2914 | if(Overflow_Error == FALSE) |
---|
2915 | { |
---|
2916 | Overflow_Error = nError; |
---|
2917 | } |
---|
2918 | return(result); |
---|
2919 | } |
---|
2920 | |
---|
2921 | /********************************************************** |
---|
2922 | * check whether a polynomial of G has least 3 monomials * |
---|
2923 | **********************************************************/ |
---|
2924 | static int lengthpoly(ideal G) |
---|
2925 | { |
---|
2926 | int i; |
---|
2927 | for(i=IDELEMS(G)-1; i>=0; i--) |
---|
2928 | { |
---|
2929 | #if 0 |
---|
2930 | if(pLength(G->m[i])>2) |
---|
2931 | { |
---|
2932 | return 1; |
---|
2933 | } |
---|
2934 | #else |
---|
2935 | if((G->m[i]!=NULL) /* len >=0 */ |
---|
2936 | && (G->m[i]->next!=NULL) /* len >=1 */ |
---|
2937 | && (G->m[i]->next->next!=NULL) /* len >=2 */ |
---|
2938 | && (G->m[i]->next->next->next!=NULL) /* len >=3 */ |
---|
2939 | //&& (G->m[i]->next->next->next->next!=NULL) /* len >=4 */ |
---|
2940 | ) |
---|
2941 | { |
---|
2942 | return 1; |
---|
2943 | } |
---|
2944 | #endif |
---|
2945 | } |
---|
2946 | return 0; |
---|
2947 | } |
---|
2948 | |
---|
2949 | /********************************************************* |
---|
2950 | * check whether a polynomial of G has least 2 monomials * |
---|
2951 | **********************************************************/ |
---|
2952 | static int islengthpoly2(ideal G) |
---|
2953 | { |
---|
2954 | int i; |
---|
2955 | for(i=IDELEMS(G)-1; i>=0; i--) |
---|
2956 | { |
---|
2957 | if((G->m[i]!=NULL) /* len >=0 */ |
---|
2958 | && (G->m[i]->next!=NULL) /* len >=1 */ |
---|
2959 | && (G->m[i]->next->next!=NULL)) /* len >=2 */ |
---|
2960 | { |
---|
2961 | return 1; |
---|
2962 | } |
---|
2963 | } |
---|
2964 | return 0; |
---|
2965 | } |
---|
2966 | |
---|
2967 | |
---|
2968 | |
---|
2969 | /* Implementation of the improved Groebner walk algorithm which is written |
---|
2970 | by Quoc-Nam Tran (2000). |
---|
2971 | One perturbs the original target weight vector, only if |
---|
2972 | the next intermediate weight vector is equal to the current target weight |
---|
2973 | vector. This must be repeated until the wanted reduced Groebner basis |
---|
2974 | to reach. |
---|
2975 | If the numbers of variables is big enough, the representation of the origin |
---|
2976 | weight vector may be very big. Therefore, it is possible the intermediate |
---|
2977 | weight vector doesn't stay in the correct Groebner cone. |
---|
2978 | In this case we have just a reduced Groebner basis of the given ideal |
---|
2979 | with respect to another monomial order. Then we have to compute |
---|
2980 | a wanted reduced Groebner basis of it with respect to the given order. |
---|
2981 | At the following subroutine we use the improved Buchberger algorithm or |
---|
2982 | the changed perturbation walk algorithm with a decrased degree. |
---|
2983 | */ |
---|
2984 | |
---|
2985 | /*************************************** |
---|
2986 | * return the initial term of an ideal * |
---|
2987 | ***************************************/ |
---|
2988 | static ideal idHeadCC(ideal h) |
---|
2989 | { |
---|
2990 | int i, nH =IDELEMS(h); |
---|
2991 | |
---|
2992 | ideal m = idInit(nH,h->rank); |
---|
2993 | |
---|
2994 | for (i=nH-1;i>=0; i--) |
---|
2995 | { |
---|
2996 | if (h->m[i]!=NULL) |
---|
2997 | { |
---|
2998 | m->m[i]=pHead(h->m[i]); |
---|
2999 | } |
---|
3000 | } |
---|
3001 | return m; |
---|
3002 | } |
---|
3003 | |
---|
3004 | /********************************************** |
---|
3005 | * check whether two head-ideals are the same * |
---|
3006 | **********************************************/ |
---|
3007 | static inline int test_G_GB_walk(ideal H0, ideal H1) |
---|
3008 | { |
---|
3009 | int i, nG = IDELEMS(H0); |
---|
3010 | |
---|
3011 | if(nG != IDELEMS(H1)) |
---|
3012 | { |
---|
3013 | return 0; |
---|
3014 | } |
---|
3015 | for(i=nG-1; i>=0; i--) |
---|
3016 | { |
---|
3017 | #if 0 |
---|
3018 | poly t; |
---|
3019 | if((t=pSub(pCopy(H0->m[i]), pCopy(H1->m[i]))) != NULL) |
---|
3020 | { |
---|
3021 | pDelete(&t); |
---|
3022 | return 0; |
---|
3023 | } |
---|
3024 | pDelete(&t); |
---|
3025 | #else |
---|
3026 | if(!pEqualPolys(H0->m[i],H1->m[i])) |
---|
3027 | { |
---|
3028 | return 0; |
---|
3029 | } |
---|
3030 | #endif |
---|
3031 | } |
---|
3032 | return 1; |
---|
3033 | } |
---|
3034 | |
---|
3035 | //unused |
---|
3036 | /***************************************************** |
---|
3037 | * find the maximal total degree of polynomials in G * |
---|
3038 | *****************************************************/ |
---|
3039 | #if 0 |
---|
3040 | static int Trandegreebound(ideal G) |
---|
3041 | { |
---|
3042 | int i, nG = IDELEMS(G); |
---|
3043 | // int np=1; |
---|
3044 | int nV = currRing->N; |
---|
3045 | int degtmp, result = 0; |
---|
3046 | intvec* ivUnit = Mivdp(nV); |
---|
3047 | |
---|
3048 | for(i=nG-1; i>=0; i--) |
---|
3049 | { |
---|
3050 | // find the maximal total degree of the polynomial G[i] |
---|
3051 | degtmp = MwalkWeightDegree(G->m[i], ivUnit); |
---|
3052 | if(degtmp > result) |
---|
3053 | { |
---|
3054 | result = degtmp; |
---|
3055 | } |
---|
3056 | } |
---|
3057 | delete ivUnit; |
---|
3058 | return result; |
---|
3059 | } |
---|
3060 | #endif |
---|
3061 | |
---|
3062 | //unused |
---|
3063 | /************************************************************************ |
---|
3064 | * perturb the weight vector iva w.r.t. the ideal G. * |
---|
3065 | * the monomial order of the current ring is the w_1 weight lex. order * |
---|
3066 | * define w := d^(n-1)w_1+ d^(n-2)w_2, ...+ dw_(n-1)+ w_n * |
---|
3067 | * where d := 1 + max{totdeg(g):g in G}*m, or * |
---|
3068 | * d := (2*maxdeg*maxdeg + (nV+1)*maxdeg)*m; * |
---|
3069 | ************************************************************************/ |
---|
3070 | #if 0 |
---|
3071 | static intvec* TranPertVector(ideal G, intvec* iva) |
---|
3072 | { |
---|
3073 | BOOLEAN nError = Overflow_Error; |
---|
3074 | Overflow_Error = FALSE; |
---|
3075 | |
---|
3076 | int i, j; |
---|
3077 | // int nG = IDELEMS(G); |
---|
3078 | int nV = currRing->N; |
---|
3079 | |
---|
3080 | // define the sequence which expresses the current monomial ordering |
---|
3081 | // w_1 = iva; w_2 = (1,0,..,0); w_n = (0,...,0,1,0) |
---|
3082 | intvec* ivMat = MivMatrixOrder(iva); |
---|
3083 | |
---|
3084 | int mtmp, m=(*iva)[0]; |
---|
3085 | |
---|
3086 | for(i=ivMat->length(); i>=0; i--) |
---|
3087 | { |
---|
3088 | mtmp = (*ivMat)[i]; |
---|
3089 | if(mtmp <0) |
---|
3090 | { |
---|
3091 | mtmp = -mtmp; |
---|
3092 | } |
---|
3093 | if(mtmp > m) |
---|
3094 | { |
---|
3095 | m = mtmp; |
---|
3096 | } |
---|
3097 | } |
---|
3098 | |
---|
3099 | // define the maximal total degree of polynomials of G |
---|
3100 | mpz_t ndeg; |
---|
3101 | mpz_init(ndeg); |
---|
3102 | |
---|
3103 | // 12 Juli 03 |
---|
3104 | #ifndef UPPER_BOUND |
---|
3105 | mpz_set_si(ndeg, Trandegreebound(G)+1); |
---|
3106 | #else |
---|
3107 | mpz_t ztmp; |
---|
3108 | mpz_init(ztmp); |
---|
3109 | |
---|
3110 | mpz_t maxdeg; |
---|
3111 | mpz_init_set_si(maxdeg, Trandegreebound(G)); |
---|
3112 | |
---|
3113 | //ndeg = (2*maxdeg*maxdeg + (nV+1)*maxdeg)*m;//Kalkbrenner (1999) |
---|
3114 | mpz_pow_ui(ztmp, maxdeg, 2); |
---|
3115 | mpz_mul_ui(ztmp, ztmp, 2); |
---|
3116 | mpz_mul_ui(maxdeg, maxdeg, nV+1); |
---|
3117 | mpz_add(ndeg, ztmp, maxdeg); |
---|
3118 | mpz_mul_ui(ndeg, ndeg, m); |
---|
3119 | |
---|
3120 | mpz_clear(ztmp); |
---|
3121 | |
---|
3122 | //PrintS("\n// with the new upper degree bound (2d^2+(n+1)d)*m "); |
---|
3123 | //Print("\n// where d = %d, n = %d and bound = %d", maxdeg, nV, ndeg); |
---|
3124 | #endif //UPPER_BOUND |
---|
3125 | |
---|
3126 | #ifdef INVEPS_SMALL_IN_TRAN |
---|
3127 | if(mpz_cmp_ui(ndeg, nV)>0 && nV > 3) |
---|
3128 | { |
---|
3129 | mpz_cdiv_q_ui(ndeg, ndeg, nV); |
---|
3130 | } |
---|
3131 | //PrintS("\n// choose the \"small\" inverse epsilon:"); |
---|
3132 | //mpz_out_str(stdout, 10, ndeg); |
---|
3133 | #endif |
---|
3134 | mpz_t deg_tmp; |
---|
3135 | mpz_init_set(deg_tmp, ndeg); |
---|
3136 | |
---|
3137 | mpz_t *ivres=( mpz_t *) omAlloc(nV*sizeof(mpz_t)); |
---|
3138 | mpz_init_set_si(ivres[nV-1],1); |
---|
3139 | |
---|
3140 | for(i=nV-2; i>=0; i--) |
---|
3141 | { |
---|
3142 | mpz_init_set(ivres[i], deg_tmp); |
---|
3143 | mpz_mul(deg_tmp, deg_tmp, ndeg); |
---|
3144 | } |
---|
3145 | |
---|
3146 | mpz_t *ivtmp=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
3147 | for(i=0; i<nV; i++) |
---|
3148 | { |
---|
3149 | mpz_init(ivtmp[i]); |
---|
3150 | } |
---|
3151 | mpz_t sing_int; |
---|
3152 | mpz_init_set_ui(sing_int, 2147483647); |
---|
3153 | |
---|
3154 | intvec* repr_vector = new intvec(nV); |
---|
3155 | |
---|
3156 | // define ivtmp := ndeg^(n-1).w_1 + ndeg^(n-2).w_2 + ... + w_n |
---|
3157 | for(i=0; i<nV; i++) |
---|
3158 | { |
---|
3159 | for(j=0; j<nV; j++) |
---|
3160 | { |
---|
3161 | if( (*ivMat)[i*nV+j] >= 0 ) |
---|
3162 | { |
---|
3163 | mpz_mul_ui(ivres[i], ivres[i], (*ivMat)[i*nV+j]); |
---|
3164 | } |
---|
3165 | else |
---|
3166 | { |
---|
3167 | mpz_mul_ui(ivres[i], ivres[i], -(*ivMat)[i*nV+j]); |
---|
3168 | mpz_neg(ivres[i], ivres[i]); |
---|
3169 | } |
---|
3170 | mpz_add(ivtmp[j], ivtmp[j], ivres[i]); |
---|
3171 | } |
---|
3172 | } |
---|
3173 | delete ivMat; |
---|
3174 | |
---|
3175 | int ntrue=0; |
---|
3176 | for(i=0; i<nV; i++) |
---|
3177 | { |
---|
3178 | (*repr_vector)[i] = mpz_get_si(ivtmp[i]); |
---|
3179 | if(mpz_cmp(ivtmp[i], sing_int)>=0) |
---|
3180 | { |
---|
3181 | ntrue++; |
---|
3182 | if(Overflow_Error == FALSE) |
---|
3183 | { |
---|
3184 | Overflow_Error = TRUE; |
---|
3185 | |
---|
3186 | PrintS("\n// ** OVERFLOW in \"Repr.Vector\": "); |
---|
3187 | mpz_out_str( stdout, 10, ivtmp[i]); |
---|
3188 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
3189 | Print("\n// So vector[%d] := %d is wrong!!\n",i+1,(*repr_vector)[i]); |
---|
3190 | } |
---|
3191 | } |
---|
3192 | } |
---|
3193 | if(Overflow_Error == TRUE) |
---|
3194 | { |
---|
3195 | ivString(repr_vector, "repvector"); |
---|
3196 | Print("\n// %d element(s) of it are overflow!!", ntrue); |
---|
3197 | } |
---|
3198 | |
---|
3199 | if(Overflow_Error == FALSE) |
---|
3200 | Overflow_Error=nError; |
---|
3201 | |
---|
3202 | omFree(ivres); |
---|
3203 | omFree(ivtmp); |
---|
3204 | |
---|
3205 | mpz_clear(sing_int); |
---|
3206 | mpz_clear(deg_tmp); |
---|
3207 | mpz_clear(ndeg); |
---|
3208 | |
---|
3209 | return repr_vector; |
---|
3210 | } |
---|
3211 | #endif |
---|
3212 | |
---|
3213 | //unused |
---|
3214 | #if 0 |
---|
3215 | static intvec* TranPertVector_lp(ideal G) |
---|
3216 | { |
---|
3217 | BOOLEAN nError = Overflow_Error; |
---|
3218 | Overflow_Error = FALSE; |
---|
3219 | // int j, nG = IDELEMS(G); |
---|
3220 | int i; |
---|
3221 | int nV = currRing->N; |
---|
3222 | |
---|
3223 | // define the maximal total degree of polynomials of G |
---|
3224 | mpz_t ndeg; |
---|
3225 | mpz_init(ndeg); |
---|
3226 | |
---|
3227 | // 12 Juli 03 |
---|
3228 | #ifndef UPPER_BOUND |
---|
3229 | mpz_set_si(ndeg, Trandegreebound(G)+1); |
---|
3230 | #else |
---|
3231 | mpz_t ztmp; |
---|
3232 | mpz_init(ztmp); |
---|
3233 | |
---|
3234 | mpz_t maxdeg; |
---|
3235 | mpz_init_set_si(maxdeg, Trandegreebound(G)); |
---|
3236 | |
---|
3237 | //ndeg = (2*maxdeg*maxdeg + (nV+1)*maxdeg);//Kalkbrenner (1999) |
---|
3238 | mpz_pow_ui(ztmp, maxdeg, 2); |
---|
3239 | mpz_mul_ui(ztmp, ztmp, 2); |
---|
3240 | mpz_mul_ui(maxdeg, maxdeg, nV+1); |
---|
3241 | mpz_add(ndeg, ztmp, maxdeg); |
---|
3242 | // PrintS("\n// with the new upper degree bound (2d^2+(n+1)d)*m "); |
---|
3243 | // Print("\n// where d = %d, n = %d and bound = %d", |
---|
3244 | // mpz_get_si(maxdeg), nV, mpz_get_si(ndeg)); |
---|
3245 | |
---|
3246 | mpz_clear(ztmp); |
---|
3247 | |
---|
3248 | #endif |
---|
3249 | |
---|
3250 | #ifdef INVEPS_SMALL_IN_TRAN |
---|
3251 | if(mpz_cmp_ui(ndeg, nV)>0 && nV > 3) |
---|
3252 | mpz_cdiv_q_ui(ndeg, ndeg, nV); |
---|
3253 | |
---|
3254 | //PrintS("\n// choose the \"small\" inverse epsilon:"); |
---|
3255 | // mpz_out_str(stdout, 10, ndeg); |
---|
3256 | #endif |
---|
3257 | |
---|
3258 | mpz_t deg_tmp; |
---|
3259 | mpz_init_set(deg_tmp, ndeg); |
---|
3260 | |
---|
3261 | mpz_t *ivres=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
3262 | mpz_init_set_si(ivres[nV-1], 1); |
---|
3263 | |
---|
3264 | for(i=nV-2; i>=0; i--) |
---|
3265 | { |
---|
3266 | mpz_init_set(ivres[i], deg_tmp); |
---|
3267 | mpz_mul(deg_tmp, deg_tmp, ndeg); |
---|
3268 | } |
---|
3269 | |
---|
3270 | mpz_t sing_int; |
---|
3271 | mpz_init_set_ui(sing_int, 2147483647); |
---|
3272 | |
---|
3273 | intvec* repr_vector = new intvec(nV); |
---|
3274 | int ntrue=0; |
---|
3275 | for(i=0; i<nV; i++) |
---|
3276 | { |
---|
3277 | (*repr_vector)[i] = mpz_get_si(ivres[i]); |
---|
3278 | |
---|
3279 | if(mpz_cmp(ivres[i], sing_int)>=0) |
---|
3280 | { |
---|
3281 | ntrue++; |
---|
3282 | if(Overflow_Error == FALSE) |
---|
3283 | { |
---|
3284 | Overflow_Error = TRUE; |
---|
3285 | PrintS("\n// ** OVERFLOW in \"Repr.Vector\": "); |
---|
3286 | mpz_out_str( stdout, 10, ivres[i]); |
---|
3287 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
3288 | Print("\n// So vector[%d] := %d is wrong!!\n",i+1,(*repr_vector)[i]); |
---|
3289 | } |
---|
3290 | } |
---|
3291 | } |
---|
3292 | if(Overflow_Error == TRUE) |
---|
3293 | { |
---|
3294 | ivString(repr_vector, "repvector"); |
---|
3295 | Print("\n// %d element(s) of it are overflow!!", ntrue); |
---|
3296 | } |
---|
3297 | if(Overflow_Error == FALSE) |
---|
3298 | Overflow_Error = nError; |
---|
3299 | |
---|
3300 | omFree(ivres); |
---|
3301 | |
---|
3302 | mpz_clear(ndeg); |
---|
3303 | mpz_clear(sing_int); |
---|
3304 | |
---|
3305 | return repr_vector; |
---|
3306 | } |
---|
3307 | #endif |
---|
3308 | |
---|
3309 | //unused |
---|
3310 | #if 0 |
---|
3311 | static intvec* RepresentationMatrix_Dp(ideal G, intvec* M) |
---|
3312 | { |
---|
3313 | BOOLEAN nError = Overflow_Error; |
---|
3314 | Overflow_Error = FALSE; |
---|
3315 | |
---|
3316 | int i, j; |
---|
3317 | int nV = currRing->N; |
---|
3318 | |
---|
3319 | intvec* ivUnit = Mivdp(nV); |
---|
3320 | int degtmp, maxdeg = 0; |
---|
3321 | |
---|
3322 | for(i=IDELEMS(G)-1; i>=0; i--) |
---|
3323 | { |
---|
3324 | // find the maximal total degree of the polynomial G[i] |
---|
3325 | degtmp = MwalkWeightDegree(G->m[i], ivUnit); |
---|
3326 | if(degtmp > maxdeg) |
---|
3327 | maxdeg = degtmp; |
---|
3328 | } |
---|
3329 | |
---|
3330 | mpz_t ztmp; |
---|
3331 | mpz_init_set_si(ztmp, maxdeg); |
---|
3332 | mpz_t *ivres=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
3333 | mpz_init_set_si(ivres[nV-1], 1); // (*ivres)[nV-1] = 1; |
---|
3334 | |
---|
3335 | for(i=nV-2; i>=0; i--) |
---|
3336 | { |
---|
3337 | mpz_init_set(ivres[i], ztmp); //(*ivres)[i] = ztmp; |
---|
3338 | mpz_mul_ui(ztmp, ztmp, maxdeg); //ztmp *=maxdeg; |
---|
3339 | } |
---|
3340 | |
---|
3341 | mpz_t *ivtmp=(mpz_t*)omAlloc(nV*sizeof(mpz_t)); |
---|
3342 | for(i=0; i<nV; i++) |
---|
3343 | mpz_init(ivtmp[i]); |
---|
3344 | |
---|
3345 | // define ivtmp := ndeg^(n-1).w_1 + ndeg^(n-2).w_2 + ... + w_n |
---|
3346 | for(i=0; i<nV; i++) |
---|
3347 | for(j=0; j<nV; j++) |
---|
3348 | { |
---|
3349 | if((*M)[i*nV+j] < 0) |
---|
3350 | { |
---|
3351 | mpz_mul_ui(ztmp, ivres[i], -(*M)[i*nV+j]); |
---|
3352 | mpz_neg(ztmp, ztmp); |
---|
3353 | } |
---|
3354 | else |
---|
3355 | mpz_mul_ui(ztmp, ivres[i], (*M)[i*nV+j]); |
---|
3356 | |
---|
3357 | mpz_add(ivtmp[j], ivtmp[j], ztmp); |
---|
3358 | } |
---|
3359 | delete ivres; |
---|
3360 | mpz_t sing_int; |
---|
3361 | mpz_init_set_ui(sing_int, 2147483647); |
---|
3362 | |
---|
3363 | int ntrue=0; |
---|
3364 | intvec* repvector = new intvec(nV); |
---|
3365 | for(i=0; i<nV; i++) |
---|
3366 | { |
---|
3367 | (*repvector)[i] = mpz_get_si(ivtmp[i]); |
---|
3368 | if(mpz_cmp(ivtmp[i], sing_int)>0) |
---|
3369 | { |
---|
3370 | ntrue++; |
---|
3371 | if(Overflow_Error == FALSE) |
---|
3372 | { |
---|
3373 | Overflow_Error = TRUE; |
---|
3374 | PrintS("\n// ** OVERFLOW in \"Repr.Matrix\": "); |
---|
3375 | mpz_out_str( stdout, 10, ivtmp[i]); |
---|
3376 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
3377 | Print("\n// So vector[%d] := %d is wrong!!\n",i+1,(*repvector)[i]); |
---|
3378 | } |
---|
3379 | } |
---|
3380 | } |
---|
3381 | if(Overflow_Error == TRUE) |
---|
3382 | { |
---|
3383 | ivString(repvector, "repvector"); |
---|
3384 | Print("\n// %d element(s) of it are overflow!!", ntrue); |
---|
3385 | } |
---|
3386 | |
---|
3387 | if(Overflow_Error == FALSE) |
---|
3388 | Overflow_Error = nError; |
---|
3389 | |
---|
3390 | mpz_clear(sing_int); |
---|
3391 | mpz_clear(ztmp); |
---|
3392 | omFree(ivtmp); |
---|
3393 | omFree(ivres); |
---|
3394 | return repvector; |
---|
3395 | } |
---|
3396 | #endif |
---|
3397 | |
---|
3398 | /***************************************************************************** |
---|
3399 | * The following subroutine is the implementation of our first improved * |
---|
3400 | * Groebner walk algorithm, i.e. the first altervative algorithm. * |
---|
3401 | * First we use the Grobner walk algorithm and then we call the changed * |
---|
3402 | * perturbation walk algorithm with decreased degree, if an intermediate * |
---|
3403 | * weight vector is equal to the current target weight vector. * |
---|
3404 | * This call will be only repeated until we get the wanted reduced Groebner * |
---|
3405 | * basis or n times, where n is the numbers of variables. * |
---|
3406 | *****************************************************************************/ |
---|
3407 | |
---|
3408 | //unused |
---|
3409 | #if 0 |
---|
3410 | static int testnegintvec(intvec* v) |
---|
3411 | { |
---|
3412 | int n = v->length(); |
---|
3413 | int i; |
---|
3414 | for(i=0; i<n; i++) |
---|
3415 | { |
---|
3416 | if((*v)[i]<0) |
---|
3417 | { |
---|
3418 | return(1); |
---|
3419 | } |
---|
3420 | } |
---|
3421 | return(0); |
---|
3422 | } |
---|
3423 | #endif |
---|
3424 | |
---|
3425 | // npwinc = 0, if curr_weight doesn't stay in the correct Groebner cone |
---|
3426 | static ideal Rec_LastGB(ideal G, intvec* curr_weight, |
---|
3427 | intvec* orig_target_weight, int tp_deg, int npwinc) |
---|
3428 | { |
---|
3429 | BOOLEAN nError = Overflow_Error; |
---|
3430 | Overflow_Error = FALSE; |
---|
3431 | // BOOLEAN nOverflow_Error = FALSE; |
---|
3432 | |
---|
3433 | clock_t tproc=0; |
---|
3434 | clock_t tinput = clock(); |
---|
3435 | |
---|
3436 | int i, nV = currRing->N; |
---|
3437 | int nwalk=0, endwalks=0, nnwinC=1; |
---|
3438 | int nlast = 0; |
---|
3439 | ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG; |
---|
3440 | ring newRing, oldRing, TargetRing; |
---|
3441 | intvec* iv_M_lp; |
---|
3442 | intvec* target_weight; |
---|
3443 | intvec* ivNull = new intvec(nV); //define (0,...,0) |
---|
3444 | ring EXXRing = currRing; |
---|
3445 | //int NEG=0; //19 juni 03 |
---|
3446 | intvec* next_weight; |
---|
3447 | #ifndef BUCHBERGER_ALG |
---|
3448 | //08 Juli 03 |
---|
3449 | intvec* hilb_func; |
---|
3450 | #endif |
---|
3451 | // to avoid (1,0,...,0) as the target vector |
---|
3452 | intvec* last_omega = new intvec(nV); |
---|
3453 | for(i=nV-1; i>0; i--) |
---|
3454 | (*last_omega)[i] = 1; |
---|
3455 | (*last_omega)[0] = 10000; |
---|
3456 | |
---|
3457 | BOOLEAN isGB = FALSE; |
---|
3458 | |
---|
3459 | // compute a pertubed weight vector of the target weight vector |
---|
3460 | if(tp_deg > 1 && tp_deg <= nV) |
---|
3461 | { |
---|
3462 | ideal H0 = idHeadCC(G); |
---|
3463 | |
---|
3464 | if (rParameter (currRing) != NULL) |
---|
3465 | { |
---|
3466 | DefRingParlp(); |
---|
3467 | } |
---|
3468 | else |
---|
3469 | { |
---|
3470 | VMrDefaultlp(); |
---|
3471 | } |
---|
3472 | TargetRing = currRing; |
---|
3473 | ssG = idrMoveR(G,EXXRing,currRing); |
---|
3474 | |
---|
3475 | ideal H0_tmp = idrMoveR(H0,EXXRing,currRing); |
---|
3476 | ideal H1 = idHeadCC(ssG); |
---|
3477 | |
---|
3478 | // Apply Lemma 2.2 in Collart et. al (1997) to check whether cone(k-1) is equal to cone(k) |
---|
3479 | if(test_G_GB_walk(H0_tmp,H1)==1) |
---|
3480 | { |
---|
3481 | idDelete(&H0_tmp); |
---|
3482 | idDelete(&H1); |
---|
3483 | G = ssG; |
---|
3484 | ssG = NULL; |
---|
3485 | newRing = currRing; |
---|
3486 | delete ivNull; |
---|
3487 | |
---|
3488 | if(npwinc != 0) |
---|
3489 | { |
---|
3490 | goto LastGB_Finish; |
---|
3491 | } |
---|
3492 | else |
---|
3493 | { |
---|
3494 | isGB = TRUE; |
---|
3495 | goto KSTD_Finish; |
---|
3496 | } |
---|
3497 | } |
---|
3498 | idDelete(&H0_tmp); |
---|
3499 | idDelete(&H1); |
---|
3500 | |
---|
3501 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
3502 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
3503 | delete iv_M_lp; |
---|
3504 | //PrintS("\n// Input is not GB!!"); |
---|
3505 | rChangeCurrRing(EXXRing); |
---|
3506 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
3507 | |
---|
3508 | if(Overflow_Error == TRUE) |
---|
3509 | { |
---|
3510 | //nOverflow_Error = Overflow_Error; |
---|
3511 | //NEG = 1; |
---|
3512 | newRing = currRing; |
---|
3513 | goto JUNI_STD; |
---|
3514 | } |
---|
3515 | } |
---|
3516 | |
---|
3517 | while(1) |
---|
3518 | { |
---|
3519 | nwalk ++; |
---|
3520 | nstep++; |
---|
3521 | |
---|
3522 | if(nwalk==1) |
---|
3523 | { |
---|
3524 | goto FIRST_STEP; |
---|
3525 | } |
---|
3526 | to=clock(); |
---|
3527 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
3528 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
3529 | xtif=xtif+clock()-to; |
---|
3530 | |
---|
3531 | #ifndef BUCHBERGER_ALG |
---|
3532 | if(isNolVector(curr_weight) == 0) |
---|
3533 | { |
---|
3534 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
3535 | } |
---|
3536 | else |
---|
3537 | { |
---|
3538 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
3539 | } |
---|
3540 | #endif // BUCHBERGER_ALG |
---|
3541 | |
---|
3542 | oldRing = currRing; |
---|
3543 | |
---|
3544 | // defiNe a new ring that its ordering is "(a(curr_weight),lp) |
---|
3545 | if (rParameter(currRing) != NULL) |
---|
3546 | { |
---|
3547 | DefRingPar(curr_weight); |
---|
3548 | } |
---|
3549 | else |
---|
3550 | { |
---|
3551 | VMrDefault(curr_weight); |
---|
3552 | } |
---|
3553 | newRing = currRing; |
---|
3554 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
3555 | to=clock(); |
---|
3556 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
3557 | #ifdef BUCHBERGER_ALG |
---|
3558 | M = MstdhomCC(Gomega1); |
---|
3559 | #else |
---|
3560 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
3561 | delete hilb_func; |
---|
3562 | #endif // BUCHBERGER_ALG |
---|
3563 | xtstd=xtstd+clock()-to; |
---|
3564 | // change the ring to oldRing |
---|
3565 | rChangeCurrRing(oldRing); |
---|
3566 | M1 = idrMoveR(M, newRing,currRing); |
---|
3567 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
3568 | |
---|
3569 | to=clock(); |
---|
3570 | // compute a reduced Groebner basis of <G> w.r.t. "newRing" by the lifting process |
---|
3571 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
3572 | xtlift=xtlift+clock()-to; |
---|
3573 | idDelete(&M1); |
---|
3574 | idDelete(&Gomega2); |
---|
3575 | idDelete(&G); |
---|
3576 | |
---|
3577 | // change the ring to newRing |
---|
3578 | rChangeCurrRing(newRing); |
---|
3579 | F1 = idrMoveR(F, oldRing,currRing); |
---|
3580 | |
---|
3581 | to=clock(); |
---|
3582 | // reduce the Groebner basis <G> w.r.t. new ring |
---|
3583 | G = kInterRedCC(F1, NULL); |
---|
3584 | xtred=xtred+clock()-to; |
---|
3585 | idDelete(&F1); |
---|
3586 | |
---|
3587 | if(endwalks == 1) |
---|
3588 | { |
---|
3589 | break; |
---|
3590 | } |
---|
3591 | FIRST_STEP: |
---|
3592 | to=clock(); |
---|
3593 | Overflow_Error = FALSE; |
---|
3594 | // compute a next weight vector |
---|
3595 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
3596 | xtnw=xtnw+clock()-to; |
---|
3597 | #ifdef PRINT_VECTORS |
---|
3598 | MivString(curr_weight, target_weight, next_weight); |
---|
3599 | #endif |
---|
3600 | |
---|
3601 | if(Overflow_Error == TRUE) |
---|
3602 | { |
---|
3603 | //PrintS("\n// ** The next vector does NOT stay in Cone!!\n"); |
---|
3604 | #ifdef TEST_OVERFLOW |
---|
3605 | goto LastGB_Finish; |
---|
3606 | #endif |
---|
3607 | |
---|
3608 | nnwinC = 0; |
---|
3609 | if(tp_deg == nV) |
---|
3610 | { |
---|
3611 | nlast = 1; |
---|
3612 | } |
---|
3613 | delete next_weight; |
---|
3614 | break; |
---|
3615 | } |
---|
3616 | |
---|
3617 | if(MivComp(next_weight, ivNull) == 1) |
---|
3618 | { |
---|
3619 | //newRing = currRing; |
---|
3620 | delete next_weight; |
---|
3621 | break; |
---|
3622 | } |
---|
3623 | |
---|
3624 | if(MivComp(next_weight, target_weight) == 1) |
---|
3625 | { |
---|
3626 | if(tp_deg == nV) |
---|
3627 | { |
---|
3628 | endwalks = 1; |
---|
3629 | } |
---|
3630 | else |
---|
3631 | { |
---|
3632 | // REC_LAST_GB_ALT2: |
---|
3633 | //nOverflow_Error = Overflow_Error; |
---|
3634 | tproc=tproc+clock()-tinput; |
---|
3635 | /* |
---|
3636 | Print("\n// takes %d steps and calls \"Rec_LastGB\" (%d):", |
---|
3637 | nwalk, tp_deg+1); |
---|
3638 | */ |
---|
3639 | G = Rec_LastGB(G,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
3640 | newRing = currRing; |
---|
3641 | delete next_weight; |
---|
3642 | break; |
---|
3643 | } |
---|
3644 | } |
---|
3645 | |
---|
3646 | for(i=nV-1; i>=0; i--) |
---|
3647 | { |
---|
3648 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
3649 | } |
---|
3650 | delete next_weight; |
---|
3651 | }//while |
---|
3652 | |
---|
3653 | delete ivNull; |
---|
3654 | |
---|
3655 | if(tp_deg != nV) |
---|
3656 | { |
---|
3657 | newRing = currRing; |
---|
3658 | |
---|
3659 | if (rParameter(currRing) != NULL) |
---|
3660 | { |
---|
3661 | DefRingParlp(); |
---|
3662 | } |
---|
3663 | else |
---|
3664 | { |
---|
3665 | VMrDefaultlp(); |
---|
3666 | } |
---|
3667 | F1 = idrMoveR(G, newRing,currRing); |
---|
3668 | |
---|
3669 | if(nnwinC == 0 || test_w_in_ConeCC(F1, target_weight) != 1 ) |
---|
3670 | { |
---|
3671 | // nOverflow_Error = Overflow_Error; |
---|
3672 | //Print("\n// takes %d steps and calls \"Rec_LastGB (%d):", tp_deg+1); |
---|
3673 | tproc=tproc+clock()-tinput; |
---|
3674 | F1 = Rec_LastGB(F1,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
3675 | } |
---|
3676 | delete target_weight; |
---|
3677 | |
---|
3678 | TargetRing = currRing; |
---|
3679 | rChangeCurrRing(EXXRing); |
---|
3680 | result = idrMoveR(F1, TargetRing,currRing); |
---|
3681 | } |
---|
3682 | else |
---|
3683 | { |
---|
3684 | if(nlast == 1) |
---|
3685 | { |
---|
3686 | JUNI_STD: |
---|
3687 | |
---|
3688 | newRing = currRing; |
---|
3689 | if (rParameter(currRing) != NULL) |
---|
3690 | { |
---|
3691 | DefRingParlp(); |
---|
3692 | } |
---|
3693 | else |
---|
3694 | { |
---|
3695 | VMrDefaultlp(); |
---|
3696 | } |
---|
3697 | KSTD_Finish: |
---|
3698 | if(isGB == FALSE) |
---|
3699 | { |
---|
3700 | F1 = idrMoveR(G, newRing,currRing); |
---|
3701 | } |
---|
3702 | else |
---|
3703 | { |
---|
3704 | F1 = G; |
---|
3705 | } |
---|
3706 | to=clock(); |
---|
3707 | // Print("\n// apply the Buchberger's alg in ring = %s",rString(currRing)); |
---|
3708 | // idElements(F1, "F1"); |
---|
3709 | G = MstdCC(F1); |
---|
3710 | xtextra=xtextra+clock()-to; |
---|
3711 | |
---|
3712 | |
---|
3713 | idDelete(&F1); |
---|
3714 | newRing = currRing; |
---|
3715 | } |
---|
3716 | |
---|
3717 | LastGB_Finish: |
---|
3718 | rChangeCurrRing(EXXRing); |
---|
3719 | result = idrMoveR(G, newRing,currRing); |
---|
3720 | } |
---|
3721 | |
---|
3722 | if(Overflow_Error == FALSE) |
---|
3723 | { |
---|
3724 | Overflow_Error=nError; |
---|
3725 | } |
---|
3726 | // Print("\n// \"Rec_LastGB\" (%d) took %d steps and %.2f sec.Overflow_Error (%d)", tp_deg, nwalk, ((double) tproc)/1000000, nOverflow_Error); |
---|
3727 | return(result); |
---|
3728 | } |
---|
3729 | |
---|
3730 | /* The following subroutine is the implementation of our second improved |
---|
3731 | Groebner walk algorithm, i.e. the second altervative algorithm. |
---|
3732 | First we use the Grobner walk algorithm and then we call the changed |
---|
3733 | perturbation walk algorithm with increased degree, if an intermediate |
---|
3734 | weight vector is equal to the current target weight vector. |
---|
3735 | This call will be only repeated until we get the wanted reduced Groebner |
---|
3736 | basis or n times, where n is the numbers of variables. |
---|
3737 | */ |
---|
3738 | |
---|
3739 | /****************************** |
---|
3740 | * walk + recursive LastGB * |
---|
3741 | ******************************/ |
---|
3742 | ideal MAltwalk2(ideal Go, intvec* curr_weight, intvec* target_weight) |
---|
3743 | { |
---|
3744 | Set_Error(FALSE); |
---|
3745 | Overflow_Error = FALSE; |
---|
3746 | //BOOLEAN nOverflow_Error = FALSE; |
---|
3747 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
3748 | |
---|
3749 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
3750 | xftinput = clock(); |
---|
3751 | clock_t tostd, tproc; |
---|
3752 | |
---|
3753 | nstep = 0; |
---|
3754 | int i, nV = currRing->N; |
---|
3755 | int nwalk=0, endwalks=0; |
---|
3756 | // int nhilb = 1; |
---|
3757 | ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G; |
---|
3758 | //ideal G1; |
---|
3759 | //ring endRing; |
---|
3760 | ring newRing, oldRing; |
---|
3761 | intvec* ivNull = new intvec(nV); |
---|
3762 | intvec* next_weight; |
---|
3763 | #if 0 |
---|
3764 | intvec* extra_curr_weight = new intvec(nV); |
---|
3765 | #endif |
---|
3766 | //intvec* hilb_func; |
---|
3767 | intvec* exivlp = Mivlp(nV); |
---|
3768 | |
---|
3769 | ring XXRing = currRing; |
---|
3770 | |
---|
3771 | //Print("\n// ring r_input = %s;", rString(currRing)); |
---|
3772 | to = clock(); |
---|
3773 | /* compute the reduced Groebner basis of the given ideal w.r.t. |
---|
3774 | a "fast" monomial order, e.g. degree reverse lex. order (dp) */ |
---|
3775 | G = MstdCC(Go); |
---|
3776 | tostd=clock()-to; |
---|
3777 | |
---|
3778 | /* |
---|
3779 | Print("\n// Computation of the first std took = %.2f sec", |
---|
3780 | ((double) tostd)/1000000); |
---|
3781 | */ |
---|
3782 | if(currRing->order[0] == ringorder_a) |
---|
3783 | { |
---|
3784 | goto NEXT_VECTOR; |
---|
3785 | } |
---|
3786 | while(1) |
---|
3787 | { |
---|
3788 | nwalk ++; |
---|
3789 | nstep ++; |
---|
3790 | to = clock(); |
---|
3791 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
3792 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
3793 | xtif=xtif+clock()-to; |
---|
3794 | #if 0 |
---|
3795 | if(Overflow_Error == TRUE) |
---|
3796 | { |
---|
3797 | for(i=nV-1; i>=0; i--) |
---|
3798 | (*curr_weight)[i] = (*extra_curr_weight)[i]; |
---|
3799 | delete extra_curr_weight; |
---|
3800 | goto LAST_GB_ALT2; |
---|
3801 | } |
---|
3802 | #endif |
---|
3803 | oldRing = currRing; |
---|
3804 | |
---|
3805 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
3806 | if (rParameter(currRing) != NULL) |
---|
3807 | { |
---|
3808 | DefRingPar(curr_weight); |
---|
3809 | } |
---|
3810 | else |
---|
3811 | { |
---|
3812 | VMrDefault(curr_weight); |
---|
3813 | } |
---|
3814 | newRing = currRing; |
---|
3815 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
3816 | to = clock(); |
---|
3817 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
3818 | M = MstdhomCC(Gomega1); |
---|
3819 | xtstd=xtstd+clock()-to; |
---|
3820 | /* change the ring to oldRing */ |
---|
3821 | rChangeCurrRing(oldRing); |
---|
3822 | M1 = idrMoveR(M, newRing,currRing); |
---|
3823 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
3824 | |
---|
3825 | to = clock(); |
---|
3826 | /* compute the reduced Groebner basis of <G> w.r.t. "newRing" |
---|
3827 | by the liftig process */ |
---|
3828 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
3829 | xtlift=xtlift+clock()-to; |
---|
3830 | idDelete(&M1); |
---|
3831 | idDelete(&Gomega2); |
---|
3832 | idDelete(&G); |
---|
3833 | |
---|
3834 | /* change the ring to newRing */ |
---|
3835 | rChangeCurrRing(newRing); |
---|
3836 | F1 = idrMoveR(F, oldRing,currRing); |
---|
3837 | |
---|
3838 | to = clock(); |
---|
3839 | /* reduce the Groebner basis <G> w.r.t. newRing */ |
---|
3840 | G = kInterRedCC(F1, NULL); |
---|
3841 | xtred=xtred+clock()-to; |
---|
3842 | idDelete(&F1); |
---|
3843 | |
---|
3844 | if(endwalks == 1) |
---|
3845 | break; |
---|
3846 | |
---|
3847 | NEXT_VECTOR: |
---|
3848 | to = clock(); |
---|
3849 | /* compute a next weight vector */ |
---|
3850 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
3851 | xtnw=xtnw+clock()-to; |
---|
3852 | #ifdef PRINT_VECTORS |
---|
3853 | MivString(curr_weight, target_weight, next_weight); |
---|
3854 | #endif |
---|
3855 | |
---|
3856 | if(Overflow_Error == TRUE) |
---|
3857 | { |
---|
3858 | /* |
---|
3859 | ivString(next_weight, "omega"); |
---|
3860 | PrintS("\n// ** The weight vector does NOT stay in Cone!!\n"); |
---|
3861 | */ |
---|
3862 | #ifdef TEST_OVERFLOW |
---|
3863 | goto TEST_OVERFLOW_OI; |
---|
3864 | #endif |
---|
3865 | |
---|
3866 | newRing = currRing; |
---|
3867 | if (rParameter(currRing) != NULL) |
---|
3868 | { |
---|
3869 | DefRingPar(target_weight); |
---|
3870 | } |
---|
3871 | else |
---|
3872 | { |
---|
3873 | VMrDefault(target_weight); |
---|
3874 | } |
---|
3875 | F1 = idrMoveR(G, newRing,currRing); |
---|
3876 | G = MstdCC(F1); |
---|
3877 | idDelete(&F1); |
---|
3878 | newRing = currRing; |
---|
3879 | break; |
---|
3880 | } |
---|
3881 | |
---|
3882 | if(MivComp(next_weight, ivNull) == 1) |
---|
3883 | { |
---|
3884 | newRing = currRing; |
---|
3885 | delete next_weight; |
---|
3886 | break; |
---|
3887 | } |
---|
3888 | |
---|
3889 | if(MivComp(next_weight, target_weight) == 1) |
---|
3890 | { |
---|
3891 | if(MivSame(target_weight, exivlp)==1) |
---|
3892 | { |
---|
3893 | // LAST_GB_ALT2: |
---|
3894 | //nOverflow_Error = Overflow_Error; |
---|
3895 | tproc = clock()-xftinput; |
---|
3896 | //Print("\n// takes %d steps and calls the recursion of level 2:", nwalk); |
---|
3897 | /* call the changed perturbation walk algorithm with degree 2 */ |
---|
3898 | G = Rec_LastGB(G, curr_weight, target_weight, 2,1); |
---|
3899 | newRing = currRing; |
---|
3900 | delete next_weight; |
---|
3901 | break; |
---|
3902 | } |
---|
3903 | endwalks = 1; |
---|
3904 | } |
---|
3905 | |
---|
3906 | for(i=nV-1; i>=0; i--) |
---|
3907 | { |
---|
3908 | //(*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
3909 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
3910 | } |
---|
3911 | delete next_weight; |
---|
3912 | } |
---|
3913 | #ifdef TEST_OVERFLOW |
---|
3914 | TEST_OVERFLOW_OI: |
---|
3915 | #endif |
---|
3916 | rChangeCurrRing(XXRing); |
---|
3917 | G = idrMoveR(G, newRing,currRing); |
---|
3918 | delete ivNull; |
---|
3919 | delete exivlp; |
---|
3920 | |
---|
3921 | #ifdef TIME_TEST |
---|
3922 | // Print("\n// \"Main procedure\" took %d steps dnd %.2f sec. Overflow_Error (%d)", nwalk, ((double) tproc)/1000000, nOverflow_Error); |
---|
3923 | |
---|
3924 | TimeStringFractal(xftinput, tostd, xtif, xtstd, xtextra,xtlift, xtred,xtnw); |
---|
3925 | |
---|
3926 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
3927 | //Print("\n// Overflow_Error? (%d)", nOverflow_Error); |
---|
3928 | Print("\n// Awalk2 took %d steps!!", nstep); |
---|
3929 | #endif |
---|
3930 | |
---|
3931 | return(G); |
---|
3932 | } |
---|
3933 | |
---|
3934 | |
---|
3935 | /************************************** |
---|
3936 | * perturb the matrix order of "lex" * |
---|
3937 | **************************************/ |
---|
3938 | static intvec* NewVectorlp(ideal I) |
---|
3939 | { |
---|
3940 | int nV = currRing->N; |
---|
3941 | intvec* iv_wlp = MivMatrixOrderlp(nV); |
---|
3942 | intvec* result = Mfpertvector(I, iv_wlp); |
---|
3943 | delete iv_wlp; |
---|
3944 | return result; |
---|
3945 | } |
---|
3946 | |
---|
3947 | int ngleich; |
---|
3948 | intvec* Xsigma; |
---|
3949 | intvec* Xtau; |
---|
3950 | int xn; |
---|
3951 | intvec* Xivinput; |
---|
3952 | intvec* Xivlp; |
---|
3953 | |
---|
3954 | /******************************** |
---|
3955 | * compute a next weight vector * |
---|
3956 | ********************************/ |
---|
3957 | static intvec* MWalkRandomNextWeight(ideal G, intvec* curr_weight, intvec* target_weight, int weight_rad, int pert_deg) |
---|
3958 | { |
---|
3959 | int i, weight_norm; |
---|
3960 | int nV = currRing->N; |
---|
3961 | intvec* next_weight2; |
---|
3962 | intvec* next_weight22 = new intvec(nV); |
---|
3963 | intvec* next_weight = MwalkNextWeightCC(curr_weight,target_weight, G); |
---|
3964 | if(MivComp(next_weight, target_weight) == 1) |
---|
3965 | { |
---|
3966 | return(next_weight); |
---|
3967 | } |
---|
3968 | else |
---|
3969 | { |
---|
3970 | //compute a perturbed next weight vector "next_weight1" |
---|
3971 | intvec* next_weight1 = MkInterRedNextWeight(MPertVectors(G, MivMatrixOrder(curr_weight), pert_deg), target_weight, G); |
---|
3972 | //Print("\n // size of next_weight1 = %d", sizeof((*next_weight1))); |
---|
3973 | |
---|
3974 | //compute a random next weight vector "next_weight2" |
---|
3975 | while(1) |
---|
3976 | { |
---|
3977 | weight_norm = 0; |
---|
3978 | while(weight_norm == 0) |
---|
3979 | { |
---|
3980 | for(i=0; i<nV; i++) |
---|
3981 | { |
---|
3982 | //Print("\n// next_weight[%d] = %d", i, (*next_weight)[i]); |
---|
3983 | (*next_weight22)[i] = rand() % 60000 - 30000; |
---|
3984 | weight_norm = weight_norm + (*next_weight22)[i]*(*next_weight22)[i]; |
---|
3985 | } |
---|
3986 | weight_norm = 1 + floor(sqrt(weight_norm)); |
---|
3987 | } |
---|
3988 | |
---|
3989 | for(i=nV-1; i>=0; i--) |
---|
3990 | { |
---|
3991 | if((*next_weight22)[i] < 0) |
---|
3992 | { |
---|
3993 | (*next_weight22)[i] = 1 + (*curr_weight)[i] + floor(weight_rad*(*next_weight22)[i]/weight_norm); |
---|
3994 | } |
---|
3995 | else |
---|
3996 | { |
---|
3997 | (*next_weight22)[i] = (*curr_weight)[i] + floor(weight_rad*(*next_weight22)[i]/weight_norm); |
---|
3998 | } |
---|
3999 | //Print("\n// next_weight22[%d] = %d", i, (*next_weight22)[i]); |
---|
4000 | } |
---|
4001 | |
---|
4002 | if(test_w_in_ConeCC(G, next_weight22) == 1) |
---|
4003 | { |
---|
4004 | //Print("\n//MWalkRandomNextWeight: next_weight2 im Kegel\n"); |
---|
4005 | next_weight2 = MkInterRedNextWeight(next_weight22, target_weight, G); |
---|
4006 | delete next_weight22; |
---|
4007 | break; |
---|
4008 | } |
---|
4009 | } |
---|
4010 | intvec* result = new intvec(nV); |
---|
4011 | ideal G_test = MwalkInitialForm(G, next_weight); |
---|
4012 | ideal G_test1 = MwalkInitialForm(G, next_weight1); |
---|
4013 | ideal G_test2 = MwalkInitialForm(G, next_weight2); |
---|
4014 | |
---|
4015 | // compare next_weights |
---|
4016 | if(IDELEMS(G_test1) < IDELEMS(G_test)) |
---|
4017 | { |
---|
4018 | if(IDELEMS(G_test2) <= IDELEMS(G_test1)) // |G_test2| <= |G_test1| < |G_test| |
---|
4019 | { |
---|
4020 | for(i=0; i<nV; i++) |
---|
4021 | { |
---|
4022 | (*result)[i] = (*next_weight2)[i]; |
---|
4023 | } |
---|
4024 | } |
---|
4025 | else // |G_test1| < |G_test|, |G_test1| < |G_test2| |
---|
4026 | { |
---|
4027 | for(i=0; i<nV; i++) |
---|
4028 | { |
---|
4029 | (*result)[i] = (*next_weight1)[i]; |
---|
4030 | } |
---|
4031 | } |
---|
4032 | } |
---|
4033 | else |
---|
4034 | { |
---|
4035 | if(IDELEMS(G_test2) <= IDELEMS(G_test)) // |G_test2| <= |G_test| <= |G_test1| |
---|
4036 | { |
---|
4037 | for(i=0; i<nV; i++) |
---|
4038 | { |
---|
4039 | (*result)[i] = (*next_weight2)[i]; |
---|
4040 | } |
---|
4041 | } |
---|
4042 | else // |G_test| <= |G_test1|, |G_test| < |G_test2| |
---|
4043 | { |
---|
4044 | for(i=0; i<nV; i++) |
---|
4045 | { |
---|
4046 | (*result)[i] = (*next_weight)[i]; |
---|
4047 | } |
---|
4048 | } |
---|
4049 | } |
---|
4050 | delete next_weight; |
---|
4051 | delete next_weight1; |
---|
4052 | idDelete(&G_test); |
---|
4053 | idDelete(&G_test1); |
---|
4054 | idDelete(&G_test2); |
---|
4055 | if(test_w_in_ConeCC(G, result) == 1) |
---|
4056 | { |
---|
4057 | delete next_weight2; |
---|
4058 | return result; |
---|
4059 | } |
---|
4060 | else |
---|
4061 | { |
---|
4062 | delete result; |
---|
4063 | return next_weight2; |
---|
4064 | } |
---|
4065 | } |
---|
4066 | } |
---|
4067 | |
---|
4068 | |
---|
4069 | /*************************************************************************** |
---|
4070 | * The procedur REC_GB_Mwalk computes a GB for <G> w.r.t. the weight order * |
---|
4071 | * otw, where G is a reduced GB w.r.t. the weight order cw. * |
---|
4072 | * The new procedur Mwalk calls REC_GB. * |
---|
4073 | ***************************************************************************/ |
---|
4074 | static ideal REC_GB_Mwalk(ideal G, intvec* curr_weight, intvec* orig_target_weight, |
---|
4075 | int tp_deg, int npwinc) |
---|
4076 | { |
---|
4077 | BOOLEAN nError = Overflow_Error; |
---|
4078 | Overflow_Error = FALSE; |
---|
4079 | |
---|
4080 | int i, nV = currRing->N; |
---|
4081 | int nwalk=0, endwalks=0, nnwinC=1, nlast = 0; |
---|
4082 | ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG; |
---|
4083 | ring newRing, oldRing, TargetRing; |
---|
4084 | intvec* target_weight; |
---|
4085 | intvec* ivNull = new intvec(nV); |
---|
4086 | #ifndef BUCHBERGER_ALG |
---|
4087 | intvec* hilb_func; |
---|
4088 | // to avoid (1,0,...,0) as the target vector |
---|
4089 | intvec* last_omega = new intvec(nV); |
---|
4090 | for(i=nV-1; i>0; i--) |
---|
4091 | { |
---|
4092 | (*last_omega)[i] = 1; |
---|
4093 | } |
---|
4094 | (*last_omega)[0] = 10000; |
---|
4095 | #endif |
---|
4096 | BOOLEAN isGB = FALSE; |
---|
4097 | |
---|
4098 | ring EXXRing = currRing; |
---|
4099 | |
---|
4100 | // compute a pertubed weight vector of the target weight vector |
---|
4101 | if(tp_deg > 1 && tp_deg <= nV) |
---|
4102 | { |
---|
4103 | ideal H0 = idHeadCC(G); |
---|
4104 | if (rParameter(currRing) != NULL) |
---|
4105 | { |
---|
4106 | DefRingPar(orig_target_weight); |
---|
4107 | } |
---|
4108 | else |
---|
4109 | { |
---|
4110 | VMrDefault(orig_target_weight); |
---|
4111 | } |
---|
4112 | TargetRing = currRing; |
---|
4113 | ssG = idrMoveR(G,EXXRing,currRing); |
---|
4114 | |
---|
4115 | ideal H0_tmp = idrMoveR(H0,EXXRing,currRing); |
---|
4116 | ideal H1 = idHeadCC(ssG); |
---|
4117 | id_Delete(&H0,EXXRing); |
---|
4118 | |
---|
4119 | if(test_G_GB_walk(H0_tmp,H1)==1) |
---|
4120 | { |
---|
4121 | //Print("\n//REC_GB_Mwalk: input in %d-th recursive is a GB!\n",tp_deg); |
---|
4122 | idDelete(&H0_tmp); |
---|
4123 | idDelete(&H1); |
---|
4124 | G = ssG; |
---|
4125 | ssG = NULL; |
---|
4126 | newRing = currRing; |
---|
4127 | delete ivNull; |
---|
4128 | if(npwinc == 0) |
---|
4129 | { |
---|
4130 | isGB = TRUE; |
---|
4131 | goto KSTD_Finish; |
---|
4132 | } |
---|
4133 | else |
---|
4134 | { |
---|
4135 | goto LastGB_Finish; |
---|
4136 | } |
---|
4137 | } |
---|
4138 | idDelete(&H0_tmp); |
---|
4139 | idDelete(&H1); |
---|
4140 | |
---|
4141 | target_weight = MPertVectors(ssG, MivMatrixOrder(orig_target_weight), tp_deg); |
---|
4142 | |
---|
4143 | rChangeCurrRing(EXXRing); |
---|
4144 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
4145 | } |
---|
4146 | |
---|
4147 | while(1) |
---|
4148 | { |
---|
4149 | nwalk ++; |
---|
4150 | nstep++; |
---|
4151 | if(nwalk == 1) |
---|
4152 | { |
---|
4153 | goto NEXT_STEP; |
---|
4154 | } |
---|
4155 | //Print("\n//REC_GB_Mwalk: Entering the %d-th step in the %d-th recursive:\n",nwalk,tp_deg); |
---|
4156 | to = clock(); |
---|
4157 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
4158 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
4159 | xtif = xtif + clock()-to; |
---|
4160 | |
---|
4161 | #ifndef BUCHBERGER_ALG |
---|
4162 | if(isNolVector(curr_weight) == 0) |
---|
4163 | { |
---|
4164 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
4165 | } |
---|
4166 | else |
---|
4167 | { |
---|
4168 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
4169 | } |
---|
4170 | #endif |
---|
4171 | |
---|
4172 | oldRing = currRing; |
---|
4173 | |
---|
4174 | // define a new ring with ordering "(a(curr_weight),lp) |
---|
4175 | if (rParameter(currRing) != NULL) |
---|
4176 | { |
---|
4177 | DefRingPar(curr_weight); |
---|
4178 | } |
---|
4179 | else |
---|
4180 | { |
---|
4181 | VMrDefault(curr_weight); |
---|
4182 | } |
---|
4183 | newRing = currRing; |
---|
4184 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
4185 | |
---|
4186 | to = clock(); |
---|
4187 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
4188 | #ifdef BUCHBERGER_ALG |
---|
4189 | M = MstdhomCC(Gomega1); |
---|
4190 | #else |
---|
4191 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
4192 | delete hilb_func; |
---|
4193 | #endif |
---|
4194 | xtstd = xtstd + clock() - to; |
---|
4195 | |
---|
4196 | // change the ring to oldRing |
---|
4197 | rChangeCurrRing(oldRing); |
---|
4198 | |
---|
4199 | M1 = idrMoveR(M, newRing,currRing); |
---|
4200 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
4201 | |
---|
4202 | to = clock(); |
---|
4203 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
4204 | xtlift = xtlift + clock() -to; |
---|
4205 | |
---|
4206 | idDelete(&M1); |
---|
4207 | idDelete(&Gomega2); |
---|
4208 | idDelete(&G); |
---|
4209 | |
---|
4210 | |
---|
4211 | // change the ring to newRing |
---|
4212 | rChangeCurrRing(newRing); |
---|
4213 | F1 = idrMoveR(F, oldRing,currRing); |
---|
4214 | |
---|
4215 | to = clock(); |
---|
4216 | // reduce the Groebner basis <G> w.r.t. new ring |
---|
4217 | G = kInterRedCC(F1, NULL); |
---|
4218 | xtred = xtred + clock() -to; |
---|
4219 | |
---|
4220 | idDelete(&F1); |
---|
4221 | |
---|
4222 | if(endwalks == 1) |
---|
4223 | { |
---|
4224 | break; |
---|
4225 | } |
---|
4226 | NEXT_STEP: |
---|
4227 | to = clock(); |
---|
4228 | // compute a next weight vector |
---|
4229 | intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
4230 | |
---|
4231 | |
---|
4232 | xtnw = xtnw + clock() - to; |
---|
4233 | |
---|
4234 | #ifdef PRINT_VECTORS |
---|
4235 | MivString(curr_weight, target_weight, next_weight); |
---|
4236 | #endif |
---|
4237 | |
---|
4238 | if(Overflow_Error == TRUE) |
---|
4239 | { |
---|
4240 | //PrintS("\n//REC_GB_Mwalk: The computed vector does NOT stay in the correct cone!!\n"); |
---|
4241 | nnwinC = 0; |
---|
4242 | if(tp_deg == nV) |
---|
4243 | { |
---|
4244 | nlast = 1; |
---|
4245 | } |
---|
4246 | delete next_weight; |
---|
4247 | break; |
---|
4248 | } |
---|
4249 | if(MivComp(next_weight, ivNull) == 1) |
---|
4250 | { |
---|
4251 | newRing = currRing; |
---|
4252 | delete next_weight; |
---|
4253 | break; |
---|
4254 | } |
---|
4255 | |
---|
4256 | if(MivComp(next_weight, target_weight) == 1) |
---|
4257 | { |
---|
4258 | if(tp_deg == nV) |
---|
4259 | { |
---|
4260 | endwalks = 1; |
---|
4261 | } |
---|
4262 | else |
---|
4263 | { |
---|
4264 | G = REC_GB_Mwalk(G,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
4265 | newRing = currRing; |
---|
4266 | delete next_weight; |
---|
4267 | break; |
---|
4268 | } |
---|
4269 | } |
---|
4270 | |
---|
4271 | for(i=nV-1; i>=0; i--) |
---|
4272 | { |
---|
4273 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
4274 | } |
---|
4275 | delete next_weight; |
---|
4276 | } |
---|
4277 | |
---|
4278 | delete ivNull; |
---|
4279 | |
---|
4280 | if(tp_deg != nV) |
---|
4281 | { |
---|
4282 | newRing = currRing; |
---|
4283 | |
---|
4284 | if (rParameter(currRing) != NULL) |
---|
4285 | { |
---|
4286 | DefRingPar(orig_target_weight); |
---|
4287 | } |
---|
4288 | else |
---|
4289 | { |
---|
4290 | VMrDefault(orig_target_weight); |
---|
4291 | } |
---|
4292 | F1 = idrMoveR(G, newRing,currRing); |
---|
4293 | |
---|
4294 | if(nnwinC == 0) |
---|
4295 | { |
---|
4296 | F1 = REC_GB_Mwalk(F1,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
4297 | } |
---|
4298 | else |
---|
4299 | { |
---|
4300 | if(test_w_in_ConeCC(F1, target_weight) != 1) |
---|
4301 | { |
---|
4302 | F1 = REC_GB_Mwalk(F1,curr_weight, orig_target_weight,tp_deg+1,nnwinC); |
---|
4303 | } |
---|
4304 | } |
---|
4305 | delete target_weight; |
---|
4306 | |
---|
4307 | TargetRing = currRing; |
---|
4308 | rChangeCurrRing(EXXRing); |
---|
4309 | result = idrMoveR(F1, TargetRing,currRing); |
---|
4310 | } |
---|
4311 | else |
---|
4312 | { |
---|
4313 | if(nlast == 1) |
---|
4314 | { |
---|
4315 | if (rParameter(currRing) != NULL) |
---|
4316 | { |
---|
4317 | DefRingPar(orig_target_weight); |
---|
4318 | } |
---|
4319 | else |
---|
4320 | { |
---|
4321 | VMrDefault(orig_target_weight); |
---|
4322 | } |
---|
4323 | KSTD_Finish: |
---|
4324 | if(isGB == FALSE) |
---|
4325 | { |
---|
4326 | F1 = idrMoveR(G, newRing,currRing); |
---|
4327 | } |
---|
4328 | else |
---|
4329 | { |
---|
4330 | F1 = G; |
---|
4331 | } |
---|
4332 | to=clock(); |
---|
4333 | // apply Buchberger alg to compute a red. GB of F1 |
---|
4334 | G = MstdCC(F1); |
---|
4335 | xtextra=clock()-to; |
---|
4336 | idDelete(&F1); |
---|
4337 | newRing = currRing; |
---|
4338 | } |
---|
4339 | |
---|
4340 | LastGB_Finish: |
---|
4341 | rChangeCurrRing(EXXRing); |
---|
4342 | result = idrMoveR(G, newRing,currRing); |
---|
4343 | } |
---|
4344 | |
---|
4345 | if(Overflow_Error == FALSE) |
---|
4346 | { |
---|
4347 | Overflow_Error = nError; |
---|
4348 | } |
---|
4349 | #ifndef BUCHBERGER_ALG |
---|
4350 | delete last_omega; |
---|
4351 | #endif |
---|
4352 | return(result); |
---|
4353 | } |
---|
4354 | |
---|
4355 | |
---|
4356 | // THE NEW GROEBNER WALK ALGORITHM |
---|
4357 | // Groebnerwalk with a recursive "second" alternative GW, called REC_GB_Mwalk that only computes the last reduced GB |
---|
4358 | ideal Mwalk(ideal Go, intvec* curr_weight, intvec* target_weight) |
---|
4359 | { |
---|
4360 | Set_Error(FALSE); |
---|
4361 | Overflow_Error = FALSE; |
---|
4362 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
4363 | |
---|
4364 | clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0; |
---|
4365 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; |
---|
4366 | tinput = clock(); |
---|
4367 | clock_t tim; |
---|
4368 | nstep=0; |
---|
4369 | int i; |
---|
4370 | int nV = currRing->N; |
---|
4371 | int nwalk=0; |
---|
4372 | int endwalks=0; |
---|
4373 | |
---|
4374 | ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G; |
---|
4375 | //ideal G1; |
---|
4376 | //ring endRing; |
---|
4377 | ring newRing, oldRing; |
---|
4378 | intvec* ivNull = new intvec(nV); |
---|
4379 | intvec* exivlp = Mivlp(nV); |
---|
4380 | #ifndef BUCHBERGER_ALG |
---|
4381 | intvec* hilb_func; |
---|
4382 | #endif |
---|
4383 | intvec* tmp_weight = new intvec(nV); |
---|
4384 | for(i=nV-1; i>=0; i--) |
---|
4385 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
4386 | |
---|
4387 | // to avoid (1,0,...,0) as the target vector |
---|
4388 | intvec* last_omega = new intvec(nV); |
---|
4389 | for(i=nV-1; i>0; i--) |
---|
4390 | (*last_omega)[i] = 1; |
---|
4391 | (*last_omega)[0] = 10000; |
---|
4392 | |
---|
4393 | ring XXRing = currRing; |
---|
4394 | |
---|
4395 | to = clock(); |
---|
4396 | // the monomial ordering of this current ring would be "dp" |
---|
4397 | G = MstdCC(Go); |
---|
4398 | tostd = clock()-to; |
---|
4399 | |
---|
4400 | if(currRing->order[0] == ringorder_a) |
---|
4401 | goto NEXT_VECTOR; |
---|
4402 | |
---|
4403 | while(1) |
---|
4404 | { |
---|
4405 | nwalk ++; |
---|
4406 | nstep ++; |
---|
4407 | to = clock(); |
---|
4408 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
4409 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
4410 | tif = tif + clock()-to; |
---|
4411 | oldRing = currRing; |
---|
4412 | |
---|
4413 | if(endwalks == 1) |
---|
4414 | { |
---|
4415 | /* compute a reduced Groebner basis of Gomega w.r.t. >>_cw by |
---|
4416 | the recursive changed perturbation walk alg. */ |
---|
4417 | tim = clock(); |
---|
4418 | /* |
---|
4419 | Print("\n// **** Grï¿œbnerwalk took %d steps and ", nwalk); |
---|
4420 | PrintS("\n// **** call the rec. Pert. Walk to compute a red GB of:"); |
---|
4421 | idElements(Gomega, "G_omega"); |
---|
4422 | */ |
---|
4423 | |
---|
4424 | if(MivSame(exivlp, target_weight)==1) |
---|
4425 | M = REC_GB_Mwalk(idCopy(Gomega), tmp_weight, curr_weight, 2,1); |
---|
4426 | else |
---|
4427 | goto NORMAL_GW; |
---|
4428 | /* |
---|
4429 | Print("\n// time for the last std(Gw) = %.2f sec", |
---|
4430 | ((double) (clock()-tim)/1000000)); |
---|
4431 | PrintS("\n// ***************************************************\n"); |
---|
4432 | */ |
---|
4433 | #ifdef CHECK_IDEAL_MWALK |
---|
4434 | idElements(Gomega, "G_omega"); |
---|
4435 | headidString(Gomega, "Gw"); |
---|
4436 | idElements(M, "M"); |
---|
4437 | //headidString(M, "M"); |
---|
4438 | #endif |
---|
4439 | to = clock(); |
---|
4440 | F = MLifttwoIdeal(Gomega, M, G); |
---|
4441 | xtlift = xtlift + clock() - to; |
---|
4442 | |
---|
4443 | idDelete(&Gomega); |
---|
4444 | idDelete(&M); |
---|
4445 | idDelete(&G); |
---|
4446 | |
---|
4447 | oldRing = currRing; |
---|
4448 | |
---|
4449 | /* create a new ring newRing */ |
---|
4450 | if (rParameter(currRing) != NULL) |
---|
4451 | { |
---|
4452 | DefRingPar(curr_weight); |
---|
4453 | } |
---|
4454 | else |
---|
4455 | { |
---|
4456 | VMrDefault(curr_weight); |
---|
4457 | } |
---|
4458 | newRing = currRing; |
---|
4459 | F1 = idrMoveR(F, oldRing,currRing); |
---|
4460 | } |
---|
4461 | else |
---|
4462 | { |
---|
4463 | NORMAL_GW: |
---|
4464 | #ifndef BUCHBERGER_ALG |
---|
4465 | if(isNolVector(curr_weight) == 0) |
---|
4466 | { |
---|
4467 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
4468 | } |
---|
4469 | else |
---|
4470 | { |
---|
4471 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
4472 | } |
---|
4473 | #endif // BUCHBERGER_ALG |
---|
4474 | |
---|
4475 | // define a new ring that its ordering is "(a(curr_weight),lp) |
---|
4476 | if (rParameter(currRing) != NULL) |
---|
4477 | { |
---|
4478 | DefRingPar(curr_weight); |
---|
4479 | } |
---|
4480 | else |
---|
4481 | { |
---|
4482 | VMrDefault(curr_weight); |
---|
4483 | } |
---|
4484 | newRing = currRing; |
---|
4485 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
4486 | |
---|
4487 | to = clock(); |
---|
4488 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
4489 | #ifdef BUCHBERGER_ALG |
---|
4490 | M = MstdhomCC(Gomega1); |
---|
4491 | #else |
---|
4492 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
4493 | delete hilb_func; |
---|
4494 | #endif // BUCHBERGER_ALG |
---|
4495 | tstd = tstd + clock() - to; |
---|
4496 | |
---|
4497 | // change the ring to oldRing |
---|
4498 | rChangeCurrRing(oldRing); |
---|
4499 | M1 = idrMoveR(M, newRing,currRing); |
---|
4500 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
4501 | |
---|
4502 | to = clock(); |
---|
4503 | // compute a representation of the generators of submod (M) with respect to those of mod (Gomega). Gomega is a reduced Groebner basis w.r.t. the current ring. |
---|
4504 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
4505 | tlift = tlift + clock() - to; |
---|
4506 | |
---|
4507 | idDelete(&M1); |
---|
4508 | idDelete(&Gomega2); |
---|
4509 | idDelete(&G); |
---|
4510 | |
---|
4511 | // change the ring to newRing |
---|
4512 | rChangeCurrRing(newRing); |
---|
4513 | F1 = idrMoveR(F, oldRing,currRing); |
---|
4514 | } |
---|
4515 | |
---|
4516 | to = clock(); |
---|
4517 | // reduce the Groebner basis <G> w.r.t. new ring |
---|
4518 | G = kInterRedCC(F1, NULL); |
---|
4519 | if(endwalks != 1) |
---|
4520 | { |
---|
4521 | tred = tred + clock() - to; |
---|
4522 | } |
---|
4523 | else |
---|
4524 | { |
---|
4525 | xtred = xtred + clock() - to; |
---|
4526 | } |
---|
4527 | idDelete(&F1); |
---|
4528 | if(endwalks == 1) |
---|
4529 | { |
---|
4530 | break; |
---|
4531 | } |
---|
4532 | NEXT_VECTOR: |
---|
4533 | to = clock(); |
---|
4534 | // compute a next weight vector |
---|
4535 | intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
4536 | tnw = tnw + clock() - to; |
---|
4537 | #ifdef PRINT_VECTORS |
---|
4538 | MivString(curr_weight, target_weight, next_weight); |
---|
4539 | #endif |
---|
4540 | |
---|
4541 | //if(test_w_in_ConeCC(G, next_weight) != 1) |
---|
4542 | if(Overflow_Error == TRUE) |
---|
4543 | { |
---|
4544 | newRing = currRing; |
---|
4545 | PrintS("\n// ** The computed vector does NOT stay in Cone!!\n"); |
---|
4546 | |
---|
4547 | if (rParameter(currRing) != NULL) |
---|
4548 | { |
---|
4549 | DefRingPar(target_weight); |
---|
4550 | } |
---|
4551 | else |
---|
4552 | { |
---|
4553 | VMrDefault(target_weight); |
---|
4554 | } |
---|
4555 | F1 = idrMoveR(G, newRing,currRing); |
---|
4556 | G = MstdCC(F1); |
---|
4557 | idDelete(&F1); |
---|
4558 | |
---|
4559 | newRing = currRing; |
---|
4560 | break; |
---|
4561 | } |
---|
4562 | |
---|
4563 | if(MivComp(next_weight, ivNull) == 1) |
---|
4564 | { |
---|
4565 | newRing = currRing; |
---|
4566 | delete next_weight; |
---|
4567 | break; |
---|
4568 | } |
---|
4569 | if(MivComp(next_weight, target_weight) == 1) |
---|
4570 | { |
---|
4571 | endwalks = 1; |
---|
4572 | } |
---|
4573 | for(i=nV-1; i>=0; i--) |
---|
4574 | { |
---|
4575 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
4576 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
4577 | } |
---|
4578 | delete next_weight; |
---|
4579 | } |
---|
4580 | rChangeCurrRing(XXRing); |
---|
4581 | G = idrMoveR(G, newRing,currRing); |
---|
4582 | |
---|
4583 | delete tmp_weight; |
---|
4584 | delete ivNull; |
---|
4585 | delete exivlp; |
---|
4586 | |
---|
4587 | #ifdef TIME_TEST |
---|
4588 | TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep); |
---|
4589 | |
---|
4590 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
4591 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
4592 | #endif |
---|
4593 | return(G); |
---|
4594 | } |
---|
4595 | |
---|
4596 | // 07.11.2012 |
---|
4597 | // THE RANDOM WALK ALGORITHM |
---|
4598 | ideal Mrwalk(ideal Go, intvec* curr_weight, intvec* target_weight, int weight_rad, int pert_deg) |
---|
4599 | { |
---|
4600 | Set_Error(FALSE); |
---|
4601 | Overflow_Error = FALSE; |
---|
4602 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
4603 | |
---|
4604 | clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0; |
---|
4605 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; |
---|
4606 | tinput = clock(); |
---|
4607 | clock_t tim; |
---|
4608 | nstep=0; |
---|
4609 | int i,nwalk,endwalks = 0; |
---|
4610 | int nV = currRing->N; |
---|
4611 | |
---|
4612 | ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G; |
---|
4613 | //ideal G1; |
---|
4614 | //ring endRing; |
---|
4615 | ring newRing, oldRing; |
---|
4616 | intvec* ivNull = new intvec(nV); |
---|
4617 | intvec* exivlp = Mivlp(nV); |
---|
4618 | intvec* tmp_weight = new intvec(nV); |
---|
4619 | for(i=nV-1; i>=0; i--) |
---|
4620 | { |
---|
4621 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
4622 | } |
---|
4623 | #ifndef BUCHBERGER_ALG |
---|
4624 | intvec* hilb_func; |
---|
4625 | // to avoid (1,0,...,0) as the target vector |
---|
4626 | intvec* last_omega = new intvec(nV); |
---|
4627 | for(i=nV-1; i>0; i--) |
---|
4628 | { |
---|
4629 | (*last_omega)[i] = 1; |
---|
4630 | } |
---|
4631 | (*last_omega)[0] = 10000; |
---|
4632 | #endif |
---|
4633 | ring XXRing = currRing; |
---|
4634 | |
---|
4635 | to = clock(); |
---|
4636 | G = MstdCC(Go); |
---|
4637 | tostd = clock()-to; |
---|
4638 | |
---|
4639 | //if(currRing->order[0] == ringorder_a) |
---|
4640 | // goto NEXT_VECTOR; |
---|
4641 | nwalk = 0; |
---|
4642 | while(1) |
---|
4643 | { |
---|
4644 | nwalk ++; |
---|
4645 | nstep ++; |
---|
4646 | to = clock(); |
---|
4647 | #ifdef CHECK_IDEAL_MWALK |
---|
4648 | idString(G,"G"); |
---|
4649 | #endif |
---|
4650 | Gomega = MwalkInitialForm(G, curr_weight);// compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
4651 | tif = tif + clock()-to; |
---|
4652 | oldRing = currRing; |
---|
4653 | #ifdef CHECK_IDEAL_MWALK |
---|
4654 | idString(Gomega,"G_omega"); |
---|
4655 | #endif |
---|
4656 | if(endwalks == 1) |
---|
4657 | { |
---|
4658 | // compute a reduced Groebner basis of Gomega w.r.t. >>_cw by the recursive changed perturbation walk alg. |
---|
4659 | tim = clock(); |
---|
4660 | Print("\n//Mrwalk: Groebnerwalk took %d steps.\n", nwalk); |
---|
4661 | //PrintS("\n//Mrwalk: call the rec. Pert. Walk to compute a red GB of:"); |
---|
4662 | //idString(Gomega, "G_omega"); |
---|
4663 | M = REC_GB_Mwalk(idCopy(Gomega), tmp_weight, curr_weight,pert_deg,1); |
---|
4664 | Print("\n//Mrwalk: time for the last std(Gw) = %.2f sec\n",((double) (clock()-tim)/1000000)); |
---|
4665 | |
---|
4666 | #ifdef CHECK_IDEAL_MWALK |
---|
4667 | idString(Gomega, "G_omega"); |
---|
4668 | idString(M, "M"); |
---|
4669 | #endif |
---|
4670 | to = clock(); |
---|
4671 | F = MLifttwoIdeal(Gomega, M, G); |
---|
4672 | xtlift = xtlift + clock() - to; |
---|
4673 | |
---|
4674 | idDelete(&Gomega); |
---|
4675 | idDelete(&M); |
---|
4676 | idDelete(&G); |
---|
4677 | |
---|
4678 | oldRing = currRing; |
---|
4679 | VMrDefault(curr_weight); //define a new ring with ordering "(a(curr_weight),lp) |
---|
4680 | |
---|
4681 | /*if (rParameter(currRing) != NULL) |
---|
4682 | { |
---|
4683 | DefRingPar(curr_weight); |
---|
4684 | } |
---|
4685 | else |
---|
4686 | { |
---|
4687 | VMrDefault(curr_weight); |
---|
4688 | }*/ |
---|
4689 | newRing = currRing; |
---|
4690 | F1 = idrMoveR(F, oldRing,currRing); |
---|
4691 | } |
---|
4692 | else |
---|
4693 | { |
---|
4694 | #ifndef BUCHBERGER_ALG |
---|
4695 | if(isNolVector(curr_weight) == 0) |
---|
4696 | { |
---|
4697 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
4698 | } |
---|
4699 | else |
---|
4700 | { |
---|
4701 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
4702 | } |
---|
4703 | #endif |
---|
4704 | /* |
---|
4705 | if (rParameter(currRing) != NULL) |
---|
4706 | { |
---|
4707 | DefRingPar(curr_weight); |
---|
4708 | } |
---|
4709 | else |
---|
4710 | { |
---|
4711 | VMrDefault(curr_weight); |
---|
4712 | }*/ |
---|
4713 | |
---|
4714 | VMrDefault(curr_weight); //define a new ring with ordering "(a(curr_weight),lp) |
---|
4715 | newRing = currRing; |
---|
4716 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
4717 | #ifdef CHECK_IDEAL_MWALK |
---|
4718 | idString(Gomega1, "G_omega1"); |
---|
4719 | #endif |
---|
4720 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
4721 | to = clock(); |
---|
4722 | #ifndef BUCHBERGER_ALG |
---|
4723 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
4724 | delete hilb_func; |
---|
4725 | #else |
---|
4726 | //M = MstdhomCC(Gomega1); |
---|
4727 | //M = MstdCC(Gomega1); |
---|
4728 | //M = kStd(Gomega1, NULL, testHomog,NULL, NULL,0,0,curr_weight); |
---|
4729 | M = kStd(Gomega1,NULL,testHomog,NULL,NULL,0,0,NULL); |
---|
4730 | #endif |
---|
4731 | tstd = tstd + clock() - to; |
---|
4732 | #ifdef CHECK_IDEAL_MWALK |
---|
4733 | idString(M, "M"); |
---|
4734 | #endif |
---|
4735 | //change the ring to oldRing |
---|
4736 | rChangeCurrRing(oldRing); |
---|
4737 | M1 = idrMoveR(M, newRing,currRing); |
---|
4738 | #ifdef CHECK_IDEAL_MWALK |
---|
4739 | idString(M1, "M1"); |
---|
4740 | #endif |
---|
4741 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
4742 | |
---|
4743 | to = clock(); |
---|
4744 | // compute a representation of the generators of submod (M) with respect to those of mod (Gomega), where Gomega is a reduced Groebner basis w.r.t. the current ring |
---|
4745 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
4746 | #ifdef CHECK_IDEAL_MWALK |
---|
4747 | idString(F, "F"); |
---|
4748 | #endif |
---|
4749 | tlift = tlift + clock() - to; |
---|
4750 | |
---|
4751 | idDelete(&M1); |
---|
4752 | idDelete(&Gomega2); |
---|
4753 | idDelete(&G); |
---|
4754 | |
---|
4755 | rChangeCurrRing(newRing); // change the ring to newRing |
---|
4756 | F1 = idrMoveR(F,oldRing,currRing); |
---|
4757 | } |
---|
4758 | |
---|
4759 | to = clock(); |
---|
4760 | G = kInterRedCC(F1, NULL); //reduce the Groebner basis <G> w.r.t. new ring |
---|
4761 | #ifdef CHECK_IDEAL_MWALK |
---|
4762 | idString(G, "G"); |
---|
4763 | #endif |
---|
4764 | idDelete(&F1); |
---|
4765 | if(endwalks == 1) |
---|
4766 | { |
---|
4767 | xtred = xtred + clock() - to; |
---|
4768 | break; |
---|
4769 | } |
---|
4770 | else |
---|
4771 | { |
---|
4772 | tred = tred + clock() - to; |
---|
4773 | } |
---|
4774 | |
---|
4775 | //NEXT_VECTOR: |
---|
4776 | to = clock(); |
---|
4777 | //intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
4778 | intvec* next_weight = MWalkRandomNextWeight(G, curr_weight, target_weight, weight_rad, pert_deg); |
---|
4779 | |
---|
4780 | tnw = tnw + clock() - to; |
---|
4781 | //#ifdef PRINT_VECTORS |
---|
4782 | MivString(curr_weight, target_weight, next_weight); |
---|
4783 | //#endif |
---|
4784 | if(Overflow_Error == TRUE) |
---|
4785 | { |
---|
4786 | newRing = currRing; |
---|
4787 | PrintS("\n//Mrwalk: The computed vector does NOT stay in Cone!!\n"); |
---|
4788 | |
---|
4789 | if (rParameter(currRing) != NULL) |
---|
4790 | { |
---|
4791 | DefRingPar(target_weight); |
---|
4792 | } |
---|
4793 | else |
---|
4794 | { |
---|
4795 | VMrDefault(target_weight); //define a new ring with ordering "(a(curr_weight),lp) |
---|
4796 | } |
---|
4797 | F1 = idrMoveR(G, newRing,currRing); |
---|
4798 | G = MstdCC(F1); |
---|
4799 | idDelete(&F1); |
---|
4800 | |
---|
4801 | newRing = currRing; |
---|
4802 | break; |
---|
4803 | } |
---|
4804 | |
---|
4805 | if(MivComp(next_weight, ivNull) == 1) |
---|
4806 | { |
---|
4807 | newRing = currRing; |
---|
4808 | delete next_weight; |
---|
4809 | break; |
---|
4810 | } |
---|
4811 | if(MivComp(next_weight, target_weight) == 1) |
---|
4812 | { |
---|
4813 | endwalks = 1; |
---|
4814 | } |
---|
4815 | for(i=nV-1; i>=0; i--) |
---|
4816 | { |
---|
4817 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
4818 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
4819 | } |
---|
4820 | delete next_weight; |
---|
4821 | } |
---|
4822 | rChangeCurrRing(XXRing); |
---|
4823 | G = idrMoveR(G, newRing,currRing); |
---|
4824 | |
---|
4825 | delete tmp_weight; |
---|
4826 | delete ivNull; |
---|
4827 | delete exivlp; |
---|
4828 | #ifndef BUCHBERGER_ALG |
---|
4829 | delete last_omega; |
---|
4830 | #endif |
---|
4831 | #ifdef TIME_TEST |
---|
4832 | TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep); |
---|
4833 | |
---|
4834 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
4835 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
4836 | #endif |
---|
4837 | return(G); |
---|
4838 | } |
---|
4839 | |
---|
4840 | //unused |
---|
4841 | #if 0 |
---|
4842 | ideal Mwalk_tst(ideal Go, intvec* curr_weight, intvec* target_weight) |
---|
4843 | { |
---|
4844 | //clock_t tinput=clock(); |
---|
4845 | //idString(Go,"Ginp"); |
---|
4846 | int i, nV = currRing->N; |
---|
4847 | int nwalk=0, endwalks=0; |
---|
4848 | |
---|
4849 | ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G; |
---|
4850 | // ideal G1; ring endRing; |
---|
4851 | ring newRing, oldRing; |
---|
4852 | intvec* ivNull = new intvec(nV); |
---|
4853 | ring XXRing = currRing; |
---|
4854 | |
---|
4855 | intvec* tmp_weight = new intvec(nV); |
---|
4856 | for(i=nV-1; i>=0; i--) |
---|
4857 | { |
---|
4858 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
4859 | } |
---|
4860 | /* the monomial ordering of this current ring would be "dp" */ |
---|
4861 | G = MstdCC(Go); |
---|
4862 | #ifndef BUCHBERGER_ALG |
---|
4863 | intvec* hilb_func; |
---|
4864 | #endif |
---|
4865 | /* to avoid (1,0,...,0) as the target vector */ |
---|
4866 | intvec* last_omega = new intvec(nV); |
---|
4867 | for(i=nV-1; i>0; i--) |
---|
4868 | (*last_omega)[i] = 1; |
---|
4869 | (*last_omega)[0] = 10000; |
---|
4870 | |
---|
4871 | while(1) |
---|
4872 | { |
---|
4873 | nwalk ++; |
---|
4874 | //Print("\n// Entering the %d-th step:", nwalk); |
---|
4875 | //Print("\n// ring r[%d] = %s;", nwalk, rString(currRing)); |
---|
4876 | idString(G,"G"); |
---|
4877 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
4878 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
4879 | //ivString(curr_weight, "omega"); |
---|
4880 | idString(Gomega,"Gw"); |
---|
4881 | |
---|
4882 | #ifndef BUCHBERGER_ALG |
---|
4883 | if(isNolVector(curr_weight) == 0) |
---|
4884 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
4885 | else |
---|
4886 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
4887 | #endif // BUCHBERGER_ALG |
---|
4888 | |
---|
4889 | |
---|
4890 | oldRing = currRing; |
---|
4891 | |
---|
4892 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
4893 | VMrDefault(curr_weight); |
---|
4894 | newRing = currRing; |
---|
4895 | |
---|
4896 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
4897 | |
---|
4898 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
4899 | #ifdef BUCHBERGER_ALG |
---|
4900 | M = MstdhomCC(Gomega1); |
---|
4901 | #else |
---|
4902 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
4903 | delete hilb_func; |
---|
4904 | #endif // BUCHBERGER_ALG |
---|
4905 | |
---|
4906 | idString(M,"M"); |
---|
4907 | |
---|
4908 | /* change the ring to oldRing */ |
---|
4909 | rChangeCurrRing(oldRing); |
---|
4910 | M1 = idrMoveR(M, newRing,currRing); |
---|
4911 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
4912 | |
---|
4913 | /* compute a representation of the generators of submod (M) |
---|
4914 | with respect to those of mod (Gomega). |
---|
4915 | Gomega is a reduced Groebner basis w.r.t. the current ring */ |
---|
4916 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
4917 | idDelete(&M1); |
---|
4918 | idDelete(&Gomega2); |
---|
4919 | idDelete(&G); |
---|
4920 | idString(F,"F"); |
---|
4921 | |
---|
4922 | /* change the ring to newRing */ |
---|
4923 | rChangeCurrRing(newRing); |
---|
4924 | F1 = idrMoveR(F, oldRing,currRing); |
---|
4925 | |
---|
4926 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
4927 | G = kInterRedCC(F1, NULL); |
---|
4928 | //idSkipZeroes(G);//done by kInterRed |
---|
4929 | idDelete(&F1); |
---|
4930 | idString(G,"G"); |
---|
4931 | if(endwalks == 1) |
---|
4932 | break; |
---|
4933 | |
---|
4934 | /* compute a next weight vector */ |
---|
4935 | intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
4936 | #ifdef PRINT_VECTORS |
---|
4937 | MivString(curr_weight, target_weight, next_weight); |
---|
4938 | #endif |
---|
4939 | |
---|
4940 | if(MivComp(next_weight, ivNull) == 1) |
---|
4941 | { |
---|
4942 | delete next_weight; |
---|
4943 | break; |
---|
4944 | } |
---|
4945 | if(MivComp(next_weight, target_weight) == 1) |
---|
4946 | endwalks = 1; |
---|
4947 | |
---|
4948 | for(i=nV-1; i>=0; i--) |
---|
4949 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
4950 | |
---|
4951 | /* 06.11.01 to free the memory: NOT Changed!!*/ |
---|
4952 | for(i=nV-1; i>=0; i--) |
---|
4953 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
4954 | delete next_weight; |
---|
4955 | } |
---|
4956 | rChangeCurrRing(XXRing); |
---|
4957 | G = idrMoveR(G, newRing,currRing); |
---|
4958 | |
---|
4959 | delete tmp_weight; |
---|
4960 | delete ivNull; |
---|
4961 | PrintLn(); |
---|
4962 | return(G); |
---|
4963 | } |
---|
4964 | #endif |
---|
4965 | |
---|
4966 | /**************************************************************/ |
---|
4967 | /* Implementation of the perturbation walk algorithm */ |
---|
4968 | /**************************************************************/ |
---|
4969 | /* If the perturbed target weight vector or an intermediate weight vector |
---|
4970 | doesn't stay in the correct Groebner cone, we have only |
---|
4971 | a reduced Groebner basis for the given ideal with respect to |
---|
4972 | a monomial order which differs to the given order. |
---|
4973 | Then we have to compute the wanted reduced Groebner basis for it. |
---|
4974 | For this, we can use |
---|
4975 | 1) the improved Buchberger algorithm or |
---|
4976 | 2) the changed perturbation walk algorithm with a decreased degree. |
---|
4977 | */ |
---|
4978 | // use kStd, if nP = 0, else call LastGB |
---|
4979 | ideal Mpwalk(ideal Go, int op_deg, int tp_deg,intvec* curr_weight, |
---|
4980 | intvec* target_weight, int nP) |
---|
4981 | { |
---|
4982 | Set_Error(FALSE ); |
---|
4983 | Overflow_Error = FALSE; |
---|
4984 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
4985 | |
---|
4986 | clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0; |
---|
4987 | xtextra=0; |
---|
4988 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; |
---|
4989 | tinput = clock(); |
---|
4990 | |
---|
4991 | clock_t tim; |
---|
4992 | |
---|
4993 | nstep = 0; |
---|
4994 | int i, ntwC=1, ntestw=1, nV = currRing->N; |
---|
4995 | int endwalks=0; |
---|
4996 | |
---|
4997 | ideal Gomega, M, F, G, Gomega1, Gomega2, M1,F1,Eresult,ssG; |
---|
4998 | ring newRing, oldRing, TargetRing; |
---|
4999 | intvec* iv_M_dp; |
---|
5000 | intvec* iv_M_lp; |
---|
5001 | intvec* exivlp = Mivlp(nV); |
---|
5002 | intvec* orig_target = target_weight; |
---|
5003 | intvec* pert_target_vector = target_weight; |
---|
5004 | intvec* ivNull = new intvec(nV); |
---|
5005 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
5006 | #ifndef BUCHBERGER_ALG |
---|
5007 | intvec* hilb_func; |
---|
5008 | #endif |
---|
5009 | intvec* next_weight; |
---|
5010 | |
---|
5011 | // to avoid (1,0,...,0) as the target vector |
---|
5012 | intvec* last_omega = new intvec(nV); |
---|
5013 | for(i=nV-1; i>0; i--) |
---|
5014 | (*last_omega)[i] = 1; |
---|
5015 | (*last_omega)[0] = 10000; |
---|
5016 | |
---|
5017 | ring XXRing = currRing; |
---|
5018 | |
---|
5019 | |
---|
5020 | to = clock(); |
---|
5021 | /* perturbs the original vector */ |
---|
5022 | if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) := "dp" |
---|
5023 | { |
---|
5024 | G = MstdCC(Go); |
---|
5025 | tostd = clock()-to; |
---|
5026 | if(op_deg != 1){ |
---|
5027 | iv_M_dp = MivMatrixOrderdp(nV); |
---|
5028 | //ivString(iv_M_dp, "iv_M_dp"); |
---|
5029 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
5030 | } |
---|
5031 | } |
---|
5032 | else |
---|
5033 | { |
---|
5034 | //define ring order := (a(curr_weight),lp); |
---|
5035 | if (rParameter(currRing) != NULL) |
---|
5036 | DefRingPar(curr_weight); |
---|
5037 | else |
---|
5038 | VMrDefault(curr_weight); |
---|
5039 | |
---|
5040 | G = idrMoveR(Go, XXRing,currRing); |
---|
5041 | G = MstdCC(G); |
---|
5042 | tostd = clock()-to; |
---|
5043 | if(op_deg != 1){ |
---|
5044 | iv_M_dp = MivMatrixOrder(curr_weight); |
---|
5045 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
5046 | } |
---|
5047 | } |
---|
5048 | delete iv_dp; |
---|
5049 | if(op_deg != 1) delete iv_M_dp; |
---|
5050 | |
---|
5051 | ring HelpRing = currRing; |
---|
5052 | |
---|
5053 | /* perturbs the target weight vector */ |
---|
5054 | if(tp_deg > 1 && tp_deg <= nV) |
---|
5055 | { |
---|
5056 | if (rParameter(currRing) != NULL) |
---|
5057 | DefRingPar(target_weight); |
---|
5058 | else |
---|
5059 | VMrDefault(target_weight); |
---|
5060 | |
---|
5061 | TargetRing = currRing; |
---|
5062 | ssG = idrMoveR(G,HelpRing,currRing); |
---|
5063 | if(MivSame(target_weight, exivlp) == 1) |
---|
5064 | { |
---|
5065 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
5066 | //ivString(iv_M_lp, "iv_M_lp"); |
---|
5067 | //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg); |
---|
5068 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
5069 | } |
---|
5070 | else |
---|
5071 | { |
---|
5072 | iv_M_lp = MivMatrixOrder(target_weight); |
---|
5073 | //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg); |
---|
5074 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
5075 | } |
---|
5076 | delete iv_M_lp; |
---|
5077 | pert_target_vector = target_weight; |
---|
5078 | rChangeCurrRing(HelpRing); |
---|
5079 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
5080 | } |
---|
5081 | /* |
---|
5082 | Print("\n// Perturbationwalkalg. vom Gradpaar (%d,%d):",op_deg,tp_deg); |
---|
5083 | ivString(curr_weight, "new sigma"); |
---|
5084 | ivString(target_weight, "new tau"); |
---|
5085 | */ |
---|
5086 | while(1) |
---|
5087 | { |
---|
5088 | nstep ++; |
---|
5089 | to = clock(); |
---|
5090 | /* compute an initial form ideal of <G> w.r.t. the weight vector |
---|
5091 | "curr_weight" */ |
---|
5092 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
5093 | |
---|
5094 | |
---|
5095 | #ifdef ENDWALKS |
---|
5096 | if(endwalks == 1){ |
---|
5097 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
5098 | idElements(G, "G"); |
---|
5099 | // idElements(Gomega, "Gw"); |
---|
5100 | headidString(G, "G"); |
---|
5101 | //headidString(Gomega, "Gw"); |
---|
5102 | } |
---|
5103 | #endif |
---|
5104 | |
---|
5105 | tif = tif + clock()-to; |
---|
5106 | |
---|
5107 | #ifndef BUCHBERGER_ALG |
---|
5108 | if(isNolVector(curr_weight) == 0) |
---|
5109 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
5110 | else |
---|
5111 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
5112 | #endif // BUCHBERGER_ALG |
---|
5113 | |
---|
5114 | oldRing = currRing; |
---|
5115 | |
---|
5116 | // define a new ring with ordering "(a(curr_weight),lp) |
---|
5117 | if (rParameter(currRing) != NULL) |
---|
5118 | DefRingPar(curr_weight); |
---|
5119 | else |
---|
5120 | VMrDefault(curr_weight); |
---|
5121 | |
---|
5122 | newRing = currRing; |
---|
5123 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
5124 | |
---|
5125 | #ifdef ENDWALKS |
---|
5126 | if(endwalks==1) |
---|
5127 | { |
---|
5128 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
5129 | idElements(Gomega1, "Gw"); |
---|
5130 | headidString(Gomega1, "headGw"); |
---|
5131 | PrintS("\n// compute a rGB of Gw:\n"); |
---|
5132 | |
---|
5133 | #ifndef BUCHBERGER_ALG |
---|
5134 | ivString(hilb_func, "w"); |
---|
5135 | #endif |
---|
5136 | } |
---|
5137 | #endif |
---|
5138 | |
---|
5139 | tim = clock(); |
---|
5140 | to = clock(); |
---|
5141 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
5142 | #ifdef BUCHBERGER_ALG |
---|
5143 | M = MstdhomCC(Gomega1); |
---|
5144 | #else |
---|
5145 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
5146 | delete hilb_func; |
---|
5147 | #endif // BUCHBERGER_ALG |
---|
5148 | |
---|
5149 | if(endwalks == 1){ |
---|
5150 | xtstd = xtstd+clock()-to; |
---|
5151 | #ifdef ENDWALKS |
---|
5152 | Print("\n// time for the last std(Gw) = %.2f sec\n", |
---|
5153 | ((double) clock())/1000000 -((double)tim) /1000000); |
---|
5154 | #endif |
---|
5155 | } |
---|
5156 | else |
---|
5157 | tstd=tstd+clock()-to; |
---|
5158 | |
---|
5159 | /* change the ring to oldRing */ |
---|
5160 | rChangeCurrRing(oldRing); |
---|
5161 | M1 = idrMoveR(M, newRing,currRing); |
---|
5162 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
5163 | |
---|
5164 | //if(endwalks==1) PrintS("\n// Lifting is working:.."); |
---|
5165 | |
---|
5166 | to=clock(); |
---|
5167 | /* compute a representation of the generators of submod (M) |
---|
5168 | with respect to those of mod (Gomega). |
---|
5169 | Gomega is a reduced Groebner basis w.r.t. the current ring */ |
---|
5170 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
5171 | if(endwalks != 1) |
---|
5172 | tlift = tlift+clock()-to; |
---|
5173 | else |
---|
5174 | xtlift=clock()-to; |
---|
5175 | |
---|
5176 | idDelete(&M1); |
---|
5177 | idDelete(&Gomega2); |
---|
5178 | idDelete(&G); |
---|
5179 | |
---|
5180 | /* change the ring to newRing */ |
---|
5181 | rChangeCurrRing(newRing); |
---|
5182 | F1 = idrMoveR(F, oldRing,currRing); |
---|
5183 | |
---|
5184 | //if(endwalks==1)PrintS("\n// InterRed is working now:"); |
---|
5185 | |
---|
5186 | to=clock(); |
---|
5187 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
5188 | G = kInterRedCC(F1, NULL); |
---|
5189 | if(endwalks != 1) |
---|
5190 | tred = tred+clock()-to; |
---|
5191 | else |
---|
5192 | xtred=clock()-to; |
---|
5193 | |
---|
5194 | idDelete(&F1); |
---|
5195 | |
---|
5196 | if(endwalks == 1) |
---|
5197 | break; |
---|
5198 | |
---|
5199 | to=clock(); |
---|
5200 | /* compute a next weight vector */ |
---|
5201 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
5202 | tnw=tnw+clock()-to; |
---|
5203 | #ifdef PRINT_VECTORS |
---|
5204 | MivString(curr_weight, target_weight, next_weight); |
---|
5205 | #endif |
---|
5206 | |
---|
5207 | if(Overflow_Error == TRUE) |
---|
5208 | { |
---|
5209 | ntwC = 0; |
---|
5210 | //ntestomega = 1; |
---|
5211 | //Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
5212 | //idElements(G, "G"); |
---|
5213 | delete next_weight; |
---|
5214 | goto FINISH_160302; |
---|
5215 | } |
---|
5216 | if(MivComp(next_weight, ivNull) == 1){ |
---|
5217 | newRing = currRing; |
---|
5218 | delete next_weight; |
---|
5219 | //Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
5220 | break; |
---|
5221 | } |
---|
5222 | if(MivComp(next_weight, target_weight) == 1) |
---|
5223 | endwalks = 1; |
---|
5224 | |
---|
5225 | for(i=nV-1; i>=0; i--) |
---|
5226 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
5227 | |
---|
5228 | delete next_weight; |
---|
5229 | }//while |
---|
5230 | |
---|
5231 | if(tp_deg != 1) |
---|
5232 | { |
---|
5233 | FINISH_160302: |
---|
5234 | if(MivSame(orig_target, exivlp) == 1) |
---|
5235 | if (rParameter(currRing) != NULL) |
---|
5236 | DefRingParlp(); |
---|
5237 | else |
---|
5238 | VMrDefaultlp(); |
---|
5239 | else |
---|
5240 | if (rParameter(currRing) != NULL) |
---|
5241 | DefRingPar(orig_target); |
---|
5242 | else |
---|
5243 | VMrDefault(orig_target); |
---|
5244 | |
---|
5245 | TargetRing=currRing; |
---|
5246 | F1 = idrMoveR(G, newRing,currRing); |
---|
5247 | #ifdef CHECK_IDEAL |
---|
5248 | headidString(G, "G"); |
---|
5249 | #endif |
---|
5250 | |
---|
5251 | |
---|
5252 | // check whether the pertubed target vector stays in the correct cone |
---|
5253 | if(ntwC != 0){ |
---|
5254 | ntestw = test_w_in_ConeCC(F1, pert_target_vector); |
---|
5255 | } |
---|
5256 | |
---|
5257 | if( ntestw != 1 || ntwC == 0) |
---|
5258 | { |
---|
5259 | /* |
---|
5260 | if(ntestw != 1){ |
---|
5261 | ivString(pert_target_vector, "tau"); |
---|
5262 | PrintS("\n// ** perturbed target vector doesn't stay in cone!!"); |
---|
5263 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
5264 | idElements(F1, "G"); |
---|
5265 | } |
---|
5266 | */ |
---|
5267 | // LastGB is "better" than the kStd subroutine |
---|
5268 | to=clock(); |
---|
5269 | ideal eF1; |
---|
5270 | if(nP == 0 || tp_deg == 1 || MivSame(orig_target, exivlp) != 1){ |
---|
5271 | // PrintS("\n// ** calls \"std\" to compute a GB"); |
---|
5272 | eF1 = MstdCC(F1); |
---|
5273 | idDelete(&F1); |
---|
5274 | } |
---|
5275 | else { |
---|
5276 | // PrintS("\n// ** calls \"LastGB\" to compute a GB"); |
---|
5277 | rChangeCurrRing(newRing); |
---|
5278 | ideal F2 = idrMoveR(F1, TargetRing,currRing); |
---|
5279 | eF1 = LastGB(F2, curr_weight, tp_deg-1); |
---|
5280 | F2=NULL; |
---|
5281 | } |
---|
5282 | xtextra=clock()-to; |
---|
5283 | ring exTargetRing = currRing; |
---|
5284 | |
---|
5285 | rChangeCurrRing(XXRing); |
---|
5286 | Eresult = idrMoveR(eF1, exTargetRing,currRing); |
---|
5287 | } |
---|
5288 | else{ |
---|
5289 | rChangeCurrRing(XXRing); |
---|
5290 | Eresult = idrMoveR(F1, TargetRing,currRing); |
---|
5291 | } |
---|
5292 | } |
---|
5293 | else { |
---|
5294 | rChangeCurrRing(XXRing); |
---|
5295 | Eresult = idrMoveR(G, newRing,currRing); |
---|
5296 | } |
---|
5297 | delete ivNull; |
---|
5298 | if(tp_deg != 1) |
---|
5299 | delete target_weight; |
---|
5300 | |
---|
5301 | if(op_deg != 1 ) |
---|
5302 | delete curr_weight; |
---|
5303 | |
---|
5304 | delete exivlp; |
---|
5305 | delete last_omega; |
---|
5306 | |
---|
5307 | #ifdef TIME_TEST |
---|
5308 | TimeStringFractal(tinput, tostd, tif+xtif, tstd+xtstd,0, tlift+xtlift, tred+xtred, |
---|
5309 | tnw+xtnw); |
---|
5310 | |
---|
5311 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
5312 | Print("\n// It took %d steps and Overflow_Error? (%d)\n", nstep, Overflow_Error); |
---|
5313 | #endif |
---|
5314 | return(Eresult); |
---|
5315 | } |
---|
5316 | |
---|
5317 | intvec* XivNull; |
---|
5318 | |
---|
5319 | // define a matrix (1 ... 1) |
---|
5320 | intvec* MMatrixone(int nV) |
---|
5321 | { |
---|
5322 | int i,j; |
---|
5323 | intvec* ivM = new intvec(nV*nV); |
---|
5324 | |
---|
5325 | for(i=0; i<nV; i++) |
---|
5326 | for(j=0; j<nV; j++) |
---|
5327 | (*ivM)[i*nV + j] = 1; |
---|
5328 | |
---|
5329 | return(ivM); |
---|
5330 | } |
---|
5331 | |
---|
5332 | int nnflow; |
---|
5333 | int Xcall; |
---|
5334 | int Xngleich; |
---|
5335 | |
---|
5336 | /*********************************************************************** |
---|
5337 | * Perturb the start weight vector at the top level, i.e. nlev = 1 * |
---|
5338 | ***********************************************************************/ |
---|
5339 | static ideal rec_fractal_call(ideal G, int nlev, intvec* omtmp) |
---|
5340 | { |
---|
5341 | Overflow_Error = FALSE; |
---|
5342 | //Print("\n\n// Entering the %d-th recursion:", nlev); |
---|
5343 | |
---|
5344 | int i, nV = currRing->N; |
---|
5345 | ring new_ring, testring; |
---|
5346 | //ring extoRing; |
---|
5347 | ideal Gomega, Gomega1, Gomega2, F, F1, Gresult, Gresult1, G1, Gt; |
---|
5348 | int nwalks = 0; |
---|
5349 | intvec* Mwlp; |
---|
5350 | #ifndef BUCHBERGER_ALG |
---|
5351 | intvec* hilb_func; |
---|
5352 | #endif |
---|
5353 | // intvec* extXtau; |
---|
5354 | intvec* next_vect; |
---|
5355 | intvec* omega2 = new intvec(nV); |
---|
5356 | intvec* altomega = new intvec(nV); |
---|
5357 | |
---|
5358 | //BOOLEAN isnewtarget = FALSE; |
---|
5359 | |
---|
5360 | // to avoid (1,0,...,0) as the target vector (Hans) |
---|
5361 | intvec* last_omega = new intvec(nV); |
---|
5362 | for(i=nV-1; i>0; i--) |
---|
5363 | (*last_omega)[i] = 1; |
---|
5364 | (*last_omega)[0] = 10000; |
---|
5365 | |
---|
5366 | intvec* omega = new intvec(nV); |
---|
5367 | for(i=0; i<nV; i++) { |
---|
5368 | if(Xsigma->length() == nV) |
---|
5369 | (*omega)[i] = (*Xsigma)[i]; |
---|
5370 | else |
---|
5371 | (*omega)[i] = (*Xsigma)[(nV*(nlev-1))+i]; |
---|
5372 | |
---|
5373 | (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i]; |
---|
5374 | } |
---|
5375 | |
---|
5376 | if(nlev == 1) Xcall = 1; |
---|
5377 | else Xcall = 0; |
---|
5378 | |
---|
5379 | ring oRing = currRing; |
---|
5380 | |
---|
5381 | while(1) |
---|
5382 | { |
---|
5383 | #ifdef FIRST_STEP_FRACTAL |
---|
5384 | // perturb the current weight vector only on the top level or |
---|
5385 | // after perturbation of the both vectors, nlev = 2 as the top level |
---|
5386 | if((nlev == 1 && Xcall == 0) || (nlev == 2 && Xngleich == 1)) |
---|
5387 | if(islengthpoly2(G) == 1) |
---|
5388 | { |
---|
5389 | Mwlp = MivWeightOrderlp(omega); |
---|
5390 | Xsigma = Mfpertvector(G, Mwlp); |
---|
5391 | delete Mwlp; |
---|
5392 | Overflow_Error = FALSE; |
---|
5393 | } |
---|
5394 | #endif |
---|
5395 | nwalks ++; |
---|
5396 | NEXT_VECTOR_FRACTAL: |
---|
5397 | to=clock(); |
---|
5398 | /* determine the next border */ |
---|
5399 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
5400 | xtnw=xtnw+clock()-to; |
---|
5401 | #ifdef PRINT_VECTORS |
---|
5402 | MivString(omega, omega2, next_vect); |
---|
5403 | #endif |
---|
5404 | oRing = currRing; |
---|
5405 | |
---|
5406 | /* We only perturb the current target vector at the recursion level 1 */ |
---|
5407 | if(Xngleich == 0 && nlev == 1) //(ngleich == 0) important, e.g. ex2, ex3 |
---|
5408 | if (MivComp(next_vect, omega2) == 1) |
---|
5409 | { |
---|
5410 | /* to dispense with taking initial (and lifting/interreducing |
---|
5411 | after the call of recursion */ |
---|
5412 | //Print("\n\n// ** Perturb the both vectors with degree %d with",nlev); |
---|
5413 | //idElements(G, "G"); |
---|
5414 | |
---|
5415 | Xngleich = 1; |
---|
5416 | nlev +=1; |
---|
5417 | |
---|
5418 | if (rParameter(currRing) != NULL) |
---|
5419 | DefRingPar(omtmp); |
---|
5420 | else |
---|
5421 | VMrDefault(omtmp); |
---|
5422 | |
---|
5423 | testring = currRing; |
---|
5424 | Gt = idrMoveR(G, oRing,currRing); |
---|
5425 | |
---|
5426 | /* perturb the original target vector w.r.t. the current GB */ |
---|
5427 | delete Xtau; |
---|
5428 | Xtau = NewVectorlp(Gt); |
---|
5429 | |
---|
5430 | rChangeCurrRing(oRing); |
---|
5431 | G = idrMoveR(Gt, testring,currRing); |
---|
5432 | |
---|
5433 | /* perturb the current vector w.r.t. the current GB */ |
---|
5434 | Mwlp = MivWeightOrderlp(omega); |
---|
5435 | Xsigma = Mfpertvector(G, Mwlp); |
---|
5436 | delete Mwlp; |
---|
5437 | |
---|
5438 | for(i=nV-1; i>=0; i--) { |
---|
5439 | (*omega2)[i] = (*Xtau)[nV+i]; |
---|
5440 | (*omega)[i] = (*Xsigma)[nV+i]; |
---|
5441 | } |
---|
5442 | |
---|
5443 | delete next_vect; |
---|
5444 | to=clock(); |
---|
5445 | |
---|
5446 | /* to avoid the value of Overflow_Error that occur in Mfpertvector*/ |
---|
5447 | Overflow_Error = FALSE; |
---|
5448 | |
---|
5449 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
5450 | xtnw=xtnw+clock()-to; |
---|
5451 | |
---|
5452 | #ifdef PRINT_VECTORS |
---|
5453 | MivString(omega, omega2, next_vect); |
---|
5454 | #endif |
---|
5455 | } |
---|
5456 | |
---|
5457 | |
---|
5458 | /* check whether the the computed vector is in the correct cone */ |
---|
5459 | /* If no, the reduced GB of an omega-homogeneous ideal will be |
---|
5460 | computed by Buchberger algorithm and stop this recursion step*/ |
---|
5461 | //if(test_w_in_ConeCC(G, next_vect) != 1) //e.g. Example s7, cyc6 |
---|
5462 | if(Overflow_Error == TRUE) |
---|
5463 | { |
---|
5464 | delete next_vect; |
---|
5465 | if (rParameter(currRing) != NULL) |
---|
5466 | { |
---|
5467 | DefRingPar(omtmp); |
---|
5468 | } |
---|
5469 | else |
---|
5470 | { |
---|
5471 | VMrDefault(omtmp); |
---|
5472 | } |
---|
5473 | #ifdef TEST_OVERFLOW |
---|
5474 | Gt = idrMoveR(G, oRing,currRing); |
---|
5475 | Gt = NULL; return(Gt); |
---|
5476 | #endif |
---|
5477 | |
---|
5478 | //Print("\n\n// apply BB's alg. in ring r = %s;", rString(currRing)); |
---|
5479 | to=clock(); |
---|
5480 | Gt = idrMoveR(G, oRing,currRing); |
---|
5481 | G1 = MstdCC(Gt); |
---|
5482 | xtextra=xtextra+clock()-to; |
---|
5483 | Gt = NULL; |
---|
5484 | |
---|
5485 | delete omega2; |
---|
5486 | delete altomega; |
---|
5487 | |
---|
5488 | //Print("\n// Leaving the %d-th recursion with %d steps", nlev, nwalks); |
---|
5489 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
5490 | nnflow ++; |
---|
5491 | |
---|
5492 | Overflow_Error = FALSE; |
---|
5493 | return (G1); |
---|
5494 | } |
---|
5495 | |
---|
5496 | |
---|
5497 | /* If the perturbed target vector stays in the correct cone, |
---|
5498 | return the current GB, |
---|
5499 | otherwise, return the computed GB by the Buchberger-algorithm. |
---|
5500 | Then we update the perturbed target vectors w.r.t. this GB. */ |
---|
5501 | |
---|
5502 | /* the computed vector is equal to the origin vector, since |
---|
5503 | t is not defined */ |
---|
5504 | if (MivComp(next_vect, XivNull) == 1) |
---|
5505 | { |
---|
5506 | if (rParameter(currRing) != NULL) |
---|
5507 | DefRingPar(omtmp); |
---|
5508 | else |
---|
5509 | VMrDefault(omtmp); |
---|
5510 | |
---|
5511 | testring = currRing; |
---|
5512 | Gt = idrMoveR(G, oRing,currRing); |
---|
5513 | |
---|
5514 | if(test_w_in_ConeCC(Gt, omega2) == 1) { |
---|
5515 | delete omega2; |
---|
5516 | delete next_vect; |
---|
5517 | delete altomega; |
---|
5518 | //Print("\n// Leaving the %d-th recursion with %d steps ",nlev, nwalks); |
---|
5519 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
5520 | |
---|
5521 | return (Gt); |
---|
5522 | } |
---|
5523 | else |
---|
5524 | { |
---|
5525 | //ivString(omega2, "tau'"); |
---|
5526 | //Print("\n// tau' doesn't stay in the correct cone!!"); |
---|
5527 | |
---|
5528 | #ifndef MSTDCC_FRACTAL |
---|
5529 | //07.08.03 |
---|
5530 | //ivString(Xtau, "old Xtau"); |
---|
5531 | intvec* Xtautmp = Mfpertvector(Gt, MivMatrixOrder(omtmp)); |
---|
5532 | #ifdef TEST_OVERFLOW |
---|
5533 | if(Overflow_Error == TRUE) |
---|
5534 | Gt = NULL; return(Gt); |
---|
5535 | #endif |
---|
5536 | |
---|
5537 | if(MivSame(Xtau, Xtautmp) == 1) |
---|
5538 | { |
---|
5539 | //PrintS("\n// Update vectors are equal to the old vectors!!"); |
---|
5540 | delete Xtautmp; |
---|
5541 | goto FRACTAL_MSTDCC; |
---|
5542 | } |
---|
5543 | |
---|
5544 | Xtau = Xtautmp; |
---|
5545 | Xtautmp = NULL; |
---|
5546 | //ivString(Xtau, "new Xtau"); |
---|
5547 | |
---|
5548 | for(i=nV-1; i>=0; i--) |
---|
5549 | (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i]; |
---|
5550 | |
---|
5551 | //Print("\n// ring tau = %s;", rString(currRing)); |
---|
5552 | rChangeCurrRing(oRing); |
---|
5553 | G = idrMoveR(Gt, testring,currRing); |
---|
5554 | |
---|
5555 | goto NEXT_VECTOR_FRACTAL; |
---|
5556 | #endif |
---|
5557 | |
---|
5558 | FRACTAL_MSTDCC: |
---|
5559 | //Print("\n// apply BB-Alg in ring = %s;", rString(currRing)); |
---|
5560 | to=clock(); |
---|
5561 | G = MstdCC(Gt); |
---|
5562 | xtextra=xtextra+clock()-to; |
---|
5563 | |
---|
5564 | oRing = currRing; |
---|
5565 | |
---|
5566 | // update the original target vector w.r.t. the current GB |
---|
5567 | if(MivSame(Xivinput, Xivlp) == 1) |
---|
5568 | if (rParameter(currRing) != NULL) |
---|
5569 | DefRingParlp(); |
---|
5570 | else |
---|
5571 | VMrDefaultlp(); |
---|
5572 | else |
---|
5573 | if (rParameter(currRing) != NULL) |
---|
5574 | DefRingPar(Xivinput); |
---|
5575 | else |
---|
5576 | VMrDefault(Xivinput); |
---|
5577 | |
---|
5578 | testring = currRing; |
---|
5579 | Gt = idrMoveR(G, oRing,currRing); |
---|
5580 | |
---|
5581 | delete Xtau; |
---|
5582 | Xtau = NewVectorlp(Gt); |
---|
5583 | |
---|
5584 | rChangeCurrRing(oRing); |
---|
5585 | G = idrMoveR(Gt, testring,currRing); |
---|
5586 | |
---|
5587 | delete omega2; |
---|
5588 | delete next_vect; |
---|
5589 | delete altomega; |
---|
5590 | /* |
---|
5591 | Print("\n// Leaving the %d-th recursion with %d steps,", nlev,nwalks); |
---|
5592 | Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
5593 | */ |
---|
5594 | if(Overflow_Error == TRUE) |
---|
5595 | nnflow ++; |
---|
5596 | |
---|
5597 | Overflow_Error = FALSE; |
---|
5598 | return(G); |
---|
5599 | } |
---|
5600 | } |
---|
5601 | |
---|
5602 | for(i=nV-1; i>=0; i--) { |
---|
5603 | (*altomega)[i] = (*omega)[i]; |
---|
5604 | (*omega)[i] = (*next_vect)[i]; |
---|
5605 | } |
---|
5606 | delete next_vect; |
---|
5607 | |
---|
5608 | to=clock(); |
---|
5609 | /* Take the initial form of <G> w.r.t. omega */ |
---|
5610 | Gomega = MwalkInitialForm(G, omega); |
---|
5611 | xtif=xtif+clock()-to; |
---|
5612 | |
---|
5613 | #ifndef BUCHBERGER_ALG |
---|
5614 | if(isNolVector(omega) == 0) |
---|
5615 | hilb_func = hFirstSeries(Gomega,NULL,NULL,omega,currRing); |
---|
5616 | else |
---|
5617 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
5618 | #endif // BUCHBERGER_ALG |
---|
5619 | |
---|
5620 | if (rParameter(currRing) != NULL) |
---|
5621 | DefRingPar(omega); |
---|
5622 | else |
---|
5623 | VMrDefault(omega); |
---|
5624 | |
---|
5625 | Gomega1 = idrMoveR(Gomega, oRing,currRing); |
---|
5626 | |
---|
5627 | /* Maximal recursion depth, to compute a red. GB */ |
---|
5628 | /* Fractal walk with the alternative recursion */ |
---|
5629 | /* alternative recursion */ |
---|
5630 | // if(nlev == nV || lengthpoly(Gomega1) == 0) |
---|
5631 | if(nlev == Xnlev || lengthpoly(Gomega1) == 0) |
---|
5632 | //if(nlev == nV) // blind recursion |
---|
5633 | { |
---|
5634 | /* |
---|
5635 | if(Xnlev != nV) |
---|
5636 | { |
---|
5637 | Print("\n// ** Xnlev = %d", Xnlev); |
---|
5638 | ivString(Xtau, "Xtau"); |
---|
5639 | } |
---|
5640 | */ |
---|
5641 | to=clock(); |
---|
5642 | #ifdef BUCHBERGER_ALG |
---|
5643 | Gresult = MstdhomCC(Gomega1); |
---|
5644 | #else |
---|
5645 | Gresult =kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,omega); |
---|
5646 | delete hilb_func; |
---|
5647 | #endif // BUCHBERGER_ALG |
---|
5648 | xtstd=xtstd+clock()-to; |
---|
5649 | } |
---|
5650 | else { |
---|
5651 | rChangeCurrRing(oRing); |
---|
5652 | Gomega1 = idrMoveR(Gomega1, oRing,currRing); |
---|
5653 | Gresult = rec_fractal_call(idCopy(Gomega1),nlev+1,omega); |
---|
5654 | } |
---|
5655 | |
---|
5656 | //convert a Groebner basis from a ring to another ring, |
---|
5657 | new_ring = currRing; |
---|
5658 | |
---|
5659 | rChangeCurrRing(oRing); |
---|
5660 | Gresult1 = idrMoveR(Gresult, new_ring,currRing); |
---|
5661 | Gomega2 = idrMoveR(Gomega1, new_ring,currRing); |
---|
5662 | |
---|
5663 | to=clock(); |
---|
5664 | /* Lifting process */ |
---|
5665 | F = MLifttwoIdeal(Gomega2, Gresult1, G); |
---|
5666 | xtlift=xtlift+clock()-to; |
---|
5667 | idDelete(&Gresult1); |
---|
5668 | idDelete(&Gomega2); |
---|
5669 | idDelete(&G); |
---|
5670 | |
---|
5671 | rChangeCurrRing(new_ring); |
---|
5672 | F1 = idrMoveR(F, oRing,currRing); |
---|
5673 | |
---|
5674 | to=clock(); |
---|
5675 | /* Interreduce G */ |
---|
5676 | G = kInterRedCC(F1, NULL); |
---|
5677 | xtred=xtred+clock()-to; |
---|
5678 | idDelete(&F1); |
---|
5679 | } |
---|
5680 | } |
---|
5681 | |
---|
5682 | /************************************************************************ |
---|
5683 | * Perturb the start weight vector at the top level with random element * |
---|
5684 | ************************************************************************/ |
---|
5685 | static ideal rec_r_fractal_call(ideal G, int nlev, intvec* omtmp, int weight_rad) |
---|
5686 | { |
---|
5687 | Overflow_Error = FALSE; |
---|
5688 | //Print("\n\n// Entering the %d-th recursion:", nlev); |
---|
5689 | |
---|
5690 | int i,k,weight_norm; |
---|
5691 | int nV = currRing->N; |
---|
5692 | ring new_ring, testring; |
---|
5693 | //ring extoRing; |
---|
5694 | ideal Gomega, Gomega1, Gomega2, F, F1, Gresult, Gresult1, G1, Gt; |
---|
5695 | int nwalks = 0; |
---|
5696 | intvec* Mwlp; |
---|
5697 | #ifndef BUCHBERGER_ALG |
---|
5698 | intvec* hilb_func; |
---|
5699 | #endif |
---|
5700 | //intvec* extXtau; |
---|
5701 | intvec* next_vect; |
---|
5702 | intvec* omega2 = new intvec(nV); |
---|
5703 | intvec* altomega = new intvec(nV); |
---|
5704 | |
---|
5705 | //BOOLEAN isnewtarget = FALSE; |
---|
5706 | |
---|
5707 | // to avoid (1,0,...,0) as the target vector (Hans) |
---|
5708 | intvec* last_omega = new intvec(nV); |
---|
5709 | for(i=nV-1; i>0; i--) |
---|
5710 | (*last_omega)[i] = 1; |
---|
5711 | (*last_omega)[0] = 10000; |
---|
5712 | |
---|
5713 | intvec* omega = new intvec(nV); |
---|
5714 | for(i=0; i<nV; i++) { |
---|
5715 | if(Xsigma->length() == nV) |
---|
5716 | (*omega)[i] = (*Xsigma)[i]; |
---|
5717 | else |
---|
5718 | (*omega)[i] = (*Xsigma)[(nV*(nlev-1))+i]; |
---|
5719 | |
---|
5720 | (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i]; |
---|
5721 | } |
---|
5722 | |
---|
5723 | if(nlev == 1) Xcall = 1; |
---|
5724 | else Xcall = 0; |
---|
5725 | |
---|
5726 | ring oRing = currRing; |
---|
5727 | |
---|
5728 | while(1) |
---|
5729 | { |
---|
5730 | #ifdef FIRST_STEP_FRACTAL |
---|
5731 | // perturb the current weight vector only on the top level or |
---|
5732 | // after perturbation of the both vectors, nlev = 2 as the top level |
---|
5733 | if((nlev == 1 && Xcall == 0) || (nlev == 2 && Xngleich == 1)) |
---|
5734 | if(islengthpoly2(G) == 1) |
---|
5735 | { |
---|
5736 | Mwlp = MivWeightOrderlp(omega); |
---|
5737 | Xsigma = Mfpertvector(G, Mwlp); |
---|
5738 | delete Mwlp; |
---|
5739 | Overflow_Error = FALSE; |
---|
5740 | } |
---|
5741 | #endif |
---|
5742 | nwalks ++; |
---|
5743 | NEXT_VECTOR_FRACTAL: |
---|
5744 | to=clock(); |
---|
5745 | /* determine the next border */ |
---|
5746 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
5747 | xtnw=xtnw+clock()-to; |
---|
5748 | #ifdef PRINT_VECTORS |
---|
5749 | MivString(omega, omega2, next_vect); |
---|
5750 | #endif |
---|
5751 | oRing = currRing; |
---|
5752 | |
---|
5753 | /* We only perturb the current target vector at the recursion level 1 */ |
---|
5754 | if(Xngleich == 0 && nlev == 1) //(ngleich == 0) important, e.g. ex2, ex3 |
---|
5755 | { |
---|
5756 | if (MivComp(next_vect, omega2) == 1) |
---|
5757 | { |
---|
5758 | /* to dispense with taking initial (and lifting/interreducing |
---|
5759 | after the call of recursion */ |
---|
5760 | //Print("\n\n// ** Perturb the both vectors with degree %d with",nlev); |
---|
5761 | //idElements(G, "G"); |
---|
5762 | |
---|
5763 | Xngleich = 1; |
---|
5764 | nlev +=1; |
---|
5765 | |
---|
5766 | if (rParameter(currRing) != NULL) |
---|
5767 | DefRingPar(omtmp); |
---|
5768 | else |
---|
5769 | VMrDefault(omtmp); |
---|
5770 | |
---|
5771 | testring = currRing; |
---|
5772 | Gt = idrMoveR(G, oRing,currRing); |
---|
5773 | |
---|
5774 | /* perturb the original target vector w.r.t. the current GB */ |
---|
5775 | delete Xtau; |
---|
5776 | Xtau = NewVectorlp(Gt); |
---|
5777 | |
---|
5778 | rChangeCurrRing(oRing); |
---|
5779 | G = idrMoveR(Gt, testring,currRing); |
---|
5780 | |
---|
5781 | /* perturb the current vector w.r.t. the current GB */ |
---|
5782 | Mwlp = MivWeightOrderlp(omega); |
---|
5783 | Xsigma = Mfpertvector(G, Mwlp); |
---|
5784 | delete Mwlp; |
---|
5785 | |
---|
5786 | for(i=nV-1; i>=0; i--) { |
---|
5787 | (*omega2)[i] = (*Xtau)[nV+i]; |
---|
5788 | (*omega)[i] = (*Xsigma)[nV+i]; |
---|
5789 | } |
---|
5790 | |
---|
5791 | delete next_vect; |
---|
5792 | to=clock(); |
---|
5793 | |
---|
5794 | /* to avoid the value of Overflow_Error that occur in Mfpertvector*/ |
---|
5795 | Overflow_Error = FALSE; |
---|
5796 | |
---|
5797 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
5798 | xtnw=xtnw+clock()-to; |
---|
5799 | |
---|
5800 | #ifdef PRINT_VECTORS |
---|
5801 | MivString(omega, omega2, next_vect); |
---|
5802 | #endif |
---|
5803 | } |
---|
5804 | else |
---|
5805 | { |
---|
5806 | // compute a perturbed next weight vector "next_vect1" |
---|
5807 | intvec* next_vect11 = MPertVectors(G, MivMatrixOrder(omega), nlev); |
---|
5808 | intvec* next_vect1 = MkInterRedNextWeight(next_vect11, omega2, G); |
---|
5809 | // Print("\n// size of next_vect = %d", sizeof((*next_vect))); |
---|
5810 | // Print("\n// size of next_vect1 = %d", sizeof((*next_vect1))); |
---|
5811 | // Print("\n// size of next_vect11 = %d", sizeof((*next_vect11))); |
---|
5812 | delete next_vect11; |
---|
5813 | |
---|
5814 | // compare next_vect and next_vect1 |
---|
5815 | ideal G_test = MwalkInitialForm(G, next_vect); |
---|
5816 | ideal G_test1 = MwalkInitialForm(G, next_vect1); |
---|
5817 | // Print("\n// G_test, G_test 1 erzeugt"); |
---|
5818 | if(IDELEMS(G_test1) <= IDELEMS(G_test)) |
---|
5819 | { |
---|
5820 | next_vect = ivCopy(next_vect1); |
---|
5821 | } |
---|
5822 | delete next_vect1; |
---|
5823 | // compute a random next weight vector "next_vect2" |
---|
5824 | intvec* next_vect22 = ivCopy(omega2); |
---|
5825 | // Print("\n// size of next_vect22 = %d", sizeof((*next_vect22))); |
---|
5826 | k = 0; |
---|
5827 | while(test_w_in_ConeCC(G, next_vect22) == 0) |
---|
5828 | { |
---|
5829 | k = k + 1; |
---|
5830 | if(k>10) |
---|
5831 | { |
---|
5832 | break; |
---|
5833 | } |
---|
5834 | weight_norm = 0; |
---|
5835 | while(weight_norm == 0) |
---|
5836 | { |
---|
5837 | for(i=nV-1; i>=0; i--) |
---|
5838 | { |
---|
5839 | (*next_vect22)[i] = rand() % 60000 - 30000; |
---|
5840 | weight_norm = weight_norm + (*next_vect22)[i]*(*next_vect22)[i]; |
---|
5841 | } |
---|
5842 | weight_norm = 1 + floor(sqrt(weight_norm)); |
---|
5843 | } |
---|
5844 | for(i=nV-1; i>=0; i--) |
---|
5845 | { |
---|
5846 | if((*next_vect22)[i] < 0) |
---|
5847 | { |
---|
5848 | (*next_vect22)[i] = 1 + (*omega)[i] + floor(weight_rad*(*next_vect22)[i]/weight_norm); |
---|
5849 | } |
---|
5850 | else |
---|
5851 | { |
---|
5852 | (*next_vect22)[i] = (*omega)[i] + floor(weight_rad*(*next_vect22)[i]/weight_norm); |
---|
5853 | } |
---|
5854 | } |
---|
5855 | } |
---|
5856 | if(test_w_in_ConeCC(G, next_vect22) == 1) |
---|
5857 | { |
---|
5858 | //compare next_weight and next_vect2 |
---|
5859 | intvec* next_vect2 = MkInterRedNextWeight(next_vect22, omega2, G); |
---|
5860 | // Print("\n// size of next_vect2 = %d", sizeof((*next_vect2))); |
---|
5861 | ideal G_test2 = MwalkInitialForm(G, next_vect2); |
---|
5862 | if(IDELEMS(G_test2) <= IDELEMS(G_test)) |
---|
5863 | { |
---|
5864 | if(IDELEMS(G_test2) <= IDELEMS(G_test1)) |
---|
5865 | { |
---|
5866 | next_vect = ivCopy(next_vect2); |
---|
5867 | } |
---|
5868 | } |
---|
5869 | idDelete(&G_test2); |
---|
5870 | delete next_vect2; |
---|
5871 | } |
---|
5872 | delete next_vect22; |
---|
5873 | idDelete(&G_test); |
---|
5874 | idDelete(&G_test1); |
---|
5875 | #ifdef PRINT_VECTORS |
---|
5876 | MivString(omega, omega2, next_vect); |
---|
5877 | #endif |
---|
5878 | } |
---|
5879 | } |
---|
5880 | |
---|
5881 | |
---|
5882 | /* check whether the the computed vector is in the correct cone */ |
---|
5883 | /* If no, the reduced GB of an omega-homogeneous ideal will be |
---|
5884 | computed by Buchberger algorithm and stop this recursion step*/ |
---|
5885 | //if(test_w_in_ConeCC(G, next_vect) != 1) //e.g. Example s7, cyc6 |
---|
5886 | if(Overflow_Error == TRUE) |
---|
5887 | { |
---|
5888 | delete next_vect; |
---|
5889 | |
---|
5890 | //OVERFLOW_IN_NEXT_VECTOR: |
---|
5891 | if (rParameter(currRing) != NULL) |
---|
5892 | DefRingPar(omtmp); |
---|
5893 | else |
---|
5894 | VMrDefault(omtmp); |
---|
5895 | |
---|
5896 | #ifdef TEST_OVERFLOW |
---|
5897 | Gt = idrMoveR(G, oRing,currRing); |
---|
5898 | Gt = NULL; return(Gt); |
---|
5899 | #endif |
---|
5900 | |
---|
5901 | //Print("\n\n// apply BB's alg. in ring r = %s;", rString(currRing)); |
---|
5902 | to=clock(); |
---|
5903 | Gt = idrMoveR(G, oRing,currRing); |
---|
5904 | G1 = MstdCC(Gt); |
---|
5905 | xtextra=xtextra+clock()-to; |
---|
5906 | Gt = NULL; |
---|
5907 | |
---|
5908 | delete omega2; |
---|
5909 | delete altomega; |
---|
5910 | |
---|
5911 | //Print("\n// Leaving the %d-th recursion with %d steps", nlev, nwalks); |
---|
5912 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
5913 | nnflow ++; |
---|
5914 | |
---|
5915 | Overflow_Error = FALSE; |
---|
5916 | return (G1); |
---|
5917 | } |
---|
5918 | |
---|
5919 | |
---|
5920 | /* If the perturbed target vector stays in the correct cone, |
---|
5921 | return the current GB, |
---|
5922 | otherwise, return the computed GB by the Buchberger-algorithm. |
---|
5923 | Then we update the perturbed target vectors w.r.t. this GB. */ |
---|
5924 | |
---|
5925 | /* the computed vector is equal to the origin vector, since |
---|
5926 | t is not defined */ |
---|
5927 | if (MivComp(next_vect, XivNull) == 1) |
---|
5928 | { |
---|
5929 | if (rParameter(currRing) != NULL) |
---|
5930 | DefRingPar(omtmp); |
---|
5931 | else |
---|
5932 | VMrDefault(omtmp); |
---|
5933 | |
---|
5934 | testring = currRing; |
---|
5935 | Gt = idrMoveR(G, oRing,currRing); |
---|
5936 | |
---|
5937 | if(test_w_in_ConeCC(Gt, omega2) == 1) { |
---|
5938 | delete omega2; |
---|
5939 | delete next_vect; |
---|
5940 | delete altomega; |
---|
5941 | //Print("\n// Leaving the %d-th recursion with %d steps ",nlev, nwalks); |
---|
5942 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
5943 | |
---|
5944 | return (Gt); |
---|
5945 | } |
---|
5946 | else |
---|
5947 | { |
---|
5948 | //ivString(omega2, "tau'"); |
---|
5949 | //Print("\n// tau' doesn't stay in the correct cone!!"); |
---|
5950 | |
---|
5951 | #ifndef MSTDCC_FRACTAL |
---|
5952 | //07.08.03 |
---|
5953 | //ivString(Xtau, "old Xtau"); |
---|
5954 | intvec* Xtautmp = Mfpertvector(Gt, MivMatrixOrder(omtmp)); |
---|
5955 | #ifdef TEST_OVERFLOW |
---|
5956 | if(Overflow_Error == TRUE) |
---|
5957 | Gt = NULL; return(Gt); |
---|
5958 | #endif |
---|
5959 | |
---|
5960 | if(MivSame(Xtau, Xtautmp) == 1) |
---|
5961 | { |
---|
5962 | //PrintS("\n// Update vectors are equal to the old vectors!!"); |
---|
5963 | delete Xtautmp; |
---|
5964 | goto FRACTAL_MSTDCC; |
---|
5965 | } |
---|
5966 | |
---|
5967 | Xtau = Xtautmp; |
---|
5968 | Xtautmp = NULL; |
---|
5969 | //ivString(Xtau, "new Xtau"); |
---|
5970 | |
---|
5971 | for(i=nV-1; i>=0; i--) |
---|
5972 | (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i]; |
---|
5973 | |
---|
5974 | //Print("\n// ring tau = %s;", rString(currRing)); |
---|
5975 | rChangeCurrRing(oRing); |
---|
5976 | G = idrMoveR(Gt, testring,currRing); |
---|
5977 | |
---|
5978 | goto NEXT_VECTOR_FRACTAL; |
---|
5979 | #endif |
---|
5980 | |
---|
5981 | FRACTAL_MSTDCC: |
---|
5982 | //Print("\n// apply BB-Alg in ring = %s;", rString(currRing)); |
---|
5983 | to=clock(); |
---|
5984 | G = MstdCC(Gt); |
---|
5985 | xtextra=xtextra+clock()-to; |
---|
5986 | |
---|
5987 | oRing = currRing; |
---|
5988 | |
---|
5989 | // update the original target vector w.r.t. the current GB |
---|
5990 | if(MivSame(Xivinput, Xivlp) == 1) |
---|
5991 | if (rParameter(currRing) != NULL) |
---|
5992 | DefRingParlp(); |
---|
5993 | else |
---|
5994 | VMrDefaultlp(); |
---|
5995 | else |
---|
5996 | if (rParameter(currRing) != NULL) |
---|
5997 | DefRingPar(Xivinput); |
---|
5998 | else |
---|
5999 | VMrDefault(Xivinput); |
---|
6000 | |
---|
6001 | testring = currRing; |
---|
6002 | Gt = idrMoveR(G, oRing,currRing); |
---|
6003 | |
---|
6004 | delete Xtau; |
---|
6005 | Xtau = NewVectorlp(Gt); |
---|
6006 | |
---|
6007 | rChangeCurrRing(oRing); |
---|
6008 | G = idrMoveR(Gt, testring,currRing); |
---|
6009 | |
---|
6010 | delete omega2; |
---|
6011 | delete next_vect; |
---|
6012 | delete altomega; |
---|
6013 | /* |
---|
6014 | Print("\n// Leaving the %d-th recursion with %d steps,", nlev,nwalks); |
---|
6015 | Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
6016 | */ |
---|
6017 | if(Overflow_Error == TRUE) |
---|
6018 | nnflow ++; |
---|
6019 | |
---|
6020 | Overflow_Error = FALSE; |
---|
6021 | return(G); |
---|
6022 | } |
---|
6023 | } |
---|
6024 | |
---|
6025 | for(i=nV-1; i>=0; i--) { |
---|
6026 | (*altomega)[i] = (*omega)[i]; |
---|
6027 | (*omega)[i] = (*next_vect)[i]; |
---|
6028 | } |
---|
6029 | delete next_vect; |
---|
6030 | |
---|
6031 | to=clock(); |
---|
6032 | /* Take the initial form of <G> w.r.t. omega */ |
---|
6033 | Gomega = MwalkInitialForm(G, omega); |
---|
6034 | xtif=xtif+clock()-to; |
---|
6035 | |
---|
6036 | #ifndef BUCHBERGER_ALG |
---|
6037 | if(isNolVector(omega) == 0) |
---|
6038 | hilb_func = hFirstSeries(Gomega,NULL,NULL,omega,currRing); |
---|
6039 | else |
---|
6040 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
6041 | #endif // BUCHBERGER_ALG |
---|
6042 | |
---|
6043 | if (rParameter(currRing) != NULL) |
---|
6044 | DefRingPar(omega); |
---|
6045 | else |
---|
6046 | VMrDefault(omega); |
---|
6047 | |
---|
6048 | Gomega1 = idrMoveR(Gomega, oRing,currRing); |
---|
6049 | |
---|
6050 | /* Maximal recursion depth, to compute a red. GB */ |
---|
6051 | /* Fractal walk with the alternative recursion */ |
---|
6052 | /* alternative recursion */ |
---|
6053 | // if(nlev == nV || lengthpoly(Gomega1) == 0) |
---|
6054 | if(nlev == Xnlev || lengthpoly(Gomega1) == 0) |
---|
6055 | //if(nlev == nV) // blind recursion |
---|
6056 | { |
---|
6057 | /* |
---|
6058 | if(Xnlev != nV) |
---|
6059 | { |
---|
6060 | Print("\n// ** Xnlev = %d", Xnlev); |
---|
6061 | ivString(Xtau, "Xtau"); |
---|
6062 | } |
---|
6063 | */ |
---|
6064 | to=clock(); |
---|
6065 | #ifdef BUCHBERGER_ALG |
---|
6066 | Gresult = MstdhomCC(Gomega1); |
---|
6067 | #else |
---|
6068 | Gresult =kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,omega); |
---|
6069 | delete hilb_func; |
---|
6070 | #endif // BUCHBERGER_ALG |
---|
6071 | xtstd=xtstd+clock()-to; |
---|
6072 | } |
---|
6073 | else { |
---|
6074 | rChangeCurrRing(oRing); |
---|
6075 | Gomega1 = idrMoveR(Gomega1, oRing,currRing); |
---|
6076 | Gresult = rec_fractal_call(idCopy(Gomega1),nlev+1,omega); |
---|
6077 | } |
---|
6078 | |
---|
6079 | //convert a Groebner basis from a ring to another ring, |
---|
6080 | new_ring = currRing; |
---|
6081 | |
---|
6082 | rChangeCurrRing(oRing); |
---|
6083 | Gresult1 = idrMoveR(Gresult, new_ring,currRing); |
---|
6084 | Gomega2 = idrMoveR(Gomega1, new_ring,currRing); |
---|
6085 | |
---|
6086 | to=clock(); |
---|
6087 | /* Lifting process */ |
---|
6088 | F = MLifttwoIdeal(Gomega2, Gresult1, G); |
---|
6089 | xtlift=xtlift+clock()-to; |
---|
6090 | idDelete(&Gresult1); |
---|
6091 | idDelete(&Gomega2); |
---|
6092 | idDelete(&G); |
---|
6093 | |
---|
6094 | rChangeCurrRing(new_ring); |
---|
6095 | F1 = idrMoveR(F, oRing,currRing); |
---|
6096 | |
---|
6097 | to=clock(); |
---|
6098 | /* Interreduce G */ |
---|
6099 | G = kInterRedCC(F1, NULL); |
---|
6100 | xtred=xtred+clock()-to; |
---|
6101 | idDelete(&F1); |
---|
6102 | } |
---|
6103 | } |
---|
6104 | |
---|
6105 | |
---|
6106 | |
---|
6107 | /******************************************************************************* |
---|
6108 | * The implementation of the fractal walk algorithm * |
---|
6109 | * * |
---|
6110 | * The main procedur Mfwalk calls the recursive Subroutine * |
---|
6111 | * rec_fractal_call to compute the wanted Grï¿œbner basis. * |
---|
6112 | * At the main procedur we compute the reduced Grï¿œbner basis w.r.t. a "fast" * |
---|
6113 | * order, e.g. "dp" and a sequence of weight vectors which are row vectors * |
---|
6114 | * of a matrix. This matrix defines the given monomial order, e.g. "lp" * |
---|
6115 | *******************************************************************************/ |
---|
6116 | ideal Mfwalk(ideal G, intvec* ivstart, intvec* ivtarget) |
---|
6117 | { |
---|
6118 | Set_Error(FALSE); |
---|
6119 | Overflow_Error = FALSE; |
---|
6120 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
6121 | //Print("\n// ring ro = %s;", rString(currRing)); |
---|
6122 | |
---|
6123 | nnflow = 0; |
---|
6124 | Xngleich = 0; |
---|
6125 | Xcall = 0; |
---|
6126 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
6127 | xftinput = clock(); |
---|
6128 | |
---|
6129 | ring oldRing = currRing; |
---|
6130 | int i, nV = currRing->N; |
---|
6131 | XivNull = new intvec(nV); |
---|
6132 | Xivinput = ivtarget; |
---|
6133 | ngleich = 0; |
---|
6134 | to=clock(); |
---|
6135 | ideal I = MstdCC(G); |
---|
6136 | G = NULL; |
---|
6137 | xftostd=clock()-to; |
---|
6138 | Xsigma = ivstart; |
---|
6139 | |
---|
6140 | Xnlev=nV; |
---|
6141 | |
---|
6142 | #ifdef FIRST_STEP_FRACTAL |
---|
6143 | ideal Gw = MwalkInitialForm(I, ivstart); |
---|
6144 | for(i=IDELEMS(Gw)-1; i>=0; i--) |
---|
6145 | { |
---|
6146 | if((Gw->m[i]!=NULL) // len >=0 |
---|
6147 | && (Gw->m[i]->next!=NULL) // len >=1 |
---|
6148 | && (Gw->m[i]->next->next!=NULL)) // len >=2 |
---|
6149 | { |
---|
6150 | intvec* iv_dp = MivUnit(nV); // define (1,1,...,1) |
---|
6151 | intvec* Mdp; |
---|
6152 | |
---|
6153 | if(MivSame(ivstart, iv_dp) != 1) |
---|
6154 | Mdp = MivWeightOrderdp(ivstart); |
---|
6155 | else |
---|
6156 | Mdp = MivMatrixOrderdp(nV); |
---|
6157 | |
---|
6158 | Xsigma = Mfpertvector(I, Mdp); |
---|
6159 | Overflow_Error = FALSE; |
---|
6160 | |
---|
6161 | delete Mdp; |
---|
6162 | delete iv_dp; |
---|
6163 | break; |
---|
6164 | } |
---|
6165 | } |
---|
6166 | idDelete(&Gw); |
---|
6167 | #endif |
---|
6168 | |
---|
6169 | ideal I1; |
---|
6170 | intvec* Mlp; |
---|
6171 | Xivlp = Mivlp(nV); |
---|
6172 | |
---|
6173 | if(MivComp(ivtarget, Xivlp) != 1) |
---|
6174 | { |
---|
6175 | if (rParameter(currRing) != NULL) |
---|
6176 | DefRingPar(ivtarget); |
---|
6177 | else |
---|
6178 | VMrDefault(ivtarget); |
---|
6179 | |
---|
6180 | I1 = idrMoveR(I, oldRing,currRing); |
---|
6181 | Mlp = MivWeightOrderlp(ivtarget); |
---|
6182 | Xtau = Mfpertvector(I1, Mlp); |
---|
6183 | } |
---|
6184 | else |
---|
6185 | { |
---|
6186 | if (rParameter(currRing) != NULL) |
---|
6187 | DefRingParlp(); |
---|
6188 | else |
---|
6189 | VMrDefaultlp(); |
---|
6190 | |
---|
6191 | I1 = idrMoveR(I, oldRing,currRing); |
---|
6192 | Mlp = MivMatrixOrderlp(nV); |
---|
6193 | Xtau = Mfpertvector(I1, Mlp); |
---|
6194 | } |
---|
6195 | delete Mlp; |
---|
6196 | Overflow_Error = FALSE; |
---|
6197 | |
---|
6198 | //ivString(Xsigma, "Xsigma"); |
---|
6199 | //ivString(Xtau, "Xtau"); |
---|
6200 | |
---|
6201 | id_Delete(&I, oldRing); |
---|
6202 | ring tRing = currRing; |
---|
6203 | |
---|
6204 | if (rParameter(currRing) != NULL) |
---|
6205 | DefRingPar(ivstart); |
---|
6206 | else |
---|
6207 | VMrDefault(ivstart); |
---|
6208 | |
---|
6209 | I = idrMoveR(I1,tRing,currRing); |
---|
6210 | to=clock(); |
---|
6211 | ideal J = MstdCC(I); |
---|
6212 | idDelete(&I); |
---|
6213 | xftostd=xftostd+clock()-to; |
---|
6214 | |
---|
6215 | ideal resF; |
---|
6216 | ring helpRing = currRing; |
---|
6217 | |
---|
6218 | J = rec_fractal_call(J, 1, ivtarget); |
---|
6219 | |
---|
6220 | rChangeCurrRing(oldRing); |
---|
6221 | resF = idrMoveR(J, helpRing,currRing); |
---|
6222 | idSkipZeroes(resF); |
---|
6223 | |
---|
6224 | delete Xivlp; |
---|
6225 | delete Xsigma; |
---|
6226 | delete Xtau; |
---|
6227 | delete XivNull; |
---|
6228 | |
---|
6229 | #ifdef TIME_TEST |
---|
6230 | TimeStringFractal(xftinput, xftostd, xtif, xtstd, xtextra, |
---|
6231 | xtlift, xtred, xtnw); |
---|
6232 | |
---|
6233 | |
---|
6234 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
6235 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
6236 | Print("\n// the numbers of Overflow_Error (%d)", nnflow); |
---|
6237 | #endif |
---|
6238 | |
---|
6239 | return(resF); |
---|
6240 | } |
---|
6241 | |
---|
6242 | ideal Mfrwalk(ideal G, intvec* ivstart, intvec* ivtarget,int weight_rad) |
---|
6243 | { |
---|
6244 | Set_Error(FALSE); |
---|
6245 | Overflow_Error = FALSE; |
---|
6246 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
6247 | //Print("\n// ring ro = %s;", rString(currRing)); |
---|
6248 | |
---|
6249 | nnflow = 0; |
---|
6250 | Xngleich = 0; |
---|
6251 | Xcall = 0; |
---|
6252 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
6253 | xftinput = clock(); |
---|
6254 | |
---|
6255 | ring oldRing = currRing; |
---|
6256 | int i, nV = currRing->N; |
---|
6257 | XivNull = new intvec(nV); |
---|
6258 | Xivinput = ivtarget; |
---|
6259 | ngleich = 0; |
---|
6260 | to=clock(); |
---|
6261 | ideal I = MstdCC(G); |
---|
6262 | G = NULL; |
---|
6263 | xftostd=clock()-to; |
---|
6264 | Xsigma = ivstart; |
---|
6265 | |
---|
6266 | Xnlev=nV; |
---|
6267 | |
---|
6268 | #ifdef FIRST_STEP_FRACTAL |
---|
6269 | ideal Gw = MwalkInitialForm(I, ivstart); |
---|
6270 | for(i=IDELEMS(Gw)-1; i>=0; i--) |
---|
6271 | { |
---|
6272 | if((Gw->m[i]!=NULL) // len >=0 |
---|
6273 | && (Gw->m[i]->next!=NULL) // len >=1 |
---|
6274 | && (Gw->m[i]->next->next!=NULL)) // len >=2 |
---|
6275 | { |
---|
6276 | intvec* iv_dp = MivUnit(nV); // define (1,1,...,1) |
---|
6277 | intvec* Mdp; |
---|
6278 | |
---|
6279 | if(MivSame(ivstart, iv_dp) != 1) |
---|
6280 | { |
---|
6281 | Mdp = MivWeightOrderdp(ivstart); |
---|
6282 | } |
---|
6283 | else |
---|
6284 | { |
---|
6285 | Mdp = MivMatrixOrderdp(nV); |
---|
6286 | } |
---|
6287 | Xsigma = Mfpertvector(I, Mdp); |
---|
6288 | Overflow_Error = FALSE; |
---|
6289 | |
---|
6290 | delete Mdp; |
---|
6291 | delete iv_dp; |
---|
6292 | break; |
---|
6293 | } |
---|
6294 | } |
---|
6295 | idDelete(&Gw); |
---|
6296 | #endif |
---|
6297 | |
---|
6298 | ideal I1; |
---|
6299 | intvec* Mlp; |
---|
6300 | Xivlp = Mivlp(nV); |
---|
6301 | |
---|
6302 | if(MivComp(ivtarget, Xivlp) != 1) |
---|
6303 | { |
---|
6304 | if (rParameter(currRing) != NULL) |
---|
6305 | DefRingPar(ivtarget); |
---|
6306 | else |
---|
6307 | VMrDefault(ivtarget); |
---|
6308 | |
---|
6309 | I1 = idrMoveR(I, oldRing,currRing); |
---|
6310 | Mlp = MivWeightOrderlp(ivtarget); |
---|
6311 | Xtau = Mfpertvector(I1, Mlp); |
---|
6312 | } |
---|
6313 | else |
---|
6314 | { |
---|
6315 | if (rParameter(currRing) != NULL) |
---|
6316 | DefRingParlp(); |
---|
6317 | else |
---|
6318 | VMrDefaultlp(); |
---|
6319 | |
---|
6320 | I1 = idrMoveR(I, oldRing,currRing); |
---|
6321 | Mlp = MivMatrixOrderlp(nV); |
---|
6322 | Xtau = Mfpertvector(I1, Mlp); |
---|
6323 | } |
---|
6324 | delete Mlp; |
---|
6325 | Overflow_Error = FALSE; |
---|
6326 | |
---|
6327 | //ivString(Xsigma, "Xsigma"); |
---|
6328 | //ivString(Xtau, "Xtau"); |
---|
6329 | |
---|
6330 | id_Delete(&I, oldRing); |
---|
6331 | ring tRing = currRing; |
---|
6332 | |
---|
6333 | if (rParameter(currRing) != NULL) |
---|
6334 | DefRingPar(ivstart); |
---|
6335 | else |
---|
6336 | VMrDefault(ivstart); |
---|
6337 | |
---|
6338 | I = idrMoveR(I1,tRing,currRing); |
---|
6339 | to=clock(); |
---|
6340 | ideal J = MstdCC(I); |
---|
6341 | idDelete(&I); |
---|
6342 | xftostd=xftostd+clock()-to; |
---|
6343 | |
---|
6344 | ideal resF; |
---|
6345 | ring helpRing = currRing; |
---|
6346 | J = rec_r_fractal_call(J,1,ivtarget,weight_rad); |
---|
6347 | rChangeCurrRing(oldRing); |
---|
6348 | resF = idrMoveR(J, helpRing,currRing); |
---|
6349 | idSkipZeroes(resF); |
---|
6350 | |
---|
6351 | delete Xivlp; |
---|
6352 | delete Xsigma; |
---|
6353 | delete Xtau; |
---|
6354 | delete XivNull; |
---|
6355 | |
---|
6356 | #ifdef TIME_TEST |
---|
6357 | TimeStringFractal(xftinput, xftostd, xtif, xtstd, xtextra, |
---|
6358 | xtlift, xtred, xtnw); |
---|
6359 | |
---|
6360 | |
---|
6361 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
6362 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
6363 | Print("\n// the numbers of Overflow_Error (%d)", nnflow); |
---|
6364 | #endif |
---|
6365 | |
---|
6366 | return(resF); |
---|
6367 | } |
---|
6368 | |
---|
6369 | /******************************************************* |
---|
6370 | * Tran's algorithm * |
---|
6371 | * * |
---|
6372 | * use kStd, if nP = 0, else call Ab_Rec_Pert (LastGB) * |
---|
6373 | *******************************************************/ |
---|
6374 | ideal TranMImprovwalk(ideal G,intvec* curr_weight,intvec* target_tmp, int nP) |
---|
6375 | { |
---|
6376 | #ifdef TIME_TEST |
---|
6377 | clock_t mtim = clock(); |
---|
6378 | #endif |
---|
6379 | Set_Error(FALSE ); |
---|
6380 | Overflow_Error = FALSE; |
---|
6381 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
6382 | //Print("\n// ring ro = %s;", rString(currRing)); |
---|
6383 | |
---|
6384 | clock_t tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0, textra=0; |
---|
6385 | #ifdef TIME_TEST |
---|
6386 | clock_t tinput = clock(); |
---|
6387 | #endif |
---|
6388 | int nsteppert=0, i, nV = currRing->N, nwalk=0, npert_tmp=0; |
---|
6389 | int *npert=(int*)omAlloc(2*nV*sizeof(int)); |
---|
6390 | ideal Gomega, M,F, G1, Gomega1, Gomega2, M1, F1; |
---|
6391 | //ring endRing; |
---|
6392 | ring newRing, oldRing, lpRing; |
---|
6393 | intvec* next_weight; |
---|
6394 | intvec* ivNull = new intvec(nV); //define (0,...,0) |
---|
6395 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
6396 | intvec* iv_lp = Mivlp(nV); //define (1,0,...,0) |
---|
6397 | ideal H0; |
---|
6398 | //ideal H1; |
---|
6399 | ideal H2, Glp; |
---|
6400 | int nGB, endwalks = 0, nwalkpert=0, npertstep=0; |
---|
6401 | intvec* Mlp = MivMatrixOrderlp(nV); |
---|
6402 | intvec* vector_tmp = new intvec(nV); |
---|
6403 | #ifndef BUCHBERGER_ALG |
---|
6404 | intvec* hilb_func; |
---|
6405 | #endif |
---|
6406 | /* to avoid (1,0,...,0) as the target vector */ |
---|
6407 | intvec* last_omega = new intvec(nV); |
---|
6408 | for(i=nV-1; i>0; i--) |
---|
6409 | (*last_omega)[i] = 1; |
---|
6410 | (*last_omega)[0] = 10000; |
---|
6411 | |
---|
6412 | // intvec* extra_curr_weight = new intvec(nV); |
---|
6413 | intvec* target_weight = new intvec(nV); |
---|
6414 | for(i=nV-1; i>=0; i--) |
---|
6415 | (*target_weight)[i] = (*target_tmp)[i]; |
---|
6416 | |
---|
6417 | ring XXRing = currRing; |
---|
6418 | newRing = currRing; |
---|
6419 | |
---|
6420 | to=clock(); |
---|
6421 | /* compute a red. GB w.r.t. the help ring */ |
---|
6422 | if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) = "dp" |
---|
6423 | G = MstdCC(G); |
---|
6424 | else |
---|
6425 | { |
---|
6426 | //rOrdStr(currRing) = (a(.c_w..),lp,C) |
---|
6427 | if (rParameter(currRing) != NULL) |
---|
6428 | DefRingPar(curr_weight); |
---|
6429 | else |
---|
6430 | VMrDefault(curr_weight); |
---|
6431 | G = idrMoveR(G, XXRing,currRing); |
---|
6432 | G = MstdCC(G); |
---|
6433 | } |
---|
6434 | tostd=clock()-to; |
---|
6435 | |
---|
6436 | #ifdef REPRESENTATION_OF_SIGMA |
---|
6437 | ideal Gw = MwalkInitialForm(G, curr_weight); |
---|
6438 | |
---|
6439 | if(islengthpoly2(Gw)==1) |
---|
6440 | { |
---|
6441 | intvec* MDp; |
---|
6442 | if(MivComp(curr_weight, iv_dp) == 1) |
---|
6443 | MDp = MatrixOrderdp(nV); //MivWeightOrderlp(iv_dp); |
---|
6444 | else |
---|
6445 | MDp = MivWeightOrderlp(curr_weight); |
---|
6446 | |
---|
6447 | curr_weight = RepresentationMatrix_Dp(G, MDp); |
---|
6448 | |
---|
6449 | delete MDp; |
---|
6450 | |
---|
6451 | ring exring = currRing; |
---|
6452 | |
---|
6453 | if (rParameter(currRing) != NULL) |
---|
6454 | DefRingPar(curr_weight); |
---|
6455 | else |
---|
6456 | VMrDefault(curr_weight); |
---|
6457 | to=clock(); |
---|
6458 | Gw = idrMoveR(G, exring,currRing); |
---|
6459 | G = MstdCC(Gw); |
---|
6460 | Gw = NULL; |
---|
6461 | tostd=tostd+clock()-to; |
---|
6462 | //ivString(curr_weight,"rep. sigma"); |
---|
6463 | goto COMPUTE_NEW_VECTOR; |
---|
6464 | } |
---|
6465 | |
---|
6466 | idDelete(&Gw); |
---|
6467 | delete iv_dp; |
---|
6468 | #endif |
---|
6469 | |
---|
6470 | |
---|
6471 | while(1) |
---|
6472 | { |
---|
6473 | to=clock(); |
---|
6474 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
6475 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
6476 | tif=tif+clock()-to; |
---|
6477 | |
---|
6478 | #ifndef BUCHBERGER_ALG |
---|
6479 | if(isNolVector(curr_weight) == 0) |
---|
6480 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
6481 | else |
---|
6482 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
6483 | #endif // BUCHBERGER_ALG |
---|
6484 | |
---|
6485 | oldRing = currRing; |
---|
6486 | |
---|
6487 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
6488 | if (rParameter(currRing) != NULL) |
---|
6489 | DefRingPar(curr_weight); |
---|
6490 | else |
---|
6491 | VMrDefault(curr_weight); |
---|
6492 | |
---|
6493 | newRing = currRing; |
---|
6494 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
6495 | |
---|
6496 | to=clock(); |
---|
6497 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
6498 | #ifdef BUCHBERGER_ALG |
---|
6499 | M = MstdhomCC(Gomega1); |
---|
6500 | #else |
---|
6501 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
6502 | delete hilb_func; |
---|
6503 | #endif // BUCHBERGER_ALG |
---|
6504 | tstd=tstd+clock()-to; |
---|
6505 | |
---|
6506 | /* change the ring to oldRing */ |
---|
6507 | rChangeCurrRing(oldRing); |
---|
6508 | M1 = idrMoveR(M, newRing,currRing); |
---|
6509 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
6510 | |
---|
6511 | to=clock(); |
---|
6512 | /* compute a representation of the generators of submod (M) |
---|
6513 | with respect to those of mod (Gomega). |
---|
6514 | Gomega is a reduced Groebner basis w.r.t. the current ring */ |
---|
6515 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
6516 | tlift=tlift+clock()-to; |
---|
6517 | |
---|
6518 | idDelete(&M1); |
---|
6519 | idDelete(&Gomega2); |
---|
6520 | idDelete(&G); |
---|
6521 | |
---|
6522 | /* change the ring to newRing */ |
---|
6523 | rChangeCurrRing(newRing); |
---|
6524 | F1 = idrMoveR(F, oldRing,currRing); |
---|
6525 | |
---|
6526 | to=clock(); |
---|
6527 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
6528 | G = kInterRedCC(F1, NULL); |
---|
6529 | tred=tred+clock()-to; |
---|
6530 | idDelete(&F1); |
---|
6531 | |
---|
6532 | |
---|
6533 | COMPUTE_NEW_VECTOR: |
---|
6534 | newRing = currRing; |
---|
6535 | nwalk++; |
---|
6536 | nwalkpert++; |
---|
6537 | to=clock(); |
---|
6538 | // compute a next weight vector |
---|
6539 | next_weight = MwalkNextWeightCC(curr_weight,target_weight, G); |
---|
6540 | tnw=tnw+clock()-to; |
---|
6541 | #ifdef PRINT_VECTORS |
---|
6542 | MivString(curr_weight, target_weight, next_weight); |
---|
6543 | #endif |
---|
6544 | |
---|
6545 | |
---|
6546 | /* check whether the computed intermediate weight vector is in |
---|
6547 | the correct cone; sometimes it is very big e.g. s7, cyc7. |
---|
6548 | If it is NOT in the correct cone, then compute directly |
---|
6549 | a reduced Groebner basis with respect to the lexicographic ordering |
---|
6550 | for the known Groebner basis that it is computed in the last step. |
---|
6551 | */ |
---|
6552 | //if(test_w_in_ConeCC(G, next_weight) != 1) |
---|
6553 | if(Overflow_Error == TRUE) |
---|
6554 | { |
---|
6555 | OMEGA_OVERFLOW_TRAN_NEW: |
---|
6556 | //Print("\n// takes %d steps!", nwalk-1); |
---|
6557 | //Print("\n//ring lastRing = %s;", rString(currRing)); |
---|
6558 | #ifdef TEST_OVERFLOW |
---|
6559 | goto BE_FINISH; |
---|
6560 | #endif |
---|
6561 | |
---|
6562 | #ifdef CHECK_IDEAL_MWALK |
---|
6563 | idElements(G, "G"); |
---|
6564 | //headidString(G, "G"); |
---|
6565 | #endif |
---|
6566 | |
---|
6567 | if(MivSame(target_tmp, iv_lp) == 1) |
---|
6568 | if (rParameter(currRing) != NULL) |
---|
6569 | DefRingParlp(); |
---|
6570 | else |
---|
6571 | VMrDefaultlp(); |
---|
6572 | else |
---|
6573 | if (rParameter(currRing) != NULL) |
---|
6574 | DefRingPar(target_tmp); |
---|
6575 | else |
---|
6576 | VMrDefault(target_tmp); |
---|
6577 | |
---|
6578 | lpRing = currRing; |
---|
6579 | G1 = idrMoveR(G, newRing,currRing); |
---|
6580 | |
---|
6581 | to=clock(); |
---|
6582 | /*apply kStd or LastGB to compute a lex. red. Groebner basis of <G>*/ |
---|
6583 | if(nP == 0 || MivSame(target_tmp, iv_lp) == 0){ |
---|
6584 | //Print("\n\n// calls \"std in ring r_%d = %s;", nwalk, rString(currRing)); |
---|
6585 | G = MstdCC(G1);//no result for qnt1 |
---|
6586 | } |
---|
6587 | else { |
---|
6588 | rChangeCurrRing(newRing); |
---|
6589 | G1 = idrMoveR(G1, lpRing,currRing); |
---|
6590 | |
---|
6591 | //Print("\n\n// calls \"LastGB\" (%d) to compute a GB", nV-1); |
---|
6592 | G = LastGB(G1, curr_weight, nV-1); //no result for kats7 |
---|
6593 | |
---|
6594 | rChangeCurrRing(lpRing); |
---|
6595 | G = idrMoveR(G, newRing,currRing); |
---|
6596 | } |
---|
6597 | textra=clock()-to; |
---|
6598 | npert[endwalks]=nwalk-npert_tmp; |
---|
6599 | npert_tmp = nwalk; |
---|
6600 | endwalks ++; |
---|
6601 | break; |
---|
6602 | } |
---|
6603 | |
---|
6604 | /* check whether the computed Groebner basis is really a Groebner basis. |
---|
6605 | If not, we perturb the target vector with the maximal "perturbation" |
---|
6606 | degree.*/ |
---|
6607 | if(MivComp(next_weight, target_weight) == 1 || |
---|
6608 | MivComp(next_weight, curr_weight) == 1 ) |
---|
6609 | { |
---|
6610 | //Print("\n//ring r_%d = %s;", nwalk, rString(currRing)); |
---|
6611 | |
---|
6612 | |
---|
6613 | //compute the number of perturbations and its step |
---|
6614 | npert[endwalks]=nwalk-npert_tmp; |
---|
6615 | npert_tmp = nwalk; |
---|
6616 | |
---|
6617 | endwalks ++; |
---|
6618 | |
---|
6619 | /*it is very important if the walk only uses one step, e.g. Fate, liu*/ |
---|
6620 | if(endwalks == 1 && MivComp(next_weight, curr_weight) == 1){ |
---|
6621 | rChangeCurrRing(XXRing); |
---|
6622 | G = idrMoveR(G, newRing,currRing); |
---|
6623 | goto FINISH; |
---|
6624 | } |
---|
6625 | H0 = id_Head(G,currRing); |
---|
6626 | |
---|
6627 | if(MivSame(target_tmp, iv_lp) == 1) |
---|
6628 | if (rParameter(currRing) != NULL) |
---|
6629 | DefRingParlp(); |
---|
6630 | else |
---|
6631 | VMrDefaultlp(); |
---|
6632 | else |
---|
6633 | if (rParameter(currRing) != NULL) |
---|
6634 | DefRingPar(target_tmp); |
---|
6635 | else |
---|
6636 | VMrDefault(target_tmp); |
---|
6637 | |
---|
6638 | lpRing = currRing; |
---|
6639 | Glp = idrMoveR(G, newRing,currRing); |
---|
6640 | H2 = idrMoveR(H0, newRing,currRing); |
---|
6641 | |
---|
6642 | /* Apply Lemma 2.2 in Collart et. al (1997) to check whether |
---|
6643 | cone(k-1) is equal to cone(k) */ |
---|
6644 | nGB = 1; |
---|
6645 | for(i=IDELEMS(Glp)-1; i>=0; i--) |
---|
6646 | { |
---|
6647 | poly t; |
---|
6648 | if((t=pSub(pHead(Glp->m[i]), pCopy(H2->m[i]))) != NULL) |
---|
6649 | { |
---|
6650 | pDelete(&t); |
---|
6651 | idDelete(&H2);//5.5.02 |
---|
6652 | nGB = 0; //i.e. Glp is no reduced Groebner basis |
---|
6653 | break; |
---|
6654 | } |
---|
6655 | pDelete(&t); |
---|
6656 | } |
---|
6657 | |
---|
6658 | idDelete(&H2);//5.5.02 |
---|
6659 | |
---|
6660 | if(nGB == 1) |
---|
6661 | { |
---|
6662 | G = Glp; |
---|
6663 | Glp = NULL; |
---|
6664 | break; |
---|
6665 | } |
---|
6666 | |
---|
6667 | /* perturb the target weight vector, if the vector target_tmp |
---|
6668 | stays in many cones */ |
---|
6669 | poly p; |
---|
6670 | BOOLEAN plength3 = FALSE; |
---|
6671 | for(i=IDELEMS(Glp)-1; i>=0; i--) |
---|
6672 | { |
---|
6673 | p = MpolyInitialForm(Glp->m[i], target_tmp); |
---|
6674 | if(p->next != NULL && |
---|
6675 | p->next->next != NULL && |
---|
6676 | p->next->next->next != NULL) |
---|
6677 | { |
---|
6678 | Overflow_Error = FALSE; |
---|
6679 | |
---|
6680 | for(i=0; i<nV; i++) |
---|
6681 | (*vector_tmp)[i] = (*target_weight)[i]; |
---|
6682 | |
---|
6683 | delete target_weight; |
---|
6684 | target_weight = MPertVectors(Glp, Mlp, nV); |
---|
6685 | |
---|
6686 | if(MivComp(vector_tmp, target_weight)==1) |
---|
6687 | { |
---|
6688 | //PrintS("\n// The old and new representaion vector are the same!!"); |
---|
6689 | G = Glp; |
---|
6690 | newRing = currRing; |
---|
6691 | goto OMEGA_OVERFLOW_TRAN_NEW; |
---|
6692 | } |
---|
6693 | |
---|
6694 | if(Overflow_Error == TRUE) |
---|
6695 | { |
---|
6696 | rChangeCurrRing(newRing); |
---|
6697 | G = idrMoveR(Glp, lpRing,currRing); |
---|
6698 | goto OMEGA_OVERFLOW_TRAN_NEW; |
---|
6699 | } |
---|
6700 | |
---|
6701 | plength3 = TRUE; |
---|
6702 | pDelete(&p); |
---|
6703 | break; |
---|
6704 | } |
---|
6705 | pDelete(&p); |
---|
6706 | } |
---|
6707 | |
---|
6708 | if(plength3 == FALSE) |
---|
6709 | { |
---|
6710 | rChangeCurrRing(newRing); |
---|
6711 | G = idrMoveR(Glp, lpRing,currRing); |
---|
6712 | goto TRAN_LIFTING; |
---|
6713 | } |
---|
6714 | |
---|
6715 | |
---|
6716 | npertstep = nwalk; |
---|
6717 | nwalkpert = 1; |
---|
6718 | nsteppert ++; |
---|
6719 | |
---|
6720 | /* |
---|
6721 | Print("\n// Subroutine needs (%d) steps.", nwalk); |
---|
6722 | idElements(Glp, "last G in walk:"); |
---|
6723 | PrintS("\n// ****************************************"); |
---|
6724 | Print("\n// Perturb the original target vector (%d): ", nsteppert); |
---|
6725 | ivString(target_weight, "new target"); |
---|
6726 | PrintS("\n// ****************************************\n"); |
---|
6727 | */ |
---|
6728 | rChangeCurrRing(newRing); |
---|
6729 | G = idrMoveR(Glp, lpRing,currRing); |
---|
6730 | |
---|
6731 | delete next_weight; |
---|
6732 | |
---|
6733 | //Print("\n// ring rNEW = %s;", rString(currRing)); |
---|
6734 | goto COMPUTE_NEW_VECTOR; |
---|
6735 | } |
---|
6736 | |
---|
6737 | TRAN_LIFTING: |
---|
6738 | for(i=nV-1; i>=0; i--) |
---|
6739 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
6740 | |
---|
6741 | delete next_weight; |
---|
6742 | }//while |
---|
6743 | #ifdef TEST_OVERFLOW |
---|
6744 | BE_FINISH: |
---|
6745 | #endif |
---|
6746 | rChangeCurrRing(XXRing); |
---|
6747 | G = idrMoveR(G, lpRing,currRing); |
---|
6748 | |
---|
6749 | FINISH: |
---|
6750 | delete ivNull; |
---|
6751 | delete next_weight; |
---|
6752 | delete iv_lp; |
---|
6753 | omFree(npert); |
---|
6754 | |
---|
6755 | #ifdef TIME_TEST |
---|
6756 | Print("\n// Computation took %d steps and %.2f sec", |
---|
6757 | nwalk, ((double) (clock()-mtim)/1000000)); |
---|
6758 | |
---|
6759 | TimeStringFractal(tinput, tostd, tif, tstd, textra, tlift, tred, tnw); |
---|
6760 | |
---|
6761 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
6762 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
6763 | #endif |
---|
6764 | |
---|
6765 | return(G); |
---|
6766 | } |
---|
6767 | |
---|
6768 | /******************************************************* |
---|
6769 | * Tran's algorithm with random element * |
---|
6770 | * * |
---|
6771 | * use kStd, if nP = 0, else call Ab_Rec_Pert (LastGB) * |
---|
6772 | *******************************************************/ |
---|
6773 | ideal TranMrImprovwalk(ideal G,intvec* curr_weight,intvec* target_tmp, int nP, int weight_rad, int pert_deg) |
---|
6774 | { |
---|
6775 | #ifdef TIME_TEST |
---|
6776 | clock_t mtim = clock(); |
---|
6777 | #endif |
---|
6778 | Set_Error(FALSE ); |
---|
6779 | Overflow_Error = FALSE; |
---|
6780 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
6781 | //Print("\n// ring ro = %s;", rString(currRing)); |
---|
6782 | |
---|
6783 | clock_t tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0, textra=0; |
---|
6784 | #ifdef TIME_TEST |
---|
6785 | clock_t tinput = clock(); |
---|
6786 | #endif |
---|
6787 | int nsteppert=0, i, nV = currRing->N, nwalk=0, npert_tmp=0; |
---|
6788 | int *npert=(int*)omAlloc(2*nV*sizeof(int)); |
---|
6789 | ideal Gomega, M,F, G1, Gomega1, Gomega2, M1, F1; |
---|
6790 | //ring endRing; |
---|
6791 | ring newRing, oldRing, lpRing; |
---|
6792 | intvec* next_weight; |
---|
6793 | intvec* ivNull = new intvec(nV); //define (0,...,0) |
---|
6794 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
6795 | intvec* iv_lp = Mivlp(nV); //define (1,0,...,0) |
---|
6796 | ideal H0; |
---|
6797 | //ideal H1; |
---|
6798 | ideal H2, Glp; |
---|
6799 | int weight_norm, nGB, endwalks = 0, nwalkpert=0, npertstep=0; |
---|
6800 | intvec* Mlp = MivMatrixOrderlp(nV); |
---|
6801 | intvec* vector_tmp = new intvec(nV); |
---|
6802 | #ifndef BUCHBERGER_ALG |
---|
6803 | intvec* hilb_func; |
---|
6804 | #endif |
---|
6805 | // to avoid (1,0,...,0) as the target vector |
---|
6806 | intvec* last_omega = new intvec(nV); |
---|
6807 | for(i=nV-1; i>0; i--) |
---|
6808 | { |
---|
6809 | (*last_omega)[i] = 1; |
---|
6810 | } |
---|
6811 | (*last_omega)[0] = 10000; |
---|
6812 | |
---|
6813 | //intvec* extra_curr_weight = new intvec(nV); |
---|
6814 | intvec* target_weight = new intvec(nV); |
---|
6815 | for(i=nV-1; i>=0; i--) |
---|
6816 | { |
---|
6817 | (*target_weight)[i] = (*target_tmp)[i]; |
---|
6818 | } |
---|
6819 | ring XXRing = currRing; |
---|
6820 | newRing = currRing; |
---|
6821 | |
---|
6822 | to=clock(); |
---|
6823 | // compute a red. GB w.r.t. the help ring |
---|
6824 | if(MivComp(curr_weight, iv_dp) == 1) |
---|
6825 | { |
---|
6826 | //rOrdStr(currRing) = "dp" |
---|
6827 | G = MstdCC(G); |
---|
6828 | } |
---|
6829 | else |
---|
6830 | { |
---|
6831 | //rOrdStr(currRing) = (a(.c_w..),lp,C) |
---|
6832 | if (rParameter(currRing) != NULL) |
---|
6833 | { |
---|
6834 | DefRingPar(curr_weight); |
---|
6835 | } |
---|
6836 | else |
---|
6837 | { |
---|
6838 | VMrDefault(curr_weight); |
---|
6839 | } |
---|
6840 | G = idrMoveR(G, XXRing,currRing); |
---|
6841 | G = MstdCC(G); |
---|
6842 | } |
---|
6843 | tostd=clock()-to; |
---|
6844 | |
---|
6845 | #ifdef REPRESENTATION_OF_SIGMA |
---|
6846 | ideal Gw = MwalkInitialForm(G, curr_weight); |
---|
6847 | |
---|
6848 | if(islengthpoly2(Gw)==1) |
---|
6849 | { |
---|
6850 | intvec* MDp; |
---|
6851 | if(MivComp(curr_weight, iv_dp) == 1) |
---|
6852 | { |
---|
6853 | MDp = MatrixOrderdp(nV); //MivWeightOrderlp(iv_dp); |
---|
6854 | } |
---|
6855 | else |
---|
6856 | { |
---|
6857 | MDp = MivWeightOrderlp(curr_weight); |
---|
6858 | } |
---|
6859 | curr_weight = RepresentationMatrix_Dp(G, MDp); |
---|
6860 | |
---|
6861 | delete MDp; |
---|
6862 | |
---|
6863 | ring exring = currRing; |
---|
6864 | |
---|
6865 | if (rParameter(currRing) != NULL) |
---|
6866 | { |
---|
6867 | DefRingPar(curr_weight); |
---|
6868 | } |
---|
6869 | else |
---|
6870 | { |
---|
6871 | VMrDefault(curr_weight); |
---|
6872 | } |
---|
6873 | to=clock(); |
---|
6874 | Gw = idrMoveR(G, exring,currRing); |
---|
6875 | G = MstdCC(Gw); |
---|
6876 | Gw = NULL; |
---|
6877 | tostd=tostd+clock()-to; |
---|
6878 | //ivString(curr_weight,"rep. sigma"); |
---|
6879 | goto COMPUTE_NEW_VECTOR; |
---|
6880 | } |
---|
6881 | |
---|
6882 | idDelete(&Gw); |
---|
6883 | delete iv_dp; |
---|
6884 | #endif |
---|
6885 | |
---|
6886 | |
---|
6887 | while(1) |
---|
6888 | { |
---|
6889 | to=clock(); |
---|
6890 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
6891 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
6892 | tif=tif+clock()-to; |
---|
6893 | |
---|
6894 | #ifndef BUCHBERGER_ALG |
---|
6895 | if(isNolVector(curr_weight) == 0) |
---|
6896 | { |
---|
6897 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
6898 | } |
---|
6899 | else |
---|
6900 | { |
---|
6901 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
6902 | } |
---|
6903 | #endif // BUCHBERGER_ALG |
---|
6904 | |
---|
6905 | oldRing = currRing; |
---|
6906 | |
---|
6907 | // define a new ring with ordering "(a(curr_weight),lp) |
---|
6908 | if (rParameter(currRing) != NULL) |
---|
6909 | { |
---|
6910 | DefRingPar(curr_weight); |
---|
6911 | } |
---|
6912 | else |
---|
6913 | { |
---|
6914 | VMrDefault(curr_weight); |
---|
6915 | } |
---|
6916 | newRing = currRing; |
---|
6917 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
6918 | |
---|
6919 | to=clock(); |
---|
6920 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
6921 | #ifdef BUCHBERGER_ALG |
---|
6922 | M = MstdhomCC(Gomega1); |
---|
6923 | #else |
---|
6924 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
6925 | delete hilb_func; |
---|
6926 | #endif |
---|
6927 | tstd=tstd+clock()-to; |
---|
6928 | |
---|
6929 | // change the ring to oldRing |
---|
6930 | rChangeCurrRing(oldRing); |
---|
6931 | M1 = idrMoveR(M, newRing,currRing); |
---|
6932 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
6933 | |
---|
6934 | to=clock(); |
---|
6935 | // compute a representation of the generators of submod (M) with respect to those of mod (Gomega). |
---|
6936 | // Gomega is a reduced Groebner basis w.r.t. the current ring |
---|
6937 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
6938 | tlift=tlift+clock()-to; |
---|
6939 | |
---|
6940 | idDelete(&M1); |
---|
6941 | idDelete(&Gomega2); |
---|
6942 | idDelete(&G); |
---|
6943 | |
---|
6944 | // change the ring to newRing |
---|
6945 | rChangeCurrRing(newRing); |
---|
6946 | F1 = idrMoveR(F, oldRing,currRing); |
---|
6947 | |
---|
6948 | to=clock(); |
---|
6949 | // reduce the Groebner basis <G> w.r.t. new ring |
---|
6950 | G = kInterRedCC(F1, NULL); |
---|
6951 | tred=tred+clock()-to; |
---|
6952 | idDelete(&F1); |
---|
6953 | |
---|
6954 | COMPUTE_NEW_VECTOR: |
---|
6955 | newRing = currRing; |
---|
6956 | nwalk++; |
---|
6957 | nwalkpert++; |
---|
6958 | to=clock(); |
---|
6959 | // compute a next weight vector |
---|
6960 | //next_weight = MwalkNextWeightCC(curr_weight,target_weight, G); |
---|
6961 | next_weight = MWalkRandomNextWeight(G, curr_weight, target_weight, weight_rad, pert_deg); |
---|
6962 | /* |
---|
6963 | next_weight = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
6964 | |
---|
6965 | if(MivComp(next_weight, target_weight) != 1) |
---|
6966 | { |
---|
6967 | // compute a perturbed next weight vector "next_weight1" |
---|
6968 | intvec* next_weight1 = MkInterRedNextWeight(MPertVectors(G, MivMatrixOrder(curr_weight), pert_deg), target_weight, G); |
---|
6969 | |
---|
6970 | // compare next_weight and next_weight1 |
---|
6971 | ideal G_test = MwalkInitialForm(G, next_weight); |
---|
6972 | ideal G_test1 = MwalkInitialForm(G, next_weight1); |
---|
6973 | if(IDELEMS(G_test1) <= IDELEMS(G_test)) |
---|
6974 | { |
---|
6975 | next_weight = ivCopy(next_weight1); |
---|
6976 | } |
---|
6977 | delete next_weight1; |
---|
6978 | // compute a random next weight vector "next_weight2" |
---|
6979 | intvec* next_weight22 = ivCopy(target_weight); |
---|
6980 | // Print("\n// size of target_weight = %d", sizeof((*target_weight))); |
---|
6981 | k = 0; |
---|
6982 | |
---|
6983 | while(test_w_in_ConeCC(G, next_weight22) == 0 && k < 11) |
---|
6984 | { |
---|
6985 | k++; |
---|
6986 | if(k>10) |
---|
6987 | { |
---|
6988 | break; |
---|
6989 | } |
---|
6990 | weight_norm = 0; |
---|
6991 | while(weight_norm == 0) |
---|
6992 | { |
---|
6993 | for(i=nV-1; i>=0; i--) |
---|
6994 | { |
---|
6995 | // Print("\n// next_weight[%d] = %d", i, (*next_weight)[i]); |
---|
6996 | (*next_weight22)[i] = rand() % 60000 - 30000; |
---|
6997 | weight_norm = weight_norm + (*next_weight22)[i]*(*next_weight22)[i]; |
---|
6998 | } |
---|
6999 | weight_norm = 1 + floor(sqrt(weight_norm)); |
---|
7000 | } |
---|
7001 | for(i=nV-1; i>=0; i--) |
---|
7002 | { |
---|
7003 | if((*next_weight22)[i] < 0) |
---|
7004 | { |
---|
7005 | (*next_weight22)[i] = 1 + (*curr_weight)[i] + floor(weight_rad*(*next_weight22)[i]/weight_norm); |
---|
7006 | } |
---|
7007 | else |
---|
7008 | { |
---|
7009 | (*next_weight22)[i] = (*curr_weight)[i] + floor(weight_rad*(*next_weight22)[i]/weight_norm); |
---|
7010 | } |
---|
7011 | // Print("\n// next_weight22[%d] = %d", i, (*next_weight22)[i]); |
---|
7012 | } |
---|
7013 | } |
---|
7014 | |
---|
7015 | if(test_w_in_ConeCC(G, next_weight22) == 1) |
---|
7016 | { |
---|
7017 | // compare next_weight and next_weight2 |
---|
7018 | // Print("\n// ZUFALL IM KEGEL"); |
---|
7019 | intvec* next_weight2 = MkInterRedNextWeight(next_weight22, target_weight, G); |
---|
7020 | |
---|
7021 | ideal G_test2 = MwalkInitialForm(G, next_weight2); |
---|
7022 | if(IDELEMS(G_test2) <= IDELEMS(G_test)) |
---|
7023 | { |
---|
7024 | if(IDELEMS(G_test2) <= IDELEMS(G_test1)) |
---|
7025 | { |
---|
7026 | // Print("\n// ZUFALL BENUTZT!\n"); |
---|
7027 | next_weight = ivCopy(next_weight2); |
---|
7028 | } |
---|
7029 | } |
---|
7030 | idDelete(&G_test2); |
---|
7031 | delete next_weight2; |
---|
7032 | } |
---|
7033 | delete next_weight22; |
---|
7034 | idDelete(&G_test); |
---|
7035 | idDelete(&G_test1); |
---|
7036 | }*/ |
---|
7037 | |
---|
7038 | tnw=tnw+clock()-to; |
---|
7039 | #ifdef PRINT_VECTORS |
---|
7040 | MivString(curr_weight, target_weight, next_weight); |
---|
7041 | #endif |
---|
7042 | |
---|
7043 | /* check whether the computed intermediate weight vector is in |
---|
7044 | the correct cone; sometimes it is very big e.g. s7, cyc7. |
---|
7045 | If it is NOT in the correct cone, then compute directly |
---|
7046 | a reduced Groebner basis with respect to the lexicographic ordering |
---|
7047 | for the known Groebner basis that it is computed in the last step. |
---|
7048 | */ |
---|
7049 | //if(test_w_in_ConeCC(G, next_weight) != 1) |
---|
7050 | if(Overflow_Error == TRUE) |
---|
7051 | { |
---|
7052 | OMEGA_OVERFLOW_TRAN_NEW: |
---|
7053 | //Print("\n// takes %d steps!", nwalk-1); |
---|
7054 | //Print("\n//ring lastRing = %s;", rString(currRing)); |
---|
7055 | #ifdef TEST_OVERFLOW |
---|
7056 | goto BE_FINISH; |
---|
7057 | #endif |
---|
7058 | |
---|
7059 | #ifdef CHECK_IDEAL_MWALK |
---|
7060 | idElements(G, "G"); |
---|
7061 | //headidString(G, "G"); |
---|
7062 | #endif |
---|
7063 | |
---|
7064 | if(MivSame(target_tmp, iv_lp) == 1) |
---|
7065 | { |
---|
7066 | if (rParameter(currRing) != NULL) |
---|
7067 | { |
---|
7068 | DefRingParlp(); |
---|
7069 | } |
---|
7070 | else |
---|
7071 | { |
---|
7072 | VMrDefaultlp(); |
---|
7073 | } |
---|
7074 | } |
---|
7075 | else |
---|
7076 | { |
---|
7077 | if (rParameter(currRing) != NULL) |
---|
7078 | { |
---|
7079 | DefRingPar(target_tmp); |
---|
7080 | } |
---|
7081 | else |
---|
7082 | { |
---|
7083 | VMrDefault(target_tmp); |
---|
7084 | } |
---|
7085 | } |
---|
7086 | lpRing = currRing; |
---|
7087 | G1 = idrMoveR(G, newRing,currRing); |
---|
7088 | |
---|
7089 | to=clock(); |
---|
7090 | // apply kStd or LastGB to compute a lex. red. Groebner basis of <G> |
---|
7091 | if(nP == 0 || MivSame(target_tmp, iv_lp) == 0) |
---|
7092 | { |
---|
7093 | //Print("\n\n// calls \"std in ring r_%d = %s;", nwalk, rString(currRing)); |
---|
7094 | G = MstdCC(G1);//no result for qnt1 |
---|
7095 | } |
---|
7096 | else |
---|
7097 | { |
---|
7098 | rChangeCurrRing(newRing); |
---|
7099 | G1 = idrMoveR(G1, lpRing,currRing); |
---|
7100 | |
---|
7101 | //Print("\n\n// calls \"LastGB\" (%d) to compute a GB", nV-1); |
---|
7102 | G = LastGB(G1, curr_weight, nV-1); //no result for kats7 |
---|
7103 | |
---|
7104 | rChangeCurrRing(lpRing); |
---|
7105 | G = idrMoveR(G, newRing,currRing); |
---|
7106 | } |
---|
7107 | textra=clock()-to; |
---|
7108 | npert[endwalks]=nwalk-npert_tmp; |
---|
7109 | npert_tmp = nwalk; |
---|
7110 | endwalks ++; |
---|
7111 | break; |
---|
7112 | } |
---|
7113 | |
---|
7114 | // check whether the computed Groebner basis is really a Groebner basis. |
---|
7115 | // If not, we perturb the target vector with the maximal "perturbation" degree. |
---|
7116 | |
---|
7117 | if(MivComp(next_weight, target_weight) == 1 || MivComp(next_weight, curr_weight) == 1 ) |
---|
7118 | { |
---|
7119 | //Print("\n//ring r_%d = %s;", nwalk, rString(currRing)); |
---|
7120 | |
---|
7121 | |
---|
7122 | //compute the number of perturbations and its step |
---|
7123 | npert[endwalks]=nwalk-npert_tmp; |
---|
7124 | npert_tmp = nwalk; |
---|
7125 | |
---|
7126 | endwalks ++; |
---|
7127 | |
---|
7128 | // it is very important if the walk only uses one step, e.g. Fate, liu |
---|
7129 | if(endwalks == 1 && MivComp(next_weight, curr_weight) == 1) |
---|
7130 | { |
---|
7131 | rChangeCurrRing(XXRing); |
---|
7132 | G = idrMoveR(G, newRing,currRing); |
---|
7133 | goto FINISH; |
---|
7134 | } |
---|
7135 | H0 = id_Head(G,currRing); |
---|
7136 | |
---|
7137 | if(MivSame(target_tmp, iv_lp) == 1) |
---|
7138 | { |
---|
7139 | if (rParameter(currRing) != NULL) |
---|
7140 | { |
---|
7141 | DefRingParlp(); |
---|
7142 | } |
---|
7143 | else |
---|
7144 | { |
---|
7145 | VMrDefaultlp(); |
---|
7146 | } |
---|
7147 | } |
---|
7148 | else |
---|
7149 | { |
---|
7150 | if (rParameter(currRing) != NULL) |
---|
7151 | { |
---|
7152 | DefRingPar(target_tmp); |
---|
7153 | } |
---|
7154 | else |
---|
7155 | { |
---|
7156 | VMrDefault(target_tmp); |
---|
7157 | } |
---|
7158 | } |
---|
7159 | lpRing = currRing; |
---|
7160 | Glp = idrMoveR(G, newRing,currRing); |
---|
7161 | H2 = idrMoveR(H0, newRing,currRing); |
---|
7162 | |
---|
7163 | // Apply Lemma 2.2 in Collart et. al (1997) to check whether cone(k-1) is equal to cone(k) |
---|
7164 | nGB = 1; |
---|
7165 | for(i=IDELEMS(Glp)-1; i>=0; i--) |
---|
7166 | { |
---|
7167 | poly t; |
---|
7168 | if((t=pSub(pHead(Glp->m[i]), pCopy(H2->m[i]))) != NULL) |
---|
7169 | { |
---|
7170 | pDelete(&t); |
---|
7171 | idDelete(&H2);//5.5.02 |
---|
7172 | nGB = 0; //i.e. Glp is no reduced Groebner basis |
---|
7173 | break; |
---|
7174 | } |
---|
7175 | pDelete(&t); |
---|
7176 | } |
---|
7177 | |
---|
7178 | idDelete(&H2);//5.5.02 |
---|
7179 | |
---|
7180 | if(nGB == 1) |
---|
7181 | { |
---|
7182 | G = Glp; |
---|
7183 | Glp = NULL; |
---|
7184 | break; |
---|
7185 | } |
---|
7186 | |
---|
7187 | // perturb the target weight vector, if the vector target_tmp stays in many cones |
---|
7188 | poly p; |
---|
7189 | BOOLEAN plength3 = FALSE; |
---|
7190 | for(i=IDELEMS(Glp)-1; i>=0; i--) |
---|
7191 | { |
---|
7192 | p = MpolyInitialForm(Glp->m[i], target_tmp); |
---|
7193 | if(p->next != NULL && |
---|
7194 | p->next->next != NULL && |
---|
7195 | p->next->next->next != NULL) |
---|
7196 | { |
---|
7197 | Overflow_Error = FALSE; |
---|
7198 | |
---|
7199 | for(i=0; i<nV; i++) |
---|
7200 | { |
---|
7201 | (*vector_tmp)[i] = (*target_weight)[i]; |
---|
7202 | } |
---|
7203 | delete target_weight; |
---|
7204 | target_weight = MPertVectors(Glp, Mlp, nV); |
---|
7205 | |
---|
7206 | if(MivComp(vector_tmp, target_weight)==1) |
---|
7207 | { |
---|
7208 | //PrintS("\n// The old and new representaion vector are the same!!"); |
---|
7209 | G = Glp; |
---|
7210 | newRing = currRing; |
---|
7211 | goto OMEGA_OVERFLOW_TRAN_NEW; |
---|
7212 | } |
---|
7213 | |
---|
7214 | if(Overflow_Error == TRUE) |
---|
7215 | { |
---|
7216 | rChangeCurrRing(newRing); |
---|
7217 | G = idrMoveR(Glp, lpRing,currRing); |
---|
7218 | goto OMEGA_OVERFLOW_TRAN_NEW; |
---|
7219 | } |
---|
7220 | |
---|
7221 | plength3 = TRUE; |
---|
7222 | pDelete(&p); |
---|
7223 | break; |
---|
7224 | } |
---|
7225 | pDelete(&p); |
---|
7226 | } |
---|
7227 | |
---|
7228 | if(plength3 == FALSE) |
---|
7229 | { |
---|
7230 | rChangeCurrRing(newRing); |
---|
7231 | G = idrMoveR(Glp, lpRing,currRing); |
---|
7232 | goto TRAN_LIFTING; |
---|
7233 | } |
---|
7234 | |
---|
7235 | |
---|
7236 | npertstep = nwalk; |
---|
7237 | nwalkpert = 1; |
---|
7238 | nsteppert ++; |
---|
7239 | |
---|
7240 | /* |
---|
7241 | Print("\n// Subroutine needs (%d) steps.", nwalk); |
---|
7242 | idElements(Glp, "last G in walk:"); |
---|
7243 | PrintS("\n// ****************************************"); |
---|
7244 | Print("\n// Perturb the original target vector (%d): ", nsteppert); |
---|
7245 | ivString(target_weight, "new target"); |
---|
7246 | PrintS("\n// ****************************************\n"); |
---|
7247 | */ |
---|
7248 | rChangeCurrRing(newRing); |
---|
7249 | G = idrMoveR(Glp, lpRing,currRing); |
---|
7250 | |
---|
7251 | delete next_weight; |
---|
7252 | |
---|
7253 | //Print("\n// ring rNEW = %s;", rString(currRing)); |
---|
7254 | goto COMPUTE_NEW_VECTOR; |
---|
7255 | } |
---|
7256 | |
---|
7257 | TRAN_LIFTING: |
---|
7258 | for(i=nV-1; i>=0; i--) |
---|
7259 | { |
---|
7260 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
7261 | } |
---|
7262 | delete next_weight; |
---|
7263 | } // end of while |
---|
7264 | #ifdef TEST_OVERFLOW |
---|
7265 | BE_FINISH: |
---|
7266 | #endif |
---|
7267 | rChangeCurrRing(XXRing); |
---|
7268 | G = idrMoveR(G, lpRing,currRing); |
---|
7269 | |
---|
7270 | FINISH: |
---|
7271 | delete ivNull; |
---|
7272 | delete next_weight; |
---|
7273 | delete iv_lp; |
---|
7274 | omFree(npert); |
---|
7275 | |
---|
7276 | #ifdef TIME_TEST |
---|
7277 | Print("\n// Computation took %d steps and %.2f sec", nwalk, ((double) (clock()-mtim)/1000000)); |
---|
7278 | |
---|
7279 | TimeStringFractal(tinput, tostd, tif, tstd, textra, tlift, tred, tnw); |
---|
7280 | |
---|
7281 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
7282 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
7283 | #endif |
---|
7284 | |
---|
7285 | return(G); |
---|
7286 | } |
---|
7287 | |
---|
7288 | |
---|
7289 | /***************************************************************** |
---|
7290 | * compute the reduced Groebner basis of an ideal <Go> w.r.t. lp * |
---|
7291 | *****************************************************************/ |
---|
7292 | static ideal Mpwalk_MAltwalk1(ideal Go, intvec* curr_weight, int tp_deg) |
---|
7293 | { |
---|
7294 | Overflow_Error = FALSE; |
---|
7295 | // BOOLEAN nOverflow_Error = FALSE; |
---|
7296 | clock_t tproc=0; |
---|
7297 | clock_t tinput=clock(); |
---|
7298 | int i, nV = currRing->N; |
---|
7299 | int nwalk=0, endwalks=0, ntestwinC=1; |
---|
7300 | int tp_deg_tmp = tp_deg; |
---|
7301 | ideal Gomega, M, F, G, M1, F1, Gomega1, Gomega2, G1; |
---|
7302 | ring newRing, oldRing, TargetRing; |
---|
7303 | intvec* next_weight; |
---|
7304 | intvec* ivNull = new intvec(nV); |
---|
7305 | |
---|
7306 | ring YXXRing = currRing; |
---|
7307 | |
---|
7308 | intvec* iv_M_dpp = MivMatrixOrderlp(nV); |
---|
7309 | intvec* target_weight;// = Mivlp(nV); |
---|
7310 | ideal ssG; |
---|
7311 | |
---|
7312 | // perturb the target vector |
---|
7313 | while(1) |
---|
7314 | { |
---|
7315 | if(Overflow_Error == FALSE) |
---|
7316 | { |
---|
7317 | if (rParameter(currRing) != NULL) |
---|
7318 | { |
---|
7319 | DefRingParlp(); |
---|
7320 | } |
---|
7321 | else |
---|
7322 | { |
---|
7323 | VMrDefaultlp(); |
---|
7324 | } |
---|
7325 | TargetRing = currRing; |
---|
7326 | ssG = idrMoveR(Go,YXXRing,currRing); |
---|
7327 | } |
---|
7328 | Overflow_Error = FALSE; |
---|
7329 | if(tp_deg != 1) |
---|
7330 | { |
---|
7331 | target_weight = MPertVectors(ssG, iv_M_dpp, tp_deg); |
---|
7332 | } |
---|
7333 | else |
---|
7334 | { |
---|
7335 | target_weight = Mivlp(nV); |
---|
7336 | break; |
---|
7337 | } |
---|
7338 | if(Overflow_Error == FALSE) |
---|
7339 | { |
---|
7340 | break; |
---|
7341 | } |
---|
7342 | Overflow_Error = TRUE; |
---|
7343 | tp_deg --; |
---|
7344 | } |
---|
7345 | if(tp_deg != tp_deg_tmp) |
---|
7346 | { |
---|
7347 | Overflow_Error = TRUE; |
---|
7348 | //nOverflow_Error = TRUE; |
---|
7349 | } |
---|
7350 | |
---|
7351 | // Print("\n// tp_deg = %d", tp_deg); |
---|
7352 | // ivString(target_weight, "pert target"); |
---|
7353 | |
---|
7354 | delete iv_M_dpp; |
---|
7355 | #ifndef BUCHBERGER_ALG |
---|
7356 | intvec* hilb_func; |
---|
7357 | #endif |
---|
7358 | // to avoid (1,0,...,0) as the target vector |
---|
7359 | intvec* last_omega = new intvec(nV); |
---|
7360 | for(i=nV-1; i>0; i--) |
---|
7361 | { |
---|
7362 | (*last_omega)[i] = 1; |
---|
7363 | } |
---|
7364 | (*last_omega)[0] = 10000; |
---|
7365 | |
---|
7366 | rChangeCurrRing(YXXRing); |
---|
7367 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
7368 | |
---|
7369 | while(1) |
---|
7370 | { |
---|
7371 | nwalk ++; |
---|
7372 | nstep ++; |
---|
7373 | |
---|
7374 | if(nwalk==1) |
---|
7375 | { |
---|
7376 | goto FIRST_STEP; |
---|
7377 | } |
---|
7378 | to=clock(); |
---|
7379 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
7380 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
7381 | xtif=xtif+clock()-to; |
---|
7382 | |
---|
7383 | #ifndef BUCHBERGER_ALG |
---|
7384 | if(isNolVector(curr_weight) == 0) |
---|
7385 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
7386 | else |
---|
7387 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
7388 | #endif |
---|
7389 | |
---|
7390 | oldRing = currRing; |
---|
7391 | |
---|
7392 | // define a new ring that its ordering is "(a(curr_weight),lp) |
---|
7393 | if (rParameter(currRing) != NULL) |
---|
7394 | { |
---|
7395 | DefRingPar(curr_weight); |
---|
7396 | } |
---|
7397 | else |
---|
7398 | { |
---|
7399 | VMrDefault(curr_weight); |
---|
7400 | } |
---|
7401 | newRing = currRing; |
---|
7402 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
7403 | |
---|
7404 | #ifdef ENDWALKS |
---|
7405 | if(endwalks == 1) |
---|
7406 | { |
---|
7407 | Print("\n// it is %d-th step!!", nwalk); |
---|
7408 | idElements(Gomega1, "Gw"); |
---|
7409 | PrintS("\n// compute a rGB of Gw:"); |
---|
7410 | } |
---|
7411 | #endif |
---|
7412 | |
---|
7413 | to=clock(); |
---|
7414 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
7415 | #ifdef BUCHBERGER_ALG |
---|
7416 | M = MstdhomCC(Gomega1); |
---|
7417 | #else |
---|
7418 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
7419 | delete hilb_func; |
---|
7420 | #endif // BUCHBERGER_ALG |
---|
7421 | xtstd=xtstd+clock()-to; |
---|
7422 | |
---|
7423 | // change the ring to oldRing |
---|
7424 | rChangeCurrRing(oldRing); |
---|
7425 | M1 = idrMoveR(M, newRing,currRing); |
---|
7426 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
7427 | to=clock(); |
---|
7428 | |
---|
7429 | // if(endwalks == 1){PrintS("\n// Lifting is still working:");} |
---|
7430 | |
---|
7431 | // compute a reduced Groebner basis of <G> w.r.t. "newRing" by the lifting process |
---|
7432 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
7433 | xtlift=xtlift+clock()-to; |
---|
7434 | |
---|
7435 | idDelete(&M1); |
---|
7436 | idDelete(&Gomega2); |
---|
7437 | idDelete(&G); |
---|
7438 | |
---|
7439 | // change the ring to newRing |
---|
7440 | rChangeCurrRing(newRing); |
---|
7441 | F1 = idrMoveR(F, oldRing,currRing); |
---|
7442 | to=clock(); |
---|
7443 | //if(endwalks == 1){ PrintS("\n// InterRed is still working:");} |
---|
7444 | // reduce the Groebner basis <G> w.r.t. the new ring |
---|
7445 | G = kInterRedCC(F1, NULL); |
---|
7446 | xtred=xtred+clock()-to; |
---|
7447 | idDelete(&F1); |
---|
7448 | |
---|
7449 | if(endwalks == 1) |
---|
7450 | break; |
---|
7451 | |
---|
7452 | FIRST_STEP: |
---|
7453 | Overflow_Error=FALSE; |
---|
7454 | to=clock(); |
---|
7455 | // compute a next weight vector |
---|
7456 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
7457 | xtnw=xtnw+clock()-to; |
---|
7458 | #ifdef PRINT_VECTORS |
---|
7459 | MivString(curr_weight, target_weight, next_weight); |
---|
7460 | #endif |
---|
7461 | |
---|
7462 | if(Overflow_Error == TRUE) |
---|
7463 | { |
---|
7464 | delete next_weight; |
---|
7465 | if(tp_deg > 1){ |
---|
7466 | //nOverflow_Error = Overflow_Error; |
---|
7467 | tproc = tproc+clock()-tinput; |
---|
7468 | //Print("\n// A subroutine takes %d steps and calls \"Mpwalk\" (1,%d):", nwalk, tp_deg-1); |
---|
7469 | G1 = Mpwalk_MAltwalk1(G, curr_weight, tp_deg-1); |
---|
7470 | goto MPW_Finish; |
---|
7471 | } |
---|
7472 | else { |
---|
7473 | newRing = currRing; |
---|
7474 | ntestwinC = 0; |
---|
7475 | break; |
---|
7476 | } |
---|
7477 | } |
---|
7478 | |
---|
7479 | if(MivComp(next_weight, ivNull) == 1) |
---|
7480 | { |
---|
7481 | newRing = currRing; |
---|
7482 | delete next_weight; |
---|
7483 | break; |
---|
7484 | } |
---|
7485 | if(MivComp(next_weight, target_weight) == 1) |
---|
7486 | { |
---|
7487 | endwalks = 1; |
---|
7488 | } |
---|
7489 | for(i=nV-1; i>=0; i--) |
---|
7490 | { |
---|
7491 | //(*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
7492 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
7493 | } |
---|
7494 | delete next_weight; |
---|
7495 | }//while |
---|
7496 | |
---|
7497 | // check whether the pertubed target vector is correct |
---|
7498 | |
---|
7499 | //define and execute ring with lex. order |
---|
7500 | if (rParameter(currRing) != NULL) |
---|
7501 | { |
---|
7502 | DefRingParlp(); |
---|
7503 | } |
---|
7504 | else |
---|
7505 | { |
---|
7506 | VMrDefaultlp(); |
---|
7507 | } |
---|
7508 | G1 = idrMoveR(G, newRing,currRing); |
---|
7509 | |
---|
7510 | if( test_w_in_ConeCC(G1, target_weight) != 1 || ntestwinC == 0) |
---|
7511 | { |
---|
7512 | PrintS("\n// The perturbed target vector doesn't STAY in the correct cone!!"); |
---|
7513 | if(tp_deg == 1) |
---|
7514 | { |
---|
7515 | //Print("\n// subroutine takes %d steps and applys \"std\"", nwalk); |
---|
7516 | to=clock(); |
---|
7517 | ideal G2 = MstdCC(G1); |
---|
7518 | xtextra=xtextra+clock()-to; |
---|
7519 | idDelete(&G1); |
---|
7520 | G1 = G2; |
---|
7521 | G2 = NULL; |
---|
7522 | } |
---|
7523 | else |
---|
7524 | { |
---|
7525 | //nOverflow_Error = Overflow_Error; |
---|
7526 | tproc = tproc+clock()-tinput; |
---|
7527 | // Print("\n// B subroutine takes %d steps and calls \"Mpwalk\" (1,%d) :", nwalk, tp_deg-1); |
---|
7528 | G1 = Mpwalk_MAltwalk1(G1, curr_weight, tp_deg-1); |
---|
7529 | } |
---|
7530 | } |
---|
7531 | |
---|
7532 | MPW_Finish: |
---|
7533 | newRing = currRing; |
---|
7534 | rChangeCurrRing(YXXRing); |
---|
7535 | ideal result = idrMoveR(G1, newRing,currRing); |
---|
7536 | |
---|
7537 | delete ivNull; |
---|
7538 | delete target_weight; |
---|
7539 | |
---|
7540 | //Print("\n// \"Mpwalk\" (1,%d) took %d steps and %.2f sec. Overflow_Error (%d)", tp_deg, nwalk, ((double) clock()-tinput)/1000000, nOverflow_Error); |
---|
7541 | |
---|
7542 | return(result); |
---|
7543 | } |
---|
7544 | |
---|
7545 | /******************************************************************* |
---|
7546 | * Implementation of the first alternative Groebner Walk Algorithm * |
---|
7547 | *******************************************************************/ |
---|
7548 | ideal MAltwalk1(ideal Go, int op_deg, int tp_deg, intvec* curr_weight, |
---|
7549 | intvec* target_weight) |
---|
7550 | { |
---|
7551 | Set_Error(FALSE ); |
---|
7552 | Overflow_Error = FALSE; |
---|
7553 | #ifdef TIME_TEST |
---|
7554 | BOOLEAN nOverflow_Error = FALSE; |
---|
7555 | #endif |
---|
7556 | // Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
7557 | |
---|
7558 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
7559 | xftinput = clock(); |
---|
7560 | clock_t tostd, tproc; |
---|
7561 | |
---|
7562 | nstep = 0; |
---|
7563 | int i, nV = currRing->N; |
---|
7564 | int nwalk=0, endwalks=0; |
---|
7565 | int op_tmp = op_deg; |
---|
7566 | ideal Gomega, M, F, G, Gomega1, Gomega2, M1, F1; |
---|
7567 | ring newRing, oldRing; |
---|
7568 | intvec* next_weight; |
---|
7569 | intvec* iv_M_dp; |
---|
7570 | intvec* ivNull = new intvec(nV); |
---|
7571 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
7572 | intvec* exivlp = Mivlp(nV); |
---|
7573 | //intvec* extra_curr_weight = new intvec(nV); |
---|
7574 | #ifndef BUCHBERGER_ALG |
---|
7575 | intvec* hilb_func; |
---|
7576 | #endif |
---|
7577 | intvec* cw_tmp = curr_weight; |
---|
7578 | |
---|
7579 | // to avoid (1,0,...,0) as the target vector |
---|
7580 | intvec* last_omega = new intvec(nV); |
---|
7581 | for(i=nV-1; i>0; i--) |
---|
7582 | { |
---|
7583 | (*last_omega)[i] = 1; |
---|
7584 | } |
---|
7585 | (*last_omega)[0] = 10000; |
---|
7586 | |
---|
7587 | ring XXRing = currRing; |
---|
7588 | |
---|
7589 | to=clock(); |
---|
7590 | /* compute a pertubed weight vector of the original weight vector. |
---|
7591 | The perturbation degree is recursive decrease until that vector |
---|
7592 | stays inn the correct cone. */ |
---|
7593 | while(1) |
---|
7594 | { |
---|
7595 | if(Overflow_Error == FALSE) |
---|
7596 | { |
---|
7597 | if(MivComp(curr_weight, iv_dp) == 1) |
---|
7598 | { |
---|
7599 | //rOrdStr(currRing) = "dp" |
---|
7600 | if(op_tmp == op_deg) |
---|
7601 | { |
---|
7602 | G = MstdCC(Go); |
---|
7603 | if(op_deg != 1) |
---|
7604 | { |
---|
7605 | iv_M_dp = MivMatrixOrderdp(nV); |
---|
7606 | } |
---|
7607 | } |
---|
7608 | } |
---|
7609 | } |
---|
7610 | else |
---|
7611 | { |
---|
7612 | if(op_tmp == op_deg) |
---|
7613 | { |
---|
7614 | //rOrdStr(currRing) = (a(...),lp,C) |
---|
7615 | if (rParameter(currRing) != NULL) |
---|
7616 | { |
---|
7617 | DefRingPar(cw_tmp); |
---|
7618 | } |
---|
7619 | else |
---|
7620 | { |
---|
7621 | VMrDefault(cw_tmp); |
---|
7622 | } |
---|
7623 | G = idrMoveR(Go, XXRing,currRing); |
---|
7624 | G = MstdCC(G); |
---|
7625 | if(op_deg != 1) |
---|
7626 | iv_M_dp = MivMatrixOrder(cw_tmp); |
---|
7627 | } |
---|
7628 | } |
---|
7629 | Overflow_Error = FALSE; |
---|
7630 | if(op_deg != 1) |
---|
7631 | { |
---|
7632 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
7633 | } |
---|
7634 | else |
---|
7635 | { |
---|
7636 | curr_weight = cw_tmp; |
---|
7637 | break; |
---|
7638 | } |
---|
7639 | if(Overflow_Error == FALSE) |
---|
7640 | { |
---|
7641 | break; |
---|
7642 | } |
---|
7643 | Overflow_Error = TRUE; |
---|
7644 | op_deg --; |
---|
7645 | } |
---|
7646 | tostd=clock()-to; |
---|
7647 | |
---|
7648 | if(op_tmp != 1 ) |
---|
7649 | delete iv_M_dp; |
---|
7650 | delete iv_dp; |
---|
7651 | |
---|
7652 | if(currRing->order[0] == ringorder_a) |
---|
7653 | goto NEXT_VECTOR; |
---|
7654 | |
---|
7655 | while(1) |
---|
7656 | { |
---|
7657 | nwalk ++; |
---|
7658 | nstep ++; |
---|
7659 | |
---|
7660 | to = clock(); |
---|
7661 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
7662 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
7663 | xtif=xtif+clock()-to; |
---|
7664 | #if 0 |
---|
7665 | if(Overflow_Error == TRUE) |
---|
7666 | { |
---|
7667 | for(i=nV-1; i>=0; i--) |
---|
7668 | (*curr_weight)[i] = (*extra_curr_weight)[i]; |
---|
7669 | delete extra_curr_weight; |
---|
7670 | |
---|
7671 | newRing = currRing; |
---|
7672 | goto MSTD_ALT1; |
---|
7673 | } |
---|
7674 | #endif |
---|
7675 | #ifndef BUCHBERGER_ALG |
---|
7676 | if(isNolVector(curr_weight) == 0) |
---|
7677 | { |
---|
7678 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
7679 | } |
---|
7680 | else |
---|
7681 | { |
---|
7682 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
7683 | } |
---|
7684 | #endif // BUCHBERGER_ALG |
---|
7685 | |
---|
7686 | oldRing = currRing; |
---|
7687 | |
---|
7688 | // define a new ring which ordering is "(a(curr_weight),lp) |
---|
7689 | if (rParameter(currRing) != NULL) |
---|
7690 | { |
---|
7691 | DefRingPar(curr_weight); |
---|
7692 | } |
---|
7693 | else |
---|
7694 | { |
---|
7695 | VMrDefault(curr_weight); |
---|
7696 | } |
---|
7697 | newRing = currRing; |
---|
7698 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
7699 | |
---|
7700 | to=clock(); |
---|
7701 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
7702 | #ifdef BUCHBERGER_ALG |
---|
7703 | M = MstdhomCC(Gomega1); |
---|
7704 | #else |
---|
7705 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
7706 | delete hilb_func; |
---|
7707 | #endif // BUCHBERGER_ALG |
---|
7708 | xtstd=xtstd+clock()-to; |
---|
7709 | |
---|
7710 | // change the ring to oldRing |
---|
7711 | rChangeCurrRing(oldRing); |
---|
7712 | M1 = idrMoveR(M, newRing,currRing); |
---|
7713 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
7714 | |
---|
7715 | to=clock(); |
---|
7716 | // compute a reduced Groebner basis of <G> w.r.t. "newRing" by the lifting process |
---|
7717 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
7718 | xtlift=xtlift+clock()-to; |
---|
7719 | |
---|
7720 | idDelete(&M1); |
---|
7721 | idDelete(&Gomega2); |
---|
7722 | idDelete(&G); |
---|
7723 | |
---|
7724 | // change the ring to newRing |
---|
7725 | rChangeCurrRing(newRing); |
---|
7726 | F1 = idrMoveR(F, oldRing,currRing); |
---|
7727 | |
---|
7728 | to=clock(); |
---|
7729 | // reduce the Groebner basis <G> w.r.t. new ring |
---|
7730 | G = kInterRedCC(F1, NULL); |
---|
7731 | xtred=xtred+clock()-to; |
---|
7732 | idDelete(&F1); |
---|
7733 | |
---|
7734 | if(endwalks == 1) |
---|
7735 | { |
---|
7736 | break; |
---|
7737 | } |
---|
7738 | NEXT_VECTOR: |
---|
7739 | to=clock(); |
---|
7740 | // compute a next weight vector |
---|
7741 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
7742 | xtnw=xtnw+clock()-to; |
---|
7743 | #ifdef PRINT_VECTORS |
---|
7744 | MivString(curr_weight, target_weight, next_weight); |
---|
7745 | #endif |
---|
7746 | |
---|
7747 | if(Overflow_Error == TRUE) |
---|
7748 | { |
---|
7749 | newRing = currRing; |
---|
7750 | |
---|
7751 | if (rParameter(currRing) != NULL) |
---|
7752 | { |
---|
7753 | DefRingPar(target_weight); |
---|
7754 | } |
---|
7755 | else |
---|
7756 | { |
---|
7757 | VMrDefault(target_weight); |
---|
7758 | } |
---|
7759 | F1 = idrMoveR(G, newRing,currRing); |
---|
7760 | G = MstdCC(F1); |
---|
7761 | idDelete(&F1); |
---|
7762 | newRing = currRing; |
---|
7763 | break; //for while |
---|
7764 | } |
---|
7765 | |
---|
7766 | |
---|
7767 | /* G is the wanted Groebner basis if next_weight == curr_weight */ |
---|
7768 | if(MivComp(next_weight, ivNull) == 1) |
---|
7769 | { |
---|
7770 | newRing = currRing; |
---|
7771 | delete next_weight; |
---|
7772 | break; //for while |
---|
7773 | } |
---|
7774 | |
---|
7775 | if(MivComp(next_weight, target_weight) == 1) |
---|
7776 | { |
---|
7777 | if(tp_deg == 1 || MivSame(target_weight, exivlp) == 0) |
---|
7778 | endwalks = 1; |
---|
7779 | else |
---|
7780 | { |
---|
7781 | // MSTD_ALT1: |
---|
7782 | #ifdef TIME_TEST |
---|
7783 | nOverflow_Error = Overflow_Error; |
---|
7784 | #endif |
---|
7785 | tproc = clock()-xftinput; |
---|
7786 | |
---|
7787 | //Print("\n// main routine takes %d steps and calls \"Mpwalk\" (1,%d):", nwalk, tp_deg); |
---|
7788 | |
---|
7789 | // compute the red. GB of <G> w.r.t. the lex order by the "recursive-modified" perturbation walk alg (1,tp_deg) |
---|
7790 | G = Mpwalk_MAltwalk1(G, curr_weight, tp_deg); |
---|
7791 | delete next_weight; |
---|
7792 | break; // for while |
---|
7793 | } |
---|
7794 | } |
---|
7795 | |
---|
7796 | //NOT Changed, to free memory |
---|
7797 | for(i=nV-1; i>=0; i--) |
---|
7798 | { |
---|
7799 | //(*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
7800 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
7801 | } |
---|
7802 | delete next_weight; |
---|
7803 | }//while |
---|
7804 | |
---|
7805 | rChangeCurrRing(XXRing); |
---|
7806 | ideal result = idrMoveR(G, newRing,currRing); |
---|
7807 | id_Delete(&G, newRing); |
---|
7808 | |
---|
7809 | delete ivNull; |
---|
7810 | if(op_deg != 1 ) |
---|
7811 | { |
---|
7812 | delete curr_weight; |
---|
7813 | } |
---|
7814 | delete exivlp; |
---|
7815 | #ifdef TIME_TEST |
---|
7816 | |
---|
7817 | Print("\n// \"Main procedure\" took %d steps, %.2f sec. and Overflow_Error(%d)", |
---|
7818 | nwalk, ((double) tproc)/1000000, nOverflow_Error); |
---|
7819 | |
---|
7820 | TimeStringFractal(xftinput, tostd, xtif, xtstd,xtextra, xtlift, xtred, xtnw); |
---|
7821 | |
---|
7822 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
7823 | Print("\n// Overflow_Error? (%d)", Overflow_Error); |
---|
7824 | Print("\n// Awalk1 took %d steps.\n", nstep); |
---|
7825 | #endif |
---|
7826 | return(result); |
---|
7827 | } |
---|