1 | /***************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | *****************************************/ |
---|
4 | /* $Id: walk.cc,v 1.9 2006-01-05 18:32:19 Singular Exp $ */ |
---|
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 Gröbner basis |
---|
34 | |
---|
35 | /* includes */ |
---|
36 | |
---|
37 | #include <stdio.h> |
---|
38 | #include <si_gmp.h> |
---|
39 | |
---|
40 | #include "mod2.h" |
---|
41 | #include "intvec.h" |
---|
42 | #include "cntrlc.h" |
---|
43 | #include "math.h" |
---|
44 | #include "structs.h" |
---|
45 | #include "omalloc.h" |
---|
46 | #include "febase.h" |
---|
47 | #include "ipshell.h" |
---|
48 | #include "ipconv.h" |
---|
49 | #include "longalg.h" |
---|
50 | #include "ffields.h" |
---|
51 | #include "subexpr.h" |
---|
52 | #include "p_Procs.h" |
---|
53 | |
---|
54 | #include "maps.h" |
---|
55 | |
---|
56 | /* include Hilbert-function */ |
---|
57 | #include "stairc.h" |
---|
58 | |
---|
59 | /** kstd2.cc */ |
---|
60 | #include "kutil.h" |
---|
61 | #include "khstd.h" |
---|
62 | |
---|
63 | // === Zeit & System (Holger Croeni === |
---|
64 | #include <time.h> |
---|
65 | #include <sys/time.h> |
---|
66 | #include <sys/stat.h> |
---|
67 | #include <unistd.h> |
---|
68 | #include <stdio.h> |
---|
69 | #include <float.h> |
---|
70 | #include <limits.h> |
---|
71 | #include <sys/types.h> |
---|
72 | |
---|
73 | #include "walk.h" |
---|
74 | #include "polys.h" |
---|
75 | #include "ideals.h" |
---|
76 | #include "ipid.h" |
---|
77 | #include "tok.h" |
---|
78 | #include "febase.h" |
---|
79 | #include "numbers.h" |
---|
80 | #include "ipid.h" |
---|
81 | #include "ring.h" |
---|
82 | #include "kstd1.h" |
---|
83 | #include "matpol.h" |
---|
84 | #include "weight.h" |
---|
85 | #include "intvec.h" |
---|
86 | #include "syz.h" |
---|
87 | #include "lists.h" |
---|
88 | #include "prCopy.h" |
---|
89 | #include "string.h" |
---|
90 | #include "longalg.h" |
---|
91 | #ifdef HAVE_FACTORY |
---|
92 | #include "clapsing.h" |
---|
93 | #endif |
---|
94 | |
---|
95 | #include "mpr_complex.h" |
---|
96 | |
---|
97 | ideal Gnull = NULL; |
---|
98 | int nstep; |
---|
99 | |
---|
100 | extern BOOLEAN ErrorCheck(); |
---|
101 | |
---|
102 | extern BOOLEAN pSetm_error; |
---|
103 | |
---|
104 | void Set_Error( BOOLEAN f) { pSetm_error=f; } |
---|
105 | |
---|
106 | BOOLEAN Overflow_Error = FALSE; |
---|
107 | |
---|
108 | clock_t xtif, xtstd, xtlift, xtred, xtnw; |
---|
109 | clock_t xftostd, xtextra, xftinput, to; |
---|
110 | |
---|
111 | /*2 |
---|
112 | *utilities for TSet, LSet |
---|
113 | */ |
---|
114 | inline static intset initec (int maxnr) |
---|
115 | { |
---|
116 | return (intset)omAlloc(maxnr*sizeof(int)); |
---|
117 | } |
---|
118 | |
---|
119 | inline static unsigned long* initsevS (int maxnr) |
---|
120 | { |
---|
121 | return (unsigned long*)omAlloc0(maxnr*sizeof(unsigned long)); |
---|
122 | } |
---|
123 | inline static int* initS_2_R (int maxnr) |
---|
124 | { |
---|
125 | return (int*)omAlloc0(maxnr*sizeof(int)); |
---|
126 | } |
---|
127 | |
---|
128 | /*2 |
---|
129 | *construct the set s from F u {P} |
---|
130 | */ |
---|
131 | static void initSSpecialCC (ideal F, ideal Q, ideal P,kStrategy strat) |
---|
132 | { |
---|
133 | int i,pos; |
---|
134 | |
---|
135 | if (Q!=NULL) i=((IDELEMS(Q)+(setmaxTinc-1))/setmaxTinc)*setmaxTinc; |
---|
136 | else i=setmaxT; |
---|
137 | |
---|
138 | strat->ecartS=initec(i); |
---|
139 | strat->sevS=initsevS(i); |
---|
140 | strat->S_2_R=initS_2_R(i); |
---|
141 | strat->fromQ=NULL; |
---|
142 | strat->Shdl=idInit(i,F->rank); |
---|
143 | strat->S=strat->Shdl->m; |
---|
144 | |
---|
145 | /*- put polys into S -*/ |
---|
146 | if (Q!=NULL) |
---|
147 | { |
---|
148 | strat->fromQ=initec(i); |
---|
149 | memset(strat->fromQ,0,i*sizeof(int)); |
---|
150 | for (i=0; i<IDELEMS(Q); i++) |
---|
151 | { |
---|
152 | if (Q->m[i]!=NULL) |
---|
153 | { |
---|
154 | LObject h; |
---|
155 | h.p = pCopy(Q->m[i]); |
---|
156 | //if (TEST_OPT_INTSTRATEGY) |
---|
157 | //{ |
---|
158 | // //pContent(h.p); |
---|
159 | // h.pCleardenom(); // also does a pContent |
---|
160 | //} |
---|
161 | //else |
---|
162 | //{ |
---|
163 | // h.pNorm(); |
---|
164 | //} |
---|
165 | strat->initEcart(&h); |
---|
166 | if (pOrdSgn==-1) |
---|
167 | { |
---|
168 | deleteHC(&h,strat); |
---|
169 | } |
---|
170 | if (h.p!=NULL) |
---|
171 | { |
---|
172 | if (strat->sl==-1) |
---|
173 | pos =0; |
---|
174 | else |
---|
175 | { |
---|
176 | pos = posInS(strat,strat->sl,h.p,h.ecart); |
---|
177 | } |
---|
178 | h.sev = pGetShortExpVector(h.p); |
---|
179 | h.SetpFDeg(); |
---|
180 | strat->enterS(h,pos,strat, strat->tl+1); |
---|
181 | enterT(h, strat); |
---|
182 | strat->fromQ[pos]=1; |
---|
183 | } |
---|
184 | } |
---|
185 | } |
---|
186 | } |
---|
187 | /*- put polys into S -*/ |
---|
188 | for (i=0; i<IDELEMS(F); i++) |
---|
189 | { |
---|
190 | if (F->m[i]!=NULL) |
---|
191 | { |
---|
192 | LObject h; |
---|
193 | h.p = pCopy(F->m[i]); |
---|
194 | if (pOrdSgn==1) |
---|
195 | { |
---|
196 | //h.p=redtailBba(h.p,strat->sl,strat); |
---|
197 | h.p=redtailBba(h.p,strat->sl,strat); |
---|
198 | } |
---|
199 | strat->initEcart(&h); |
---|
200 | if (pOrdSgn==-1) |
---|
201 | { |
---|
202 | deleteHC(&h,strat); |
---|
203 | } |
---|
204 | if (h.p!=NULL) |
---|
205 | { |
---|
206 | if (strat->sl==-1) |
---|
207 | pos =0; |
---|
208 | else |
---|
209 | pos = posInS(strat,strat->sl,h.p,h.ecart); |
---|
210 | h.sev = pGetShortExpVector(h.p); |
---|
211 | strat->enterS(h,pos,strat, strat->tl+1); |
---|
212 | h.length = pLength(h.p); |
---|
213 | h.SetpFDeg(); |
---|
214 | enterT(h,strat); |
---|
215 | } |
---|
216 | } |
---|
217 | } |
---|
218 | #ifdef INITSSPECIAL |
---|
219 | for (i=0; i<IDELEMS(P); i++) |
---|
220 | { |
---|
221 | if (P->m[i]!=NULL) |
---|
222 | { |
---|
223 | LObject h; |
---|
224 | h.p=pCopy(P->m[i]); |
---|
225 | strat->initEcart(&h); |
---|
226 | h.length = pLength(h.p); |
---|
227 | if (TEST_OPT_INTSTRATEGY) |
---|
228 | { |
---|
229 | h.pCleardenom(); |
---|
230 | } |
---|
231 | else |
---|
232 | { |
---|
233 | h.pNorm(); |
---|
234 | } |
---|
235 | if(strat->sl>=0) |
---|
236 | { |
---|
237 | if (pOrdSgn==1) |
---|
238 | { |
---|
239 | h.p=redBba(h.p,strat->sl,strat); |
---|
240 | if (h.p!=NULL) |
---|
241 | h.p=redtailBba(h.p,strat->sl,strat); |
---|
242 | } |
---|
243 | else |
---|
244 | { |
---|
245 | h.p=redMora(h.p,strat->sl,strat); |
---|
246 | strat->initEcart(&h); |
---|
247 | } |
---|
248 | if(h.p!=NULL) |
---|
249 | { |
---|
250 | if (TEST_OPT_INTSTRATEGY) |
---|
251 | { |
---|
252 | h.pCleardenom(); |
---|
253 | } |
---|
254 | else |
---|
255 | { |
---|
256 | h.is_normalized = 0; |
---|
257 | h.pNorm(); |
---|
258 | } |
---|
259 | h.sev = pGetShortExpVector(h.p); |
---|
260 | h.SetpFDeg(); |
---|
261 | pos = posInS(strat->S,strat->sl,h.p,h.ecart); |
---|
262 | enterpairsSpecial(h.p,strat->sl,h.ecart,pos,strat,strat->tl+1); |
---|
263 | strat->enterS(h,pos,strat, strat->tl+1); |
---|
264 | enterT(h,strat); |
---|
265 | } |
---|
266 | } |
---|
267 | else |
---|
268 | { |
---|
269 | h.sev = pGetShortExpVector(h.p); |
---|
270 | h.SetpFDeg(); |
---|
271 | strat->enterS(h,0,strat, strat->tl+1); |
---|
272 | enterT(h,strat); |
---|
273 | } |
---|
274 | } |
---|
275 | } |
---|
276 | #endif |
---|
277 | } |
---|
278 | |
---|
279 | /*2 |
---|
280 | *interreduces F |
---|
281 | */ |
---|
282 | static ideal kInterRedCC(ideal F, ideal Q) |
---|
283 | { |
---|
284 | int j; |
---|
285 | kStrategy strat = new skStrategy; |
---|
286 | |
---|
287 | // if (TEST_OPT_PROT) |
---|
288 | // { |
---|
289 | // writeTime("start InterRed:"); |
---|
290 | // mflush(); |
---|
291 | // } |
---|
292 | //strat->syzComp = 0; |
---|
293 | strat->kHEdgeFound = ppNoether != NULL; |
---|
294 | strat->kNoether=pCopy(ppNoether); |
---|
295 | strat->ak = idRankFreeModule(F); |
---|
296 | initBuchMoraCrit(strat); |
---|
297 | strat->NotUsedAxis = (BOOLEAN *)omAlloc((pVariables+1)*sizeof(BOOLEAN)); |
---|
298 | for (j=pVariables; j>0; j--) strat->NotUsedAxis[j] = TRUE; |
---|
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 (pOrdSgn == -1) strat->honey = TRUE; |
---|
309 | |
---|
310 | |
---|
311 | //initSCC(F,Q,strat); |
---|
312 | initS(F,Q,strat); |
---|
313 | |
---|
314 | /* |
---|
315 | timetmp=clock();//22.01.02 |
---|
316 | initSSpecialCC(F,Q,NULL,strat); |
---|
317 | tininitS=tininitS+clock()-timetmp;//22.01.02 |
---|
318 | */ |
---|
319 | if (TEST_OPT_REDSB) |
---|
320 | strat->noTailReduction=FALSE; |
---|
321 | |
---|
322 | updateS(TRUE,strat); |
---|
323 | |
---|
324 | if (TEST_OPT_REDSB && TEST_OPT_INTSTRATEGY) |
---|
325 | completeReduce(strat); |
---|
326 | pDelete(&strat->kHEdge); |
---|
327 | omFreeSize((ADDRESS)strat->T,strat->tmax*sizeof(TObject)); |
---|
328 | omFreeSize((ADDRESS)strat->ecartS,IDELEMS(strat->Shdl)*sizeof(int)); |
---|
329 | omFreeSize((ADDRESS)strat->sevS,IDELEMS(strat->Shdl)*sizeof(unsigned long)); |
---|
330 | omFreeSize((ADDRESS)strat->NotUsedAxis,(pVariables+1)*sizeof(BOOLEAN)); |
---|
331 | omfree(strat->sevT); |
---|
332 | omfree(strat->S_2_R); |
---|
333 | omfree(strat->R); |
---|
334 | |
---|
335 | if (strat->fromQ) |
---|
336 | { |
---|
337 | for (j=0;j<IDELEMS(strat->Shdl);j++) |
---|
338 | { |
---|
339 | if(strat->fromQ[j]) pDelete(&strat->Shdl->m[j]); |
---|
340 | } |
---|
341 | omFreeSize((ADDRESS)strat->fromQ,IDELEMS(strat->Shdl)*sizeof(int)); |
---|
342 | strat->fromQ=NULL; |
---|
343 | } |
---|
344 | // if (TEST_OPT_PROT) |
---|
345 | // { |
---|
346 | // writeTime("end Interred:"); |
---|
347 | // mflush(); |
---|
348 | // } |
---|
349 | ideal shdl=strat->Shdl; |
---|
350 | idSkipZeroes(shdl); |
---|
351 | delete(strat); |
---|
352 | |
---|
353 | return shdl; |
---|
354 | } |
---|
355 | |
---|
356 | static void TimeString(clock_t tinput, clock_t tostd, clock_t tif,clock_t tstd, |
---|
357 | clock_t tlf,clock_t tred, clock_t tnw, int step) |
---|
358 | { |
---|
359 | double totm = ((double) (clock() - tinput))/1000000; |
---|
360 | double ostd,mostd, mif, mstd, mextra, mlf, mred, mnw, mxif,mxstd,mxlf,mxred,mxnw,tot; |
---|
361 | |
---|
362 | Print("\n// total time = %.2f sec", totm); |
---|
363 | Print("\n// tostd = %.2f sec = %.2f %", ostd=((double) tostd)/1000000, |
---|
364 | mostd=((((double) tostd)/1000000)/totm)*100); |
---|
365 | Print("\n// tif = %.2f sec = %.2f %", ((double) tif)/1000000, |
---|
366 | mif=((((double) tif)/1000000)/totm)*100); |
---|
367 | Print("\n// std = %.2f sec = %.2f %", ((double) tstd)/1000000, |
---|
368 | mstd=((((double) tstd)/1000000)/totm)*100); |
---|
369 | Print("\n// lift = %.2f sec = %.2f %", ((double) tlf)/1000000, |
---|
370 | mlf=((((double) tlf)/1000000)/totm)*100); |
---|
371 | Print("\n// ired = %.2f sec = %.2f %", ((double) tred)/1000000, |
---|
372 | mred=((((double) tred)/1000000)/totm)*100); |
---|
373 | Print("\n// nextw = %.2f sec = %.2f %", ((double) tnw)/1000000, |
---|
374 | mnw=((((double) tnw)/1000000)/totm)*100); |
---|
375 | PrintS("\n Time for the last step:"); |
---|
376 | Print("\n// xinfo = %.2f sec = %.2f %", ((double) xtif)/1000000, |
---|
377 | mxif=((((double) xtif)/1000000)/totm)*100); |
---|
378 | Print("\n// xstd = %.2f sec = %.2f %", ((double) xtstd)/1000000, |
---|
379 | mxstd=((((double) xtstd)/1000000)/totm)*100); |
---|
380 | Print("\n// xlift = %.2f sec = %.2f %", ((double) xtlift)/1000000, |
---|
381 | mxlf=((((double) xtlift)/1000000)/totm)*100); |
---|
382 | Print("\n// xired = %.2f sec = %.2f %", ((double) xtred)/1000000, |
---|
383 | mxred=((((double) xtred)/1000000)/totm)*100); |
---|
384 | Print("\n// xnextw= %.2f sec = %.2f %", ((double) xtnw)/1000000, |
---|
385 | mxnw=((((double) xtnw)/1000000)/totm)*100); |
---|
386 | |
---|
387 | tot=mostd+mif+mstd+mlf+mred+mnw+mxif+mxstd+mxlf+mxred+mxnw; |
---|
388 | double res = (double) 100 - tot; |
---|
389 | Print("\n// &%d&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f(%.2f)\\ \\", |
---|
390 | step, ostd, totm, mostd,mif,mstd,mlf,mred,mnw,mxif,mxstd,mxlf,mxred,mxnw,tot,res, |
---|
391 | ((((double) xtextra)/1000000)/totm)*100); |
---|
392 | } |
---|
393 | |
---|
394 | static void TimeStringFractal(clock_t tinput, clock_t tostd, clock_t tif,clock_t tstd, |
---|
395 | clock_t textra, clock_t tlf,clock_t tred, clock_t tnw) |
---|
396 | { |
---|
397 | |
---|
398 | double totm = ((double) (clock() - tinput))/1000000; |
---|
399 | double ostd, mostd, mif, mstd, mextra, mlf, mred, mnw, tot, res; |
---|
400 | Print("\n// total time = %.2f sec", totm); |
---|
401 | Print("\n// tostd = %.2f sec = %.2f %", ostd=((double) tostd)/1000000, |
---|
402 | mostd=((((double) tostd)/1000000)/totm)*100); |
---|
403 | Print("\n// tif = %.2f sec = %.2f %", ((double) tif)/1000000, |
---|
404 | mif=((((double) tif)/1000000)/totm)*100); |
---|
405 | Print("\n// std = %.2f sec = %.2f %", ((double) tstd)/1000000, |
---|
406 | mstd=((((double) tstd)/1000000)/totm)*100); |
---|
407 | Print("\n// xstd = %.2f sec = %.2f %", ((double) textra)/1000000, |
---|
408 | mextra=((((double) textra)/1000000)/totm)*100); |
---|
409 | Print("\n// lift = %.2f sec = %.2f %", ((double) tlf)/1000000, |
---|
410 | mlf=((((double) tlf)/1000000)/totm)*100); |
---|
411 | Print("\n// ired = %.2f sec = %.2f %", ((double) tred)/1000000, |
---|
412 | mred=((((double) tred)/1000000)/totm)*100); |
---|
413 | Print("\n// nextw = %.2f sec = %.2f %", ((double) tnw)/1000000, |
---|
414 | mnw=((((double) tnw)/1000000)/totm)*100); |
---|
415 | tot = mostd+mif+mstd+mextra+mlf+mred+mnw; |
---|
416 | res = (double) 100.00-tot; |
---|
417 | Print("\n// &%.2f &%.2f&%.2f &%.2f &%.2f &%.2f &%.2f &%.2f &%.2f&%.2f&%.2f\\ \\ ", |
---|
418 | ostd,totm,mostd,mif,mstd,mextra,mlf,mred,mnw,tot,res); |
---|
419 | } |
---|
420 | |
---|
421 | static void idString(ideal L, char* st) |
---|
422 | { |
---|
423 | int i, nL = IDELEMS(L); |
---|
424 | |
---|
425 | Print("\n// ideal %s = ", st); |
---|
426 | for(i=0; i<nL-1; i++) |
---|
427 | Print(" %s, ", pString(L->m[i])); |
---|
428 | |
---|
429 | Print(" %s;", pString(L->m[nL-1])); |
---|
430 | } |
---|
431 | |
---|
432 | static void headidString(ideal L, char* st) |
---|
433 | { |
---|
434 | int i, nL = IDELEMS(L); |
---|
435 | |
---|
436 | Print("\n// ideal %s = ", st); |
---|
437 | for(i=0; i<nL-1; i++) |
---|
438 | Print(" %s, ", pString(pHead(L->m[i]))); |
---|
439 | |
---|
440 | Print(" %s;", pString(pHead(L->m[nL-1]))); |
---|
441 | } |
---|
442 | |
---|
443 | static void idElements(ideal L, char* st) |
---|
444 | { |
---|
445 | int i, nL = IDELEMS(L); |
---|
446 | int *K=(int *)omAlloc(nL*sizeof(int)); |
---|
447 | |
---|
448 | Print("\n// #monoms of %s = ", st); |
---|
449 | for(i=0; i<nL; i++) |
---|
450 | K[i] = pLength(L->m[i]); |
---|
451 | |
---|
452 | int j, nsame, nk=0; |
---|
453 | for(i=0; i<nL; i++) |
---|
454 | { |
---|
455 | if(K[i]!=0) |
---|
456 | { |
---|
457 | nsame = 1; |
---|
458 | for(j=i+1; j<nL; j++){ |
---|
459 | if(K[j]==K[i]){ |
---|
460 | nsame ++; |
---|
461 | K[j]=0; |
---|
462 | } |
---|
463 | } |
---|
464 | if(nsame == 1) |
---|
465 | Print("%d, ",K[i]); |
---|
466 | else |
---|
467 | Print("%d[%d], ", K[i], nsame); |
---|
468 | } |
---|
469 | } |
---|
470 | omFree(K); |
---|
471 | } |
---|
472 | |
---|
473 | |
---|
474 | |
---|
475 | static void ivString(intvec* iv, char* ch) |
---|
476 | { |
---|
477 | int nV = iv->length()-1; |
---|
478 | //Print("\n// vector %s = (", ch); |
---|
479 | Print("\n// intvec %s = ", ch); |
---|
480 | |
---|
481 | for(int i=0; i<nV; i++) |
---|
482 | Print("%d, ", (*iv)[i]); |
---|
483 | Print("%d;", (*iv)[nV]); |
---|
484 | } |
---|
485 | |
---|
486 | static void MivString(intvec* iva, intvec* ivb, intvec* ivc) |
---|
487 | { |
---|
488 | int nV = iva->length()-1; |
---|
489 | int i; |
---|
490 | PrintS("\n// ("); |
---|
491 | for(i=0; i<nV; i++) |
---|
492 | Print("%d, ", (*iva)[i]); |
---|
493 | Print("%d) ==> (", (*iva)[nV]); |
---|
494 | |
---|
495 | for(i=0; i<nV; i++) |
---|
496 | Print("%d, ", (*ivb)[i]); |
---|
497 | Print("%d) := (", (*ivb)[nV]); |
---|
498 | |
---|
499 | for(i=0; i<nV; i++) |
---|
500 | Print("%d, ", (*ivc)[i]); |
---|
501 | Print("%d)", (*ivc)[nV]); |
---|
502 | } |
---|
503 | |
---|
504 | |
---|
505 | // returns gcd of integers a and b |
---|
506 | static inline long gcd(const long a, const long b) |
---|
507 | { |
---|
508 | long r, p0 = a, p1 = b; |
---|
509 | //assume(p0 >= 0 && p1 >= 0); |
---|
510 | if(p0 < 0) |
---|
511 | p0 = -p0; |
---|
512 | |
---|
513 | if(p1 < 0) |
---|
514 | p1 = -p1; |
---|
515 | |
---|
516 | while(p1 != 0) |
---|
517 | { |
---|
518 | r = p0 % p1; |
---|
519 | p0 = p1; |
---|
520 | p1 = r; |
---|
521 | } |
---|
522 | return p0; |
---|
523 | } |
---|
524 | |
---|
525 | // cancel gcd of integers zaehler and nenner |
---|
526 | static void cancel(mpz_t zaehler, mpz_t nenner) |
---|
527 | { |
---|
528 | // assume(zaehler >= 0 && nenner > 0); |
---|
529 | mpz_t g; |
---|
530 | mpz_init(g); |
---|
531 | mpz_gcd(g, zaehler, nenner); |
---|
532 | |
---|
533 | mpz_div(zaehler , zaehler, g); |
---|
534 | mpz_div(nenner , nenner, g); |
---|
535 | |
---|
536 | mpz_clear(g); |
---|
537 | } |
---|
538 | |
---|
539 | /* 23.07.03 */ |
---|
540 | static int isVectorNeg(intvec* omega) |
---|
541 | { |
---|
542 | int i; |
---|
543 | |
---|
544 | for(i=omega->length(); i>=0; i--) |
---|
545 | if((*omega)[i]<0) |
---|
546 | return 1; |
---|
547 | |
---|
548 | return 0; |
---|
549 | } |
---|
550 | |
---|
551 | /******************************************************************** |
---|
552 | * compute a weight degree of a monomial p w.r.t. a weight_vector * |
---|
553 | ********************************************************************/ |
---|
554 | static inline int MLmWeightedDegree(const poly p, intvec* weight) |
---|
555 | { |
---|
556 | /* 2147483647 is max. integer representation in SINGULAR */ |
---|
557 | mpz_t sing_int; |
---|
558 | mpz_init_set_ui(sing_int, 2147483647); |
---|
559 | |
---|
560 | int i, wgrad; |
---|
561 | |
---|
562 | mpz_t zmul; |
---|
563 | mpz_init(zmul); |
---|
564 | mpz_t zvec; |
---|
565 | mpz_init(zvec); |
---|
566 | mpz_t zsum; |
---|
567 | mpz_init(zsum); |
---|
568 | |
---|
569 | for (i=pVariables; i>0; i--) |
---|
570 | { |
---|
571 | mpz_set_si(zvec, (*weight)[i-1]); |
---|
572 | mpz_mul_ui(zmul, zvec, pGetExp(p, i)); |
---|
573 | mpz_add(zsum, zsum, zmul); |
---|
574 | } |
---|
575 | |
---|
576 | wgrad = mpz_get_ui(zsum); |
---|
577 | |
---|
578 | if(mpz_cmp(zsum, sing_int)>0) |
---|
579 | { |
---|
580 | if(Overflow_Error == FALSE) { |
---|
581 | PrintLn(); |
---|
582 | PrintS("\n// ** OVERFLOW in \"MwalkInitialForm\": "); |
---|
583 | mpz_out_str( stdout, 10, zsum); |
---|
584 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
585 | Overflow_Error = TRUE; |
---|
586 | } |
---|
587 | } |
---|
588 | |
---|
589 | return wgrad; |
---|
590 | } |
---|
591 | |
---|
592 | /******************************************************************** |
---|
593 | * compute a weight degree of a polynomial p w.r.t. a weight_vector * |
---|
594 | ********************************************************************/ |
---|
595 | static inline int MwalkWeightDegree(poly p, intvec* weight_vector) |
---|
596 | { |
---|
597 | assume(weight_vector->length() >= pVariables); |
---|
598 | int max = 0, maxtemp; |
---|
599 | |
---|
600 | while(p != NULL) |
---|
601 | { |
---|
602 | maxtemp = MLmWeightedDegree(p, weight_vector); |
---|
603 | pIter(p); |
---|
604 | |
---|
605 | if (maxtemp > max) |
---|
606 | max = maxtemp; |
---|
607 | } |
---|
608 | return max; |
---|
609 | } |
---|
610 | |
---|
611 | |
---|
612 | /******************************************************************** |
---|
613 | * compute a weight degree of a monomial p w.r.t. a weight_vector * |
---|
614 | ********************************************************************/ |
---|
615 | static void MLmWeightedDegree_gmp(mpz_t result, const poly p, intvec* weight) |
---|
616 | { |
---|
617 | /* 2147483647 is max. integer representation in SINGULAR */ |
---|
618 | mpz_t sing_int; |
---|
619 | mpz_init_set_ui(sing_int, 2147483647); |
---|
620 | |
---|
621 | int i, wgrad; |
---|
622 | |
---|
623 | mpz_t zmul; |
---|
624 | mpz_init(zmul); |
---|
625 | mpz_t zvec; |
---|
626 | mpz_init(zvec); |
---|
627 | mpz_t ztmp; |
---|
628 | mpz_init(ztmp); |
---|
629 | |
---|
630 | for (i=pVariables; i>0; i--) |
---|
631 | { |
---|
632 | mpz_set_si(zvec, (*weight)[i-1]); |
---|
633 | mpz_mul_ui(zmul, zvec, pGetExp(p, i)); |
---|
634 | mpz_add(ztmp, ztmp, zmul); |
---|
635 | } |
---|
636 | mpz_init_set(result, ztmp); |
---|
637 | mpz_clear(ztmp); |
---|
638 | mpz_clear(sing_int); |
---|
639 | mpz_clear(zvec); |
---|
640 | mpz_clear(zmul); |
---|
641 | } |
---|
642 | |
---|
643 | |
---|
644 | /***************************************************************************** |
---|
645 | * return an initial form of the polynom g w.r.t. a weight vector curr_weight * |
---|
646 | *****************************************************************************/ |
---|
647 | static poly MpolyInitialForm(poly g, intvec* curr_weight) |
---|
648 | { |
---|
649 | if(g == NULL) |
---|
650 | return NULL; |
---|
651 | |
---|
652 | mpz_t max; mpz_init(max); |
---|
653 | mpz_t maxtmp; mpz_init(maxtmp); |
---|
654 | |
---|
655 | poly hg, in_w_g = NULL; |
---|
656 | |
---|
657 | while(g != NULL) |
---|
658 | { |
---|
659 | hg = g; |
---|
660 | pIter(g); |
---|
661 | MLmWeightedDegree_gmp(maxtmp, hg, curr_weight); |
---|
662 | |
---|
663 | if(mpz_cmp(maxtmp, max)>0) |
---|
664 | { |
---|
665 | mpz_init_set(max, maxtmp); |
---|
666 | pDelete(&in_w_g); |
---|
667 | in_w_g = pHead(hg); |
---|
668 | } |
---|
669 | else { |
---|
670 | if(mpz_cmp(maxtmp, max)==0) |
---|
671 | in_w_g = pAdd(in_w_g, pHead(hg)); |
---|
672 | } |
---|
673 | } |
---|
674 | return in_w_g; |
---|
675 | } |
---|
676 | |
---|
677 | /************************************************************************ |
---|
678 | * compute the initial form of an ideal <G> w.r.t. a weight vector iva * |
---|
679 | ************************************************************************/ |
---|
680 | ideal MwalkInitialForm(ideal G, intvec* ivw) |
---|
681 | { |
---|
682 | BOOLEAN nError = Overflow_Error; |
---|
683 | Overflow_Error = FALSE; |
---|
684 | |
---|
685 | int i, nG = IDELEMS(G); |
---|
686 | ideal Gomega = idInit(nG, 1); |
---|
687 | |
---|
688 | for(i=nG-1; i>=0; i--) |
---|
689 | Gomega->m[i] = MpolyInitialForm(G->m[i], ivw); |
---|
690 | |
---|
691 | if(Overflow_Error == FALSE) |
---|
692 | Overflow_Error = nError; |
---|
693 | |
---|
694 | return Gomega; |
---|
695 | } |
---|
696 | |
---|
697 | /************************************************************************ |
---|
698 | * test whether the weight vector iv is in the cone of the ideal G * |
---|
699 | * i.e. are in(in_w(g)) =? in(g), for all g in G * |
---|
700 | ************************************************************************/ |
---|
701 | |
---|
702 | static int test_w_in_ConeCC(ideal G, intvec* iv) |
---|
703 | { |
---|
704 | if(G->m[0] == NULL) |
---|
705 | { |
---|
706 | PrintS("//** the result may be WRONG, i.e. 0!!\n"); |
---|
707 | return 0; |
---|
708 | } |
---|
709 | |
---|
710 | BOOLEAN nError = Overflow_Error; |
---|
711 | Overflow_Error = FALSE; |
---|
712 | |
---|
713 | int i, nG = IDELEMS(G); |
---|
714 | poly mi, gi; |
---|
715 | |
---|
716 | for(i=nG-1; i>=0; i--) |
---|
717 | { |
---|
718 | mi = MpolyInitialForm(G->m[i], iv); |
---|
719 | gi = G->m[i]; |
---|
720 | |
---|
721 | if(mi == NULL) |
---|
722 | { |
---|
723 | pDelete(&mi); |
---|
724 | |
---|
725 | if(Overflow_Error == FALSE) |
---|
726 | Overflow_Error = nError; |
---|
727 | |
---|
728 | return 0; |
---|
729 | } |
---|
730 | if(!pLmEqual(mi, gi)) |
---|
731 | { |
---|
732 | pDelete(&mi); |
---|
733 | |
---|
734 | if(Overflow_Error == FALSE) |
---|
735 | Overflow_Error = nError; |
---|
736 | |
---|
737 | return 0; |
---|
738 | } |
---|
739 | |
---|
740 | pDelete(&mi); |
---|
741 | } |
---|
742 | |
---|
743 | if(Overflow_Error == FALSE) |
---|
744 | Overflow_Error = nError; |
---|
745 | |
---|
746 | return 1; |
---|
747 | } |
---|
748 | |
---|
749 | |
---|
750 | //compute a least common multiple of two integers |
---|
751 | static inline long Mlcm(long &i1, long &i2) |
---|
752 | { |
---|
753 | long temp = gcd(i1, i2); |
---|
754 | return ((i1 / temp)* i2); |
---|
755 | } |
---|
756 | |
---|
757 | |
---|
758 | /*************************************************** |
---|
759 | * return the dot product of two intvecs a and b * |
---|
760 | ***************************************************/ |
---|
761 | static inline long MivDotProduct(intvec* a, intvec* b) |
---|
762 | { |
---|
763 | assume( a->length() == b->length()); |
---|
764 | int i, n = a->length(); |
---|
765 | long result = 0; |
---|
766 | |
---|
767 | for(i=n-1; i>=0; i--) |
---|
768 | result += (*a)[i] * (*b)[i]; |
---|
769 | |
---|
770 | return result; |
---|
771 | } |
---|
772 | |
---|
773 | |
---|
774 | static intvec* MivSub(intvec* a, intvec* b) |
---|
775 | { |
---|
776 | assume( a->length() == b->length()); |
---|
777 | int i, n = a->length(); |
---|
778 | intvec* result = new intvec(n); |
---|
779 | |
---|
780 | for(i=n-1; i>=0; i--) |
---|
781 | (*result)[i] = (*a)[i] - (*b)[i]; |
---|
782 | |
---|
783 | return result; |
---|
784 | } |
---|
785 | |
---|
786 | /**21.10.00******************************************* |
---|
787 | * return the "intvec" lead exponent of a polynomial * |
---|
788 | *****************************************************/ |
---|
789 | static intvec* MExpPol(poly f) |
---|
790 | { |
---|
791 | int i, nR = currRing->N; |
---|
792 | intvec* result = new intvec(nR); |
---|
793 | |
---|
794 | for(i=nR-1; i>=0; i--) |
---|
795 | (*result)[i] = pGetExp(f,i+1); |
---|
796 | |
---|
797 | return result; |
---|
798 | } |
---|
799 | |
---|
800 | /* return 1, if two given intvecs are the same, otherwise 0*/ |
---|
801 | int MivSame(intvec* u , intvec* v) |
---|
802 | { |
---|
803 | assume(u->length() == v->length()); |
---|
804 | |
---|
805 | int i, niv = u->length(); |
---|
806 | |
---|
807 | for (i=0; i<niv; i++) |
---|
808 | if ((*u)[i] != (*v)[i]) |
---|
809 | return 0; |
---|
810 | |
---|
811 | return 1; |
---|
812 | } |
---|
813 | |
---|
814 | int M3ivSame(intvec* temp, intvec* u , intvec* v) |
---|
815 | { |
---|
816 | assume(temp->length() == u->length() && u->length() == v->length()); |
---|
817 | |
---|
818 | if((MivSame(temp, u)) == 1) |
---|
819 | return 0; |
---|
820 | |
---|
821 | if((MivSame(temp, v)) == 1) |
---|
822 | return 1; |
---|
823 | |
---|
824 | return 2; |
---|
825 | } |
---|
826 | |
---|
827 | |
---|
828 | /* compute a Groebner basis of an ideal */ |
---|
829 | static ideal MstdCC(ideal G) |
---|
830 | { |
---|
831 | int save_test=test; |
---|
832 | test|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB)); |
---|
833 | ideal G1 = kStd(G, NULL, testHomog, NULL); |
---|
834 | test=save_test; |
---|
835 | |
---|
836 | idSkipZeroes(G1); |
---|
837 | return G1; |
---|
838 | } |
---|
839 | |
---|
840 | |
---|
841 | /* compute a Groebner basis of a homogenoues ideal */ |
---|
842 | static ideal MstdhomCC(ideal G) |
---|
843 | { |
---|
844 | int save_test=test; |
---|
845 | test|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB)); |
---|
846 | ideal G1 = kStd(G, NULL, isHomog, NULL); |
---|
847 | test=save_test; |
---|
848 | |
---|
849 | idSkipZeroes(G1); |
---|
850 | return G1; |
---|
851 | } |
---|
852 | |
---|
853 | |
---|
854 | /***************************************************************************** |
---|
855 | * create a weight matrix order as intvec of an extra weight vector (a(iv),lp)* |
---|
856 | ******************************************************************************/ |
---|
857 | intvec* MivMatrixOrder(intvec* iv) |
---|
858 | { |
---|
859 | int i,j, nR = iv->length(); |
---|
860 | intvec* ivm = new intvec(nR*nR); |
---|
861 | |
---|
862 | for(i=0; i<nR; i++) |
---|
863 | (*ivm)[i] = (*iv)[i]; |
---|
864 | |
---|
865 | for(i=1; i<nR; i++) |
---|
866 | (*ivm)[i*nR+i-1] = 1; |
---|
867 | |
---|
868 | return ivm; |
---|
869 | } |
---|
870 | |
---|
871 | /* return intvec = (1, ..., 1) */ |
---|
872 | intvec* Mivdp(int nR) |
---|
873 | { |
---|
874 | int i; |
---|
875 | intvec* ivm = new intvec(nR); |
---|
876 | |
---|
877 | for(i=nR-1; i>=0; i--) |
---|
878 | (*ivm)[i] = 1; |
---|
879 | |
---|
880 | return ivm; |
---|
881 | } |
---|
882 | |
---|
883 | /* return intvvec = (1,0, ..., 0) */ |
---|
884 | intvec* Mivlp(int nR) |
---|
885 | { |
---|
886 | int i; |
---|
887 | intvec* ivm = new intvec(nR); |
---|
888 | (*ivm)[0] = 1; |
---|
889 | |
---|
890 | return ivm; |
---|
891 | } |
---|
892 | |
---|
893 | /**** 28.10.02 print the max total degree and the max coefficient of G***/ |
---|
894 | static void checkComplexity(ideal G, char* cG) |
---|
895 | { |
---|
896 | int nV = currRing->N; |
---|
897 | int nG = IDELEMS(G); |
---|
898 | intvec* ivUnit = Mivdp(nV);//19.02 |
---|
899 | int i,j, tmpdeg, maxdeg=0; |
---|
900 | number tmpcoeff , maxcoeff=nNULL; |
---|
901 | poly p; |
---|
902 | for(i=nG-1; i>=0; i--) |
---|
903 | { |
---|
904 | tmpdeg = MwalkWeightDegree(G->m[i], ivUnit); |
---|
905 | if (tmpdeg > maxdeg ) |
---|
906 | maxdeg = tmpdeg; |
---|
907 | } |
---|
908 | |
---|
909 | for(i=nG-1; i>=0; i--) |
---|
910 | { |
---|
911 | p = pCopy(G->m[i]); |
---|
912 | while(p != NULL) |
---|
913 | { |
---|
914 | //tmpcoeff = pGetCoeff(pHead(p)); |
---|
915 | tmpcoeff = pGetCoeff(p); |
---|
916 | if(nGreater(tmpcoeff,maxcoeff)) |
---|
917 | maxcoeff = nCopy(tmpcoeff); |
---|
918 | pIter(p); |
---|
919 | } |
---|
920 | pDelete(&p); |
---|
921 | } |
---|
922 | p = pNSet(maxcoeff); |
---|
923 | char* pStr = pString(p); |
---|
924 | Print("// max total degree of %s = %d\n",cG, maxdeg); |
---|
925 | Print("// max coefficient of %s = %s", cG, pStr);//ing(p)); |
---|
926 | Print(" which consists of %d digits", strlen(pStr)); |
---|
927 | PrintLn(); |
---|
928 | } |
---|
929 | |
---|
930 | |
---|
931 | |
---|
932 | /***************************************************************************** |
---|
933 | * If target_ord = intmat(A1, ..., An) then calculate the perturbation * |
---|
934 | * vectors * |
---|
935 | * tau_p_dep = inveps^(p_deg-1)*A1 + inveps^(p_deg-2)*A2 +... + A_p_deg * |
---|
936 | * where * |
---|
937 | * inveps > totaldegree(G)*(max(A2)+...+max(A_p_deg)) * |
---|
938 | * intmat target_ord is an integer order matrix of the monomial ordering of * |
---|
939 | * basering. * |
---|
940 | * This programm computes a perturbated vector with a p_deg perturbation * |
---|
941 | * degree which smaller than the numbers of variables * |
---|
942 | ******************************************************************************/ |
---|
943 | /* ivtarget is a matrix order of a degree reverse lex. order */ |
---|
944 | intvec* MPertVectors(ideal G, intvec* ivtarget, int pdeg) |
---|
945 | { |
---|
946 | int nV = currRing->N; |
---|
947 | //assume(pdeg <= nV && pdeg >= 0); |
---|
948 | |
---|
949 | int i, j, nG = IDELEMS(G); |
---|
950 | intvec* v_null = new intvec(nV); |
---|
951 | |
---|
952 | |
---|
953 | //Checking that the perturbed degree is valid |
---|
954 | if(pdeg > nV || pdeg <= 0) |
---|
955 | { |
---|
956 | WerrorS("//** The perturbed degree is wrong!!"); |
---|
957 | return v_null; |
---|
958 | } |
---|
959 | delete v_null; |
---|
960 | |
---|
961 | if(pdeg == 1) |
---|
962 | return ivtarget; |
---|
963 | |
---|
964 | mpz_t *pert_vector=(mpz_t*)omAlloc(nV*sizeof(mpz_t)); |
---|
965 | |
---|
966 | for(i=0; i<nV; i++) |
---|
967 | mpz_init_set_si(pert_vector[i], (*ivtarget)[i]); |
---|
968 | |
---|
969 | |
---|
970 | // Calculate max1 = Max(A2)+Max(A3)+...+Max(Apdeg), |
---|
971 | // where the Ai are the i-te rows of the matrix target_ord. |
---|
972 | |
---|
973 | int ntemp, maxAi, maxA=0; |
---|
974 | for(i=1; i<pdeg; i++) |
---|
975 | { |
---|
976 | maxAi = (*ivtarget)[i*nV]; |
---|
977 | if(maxAi<0) maxAi = -maxAi; |
---|
978 | |
---|
979 | for(j=i*nV+1; j<(i+1)*nV; j++) |
---|
980 | { |
---|
981 | ntemp = (*ivtarget)[j]; |
---|
982 | if(ntemp < 0) ntemp = -ntemp; |
---|
983 | |
---|
984 | if(ntemp > maxAi) |
---|
985 | maxAi = ntemp; |
---|
986 | } |
---|
987 | maxA += maxAi; |
---|
988 | } |
---|
989 | |
---|
990 | // Calculate inveps = 1/eps, where 1/eps > totaldeg(p)*max1 for all p in G. |
---|
991 | |
---|
992 | intvec* ivUnit = Mivdp(nV); |
---|
993 | |
---|
994 | mpz_t tot_deg; mpz_init(tot_deg); |
---|
995 | mpz_t maxdeg; mpz_init(maxdeg); |
---|
996 | mpz_t inveps; mpz_init(inveps); |
---|
997 | |
---|
998 | |
---|
999 | for(i=nG-1; i>=0; i--) |
---|
1000 | { |
---|
1001 | mpz_set_ui(maxdeg, MwalkWeightDegree(G->m[i], ivUnit)); |
---|
1002 | if (mpz_cmp(maxdeg, tot_deg) > 0 ) |
---|
1003 | mpz_set(tot_deg, maxdeg); |
---|
1004 | } |
---|
1005 | |
---|
1006 | delete ivUnit; |
---|
1007 | mpz_mul_ui(inveps, tot_deg, maxA); |
---|
1008 | mpz_add_ui(inveps, inveps, 1); |
---|
1009 | |
---|
1010 | |
---|
1011 | //xx1.06.02 takes "small" inveps |
---|
1012 | #ifdef INVEPS_SMALL_IN_MPERTVECTOR |
---|
1013 | if(mpz_cmp_ui(inveps, pdeg)>0 && pdeg > 3) |
---|
1014 | { |
---|
1015 | /* |
---|
1016 | Print("\n// choose the\"small\" inverse epsilon := %d / %d = ", |
---|
1017 | mpz_get_si(inveps), pdeg); |
---|
1018 | */ |
---|
1019 | mpz_fdiv_q_ui(inveps, inveps, pdeg); |
---|
1020 | //mpz_out_str(stdout, 10, inveps); |
---|
1021 | } |
---|
1022 | #else |
---|
1023 | //PrintS("\n// the \"big\" inverse epsilon: "); |
---|
1024 | mpz_out_str(stdout, 10, inveps); |
---|
1025 | #endif |
---|
1026 | |
---|
1027 | // pert(A1) = inveps^(pdeg-1)*A1 + inveps^(pdeg-2)*A2+...+A_pdeg, |
---|
1028 | // pert_vector := A1 |
---|
1029 | for ( i=1; i < pdeg; i++ ) |
---|
1030 | for(j=0; j<nV; j++) |
---|
1031 | { |
---|
1032 | mpz_mul(pert_vector[j], pert_vector[j], inveps); |
---|
1033 | if((*ivtarget)[i*nV+j]<0) |
---|
1034 | mpz_sub_ui(pert_vector[j], pert_vector[j],-(*ivtarget)[i*nV+j]); |
---|
1035 | else |
---|
1036 | mpz_add_ui(pert_vector[j], pert_vector[j],(*ivtarget)[i*nV+j]); |
---|
1037 | } |
---|
1038 | |
---|
1039 | mpz_t ztemp; |
---|
1040 | mpz_init(ztemp); |
---|
1041 | mpz_set(ztemp, pert_vector[0]); |
---|
1042 | for(i=1; i<nV; i++) |
---|
1043 | { |
---|
1044 | mpz_gcd(ztemp, ztemp, pert_vector[i]); |
---|
1045 | if(mpz_cmp_si(ztemp, 1) == 0) |
---|
1046 | break; |
---|
1047 | } |
---|
1048 | if(mpz_cmp_si(ztemp, 1) != 0) |
---|
1049 | for(i=0; i<nV; i++) |
---|
1050 | mpz_divexact(pert_vector[i], pert_vector[i], ztemp); |
---|
1051 | |
---|
1052 | intvec* result = new intvec(nV); |
---|
1053 | /* 2147483647 is max. integer representation in SINGULAR */ |
---|
1054 | mpz_t sing_int; |
---|
1055 | mpz_init_set_ui(sing_int, 2147483647); |
---|
1056 | |
---|
1057 | int ntrue=0; |
---|
1058 | for(i=0; i<nV; i++) |
---|
1059 | { |
---|
1060 | (*result)[i] = mpz_get_si(pert_vector[i]); |
---|
1061 | |
---|
1062 | if(mpz_cmp(pert_vector[i], sing_int)>=0) |
---|
1063 | { |
---|
1064 | ntrue++; |
---|
1065 | if(Overflow_Error == FALSE) |
---|
1066 | { |
---|
1067 | Overflow_Error = TRUE; |
---|
1068 | PrintS("\n// ** OVERFLOW in \"MPertvectors\": "); |
---|
1069 | mpz_out_str( stdout, 10, pert_vector[i]); |
---|
1070 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
1071 | Print("\n// So vector[%d] := %d is wrong!!", i+1, (*result)[i]); |
---|
1072 | } |
---|
1073 | } |
---|
1074 | } |
---|
1075 | |
---|
1076 | if(Overflow_Error == TRUE) |
---|
1077 | { |
---|
1078 | ivString(result, "pert_vector"); |
---|
1079 | Print("\n// %d element(s) of it is overflow!!", ntrue); |
---|
1080 | } |
---|
1081 | |
---|
1082 | mpz_clear(ztemp); |
---|
1083 | mpz_clear(sing_int); |
---|
1084 | omFree(pert_vector); |
---|
1085 | return result; |
---|
1086 | } |
---|
1087 | |
---|
1088 | |
---|
1089 | /* ivtarget is a matrix order of the lex. order */ |
---|
1090 | intvec* MPertVectorslp(ideal G, intvec* ivtarget, int pdeg) |
---|
1091 | { |
---|
1092 | int nV = currRing->N; |
---|
1093 | //assume(pdeg <= nV && pdeg >= 0); |
---|
1094 | |
---|
1095 | int i, j, nG = IDELEMS(G); |
---|
1096 | intvec* pert_vector = new intvec(nV); |
---|
1097 | |
---|
1098 | //Checking that the perturbated degree is valid |
---|
1099 | if(pdeg > nV || pdeg <= 0) |
---|
1100 | { |
---|
1101 | WerrorS("//** The perturbed degree is wrong!!"); |
---|
1102 | return pert_vector; |
---|
1103 | } |
---|
1104 | for(i=0; i<nV; i++) |
---|
1105 | (*pert_vector)[i]=(*ivtarget)[i]; |
---|
1106 | |
---|
1107 | if(pdeg == 1) |
---|
1108 | return pert_vector; |
---|
1109 | |
---|
1110 | // Calculate max1 = Max(A2)+Max(A3)+...+Max(Apdeg), |
---|
1111 | // where the Ai are the i-te rows of the matrix target_ord. |
---|
1112 | int ntemp, maxAi, maxA=0; |
---|
1113 | for(i=1; i<pdeg; i++) |
---|
1114 | { |
---|
1115 | maxAi = (*ivtarget)[i*nV]; |
---|
1116 | for(j=i*nV+1; j<(i+1)*nV; j++) |
---|
1117 | { |
---|
1118 | ntemp = (*ivtarget)[j]; |
---|
1119 | if(ntemp > maxAi) |
---|
1120 | maxAi = ntemp; |
---|
1121 | } |
---|
1122 | maxA += maxAi; |
---|
1123 | } |
---|
1124 | |
---|
1125 | // Calculate inveps := 1/eps, where 1/eps > deg(p)*max1 for all p in G. |
---|
1126 | int inveps, tot_deg = 0, maxdeg; |
---|
1127 | |
---|
1128 | intvec* ivUnit = Mivdp(nV);//19.02 |
---|
1129 | for(i=nG-1; i>=0; i--) |
---|
1130 | { |
---|
1131 | //maxdeg = pTotaldegree(G->m[i], currRing); //it's wrong for ex1,2,rose |
---|
1132 | maxdeg = MwalkWeightDegree(G->m[i], ivUnit); |
---|
1133 | if (maxdeg > tot_deg ) |
---|
1134 | tot_deg = maxdeg; |
---|
1135 | } |
---|
1136 | delete ivUnit; |
---|
1137 | |
---|
1138 | inveps = (tot_deg * maxA) + 1; |
---|
1139 | |
---|
1140 | //9.10.01 |
---|
1141 | #ifdef INVEPS_SMALL_IN_FRACTAL |
---|
1142 | /* |
---|
1143 | Print("\n// choose the\"small\" inverse epsilon := %d / %d = ", |
---|
1144 | inveps, pdeg); |
---|
1145 | */ |
---|
1146 | if(inveps > pdeg && pdeg > 3) |
---|
1147 | inveps = inveps / pdeg; |
---|
1148 | |
---|
1149 | //Print(" %d", inveps); |
---|
1150 | #else |
---|
1151 | PrintS("\n// the \"big\" inverse epsilon %d", inveps); |
---|
1152 | #endif |
---|
1153 | |
---|
1154 | // Pert(A1) = inveps^(pdeg-1)*A1 + inveps^(pdeg-2)*A2+...+A_pdeg, |
---|
1155 | for ( i=1; i < pdeg; i++ ) |
---|
1156 | for(j=0; j<nV; j++) |
---|
1157 | (*pert_vector)[j] = inveps*((*pert_vector)[j]) + (*ivtarget)[i*nV+j]; |
---|
1158 | |
---|
1159 | int temp = (*pert_vector)[0]; |
---|
1160 | for(i=1; i<nV; i++) |
---|
1161 | { |
---|
1162 | temp = gcd(temp, (*pert_vector)[i]); |
---|
1163 | if(temp == 1) |
---|
1164 | break; |
---|
1165 | } |
---|
1166 | if(temp != 1) |
---|
1167 | for(i=0; i<nV; i++) |
---|
1168 | (*pert_vector)[i] = (*pert_vector)[i] / temp; |
---|
1169 | |
---|
1170 | intvec* result = pert_vector; |
---|
1171 | pert_vector = NULL; |
---|
1172 | return result; |
---|
1173 | } |
---|
1174 | |
---|
1175 | |
---|
1176 | /* define a lexicographic order matrix as intvec */ |
---|
1177 | intvec* MivMatrixOrderlp(int nV) |
---|
1178 | { |
---|
1179 | int i; |
---|
1180 | intvec* ivM = new intvec(nV*nV); |
---|
1181 | |
---|
1182 | for(i=0; i<nV; i++) |
---|
1183 | (*ivM)[i*nV + i] = 1; |
---|
1184 | |
---|
1185 | return(ivM); |
---|
1186 | } |
---|
1187 | |
---|
1188 | /* define a rlex order (dp) matrix as intvec */ |
---|
1189 | intvec* MivMatrixOrderdp(int nV) |
---|
1190 | { |
---|
1191 | int i; |
---|
1192 | intvec* ivM = new intvec(nV*nV); |
---|
1193 | |
---|
1194 | for(i=0; i<nV; i++) |
---|
1195 | (*ivM)[i] = 1; |
---|
1196 | |
---|
1197 | for(i=1; i<nV; i++) |
---|
1198 | (*ivM)[(i+1)*nV - i] = -1; |
---|
1199 | |
---|
1200 | return(ivM); |
---|
1201 | } |
---|
1202 | |
---|
1203 | //creates an intvec of the monomial order Wp(ivstart) |
---|
1204 | intvec* MivWeightOrderlp(intvec* ivstart) |
---|
1205 | { |
---|
1206 | int i; |
---|
1207 | int nV = ivstart->length(); |
---|
1208 | intvec* ivM = new intvec(nV*nV); |
---|
1209 | |
---|
1210 | for(i=0; i<nV; i++) |
---|
1211 | (*ivM)[i] = (*ivstart)[i]; |
---|
1212 | |
---|
1213 | for(i=1; i<nV; i++) |
---|
1214 | (*ivM)[i*nV + i-1] = 1; |
---|
1215 | |
---|
1216 | return(ivM); |
---|
1217 | } |
---|
1218 | |
---|
1219 | intvec* MivWeightOrderdp(intvec* ivstart) |
---|
1220 | { |
---|
1221 | int i; |
---|
1222 | int nV = ivstart->length(); |
---|
1223 | intvec* ivM = new intvec(nV*nV); |
---|
1224 | |
---|
1225 | for(i=0; i<nV; i++) |
---|
1226 | (*ivM)[i] = (*ivstart)[i]; |
---|
1227 | |
---|
1228 | for(i=0; i<nV; i++) |
---|
1229 | (*ivM)[nV+i] = 1; |
---|
1230 | |
---|
1231 | for(i=2; i<nV; i++) |
---|
1232 | (*ivM)[(i+1)*nV - i] = -1; |
---|
1233 | |
---|
1234 | return(ivM); |
---|
1235 | } |
---|
1236 | |
---|
1237 | static intvec* MatrixOrderdp(int nV) |
---|
1238 | { |
---|
1239 | int i; |
---|
1240 | intvec* ivM = new intvec(nV*nV); |
---|
1241 | |
---|
1242 | for(i=0; i<nV; i++) |
---|
1243 | (*ivM)[i] = 1; |
---|
1244 | |
---|
1245 | for(i=1; i<nV; i++) |
---|
1246 | (*ivM)[(i+1)*nV - i] = -1; |
---|
1247 | |
---|
1248 | return(ivM); |
---|
1249 | } |
---|
1250 | |
---|
1251 | intvec* MivUnit(int nV) |
---|
1252 | { |
---|
1253 | int i; |
---|
1254 | intvec* ivM = new intvec(nV); |
---|
1255 | |
---|
1256 | for(i=nV-1; i>=0; i--) |
---|
1257 | (*ivM)[i] = 1; |
---|
1258 | |
---|
1259 | return(ivM); |
---|
1260 | } |
---|
1261 | |
---|
1262 | |
---|
1263 | /************************************************************************ |
---|
1264 | * compute a perturbed weight vector of a matrix order w.r.t. an ideal * |
---|
1265 | *************************************************************************/ |
---|
1266 | int Xnlev; |
---|
1267 | |
---|
1268 | intvec* Mfpertvector(ideal G, intvec* ivtarget) |
---|
1269 | { |
---|
1270 | int i, j, nG = IDELEMS(G); |
---|
1271 | int nV = currRing->N; |
---|
1272 | int niv = nV*nV; |
---|
1273 | |
---|
1274 | // Calculate max1 = Max(A2) + Max(A3) + ... + Max(AnV), |
---|
1275 | // where the Ai are the i-te rows of the matrix 'targer_ord'. |
---|
1276 | int ntemp, maxAi, maxA=0; |
---|
1277 | for(i=1; i<nV; i++) |
---|
1278 | { |
---|
1279 | maxAi = (*ivtarget)[i*nV]; |
---|
1280 | if(maxAi<0) maxAi = -maxAi; |
---|
1281 | |
---|
1282 | for(j=i*nV+1; j<(i+1)*nV; j++) |
---|
1283 | { |
---|
1284 | ntemp = (*ivtarget)[j]; |
---|
1285 | if(ntemp < 0) ntemp = -ntemp; |
---|
1286 | |
---|
1287 | if(ntemp > maxAi) |
---|
1288 | maxAi = ntemp; |
---|
1289 | } |
---|
1290 | maxA = maxA + maxAi; |
---|
1291 | } |
---|
1292 | intvec* ivUnit = Mivdp(nV); |
---|
1293 | |
---|
1294 | // Calculate inveps = 1/eps, where 1/eps > deg(p)*max1 for all p in G. |
---|
1295 | mpz_t tot_deg; mpz_init(tot_deg); |
---|
1296 | mpz_t maxdeg; mpz_init(maxdeg); |
---|
1297 | mpz_t inveps; mpz_init(inveps); |
---|
1298 | |
---|
1299 | |
---|
1300 | for(i=nG-1; i>=0; i--) |
---|
1301 | { |
---|
1302 | mpz_set_ui(maxdeg, MwalkWeightDegree(G->m[i], ivUnit)); |
---|
1303 | if (mpz_cmp(maxdeg, tot_deg) > 0 ) |
---|
1304 | mpz_set(tot_deg, maxdeg); |
---|
1305 | } |
---|
1306 | |
---|
1307 | delete ivUnit; |
---|
1308 | //inveps = (tot_deg * maxA) + 1; |
---|
1309 | mpz_mul_ui(inveps, tot_deg, maxA); |
---|
1310 | mpz_add_ui(inveps, inveps, 1); |
---|
1311 | |
---|
1312 | //xx1.06.02 takes "small" inveps |
---|
1313 | #ifdef INVEPS_SMALL_IN_FRACTAL |
---|
1314 | if(mpz_cmp_ui(inveps, nV)>0 && nV > 3) |
---|
1315 | mpz_cdiv_q_ui(inveps, inveps, nV); |
---|
1316 | |
---|
1317 | //PrintS("\n// choose the \"small\" inverse epsilon!"); |
---|
1318 | #endif |
---|
1319 | |
---|
1320 | // PrintLn(); mpz_out_str(stdout, 10, inveps); |
---|
1321 | |
---|
1322 | // Calculate the perturbed target orders: |
---|
1323 | mpz_t *ivtemp=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
1324 | mpz_t *pert_vector=(mpz_t *)omAlloc(niv*sizeof(mpz_t)); |
---|
1325 | |
---|
1326 | for(i=0; i<nV; i++) |
---|
1327 | { |
---|
1328 | mpz_init_set_si(ivtemp[i], (*ivtarget)[i]); |
---|
1329 | mpz_init_set_si(pert_vector[i], (*ivtarget)[i]); |
---|
1330 | } |
---|
1331 | |
---|
1332 | mpz_t ztmp; mpz_init(ztmp); |
---|
1333 | BOOLEAN isneg = FALSE; |
---|
1334 | |
---|
1335 | for(i=1; i<nV; i++) |
---|
1336 | { |
---|
1337 | for(j=0; j<nV; j++) |
---|
1338 | { |
---|
1339 | mpz_mul(ztmp, inveps, ivtemp[j]); |
---|
1340 | |
---|
1341 | if((*ivtarget)[i*nV+j]<0) |
---|
1342 | mpz_sub_ui(ivtemp[j], ztmp, -(*ivtarget)[i*nV+j]); |
---|
1343 | else |
---|
1344 | mpz_add_ui(ivtemp[j], ztmp,(*ivtarget)[i*nV+j]); |
---|
1345 | } |
---|
1346 | |
---|
1347 | for(j=0; j<nV; j++) |
---|
1348 | mpz_init_set(pert_vector[i*nV+j],ivtemp[j]); |
---|
1349 | } |
---|
1350 | |
---|
1351 | /* 2147483647 is max. integer representation in SINGULAR */ |
---|
1352 | mpz_t sing_int; |
---|
1353 | mpz_init_set_ui(sing_int, 2147483647); |
---|
1354 | |
---|
1355 | intvec* result = new intvec(niv); |
---|
1356 | BOOLEAN nflow = FALSE; |
---|
1357 | |
---|
1358 | // computes gcd |
---|
1359 | mpz_set(ztmp, pert_vector[0]); |
---|
1360 | for(i=0; i<niv; i++) |
---|
1361 | { |
---|
1362 | mpz_gcd(ztmp, ztmp, pert_vector[i]); |
---|
1363 | if(mpz_cmp_si(ztmp, 1)==0) |
---|
1364 | break; |
---|
1365 | } |
---|
1366 | |
---|
1367 | for(i=0; i<niv; i++) |
---|
1368 | { |
---|
1369 | mpz_divexact(pert_vector[i], pert_vector[i], ztmp); |
---|
1370 | (* result)[i] = mpz_get_si(pert_vector[i]); |
---|
1371 | |
---|
1372 | if(mpz_cmp(pert_vector[i], sing_int)>0) |
---|
1373 | if(nflow == FALSE) |
---|
1374 | { |
---|
1375 | Xnlev = i / nV; |
---|
1376 | nflow = TRUE; |
---|
1377 | Overflow_Error = TRUE; |
---|
1378 | |
---|
1379 | Print("\n// Xlev = %d and the %d-th element is", Xnlev, i+1); |
---|
1380 | PrintS("\n// ** OVERFLOW in \"Mfpertvector\": "); |
---|
1381 | mpz_out_str( stdout, 10, pert_vector[i]); |
---|
1382 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
1383 | Print("\n// So vector[%d] := %d is wrong!!", i+1, (*result)[i]); |
---|
1384 | } |
---|
1385 | } |
---|
1386 | |
---|
1387 | if(Overflow_Error == TRUE) |
---|
1388 | ivString(result, "new_vector"); |
---|
1389 | |
---|
1390 | omFree(pert_vector); |
---|
1391 | omFree(ivtemp); |
---|
1392 | mpz_clear(ztmp); |
---|
1393 | |
---|
1394 | return result; |
---|
1395 | } |
---|
1396 | |
---|
1397 | /**************************************************************** |
---|
1398 | * Multiplikation of two ideals by elementwise * |
---|
1399 | * i.e. Let be A := (a_i) and B := (b_i), return C := (a_i*b_i) * |
---|
1400 | * destroy A, keeps B * |
---|
1401 | ****************************************************************/ |
---|
1402 | static ideal MidMult(ideal A, ideal B) |
---|
1403 | { |
---|
1404 | int mA = IDELEMS(A), mB = IDELEMS(B); |
---|
1405 | |
---|
1406 | if(A==NULL || B==NULL) |
---|
1407 | return NULL; |
---|
1408 | |
---|
1409 | if(mB < mA) |
---|
1410 | mA = mB; |
---|
1411 | |
---|
1412 | ideal result = idInit(mA, 1); |
---|
1413 | |
---|
1414 | int i, k=0; |
---|
1415 | for(i=0; i<mA; i++) |
---|
1416 | { |
---|
1417 | result->m[k] = pMult(A->m[i], pCopy(B->m[i])); |
---|
1418 | A->m[i]=NULL; |
---|
1419 | if (result->m[k]!=NULL) k++; |
---|
1420 | } |
---|
1421 | |
---|
1422 | idDelete(&A); |
---|
1423 | idSkipZeroes(result); |
---|
1424 | return result; |
---|
1425 | } |
---|
1426 | |
---|
1427 | /********************************************************************* |
---|
1428 | * G is a red. Groebner basis w.r.t. <_1 * |
---|
1429 | * Gomega is an initial form ideal of <G> w.r.t. a weight vector w * |
---|
1430 | * M is a subideal of <Gomega> and M selft is a red. Groebner basis * |
---|
1431 | * of the ideal <Gomega> w.r.t. <_w * |
---|
1432 | * Let m_i = h1.gw1 + ... + hs.gws for each m_i in M; gwi in Gomega * |
---|
1433 | * return F with n(F) = n(M) and f_i = h1.g1 + ... + hs.gs for each i* |
---|
1434 | ********************************************************************/ |
---|
1435 | static ideal MLifttwoIdeal(ideal Gw, ideal M, ideal G) |
---|
1436 | { |
---|
1437 | ideal Mtmp = idLift(Gw, M, NULL, FALSE, TRUE, TRUE, NULL); |
---|
1438 | |
---|
1439 | //3.12.02 Note: if Gw is a GB, then isSB = TRUE, otherwise FALSE |
---|
1440 | //So, it is better, if one tests whether Gw is a GB |
---|
1441 | //in ideals.cc: |
---|
1442 | //idLift (ideal mod, ideal submod,ideal * rest, BOOLEAN goodShape, |
---|
1443 | // BOOLEAN isSB,BOOLEAN divide,matrix * unit) |
---|
1444 | |
---|
1445 | /* Let be Mtmp = {m1,...,ms}, where mi=sum hij.in_gj, for all i=1,...,s |
---|
1446 | We compute F = {f1,...,fs}, where fi=sum hij.gj */ |
---|
1447 | int i, j, nM = IDELEMS(Mtmp); |
---|
1448 | ideal idpol, idLG; |
---|
1449 | ideal F = idInit(nM, 1); |
---|
1450 | |
---|
1451 | for(i=0; i<nM; i++) |
---|
1452 | { |
---|
1453 | idpol = idVec2Ideal(Mtmp->m[i]); |
---|
1454 | idLG = MidMult(idpol, G); |
---|
1455 | idpol = NULL; |
---|
1456 | F->m[i] = NULL; |
---|
1457 | for(j=IDELEMS(idLG)-1; j>=0; j--) |
---|
1458 | { |
---|
1459 | F->m[i] = pAdd(F->m[i], idLG->m[j]); |
---|
1460 | idLG->m[j]=NULL; |
---|
1461 | } |
---|
1462 | idDelete(&idLG); |
---|
1463 | } |
---|
1464 | idDelete(&Mtmp); |
---|
1465 | return F; |
---|
1466 | } |
---|
1467 | |
---|
1468 | |
---|
1469 | static void checkidealCC(ideal G, char* Ch) |
---|
1470 | { |
---|
1471 | int i,nmon=0,ntmp; |
---|
1472 | int nG = IDELEMS(G); |
---|
1473 | int n = nG-1; |
---|
1474 | Print("\n//** Ideal %s besteht aus %d Polynomen mit ", Ch, nG); |
---|
1475 | |
---|
1476 | for(i=0; i<nG; i++) |
---|
1477 | { |
---|
1478 | ntmp = pLength(G->m[i]); |
---|
1479 | nmon += ntmp; |
---|
1480 | |
---|
1481 | if(i != n) |
---|
1482 | Print("%d, ", ntmp); |
---|
1483 | else |
---|
1484 | Print(" bzw. %d ", ntmp); |
---|
1485 | } |
---|
1486 | PrintS(" Monomen.\n"); |
---|
1487 | Print("//** %s besitzt %d Monome.", Ch, nmon); |
---|
1488 | PrintLn(); |
---|
1489 | } |
---|
1490 | |
---|
1491 | static void HeadidString(ideal L, char* st) |
---|
1492 | { |
---|
1493 | int i, nL = IDELEMS(L)-1; |
---|
1494 | |
---|
1495 | Print("// The head terms of the ideal %s = ", st); |
---|
1496 | for(i=0; i<nL; i++) |
---|
1497 | Print(" %s, ", pString(pHead(L->m[i]))); |
---|
1498 | |
---|
1499 | Print(" %s;\n", pString(pHead(L->m[nL]))); |
---|
1500 | } |
---|
1501 | |
---|
1502 | static inline int MivComp(intvec* iva, intvec* ivb) |
---|
1503 | { |
---|
1504 | assume(iva->length() == ivb->length()); |
---|
1505 | int i; |
---|
1506 | |
---|
1507 | for(i=iva->length()-1; i>=0; i--) |
---|
1508 | if((*iva)[i] - (*ivb)[i] != 0) |
---|
1509 | return 0; |
---|
1510 | |
---|
1511 | return 1; |
---|
1512 | } |
---|
1513 | |
---|
1514 | |
---|
1515 | /* |
---|
1516 | compute a next weight vector between curr_weight and target_weight |
---|
1517 | with respect to an ideal G. |
---|
1518 | */ |
---|
1519 | static intvec* MwalkNextWeightCC(intvec* curr_weight, intvec* target_weight, |
---|
1520 | ideal G) |
---|
1521 | { |
---|
1522 | BOOLEAN nError = Overflow_Error; |
---|
1523 | Overflow_Error = FALSE; |
---|
1524 | |
---|
1525 | assume(currRing != NULL && curr_weight != NULL && |
---|
1526 | target_weight != NULL && G != NULL); |
---|
1527 | |
---|
1528 | int nRing = currRing->N; |
---|
1529 | int j, nG = IDELEMS(G); |
---|
1530 | intvec* ivtemp; |
---|
1531 | |
---|
1532 | mpz_t t_zaehler, t_nenner; |
---|
1533 | mpz_init(t_zaehler); |
---|
1534 | mpz_init(t_nenner); |
---|
1535 | |
---|
1536 | mpz_t s_zaehler, s_nenner, temp, MwWd; |
---|
1537 | mpz_init(s_zaehler); |
---|
1538 | mpz_init(s_nenner); |
---|
1539 | mpz_init(temp); |
---|
1540 | mpz_init(MwWd); |
---|
1541 | |
---|
1542 | |
---|
1543 | mpz_t deg_w0_p1, deg_d0_p1; |
---|
1544 | mpz_init(deg_w0_p1); |
---|
1545 | mpz_init(deg_d0_p1); |
---|
1546 | |
---|
1547 | mpz_t sztn, sntz; |
---|
1548 | mpz_init(sztn); |
---|
1549 | mpz_init(sntz); |
---|
1550 | mpz_t t_null; |
---|
1551 | mpz_init(t_null); |
---|
1552 | |
---|
1553 | mpz_t ggt; |
---|
1554 | |
---|
1555 | int tn0, tn1, tz1, ncmp, gcd_tmp, ntmp; |
---|
1556 | intvec* diff_weight = MivSub(target_weight, curr_weight); |
---|
1557 | |
---|
1558 | poly g, gw; |
---|
1559 | for (j=0; j<nG; j++) |
---|
1560 | { |
---|
1561 | g = G->m[j]; |
---|
1562 | if (g != NULL) |
---|
1563 | { |
---|
1564 | ivtemp = MExpPol(g); |
---|
1565 | mpz_set_si(deg_w0_p1, MivDotProduct(ivtemp, curr_weight)); |
---|
1566 | mpz_set_si(deg_d0_p1, MivDotProduct(ivtemp, diff_weight)); |
---|
1567 | delete ivtemp; |
---|
1568 | |
---|
1569 | pIter(g); |
---|
1570 | while (g != NULL) |
---|
1571 | { |
---|
1572 | ivtemp = MExpPol(g); |
---|
1573 | mpz_set_si(MwWd, MivDotProduct(ivtemp, curr_weight)); |
---|
1574 | mpz_sub(s_zaehler, deg_w0_p1, MwWd); |
---|
1575 | |
---|
1576 | if(mpz_cmp(s_zaehler, t_null) != 0) |
---|
1577 | { |
---|
1578 | mpz_set_si(MwWd, MivDotProduct(ivtemp, diff_weight)); |
---|
1579 | mpz_sub(s_nenner, MwWd, deg_d0_p1); |
---|
1580 | |
---|
1581 | // check for 0 < s <= 1 |
---|
1582 | if( (mpz_cmp(s_zaehler,t_null) > 0 && |
---|
1583 | mpz_cmp(s_nenner, s_zaehler)>=0) || |
---|
1584 | (mpz_cmp(s_zaehler, t_null) < 0 && |
---|
1585 | mpz_cmp(s_nenner, s_zaehler)<=0)) |
---|
1586 | { |
---|
1587 | // make both positive |
---|
1588 | if (mpz_cmp(s_zaehler, t_null) < 0) |
---|
1589 | { |
---|
1590 | mpz_neg(s_zaehler, s_zaehler); |
---|
1591 | mpz_neg(s_nenner, s_nenner); |
---|
1592 | } |
---|
1593 | |
---|
1594 | //compute a simply fraction of s |
---|
1595 | cancel(s_zaehler, s_nenner); |
---|
1596 | |
---|
1597 | if(mpz_cmp(t_nenner, t_null) != 0) |
---|
1598 | { |
---|
1599 | mpz_mul(sztn, s_zaehler, t_nenner); |
---|
1600 | mpz_mul(sntz, s_nenner, t_zaehler); |
---|
1601 | |
---|
1602 | if(mpz_cmp(sztn,sntz) < 0) |
---|
1603 | { |
---|
1604 | mpz_add(t_nenner, t_null, s_nenner); |
---|
1605 | mpz_add(t_zaehler,t_null, s_zaehler); |
---|
1606 | } |
---|
1607 | } |
---|
1608 | else |
---|
1609 | { |
---|
1610 | mpz_add(t_nenner, t_null, s_nenner); |
---|
1611 | mpz_add(t_zaehler,t_null, s_zaehler); |
---|
1612 | } |
---|
1613 | } |
---|
1614 | } |
---|
1615 | pIter(g); |
---|
1616 | delete ivtemp; |
---|
1617 | } |
---|
1618 | } |
---|
1619 | } |
---|
1620 | |
---|
1621 | mpz_t *vec=(mpz_t*)omAlloc(nRing*sizeof(mpz_t)); |
---|
1622 | |
---|
1623 | /* there is no 0<t<1 and define the next weight vector that is equal to |
---|
1624 | the current weight vector */ |
---|
1625 | if(mpz_cmp(t_nenner, t_null) == 0) |
---|
1626 | { |
---|
1627 | delete diff_weight; |
---|
1628 | diff_weight = ivCopy(curr_weight);//take memory |
---|
1629 | goto FINISH; |
---|
1630 | } |
---|
1631 | |
---|
1632 | /* define the target vector as the next weight vector, if t = 1 */ |
---|
1633 | if(mpz_cmp_si(t_nenner, 1)==0 && mpz_cmp_si(t_zaehler,1)==0) |
---|
1634 | { |
---|
1635 | delete diff_weight; |
---|
1636 | diff_weight = ivCopy(target_weight); //this takes memory |
---|
1637 | goto FINISH; |
---|
1638 | } |
---|
1639 | |
---|
1640 | |
---|
1641 | //14.08.03 simplify the both vectors curr_weight and diff_weight (C-int) |
---|
1642 | gcd_tmp = (*curr_weight)[0]; |
---|
1643 | |
---|
1644 | for (j=1; j<nRing; j++) |
---|
1645 | { |
---|
1646 | gcd_tmp = gcd(gcd_tmp, (*curr_weight)[j]); |
---|
1647 | if(gcd_tmp == 1) |
---|
1648 | break; |
---|
1649 | } |
---|
1650 | |
---|
1651 | if(gcd_tmp != 1) |
---|
1652 | for (j=0; j<nRing; j++) |
---|
1653 | { |
---|
1654 | gcd_tmp = gcd(gcd_tmp, (*diff_weight)[j]); |
---|
1655 | if(gcd_tmp == 1) |
---|
1656 | break; |
---|
1657 | } |
---|
1658 | |
---|
1659 | if(gcd_tmp != 1) |
---|
1660 | for (j=0; j<nRing; j++) |
---|
1661 | { |
---|
1662 | (*curr_weight)[j] = (*curr_weight)[j]/gcd_tmp; |
---|
1663 | (*diff_weight)[j] = (*diff_weight)[j]/gcd_tmp; |
---|
1664 | } |
---|
1665 | #ifdef NEXT_VECTORS_CC |
---|
1666 | Print("\n// gcd of the weight vectors (current and target) = %d", gcd_tmp); |
---|
1667 | ivString(curr_weight, "new cw"); |
---|
1668 | ivString(diff_weight, "new dw"); |
---|
1669 | |
---|
1670 | PrintS("\n// t_zaehler: "); mpz_out_str( stdout, 10, t_zaehler); |
---|
1671 | PrintS(", t_nenner: "); mpz_out_str( stdout, 10, t_nenner); |
---|
1672 | #endif |
---|
1673 | |
---|
1674 | mpz_t ddf; mpz_init(ddf); |
---|
1675 | mpz_t dcw; mpz_init(dcw); |
---|
1676 | BOOLEAN isdwpos; |
---|
1677 | |
---|
1678 | // construct a new weight vector |
---|
1679 | for (j=0; j<nRing; j++) |
---|
1680 | { |
---|
1681 | mpz_set_si(dcw, (*curr_weight)[j]); |
---|
1682 | mpz_mul(s_nenner, t_nenner, dcw); |
---|
1683 | |
---|
1684 | if( (*diff_weight)[j]>0) |
---|
1685 | mpz_mul_ui(s_zaehler, t_zaehler, (*diff_weight)[j]); |
---|
1686 | else |
---|
1687 | { |
---|
1688 | mpz_mul_ui(s_zaehler, t_zaehler, -(*diff_weight)[j]); |
---|
1689 | mpz_neg(s_zaehler, s_zaehler); |
---|
1690 | } |
---|
1691 | |
---|
1692 | mpz_add(sntz, s_nenner, s_zaehler); |
---|
1693 | |
---|
1694 | mpz_init_set(vec[j], sntz); |
---|
1695 | |
---|
1696 | #ifdef NEXT_VECTORS_CC |
---|
1697 | Print("\n// j = %d ==> ", j); |
---|
1698 | PrintS("("); |
---|
1699 | mpz_out_str( stdout, 10, t_nenner); |
---|
1700 | Print(" * %d)", (*curr_weight)[j]); |
---|
1701 | Print(" + ("); mpz_out_str( stdout, 10, t_zaehler); |
---|
1702 | Print(" * %d) = ", (*diff_weight)[j]); |
---|
1703 | mpz_out_str( stdout, 10, s_nenner); |
---|
1704 | PrintS(" + "); |
---|
1705 | mpz_out_str( stdout, 10, s_zaehler); |
---|
1706 | PrintS(" = "); mpz_out_str( stdout, 10, sntz); |
---|
1707 | Print(" ==> vector[%d]: ", j); mpz_out_str(stdout, 10, vec[j]); |
---|
1708 | #endif |
---|
1709 | |
---|
1710 | if(j==0) |
---|
1711 | mpz_init_set(ggt, sntz); |
---|
1712 | else |
---|
1713 | if(mpz_cmp_si(ggt,1) != 0) |
---|
1714 | mpz_gcd(ggt, ggt, sntz); |
---|
1715 | |
---|
1716 | } |
---|
1717 | |
---|
1718 | #ifdef NEXT_VECTORS_CC |
---|
1719 | PrintS("\n// gcd of elements of the vector: "); |
---|
1720 | mpz_out_str( stdout, 10, ggt); |
---|
1721 | #endif |
---|
1722 | |
---|
1723 | mpz_t omega; |
---|
1724 | mpz_t sing_int; |
---|
1725 | mpz_init_set_ui(sing_int, 2147483647); |
---|
1726 | |
---|
1727 | /* construct a new weight vector and check whether vec[j] is overflow!! |
---|
1728 | i.e. vec[j] > 2^31. |
---|
1729 | If vec[j] doesn't overflow, define a weight vector |
---|
1730 | otherwise, report that overflow appears. |
---|
1731 | In the second case test whether the defined new vector correct is |
---|
1732 | plays an important rolle */ |
---|
1733 | |
---|
1734 | for (j=0; j<nRing; j++) |
---|
1735 | { |
---|
1736 | if(mpz_cmp_si(ggt,1)==0) |
---|
1737 | (*diff_weight)[j] = mpz_get_si(vec[j]); |
---|
1738 | else |
---|
1739 | { |
---|
1740 | mpz_divexact(vec[j], vec[j], ggt); |
---|
1741 | (*diff_weight)[j] = mpz_get_si(vec[j]); |
---|
1742 | } |
---|
1743 | |
---|
1744 | if(mpz_cmp(vec[j], sing_int)>=0) |
---|
1745 | if(Overflow_Error == FALSE) |
---|
1746 | { |
---|
1747 | Overflow_Error = TRUE; |
---|
1748 | |
---|
1749 | PrintS("\n// ** OVERFLOW in \"NextVector\": "); |
---|
1750 | mpz_out_str( stdout, 10, vec[j]); |
---|
1751 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
1752 | Print("\n// So vector[%d] := %d is wrong!!\n",j+1, (*diff_weight)[j]); |
---|
1753 | } |
---|
1754 | } |
---|
1755 | |
---|
1756 | FINISH: |
---|
1757 | |
---|
1758 | mpz_clear(t_zaehler); |
---|
1759 | mpz_clear(t_nenner); |
---|
1760 | mpz_clear(sntz); |
---|
1761 | mpz_clear(sztn); |
---|
1762 | mpz_clear(temp); |
---|
1763 | mpz_clear(MwWd); |
---|
1764 | mpz_clear(deg_w0_p1); |
---|
1765 | mpz_clear(deg_d0_p1); |
---|
1766 | omFree(vec); |
---|
1767 | |
---|
1768 | if(Overflow_Error == FALSE) |
---|
1769 | Overflow_Error = nError; |
---|
1770 | |
---|
1771 | return diff_weight; |
---|
1772 | } |
---|
1773 | |
---|
1774 | /* |
---|
1775 | compute an intermediate weight vector from iva to ivb w.r.t. |
---|
1776 | the reduced Groebner basis G. |
---|
1777 | Return NULL, if it is equal to iva or iva = avb. |
---|
1778 | */ |
---|
1779 | intvec* MkInterRedNextWeight(intvec* iva, intvec* ivb, ideal G) |
---|
1780 | { |
---|
1781 | intvec* tmp = new intvec(iva->length()); |
---|
1782 | intvec* result; |
---|
1783 | |
---|
1784 | if(G == NULL) |
---|
1785 | return tmp; |
---|
1786 | |
---|
1787 | if(MivComp(iva, ivb) == 1) |
---|
1788 | return tmp; |
---|
1789 | |
---|
1790 | result = MwalkNextWeightCC(iva, ivb, G); |
---|
1791 | |
---|
1792 | if(MivComp(result, iva) == 1) |
---|
1793 | { |
---|
1794 | delete result; |
---|
1795 | return tmp; |
---|
1796 | } |
---|
1797 | |
---|
1798 | delete tmp; |
---|
1799 | return result; |
---|
1800 | } |
---|
1801 | |
---|
1802 | /* 01.11.01 */ |
---|
1803 | /* define and execute a new ring which order is (a(va),lp,C) */ |
---|
1804 | static void VMrDefault(intvec* va) |
---|
1805 | { |
---|
1806 | idhdl tmp = enterid(IDID(currRingHdl),IDLEV(currRingHdl)+1,RING_CMD,&IDROOT,TRUE); |
---|
1807 | //3.11.01 |
---|
1808 | |
---|
1809 | if (ppNoether!=NULL) |
---|
1810 | pDelete(&ppNoether); |
---|
1811 | |
---|
1812 | if (((sLastPrinted.rtyp>BEGIN_RING) && (sLastPrinted.rtyp<END_RING)) || |
---|
1813 | ((sLastPrinted.rtyp==LIST_CMD)&&(lRingDependend((lists)sLastPrinted.data)))) |
---|
1814 | |
---|
1815 | { |
---|
1816 | sLastPrinted.CleanUp(); |
---|
1817 | memset(&sLastPrinted,0,sizeof(sleftv)); |
---|
1818 | } |
---|
1819 | |
---|
1820 | ring r = IDRING(tmp); |
---|
1821 | int i, nv = currRing->N; |
---|
1822 | |
---|
1823 | r->ch = currRing->ch; |
---|
1824 | r->N = currRing->N; |
---|
1825 | int nb = rBlocks(currRing) + 1;//31.10.01 (+1) |
---|
1826 | |
---|
1827 | /*names*/ |
---|
1828 | char* Q; //30.10.01 to avoid the corrupted memory, NOT change!! |
---|
1829 | r->names = (char **) omAlloc0(nv * sizeof(char_ptr)); |
---|
1830 | for(i=0; i<nv; i++) |
---|
1831 | { |
---|
1832 | Q = currRing->names[i]; |
---|
1833 | r->names[i] = omStrDup(Q); |
---|
1834 | } |
---|
1835 | |
---|
1836 | intvec* iva = va; //why? |
---|
1837 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
1838 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
1839 | r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int)); |
---|
1840 | for(i=0; i<nv; i++) |
---|
1841 | r->wvhdl[0][i] = (*iva)[i]; |
---|
1842 | |
---|
1843 | /* order: a,lp,C,0 */ |
---|
1844 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
1845 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
1846 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
1847 | |
---|
1848 | /* ringorder a for the first block: var 1..nv */ |
---|
1849 | r->order[0] = ringorder_a; |
---|
1850 | r->block0[0] = 1; |
---|
1851 | r->block1[0] = nv; |
---|
1852 | |
---|
1853 | /* ringorder lp for the second block: var 1..nv */ |
---|
1854 | r->order[1] = ringorder_lp; |
---|
1855 | r->block0[1] = 1; |
---|
1856 | r->block1[1] = nv; |
---|
1857 | |
---|
1858 | /* ringorder C for the third block */ |
---|
1859 | // it is very important within "idLift", |
---|
1860 | // especially, by ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
1861 | // therefore, nb must be (nBlocks(currRing) + 1) |
---|
1862 | r->order[2] = ringorder_C; |
---|
1863 | |
---|
1864 | /* the last block: everything is 0 */ |
---|
1865 | r->order[3] = 0; |
---|
1866 | |
---|
1867 | /*polynomial ring*/ |
---|
1868 | r->OrdSgn = 1; |
---|
1869 | |
---|
1870 | /* complete ring intializations */ |
---|
1871 | rComplete(r); |
---|
1872 | |
---|
1873 | rChangeCurrRing(r); |
---|
1874 | currRingHdl = tmp; |
---|
1875 | } |
---|
1876 | |
---|
1877 | /* 03.11.01 */ |
---|
1878 | /* define and execute a new ring which order is a lexicographic order */ |
---|
1879 | static void VMrDefaultlp(void) |
---|
1880 | { |
---|
1881 | idhdl tmp = enterid(IDID(currRingHdl),IDLEV(currRingHdl)+1,RING_CMD,&IDROOT,TRUE); |
---|
1882 | |
---|
1883 | |
---|
1884 | if (ppNoether!=NULL) |
---|
1885 | pDelete(&ppNoether); |
---|
1886 | |
---|
1887 | if (((sLastPrinted.rtyp>BEGIN_RING) && (sLastPrinted.rtyp<END_RING)) || |
---|
1888 | ((sLastPrinted.rtyp==LIST_CMD)&&(lRingDependend((lists)sLastPrinted.data)))) |
---|
1889 | |
---|
1890 | { |
---|
1891 | sLastPrinted.CleanUp(); |
---|
1892 | memset(&sLastPrinted,0,sizeof(sleftv)); |
---|
1893 | } |
---|
1894 | |
---|
1895 | ring r = IDRING(tmp); |
---|
1896 | int i, nv = currRing->N; |
---|
1897 | |
---|
1898 | r->ch = currRing->ch; |
---|
1899 | r->N = currRing->N; |
---|
1900 | int nb = rBlocks(currRing) + 1;//31.10.01 (+1) |
---|
1901 | |
---|
1902 | /*names*/ |
---|
1903 | char* Q; //30.10.01 to avoid the corrupted memory, NOT change!! |
---|
1904 | r->names = (char **) omAlloc0(nv * sizeof(char_ptr)); |
---|
1905 | for(i=0; i<nv; i++) |
---|
1906 | { |
---|
1907 | Q = currRing->names[i]; |
---|
1908 | r->names[i] = omStrDup(Q); |
---|
1909 | } |
---|
1910 | |
---|
1911 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
1912 | |
---|
1913 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
1914 | |
---|
1915 | /* order: lp,C,0 */ |
---|
1916 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
1917 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
1918 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
1919 | |
---|
1920 | /* ringorder lp for the first block: var 1..nv */ |
---|
1921 | r->order[0] = ringorder_lp; |
---|
1922 | r->block0[0] = 1; |
---|
1923 | r->block1[0] = nv; |
---|
1924 | |
---|
1925 | /* ringorder C for the second block */ |
---|
1926 | r->order[1] = ringorder_C; |
---|
1927 | |
---|
1928 | /* the last block: everything is 0 */ |
---|
1929 | r->order[2] = 0; |
---|
1930 | |
---|
1931 | /*polynomial ring*/ |
---|
1932 | r->OrdSgn = 1; |
---|
1933 | |
---|
1934 | /* complete ring intializations */ |
---|
1935 | rComplete(r); |
---|
1936 | |
---|
1937 | //rSetHdl(tmp); |
---|
1938 | |
---|
1939 | rChangeCurrRing(r); |
---|
1940 | currRingHdl = tmp; |
---|
1941 | } |
---|
1942 | |
---|
1943 | |
---|
1944 | /* define a ring with parameters und change to it */ |
---|
1945 | /* DefRingPar and DefRingParlp corrupt still memory */ |
---|
1946 | static void DefRingPar(intvec* va) |
---|
1947 | { |
---|
1948 | int i, nv = currRing->N; |
---|
1949 | int nb = rBlocks(currRing) + 1; |
---|
1950 | |
---|
1951 | ring res=(ring)omAllocBin(ip_sring_bin); |
---|
1952 | |
---|
1953 | memcpy4(res,currRing,sizeof(ip_sring)); |
---|
1954 | |
---|
1955 | res->VarOffset = NULL; |
---|
1956 | res->ref=0; |
---|
1957 | if (currRing->algring!=NULL) |
---|
1958 | currRing->algring->ref++; |
---|
1959 | |
---|
1960 | if (currRing->parameter!=NULL) |
---|
1961 | { |
---|
1962 | res->minpoly=nCopy(currRing->minpoly); |
---|
1963 | int l=rPar(currRing); |
---|
1964 | res->parameter=(char **)omAlloc(l*sizeof(char_ptr)); |
---|
1965 | |
---|
1966 | for(i=l-1;i>=0;i--) |
---|
1967 | res->parameter[i]=omStrDup(currRing->parameter[i]); |
---|
1968 | } |
---|
1969 | |
---|
1970 | intvec* iva = va; |
---|
1971 | |
---|
1972 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
1973 | res->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
1974 | res->wvhdl[0] = (int*) omAlloc(nv*sizeof(int)); |
---|
1975 | for(i=0; i<nv; i++) |
---|
1976 | res->wvhdl[0][i] = (*iva)[i]; |
---|
1977 | |
---|
1978 | /* order: a,lp,C,0 */ |
---|
1979 | res->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
1980 | res->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
1981 | res->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
1982 | |
---|
1983 | /* ringorder a for the first block: var 1..nv */ |
---|
1984 | res->order[0] = ringorder_a; |
---|
1985 | res->block0[0] = 1; |
---|
1986 | res->block1[0] = nv; |
---|
1987 | |
---|
1988 | /* ringorder lp for the second block: var 1..nv */ |
---|
1989 | res->order[1] = ringorder_lp; |
---|
1990 | res->block0[1] = 1; |
---|
1991 | res->block1[1] = nv; |
---|
1992 | |
---|
1993 | /* ringorder C for the third block */ |
---|
1994 | // it is very important within "idLift", |
---|
1995 | // especially, by ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
1996 | // therefore, nb must be (nBlocks(currRing) + 1) |
---|
1997 | res->order[2] = ringorder_C; |
---|
1998 | |
---|
1999 | /* the last block: everything is 0 */ |
---|
2000 | res->order[3] = 0; |
---|
2001 | |
---|
2002 | /*polynomial ring*/ |
---|
2003 | res->OrdSgn = 1; |
---|
2004 | |
---|
2005 | |
---|
2006 | res->names = (char **)omAlloc0(nv * sizeof(char_ptr)); |
---|
2007 | for (i=nv-1; i>=0; i--) |
---|
2008 | res->names[i] = omStrDup(currRing->names[i]); |
---|
2009 | |
---|
2010 | /* complete ring intializations */ |
---|
2011 | rComplete(res); |
---|
2012 | |
---|
2013 | |
---|
2014 | // clean up history |
---|
2015 | if (sLastPrinted.RingDependend()) |
---|
2016 | { |
---|
2017 | sLastPrinted.CleanUp(); |
---|
2018 | memset(&sLastPrinted,0,sizeof(sleftv)); |
---|
2019 | } |
---|
2020 | |
---|
2021 | |
---|
2022 | /* execute the created ring */ |
---|
2023 | rChangeCurrRing(res); |
---|
2024 | } |
---|
2025 | |
---|
2026 | |
---|
2027 | static void DefRingParlp(void) |
---|
2028 | { |
---|
2029 | int i, nv = currRing->N; |
---|
2030 | |
---|
2031 | ring r=(ring)omAllocBin(ip_sring_bin); |
---|
2032 | |
---|
2033 | memcpy4(r,currRing,sizeof(ip_sring)); |
---|
2034 | |
---|
2035 | r->VarOffset = NULL; |
---|
2036 | r->ref=0; |
---|
2037 | if (currRing->algring!=NULL) |
---|
2038 | currRing->algring->ref++; |
---|
2039 | |
---|
2040 | if (currRing->parameter!=NULL) |
---|
2041 | { |
---|
2042 | r->minpoly=nCopy(currRing->minpoly); |
---|
2043 | int l=rPar(currRing); |
---|
2044 | r->parameter=(char **)omAlloc(l*sizeof(char_ptr)); |
---|
2045 | |
---|
2046 | for(i=l-1;i>=0;i--) |
---|
2047 | r->parameter[i]=omStrDup(currRing->parameter[i]); |
---|
2048 | } |
---|
2049 | |
---|
2050 | |
---|
2051 | r->ch = currRing->ch; |
---|
2052 | r->N = currRing->N; |
---|
2053 | int nb = rBlocks(currRing) + 1;//31.10.01 (+1) |
---|
2054 | |
---|
2055 | /*names*/ |
---|
2056 | char* Q; |
---|
2057 | r->names = (char **) omAlloc0(nv * sizeof(char_ptr)); |
---|
2058 | for(i=nv-1; i>=0; i--) |
---|
2059 | { |
---|
2060 | Q = currRing->names[i]; |
---|
2061 | r->names[i] = omStrDup(Q); |
---|
2062 | } |
---|
2063 | |
---|
2064 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
2065 | |
---|
2066 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2067 | |
---|
2068 | /* order: lp,C,0 */ |
---|
2069 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2070 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2071 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2072 | |
---|
2073 | /* ringorder lp for the first block: var 1..nv */ |
---|
2074 | r->order[0] = ringorder_lp; |
---|
2075 | r->block0[0] = 1; |
---|
2076 | r->block1[0] = nv; |
---|
2077 | |
---|
2078 | /* ringorder C for the second block */ |
---|
2079 | r->order[1] = ringorder_C; |
---|
2080 | |
---|
2081 | /* the last block: everything is 0 */ |
---|
2082 | r->order[2] = 0; |
---|
2083 | |
---|
2084 | /*polynomial ring*/ |
---|
2085 | r->OrdSgn = 1; |
---|
2086 | |
---|
2087 | |
---|
2088 | if (currRing->parameter!=NULL) |
---|
2089 | { |
---|
2090 | r->minpoly=nCopy(currRing->minpoly); |
---|
2091 | int l=rPar(currRing); |
---|
2092 | r->parameter=(char **)omAlloc(l*sizeof(char_ptr)); |
---|
2093 | |
---|
2094 | for(i=l-1;i>=0;i--) |
---|
2095 | r->parameter[i]=omStrDup(currRing->parameter[i]); |
---|
2096 | } |
---|
2097 | |
---|
2098 | /* complete ring intializations */ |
---|
2099 | rComplete(r); |
---|
2100 | |
---|
2101 | // clean up history |
---|
2102 | if (sLastPrinted.RingDependend()) |
---|
2103 | { |
---|
2104 | sLastPrinted.CleanUp(); |
---|
2105 | memset(&sLastPrinted,0,sizeof(sleftv)); |
---|
2106 | } |
---|
2107 | |
---|
2108 | /* execute the created ring */ |
---|
2109 | rChangeCurrRing(r); |
---|
2110 | } |
---|
2111 | |
---|
2112 | /* check wheather one or more components of a vector are zero */ |
---|
2113 | static int isNolVector(intvec* hilb) |
---|
2114 | { |
---|
2115 | int i; |
---|
2116 | for(i=hilb->length()-1; i>=0; i--) |
---|
2117 | if((* hilb)[i]==0) |
---|
2118 | return 1; |
---|
2119 | |
---|
2120 | return 0; |
---|
2121 | } |
---|
2122 | |
---|
2123 | |
---|
2124 | /****************************** Februar 2002 **************************** |
---|
2125 | * G is a Groebner basis w.r.t. (a(curr_weight),lp) and * |
---|
2126 | * we compute a GB of <G> w.r.t. the lex. order by the perturbation walk * |
---|
2127 | * its perturbation degree is tp_deg * |
---|
2128 | * We call the following subfunction LastGB, if * |
---|
2129 | * the computed intermediate weight vector or * |
---|
2130 | * the perturbed target weight vector * |
---|
2131 | * does NOT in the correct cone. * |
---|
2132 | **************************************************************************/ |
---|
2133 | |
---|
2134 | static ideal LastGB(ideal G, intvec* curr_weight,int tp_deg) |
---|
2135 | { |
---|
2136 | BOOLEAN nError = Overflow_Error; |
---|
2137 | Overflow_Error = FALSE; |
---|
2138 | |
---|
2139 | int i, nV = currRing->N; |
---|
2140 | int nwalk=0, endwalks=0, nnwinC=1; |
---|
2141 | int nlast = 0; |
---|
2142 | ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG; |
---|
2143 | ring newRing, oldRing, TargetRing; |
---|
2144 | intvec* iv_M_lp; |
---|
2145 | intvec* target_weight; |
---|
2146 | intvec* iv_lp = Mivlp(nV); //define (1,0,...,0) |
---|
2147 | intvec* pert_target_vector; |
---|
2148 | intvec* ivNull = new intvec(nV); |
---|
2149 | intvec* extra_curr_weight = new intvec(nV); |
---|
2150 | intvec* hilb_func; |
---|
2151 | intvec* next_weight; |
---|
2152 | |
---|
2153 | /* to avoid (1,0,...,0) as the target vector */ |
---|
2154 | intvec* last_omega = new intvec(nV); |
---|
2155 | for(i=nV-1; i>0; i--) |
---|
2156 | (*last_omega)[i] = 1; |
---|
2157 | (*last_omega)[0] = 10000; |
---|
2158 | |
---|
2159 | ring EXXRing = currRing; |
---|
2160 | |
---|
2161 | /* compute a pertubed weight vector of the target weight vector */ |
---|
2162 | if(tp_deg > 1 && tp_deg <= nV) |
---|
2163 | { |
---|
2164 | //..25.03.03 VMrDefaultlp();// VMrDefault(target_weight); |
---|
2165 | if (currRing->parameter != NULL) |
---|
2166 | DefRingParlp(); |
---|
2167 | else |
---|
2168 | VMrDefaultlp(); |
---|
2169 | |
---|
2170 | TargetRing = currRing; |
---|
2171 | ssG = idrMoveR(G,EXXRing); |
---|
2172 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
2173 | //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg); |
---|
2174 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
2175 | delete iv_M_lp; |
---|
2176 | pert_target_vector = target_weight; |
---|
2177 | |
---|
2178 | rChangeCurrRing(EXXRing); |
---|
2179 | G = idrMoveR(ssG, TargetRing); |
---|
2180 | } |
---|
2181 | else |
---|
2182 | target_weight = Mivlp(nV); |
---|
2183 | |
---|
2184 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2185 | |
---|
2186 | while(1) |
---|
2187 | { |
---|
2188 | nwalk++; |
---|
2189 | nstep++; |
---|
2190 | to=clock(); |
---|
2191 | /* compute a next weight vector */ |
---|
2192 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
2193 | xtnw=xtnw+clock()-to; |
---|
2194 | #ifdef PRINT_VECTORS |
---|
2195 | MivString(curr_weight, target_weight, next_weight); |
---|
2196 | #endif |
---|
2197 | |
---|
2198 | if(Overflow_Error == TRUE){ |
---|
2199 | newRing = currRing; |
---|
2200 | nnwinC = 0; |
---|
2201 | if(tp_deg == 1) |
---|
2202 | nlast = 1; |
---|
2203 | delete next_weight; |
---|
2204 | |
---|
2205 | //idElements(G, "G"); |
---|
2206 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2207 | |
---|
2208 | break; |
---|
2209 | } |
---|
2210 | |
---|
2211 | if(MivComp(next_weight, ivNull) == 1){ |
---|
2212 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2213 | newRing = currRing; |
---|
2214 | delete next_weight; |
---|
2215 | break; |
---|
2216 | } |
---|
2217 | |
---|
2218 | if(MivComp(next_weight, target_weight) == 1) |
---|
2219 | endwalks = 1; |
---|
2220 | |
---|
2221 | for(i=nV-1; i>=0; i--) |
---|
2222 | (*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
2223 | |
---|
2224 | /* 06.11.01 NOT Changed */ |
---|
2225 | for(i=nV-1; i>=0; i--) |
---|
2226 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
2227 | |
---|
2228 | oldRing = currRing; |
---|
2229 | to=clock(); |
---|
2230 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
2231 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
2232 | xtif=xtif+clock()-to; |
---|
2233 | |
---|
2234 | #ifdef ENDWALKS |
---|
2235 | if(endwalks == 1){ |
---|
2236 | Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2237 | idElements(Gomega, "Gw"); |
---|
2238 | headidString(Gomega, "Gw"); |
---|
2239 | } |
---|
2240 | #endif |
---|
2241 | |
---|
2242 | #ifndef BUCHBERGER_ALG |
---|
2243 | if(isNolVector(curr_weight) == 0) |
---|
2244 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
2245 | else |
---|
2246 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
2247 | #endif // BUCHBERGER_ALG |
---|
2248 | |
---|
2249 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
2250 | //..25.03.03 VMrDefault(curr_weight); |
---|
2251 | if (currRing->parameter != NULL) |
---|
2252 | DefRingPar(curr_weight); |
---|
2253 | else |
---|
2254 | VMrDefault(curr_weight); |
---|
2255 | |
---|
2256 | newRing = currRing; |
---|
2257 | Gomega1 = idrMoveR(Gomega, oldRing); |
---|
2258 | |
---|
2259 | to=clock(); |
---|
2260 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
2261 | #ifdef BUCHBERGER_ALG |
---|
2262 | M = MstdhomCC(Gomega1); |
---|
2263 | #else |
---|
2264 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
2265 | delete hilb_func; |
---|
2266 | #endif // BUCHBERGER_ALG |
---|
2267 | xtstd=xtstd+clock()-to; |
---|
2268 | /* change the ring to oldRing */ |
---|
2269 | rChangeCurrRing(oldRing); |
---|
2270 | M1 = idrMoveR(M, newRing); |
---|
2271 | Gomega2 = idrMoveR(Gomega1, newRing); |
---|
2272 | |
---|
2273 | to=clock(); |
---|
2274 | /* compute a reduced Groebner basis of <G> w.r.t. "newRing" */ |
---|
2275 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
2276 | xtlift=xtlift+clock()-to; |
---|
2277 | |
---|
2278 | idDelete(&M1); |
---|
2279 | idDelete(&G); |
---|
2280 | |
---|
2281 | /* change the ring to newRing */ |
---|
2282 | rChangeCurrRing(newRing); |
---|
2283 | F1 = idrMoveR(F, oldRing); |
---|
2284 | |
---|
2285 | to=clock(); |
---|
2286 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
2287 | G = kInterRedCC(F1, NULL); |
---|
2288 | xtred=xtred+clock()-to; |
---|
2289 | idDelete(&F1); |
---|
2290 | |
---|
2291 | if(endwalks == 1){ |
---|
2292 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2293 | break; |
---|
2294 | } |
---|
2295 | |
---|
2296 | delete next_weight; |
---|
2297 | }//while |
---|
2298 | |
---|
2299 | delete ivNull; |
---|
2300 | |
---|
2301 | if(tp_deg != 1) |
---|
2302 | { |
---|
2303 | //..25.03.03 VMrDefaultlp();//define and execute the ring "lp" |
---|
2304 | if (currRing->parameter != NULL) |
---|
2305 | DefRingParlp(); |
---|
2306 | else |
---|
2307 | VMrDefaultlp(); |
---|
2308 | |
---|
2309 | F1 = idrMoveR(G, newRing); |
---|
2310 | |
---|
2311 | if(nnwinC == 0 || test_w_in_ConeCC(F1, pert_target_vector) != 1) |
---|
2312 | { |
---|
2313 | oldRing = currRing; |
---|
2314 | rChangeCurrRing(newRing); |
---|
2315 | G = idrMoveR(F1, oldRing); |
---|
2316 | Print("\n// takes %d steps and calls the recursion of level %d:", |
---|
2317 | nwalk, tp_deg-1); |
---|
2318 | |
---|
2319 | F1 = LastGB(G,curr_weight, tp_deg-1); |
---|
2320 | } |
---|
2321 | |
---|
2322 | TargetRing = currRing; |
---|
2323 | rChangeCurrRing(EXXRing); |
---|
2324 | result = idrMoveR(F1, TargetRing); |
---|
2325 | } |
---|
2326 | else |
---|
2327 | { |
---|
2328 | if(nlast == 1) |
---|
2329 | { |
---|
2330 | //OMEGA_OVERFLOW_LASTGB: |
---|
2331 | /* |
---|
2332 | if(MivSame(curr_weight, iv_lp) == 1) |
---|
2333 | if (currRing->parameter != NULL) |
---|
2334 | DefRingParlp(); |
---|
2335 | else |
---|
2336 | VMrDefaultlp(); |
---|
2337 | else |
---|
2338 | if (currRing->parameter != NULL) |
---|
2339 | DefRingPar(curr_weight); |
---|
2340 | else |
---|
2341 | VMrDefault(curr_weight); |
---|
2342 | */ |
---|
2343 | |
---|
2344 | //..25.03.03 VMrDefaultlp();//define and execute the ring "lp" |
---|
2345 | if (currRing->parameter != NULL) |
---|
2346 | DefRingParlp(); |
---|
2347 | else |
---|
2348 | VMrDefaultlp(); |
---|
2349 | |
---|
2350 | |
---|
2351 | F1 = idrMoveR(G, newRing); |
---|
2352 | //Print("\n// Apply \"std\" in ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
2353 | |
---|
2354 | G = MstdCC(F1); |
---|
2355 | idDelete(&F1); |
---|
2356 | newRing = currRing; |
---|
2357 | } |
---|
2358 | |
---|
2359 | rChangeCurrRing(EXXRing); |
---|
2360 | result = idrMoveR(G, newRing); |
---|
2361 | } |
---|
2362 | delete target_weight; |
---|
2363 | delete last_omega; |
---|
2364 | delete iv_lp; |
---|
2365 | |
---|
2366 | if(Overflow_Error == FALSE) |
---|
2367 | Overflow_Error = nError; |
---|
2368 | |
---|
2369 | return(result); |
---|
2370 | } |
---|
2371 | |
---|
2372 | |
---|
2373 | /* check whether a polynomial of G has least 3 monomials */ |
---|
2374 | static int lengthpoly(ideal G) |
---|
2375 | { |
---|
2376 | int i; |
---|
2377 | for(i=IDELEMS(G)-1; i>=0; i--) |
---|
2378 | #if 0 |
---|
2379 | if(pLength(G->m[i])>2) |
---|
2380 | return 1; |
---|
2381 | #else |
---|
2382 | if((G->m[i]!=NULL) /* len >=0 */ |
---|
2383 | && (G->m[i]->next!=NULL) /* len >=1 */ |
---|
2384 | && (G->m[i]->next->next!=NULL) /* len >=2 */ |
---|
2385 | && (G->m[i]->next->next->next!=NULL) /* len >=3 */ |
---|
2386 | //&& (G->m[i]->next->next->next->next!=NULL) /* len >=4 */ |
---|
2387 | ) return 1; |
---|
2388 | #endif |
---|
2389 | return 0; |
---|
2390 | } |
---|
2391 | |
---|
2392 | /* check whether a polynomial of G has least 2 monomials */ |
---|
2393 | static int islengthpoly2(ideal G) |
---|
2394 | { |
---|
2395 | int i; |
---|
2396 | for(i=IDELEMS(G)-1; i>=0; i--) |
---|
2397 | if((G->m[i]!=NULL) /* len >=0 */ |
---|
2398 | && (G->m[i]->next!=NULL) /* len >=1 */ |
---|
2399 | && (G->m[i]->next->next!=NULL)) /* len >=2 */ |
---|
2400 | return 1; |
---|
2401 | |
---|
2402 | return 0; |
---|
2403 | } |
---|
2404 | |
---|
2405 | |
---|
2406 | |
---|
2407 | /* Implementation of the improved Groebner walk algorithm which is written |
---|
2408 | by Quoc-Nam Tran (2000). |
---|
2409 | One perturbs the original target weight vector, only if |
---|
2410 | the next intermediate weight vector is equal to the current target weight |
---|
2411 | vector. This must be repeated until the wanted reduced Groebner basis |
---|
2412 | to reach. |
---|
2413 | If the numbers of variables is big enough, the representation of the origin |
---|
2414 | weight vector may be very big. Therefore, it is possible the intermediate |
---|
2415 | weight vector doesn't stay in the correct Groebner cone. |
---|
2416 | In this case we have just a reduced Groebner basis of the given ideal |
---|
2417 | with respect to another monomial order. Then we have to compute |
---|
2418 | a wanted reduced Groebner basis of it with respect to the given order. |
---|
2419 | At the following subroutine we use the improved Buchberger algorithm or |
---|
2420 | the changed perturbation walk algorithm with a decrased degree. |
---|
2421 | */ |
---|
2422 | |
---|
2423 | /*2 |
---|
2424 | * return the initial term of an ideal |
---|
2425 | */ |
---|
2426 | static ideal idHeadCC(ideal h) |
---|
2427 | { |
---|
2428 | int i, nH =IDELEMS(h); |
---|
2429 | |
---|
2430 | ideal m = idInit(nH,h->rank); |
---|
2431 | |
---|
2432 | for (i=nH-1;i>=0; i--) |
---|
2433 | { |
---|
2434 | if (h->m[i]!=NULL) |
---|
2435 | m->m[i]=pHead(h->m[i]); |
---|
2436 | } |
---|
2437 | return m; |
---|
2438 | } |
---|
2439 | |
---|
2440 | /* check whether two head-ideals are the same */ |
---|
2441 | static inline int test_G_GB_walk(ideal H0, ideal H1) |
---|
2442 | { |
---|
2443 | int i, nG = IDELEMS(H0); |
---|
2444 | |
---|
2445 | if(nG != IDELEMS(H1)) |
---|
2446 | return 0; |
---|
2447 | |
---|
2448 | for(i=nG-1; i>=0; i--) |
---|
2449 | { |
---|
2450 | #if 0 |
---|
2451 | poly t; |
---|
2452 | if((t=pSub(pCopy(H0->m[i]), pCopy(H1->m[i]))) != NULL) |
---|
2453 | { |
---|
2454 | pDelete(&t); |
---|
2455 | return 0; |
---|
2456 | } |
---|
2457 | pDelete(&t); |
---|
2458 | #else |
---|
2459 | if(!pEqualPolys(H0->m[i],H1->m[i])) |
---|
2460 | return 0; |
---|
2461 | #endif |
---|
2462 | } |
---|
2463 | |
---|
2464 | return 1; |
---|
2465 | } |
---|
2466 | |
---|
2467 | /* 19.11.01 */ |
---|
2468 | /* find the maximal total degree of polynomials in G */ |
---|
2469 | static int Trandegreebound(ideal G) |
---|
2470 | { |
---|
2471 | int i, nG = IDELEMS(G); |
---|
2472 | int np=1, nV = currRing->N; |
---|
2473 | int degtmp, result = 0; |
---|
2474 | intvec* ivUnit = Mivdp(nV); |
---|
2475 | |
---|
2476 | for(i=nG-1; i>=0; i--) |
---|
2477 | { |
---|
2478 | /* find the maximal total degree of the polynomial G[i] */ |
---|
2479 | degtmp = MwalkWeightDegree(G->m[i], ivUnit); |
---|
2480 | if(degtmp > result) |
---|
2481 | result = degtmp; |
---|
2482 | } |
---|
2483 | delete ivUnit; |
---|
2484 | return result; |
---|
2485 | } |
---|
2486 | |
---|
2487 | /* perturb the weight vector iva w.r.t. the ideal G. |
---|
2488 | the monomial order of the current ring is the w_1 weight lex. order. |
---|
2489 | define w := d^(n-1)w_1+ d^(n-2)w_2, ...+ dw_(n-1)+ w_n |
---|
2490 | where d := 1 + max{totdeg(g):g in G}*m, or |
---|
2491 | d := (2*maxdeg*maxdeg + (nV+1)*maxdeg)*m; |
---|
2492 | */ |
---|
2493 | |
---|
2494 | //GMP |
---|
2495 | static intvec* TranPertVector(ideal G, intvec* iva) |
---|
2496 | { |
---|
2497 | BOOLEAN nError = Overflow_Error; |
---|
2498 | Overflow_Error = FALSE; |
---|
2499 | |
---|
2500 | int i, j, nG = IDELEMS(G); |
---|
2501 | int nV = currRing->N; |
---|
2502 | |
---|
2503 | // define the sequence which expresses the current monomial ordering |
---|
2504 | // w_1 = iva; w_2 = (1,0,..,0); w_n = (0,...,0,1,0) |
---|
2505 | intvec* ivMat = MivMatrixOrder(iva); |
---|
2506 | |
---|
2507 | int mtmp, m=(*iva)[0]; |
---|
2508 | |
---|
2509 | for(i=ivMat->length(); i>=0; i--) |
---|
2510 | { |
---|
2511 | mtmp = (*ivMat)[i]; |
---|
2512 | |
---|
2513 | if(mtmp <0) mtmp = -mtmp; |
---|
2514 | |
---|
2515 | if(mtmp > m) |
---|
2516 | m = mtmp; |
---|
2517 | } |
---|
2518 | |
---|
2519 | /* define the maximal total degree of polynomials of G */ |
---|
2520 | mpz_t ndeg; |
---|
2521 | mpz_init(ndeg); |
---|
2522 | |
---|
2523 | // 12 Juli 03 |
---|
2524 | #ifndef UPPER_BOUND |
---|
2525 | mpz_set_si(ndeg, Trandegreebound(G)+1); |
---|
2526 | #else |
---|
2527 | mpz_t ztmp; |
---|
2528 | mpz_init(ztmp); |
---|
2529 | |
---|
2530 | mpz_t maxdeg; |
---|
2531 | mpz_init_set_si(maxdeg, Trandegreebound(G)); |
---|
2532 | |
---|
2533 | //ndeg = (2*maxdeg*maxdeg + (nV+1)*maxdeg)*m;//Kalkbrenner (1999) |
---|
2534 | mpz_pow_ui(ztmp, maxdeg, 2); |
---|
2535 | mpz_mul_ui(ztmp, ztmp, 2); |
---|
2536 | mpz_mul_ui(maxdeg, maxdeg, nV+1); |
---|
2537 | mpz_add(ndeg, ztmp, maxdeg); |
---|
2538 | mpz_mul_ui(ndeg, ndeg, m); |
---|
2539 | |
---|
2540 | //PrintS("\n// with the new upper degree bound (2d^2+(n+1)d)*m "); |
---|
2541 | //Print("\n// where d = %d, n = %d and bound = %d", maxdeg, nV, ndeg); |
---|
2542 | #endif //UPPER_BOUND |
---|
2543 | |
---|
2544 | /* 29.08.03*/ |
---|
2545 | #ifdef INVEPS_SMALL_IN_TRAN |
---|
2546 | if(mpz_cmp_ui(ndeg, nV)>0 && nV > 3) |
---|
2547 | mpz_cdiv_q_ui(ndeg, ndeg, nV); |
---|
2548 | |
---|
2549 | //PrintS("\n// choose the \"small\" inverse epsilon:"); |
---|
2550 | //mpz_out_str(stdout, 10, ndeg); |
---|
2551 | #endif |
---|
2552 | mpz_t deg_tmp; |
---|
2553 | mpz_init_set(deg_tmp, ndeg); |
---|
2554 | |
---|
2555 | mpz_t *ivres=( mpz_t *) omAlloc(nV*sizeof(mpz_t)); |
---|
2556 | mpz_init_set_si(ivres[nV-1],1); |
---|
2557 | |
---|
2558 | for(i=nV-2; i>=0; i--) |
---|
2559 | { |
---|
2560 | mpz_init_set(ivres[i], deg_tmp); |
---|
2561 | mpz_mul(deg_tmp, deg_tmp, ndeg); |
---|
2562 | } |
---|
2563 | |
---|
2564 | mpz_t *ivtmp=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
2565 | for(i=0; i<nV; i++) |
---|
2566 | mpz_init(ivtmp[i]); |
---|
2567 | |
---|
2568 | mpz_t sing_int; |
---|
2569 | mpz_init_set_ui(sing_int, 2147483647); |
---|
2570 | |
---|
2571 | intvec* repr_vector = new intvec(nV); |
---|
2572 | |
---|
2573 | /* define ivtmp := ndeg^(n-1).w_1 + ndeg^(n-2).w_2 + ... + w_n */ |
---|
2574 | for(i=0; i<nV; i++) |
---|
2575 | for(j=0; j<nV; j++) |
---|
2576 | { |
---|
2577 | if( (*ivMat)[i*nV+j] >= 0 ) |
---|
2578 | mpz_mul_ui(ivres[i], ivres[i], (*ivMat)[i*nV+j]); |
---|
2579 | else |
---|
2580 | { |
---|
2581 | mpz_mul_ui(ivres[i], ivres[i], -(*ivMat)[i*nV+j]); |
---|
2582 | mpz_neg(ivres[i], ivres[i]); |
---|
2583 | } |
---|
2584 | mpz_add(ivtmp[j], ivtmp[j], ivres[i]); |
---|
2585 | } |
---|
2586 | |
---|
2587 | delete ivMat; |
---|
2588 | |
---|
2589 | int ntrue=0; |
---|
2590 | for(i=0; i<nV; i++) |
---|
2591 | { |
---|
2592 | (*repr_vector)[i] = mpz_get_si(ivtmp[i]); |
---|
2593 | if(mpz_cmp(ivtmp[i], sing_int)>=0) |
---|
2594 | { |
---|
2595 | ntrue++; |
---|
2596 | if(Overflow_Error == FALSE) |
---|
2597 | { |
---|
2598 | Overflow_Error = TRUE; |
---|
2599 | |
---|
2600 | PrintS("\n// ** OVERFLOW in \"Repr.Vector\": "); |
---|
2601 | mpz_out_str( stdout, 10, ivtmp[i]); |
---|
2602 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
2603 | Print("\n// So vector[%d] := %d is wrong!!\n",i+1,(*repr_vector)[i]); |
---|
2604 | } |
---|
2605 | } |
---|
2606 | } |
---|
2607 | if(Overflow_Error == TRUE) |
---|
2608 | { |
---|
2609 | ivString(repr_vector, "repvector"); |
---|
2610 | Print("\n// %d element(s) of it are overflow!!", ntrue); |
---|
2611 | } |
---|
2612 | |
---|
2613 | if(Overflow_Error == FALSE) |
---|
2614 | Overflow_Error=nError; |
---|
2615 | |
---|
2616 | omFree(ivres); |
---|
2617 | omFree(ivtmp); |
---|
2618 | return repr_vector; |
---|
2619 | } |
---|
2620 | |
---|
2621 | |
---|
2622 | |
---|
2623 | static intvec* TranPertVector_lp(ideal G) |
---|
2624 | { |
---|
2625 | BOOLEAN nError = Overflow_Error; |
---|
2626 | Overflow_Error = FALSE; |
---|
2627 | |
---|
2628 | int i, j, nG = IDELEMS(G); |
---|
2629 | int nV = currRing->N; |
---|
2630 | |
---|
2631 | /* define the maximal total degree of polynomials of G */ |
---|
2632 | mpz_t ndeg; |
---|
2633 | mpz_init(ndeg); |
---|
2634 | |
---|
2635 | // 12 Juli 03 |
---|
2636 | #ifndef UPPER_BOUND |
---|
2637 | mpz_set_si(ndeg, Trandegreebound(G)+1); |
---|
2638 | #else |
---|
2639 | mpz_t ztmp; |
---|
2640 | mpz_init(ztmp); |
---|
2641 | |
---|
2642 | mpz_t maxdeg; |
---|
2643 | mpz_init_set_si(maxdeg, Trandegreebound(G)); |
---|
2644 | |
---|
2645 | //ndeg = (2*maxdeg*maxdeg + (nV+1)*maxdeg);//Kalkbrenner (1999) |
---|
2646 | mpz_pow_ui(ztmp, maxdeg, 2); |
---|
2647 | mpz_mul_ui(ztmp, ztmp, 2); |
---|
2648 | mpz_mul_ui(maxdeg, maxdeg, nV+1); |
---|
2649 | mpz_add(ndeg, ztmp, maxdeg); |
---|
2650 | /* |
---|
2651 | PrintS("\n// with the new upper degree bound (2d^2+(n+1)d)*m "); |
---|
2652 | Print("\n// where d = %d, n = %d and bound = %d", |
---|
2653 | mpz_get_si(maxdeg), nV, mpz_get_si(ndeg)); |
---|
2654 | */ |
---|
2655 | #endif //UPPER_BOUND |
---|
2656 | |
---|
2657 | #ifdef INVEPS_SMALL_IN_TRAN |
---|
2658 | if(mpz_cmp_ui(ndeg, nV)>0 && nV > 3) |
---|
2659 | mpz_cdiv_q_ui(ndeg, ndeg, nV); |
---|
2660 | |
---|
2661 | //PrintS("\n// choose the \"small\" inverse epsilon:"); |
---|
2662 | // mpz_out_str(stdout, 10, ndeg); |
---|
2663 | #endif |
---|
2664 | |
---|
2665 | mpz_t deg_tmp; |
---|
2666 | mpz_init_set(deg_tmp, ndeg); |
---|
2667 | |
---|
2668 | mpz_t *ivres=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
2669 | mpz_init_set_si(ivres[nV-1], 1); |
---|
2670 | |
---|
2671 | for(i=nV-2; i>=0; i--) |
---|
2672 | { |
---|
2673 | mpz_init_set(ivres[i], deg_tmp); |
---|
2674 | mpz_mul(deg_tmp, deg_tmp, ndeg); |
---|
2675 | } |
---|
2676 | |
---|
2677 | mpz_t sing_int; |
---|
2678 | mpz_init_set_ui(sing_int, 2147483647); |
---|
2679 | |
---|
2680 | intvec* repr_vector = new intvec(nV); |
---|
2681 | int ntrue; |
---|
2682 | for(i=0; i<nV; i++) |
---|
2683 | { |
---|
2684 | (*repr_vector)[i] = mpz_get_si(ivres[i]); |
---|
2685 | |
---|
2686 | if(mpz_cmp(ivres[i], sing_int)>=0) |
---|
2687 | { |
---|
2688 | ntrue++; |
---|
2689 | if(Overflow_Error == FALSE) |
---|
2690 | { |
---|
2691 | Overflow_Error = TRUE; |
---|
2692 | PrintS("\n// ** OVERFLOW in \"Repr.Vector\": "); |
---|
2693 | mpz_out_str( stdout, 10, ivres[i]); |
---|
2694 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
2695 | Print("\n// So vector[%d] := %d is wrong!!\n",i+1,(*repr_vector)[i]); |
---|
2696 | } |
---|
2697 | } |
---|
2698 | } |
---|
2699 | if(Overflow_Error == TRUE) |
---|
2700 | { |
---|
2701 | ivString(repr_vector, "repvector"); |
---|
2702 | Print("\n// %d element(s) of it are overflow!!", ntrue); |
---|
2703 | } |
---|
2704 | if(Overflow_Error == FALSE) |
---|
2705 | Overflow_Error = nError; |
---|
2706 | |
---|
2707 | omFree(ivres); |
---|
2708 | return repr_vector; |
---|
2709 | } |
---|
2710 | |
---|
2711 | |
---|
2712 | //GMP |
---|
2713 | static intvec* RepresentationMatrix_Dp(ideal G, intvec* M) |
---|
2714 | { |
---|
2715 | BOOLEAN nError = Overflow_Error; |
---|
2716 | Overflow_Error = FALSE; |
---|
2717 | |
---|
2718 | int i, j; |
---|
2719 | int nV = currRing->N; |
---|
2720 | |
---|
2721 | intvec* ivUnit = Mivdp(nV); |
---|
2722 | int degtmp, maxdeg = 0; |
---|
2723 | |
---|
2724 | for(i=IDELEMS(G)-1; i>=0; i--) |
---|
2725 | { |
---|
2726 | /* find the maximal total degree of the polynomial G[i] */ |
---|
2727 | degtmp = MwalkWeightDegree(G->m[i], ivUnit); |
---|
2728 | if(degtmp > maxdeg) |
---|
2729 | maxdeg = degtmp; |
---|
2730 | } |
---|
2731 | |
---|
2732 | mpz_t ztmp; |
---|
2733 | mpz_init_set_si(ztmp, maxdeg); |
---|
2734 | mpz_t *ivres=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
2735 | mpz_init_set_si(ivres[nV-1], 1); // (*ivres)[nV-1] = 1; |
---|
2736 | |
---|
2737 | for(i=nV-2; i>=0; i--) |
---|
2738 | { |
---|
2739 | mpz_init_set(ivres[i], ztmp); //(*ivres)[i] = ztmp; |
---|
2740 | mpz_mul_ui(ztmp, ztmp, maxdeg); //ztmp *=maxdeg; |
---|
2741 | } |
---|
2742 | |
---|
2743 | mpz_t *ivtmp=(mpz_t*)omAlloc(nV*sizeof(mpz_t)); |
---|
2744 | for(i=0; i<nV; i++) |
---|
2745 | mpz_init(ivtmp[i]); |
---|
2746 | |
---|
2747 | /* define ivtmp := ndeg^(n-1).w_1 + ndeg^(n-2).w_2 + ... + w_n */ |
---|
2748 | for(i=0; i<nV; i++) |
---|
2749 | for(j=0; j<nV; j++) |
---|
2750 | { |
---|
2751 | if((*M)[i*nV+j] < 0) |
---|
2752 | { |
---|
2753 | mpz_mul_ui(ztmp, ivres[i], -(*M)[i*nV+j]); |
---|
2754 | mpz_neg(ztmp, ztmp); |
---|
2755 | } |
---|
2756 | else |
---|
2757 | mpz_mul_ui(ztmp, ivres[i], (*M)[i*nV+j]); |
---|
2758 | |
---|
2759 | mpz_add(ivtmp[j], ivtmp[j], ztmp); |
---|
2760 | } |
---|
2761 | |
---|
2762 | mpz_t sing_int; |
---|
2763 | mpz_init_set_ui(sing_int, 2147483647); |
---|
2764 | |
---|
2765 | int ntrue; |
---|
2766 | intvec* repvector = new intvec(nV); |
---|
2767 | for(i=0; i<nV; i++) |
---|
2768 | { |
---|
2769 | (*repvector)[i] = mpz_get_si(ivtmp[i]); |
---|
2770 | if(mpz_cmp(ivtmp[i], sing_int)>0) |
---|
2771 | { |
---|
2772 | ntrue++; |
---|
2773 | if(Overflow_Error == FALSE) |
---|
2774 | { |
---|
2775 | Overflow_Error = TRUE; |
---|
2776 | PrintS("\n// ** OVERFLOW in \"Repr.Matrix\": "); |
---|
2777 | mpz_out_str( stdout, 10, ivtmp[i]); |
---|
2778 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
2779 | Print("\n// So vector[%d] := %d is wrong!!\n",i+1,(*repvector)[i]); |
---|
2780 | } |
---|
2781 | } |
---|
2782 | } |
---|
2783 | if(Overflow_Error == TRUE) |
---|
2784 | { |
---|
2785 | ivString(repvector, "repvector"); |
---|
2786 | Print("\n// %d element(s) of it are overflow!!", ntrue); |
---|
2787 | } |
---|
2788 | |
---|
2789 | if(Overflow_Error == FALSE) |
---|
2790 | Overflow_Error = nError; |
---|
2791 | |
---|
2792 | mpz_clear(ztmp); |
---|
2793 | omFree(ivtmp); |
---|
2794 | omFree(ivres); |
---|
2795 | return repvector; |
---|
2796 | } |
---|
2797 | |
---|
2798 | |
---|
2799 | |
---|
2800 | |
---|
2801 | |
---|
2802 | /* The following subroutine is the implementation of our first improved |
---|
2803 | Groebner walk algorithm, i.e. the first altervative algorithm. |
---|
2804 | First we use the Grobner walk algorithm and then we call the changed |
---|
2805 | perturbation walk algorithm with decreased degree, if an intermediate |
---|
2806 | weight vector is equal to the current target weight vector. |
---|
2807 | This call will be only repeated until we get the wanted reduced Groebner |
---|
2808 | basis or n times, where n is the numbers of variables. |
---|
2809 | */ |
---|
2810 | |
---|
2811 | // 19 Juni 2003 |
---|
2812 | static int testnegintvec(intvec* v) |
---|
2813 | { |
---|
2814 | int n = v->length(); |
---|
2815 | int i; |
---|
2816 | for(i=0; i<n; i++){ |
---|
2817 | if((*v)[i]<0) |
---|
2818 | return(1); |
---|
2819 | } |
---|
2820 | return(0); |
---|
2821 | } |
---|
2822 | |
---|
2823 | |
---|
2824 | /* 7 Februar 2002 */ |
---|
2825 | /* npwinc = 0, if curr_weight doesn't stay in the correct Groebner cone */ |
---|
2826 | static ideal Rec_LastGB(ideal G, intvec* curr_weight, |
---|
2827 | intvec* orig_target_weight, int tp_deg, int npwinc) |
---|
2828 | { |
---|
2829 | BOOLEAN nError = Overflow_Error; |
---|
2830 | Overflow_Error = FALSE; |
---|
2831 | BOOLEAN nOverflow_Error = FALSE; |
---|
2832 | |
---|
2833 | clock_t tproc=0; |
---|
2834 | clock_t tinput = clock(); |
---|
2835 | |
---|
2836 | int i, nV = currRing->N; |
---|
2837 | int nwalk=0, endwalks=0, nnwinC=1; |
---|
2838 | int nlast = 0; |
---|
2839 | ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG; |
---|
2840 | ring newRing, oldRing, TargetRing; |
---|
2841 | intvec* iv_M_lp; |
---|
2842 | intvec* target_weight; |
---|
2843 | intvec* ivNull = new intvec(nV); //define (0,...,0) |
---|
2844 | ring EXXRing = currRing; |
---|
2845 | int NEG=0; //19 juni 03 |
---|
2846 | intvec* extra_curr_weight = new intvec(nV); |
---|
2847 | intvec* next_weight; |
---|
2848 | |
---|
2849 | //08 Juli 03 |
---|
2850 | intvec* hilb_func; |
---|
2851 | /* to avoid (1,0,...,0) as the target vector */ |
---|
2852 | intvec* last_omega = new intvec(nV); |
---|
2853 | for(i=nV-1; i>0; i--) |
---|
2854 | (*last_omega)[i] = 1; |
---|
2855 | (*last_omega)[0] = 10000; |
---|
2856 | |
---|
2857 | BOOLEAN isGB = FALSE; |
---|
2858 | |
---|
2859 | /* compute a pertubed weight vector of the target weight vector */ |
---|
2860 | if(tp_deg > 1 && tp_deg <= nV) { |
---|
2861 | ideal H0 = idHeadCC(G); |
---|
2862 | |
---|
2863 | if (currRing->parameter != NULL) |
---|
2864 | DefRingParlp(); |
---|
2865 | else |
---|
2866 | VMrDefaultlp(); |
---|
2867 | |
---|
2868 | TargetRing = currRing; |
---|
2869 | ssG = idrMoveR(G,EXXRing); |
---|
2870 | |
---|
2871 | ideal H0_tmp = idrMoveR(H0,EXXRing); |
---|
2872 | ideal H1 = idHeadCC(ssG); |
---|
2873 | |
---|
2874 | /* Apply Lemma 2.2 in Collart et. al (1997) to check whether |
---|
2875 | cone(k-1) is equal to cone(k) */ |
---|
2876 | if(test_G_GB_walk(H0_tmp,H1)==1) { |
---|
2877 | idDelete(&H0_tmp); |
---|
2878 | idDelete(&H1); |
---|
2879 | G = ssG; |
---|
2880 | ssG = NULL; |
---|
2881 | newRing = currRing; |
---|
2882 | delete ivNull; |
---|
2883 | |
---|
2884 | if(npwinc != 0) |
---|
2885 | goto LastGB_Finish; |
---|
2886 | else { |
---|
2887 | isGB = TRUE; |
---|
2888 | goto KSTD_Finish; |
---|
2889 | } |
---|
2890 | } |
---|
2891 | idDelete(&H0_tmp); |
---|
2892 | idDelete(&H1); |
---|
2893 | |
---|
2894 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
2895 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
2896 | delete iv_M_lp; |
---|
2897 | //PrintS("\n// Input is not GB!!"); |
---|
2898 | rChangeCurrRing(EXXRing); |
---|
2899 | G = idrMoveR(ssG, TargetRing); |
---|
2900 | |
---|
2901 | if(Overflow_Error == TRUE) { |
---|
2902 | nOverflow_Error = Overflow_Error; |
---|
2903 | NEG = 1; |
---|
2904 | newRing = currRing; |
---|
2905 | goto JUNI_STD; |
---|
2906 | } |
---|
2907 | } |
---|
2908 | |
---|
2909 | while(1) |
---|
2910 | { |
---|
2911 | nwalk ++; |
---|
2912 | nstep++; |
---|
2913 | |
---|
2914 | if(nwalk==1) |
---|
2915 | goto FIRST_STEP; |
---|
2916 | |
---|
2917 | to=clock(); |
---|
2918 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
2919 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
2920 | xtif=xtif+clock()-to; |
---|
2921 | |
---|
2922 | #ifndef BUCHBERGER_ALG |
---|
2923 | if(isNolVector(curr_weight) == 0) |
---|
2924 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
2925 | else |
---|
2926 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
2927 | #endif // BUCHBERGER_ALG |
---|
2928 | |
---|
2929 | oldRing = currRing; |
---|
2930 | |
---|
2931 | /* defiNe a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
2932 | if (currRing->parameter != NULL) |
---|
2933 | DefRingPar(curr_weight); |
---|
2934 | else |
---|
2935 | VMrDefault(curr_weight); |
---|
2936 | |
---|
2937 | newRing = currRing; |
---|
2938 | Gomega1 = idrMoveR(Gomega, oldRing); |
---|
2939 | to=clock(); |
---|
2940 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
2941 | #ifdef BUCHBERGER_ALG |
---|
2942 | M = MstdhomCC(Gomega1); |
---|
2943 | #else |
---|
2944 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
2945 | delete hilb_func; |
---|
2946 | #endif // BUCHBERGER_ALG |
---|
2947 | xtstd=xtstd+clock()-to; |
---|
2948 | /* change the ring to oldRing */ |
---|
2949 | rChangeCurrRing(oldRing); |
---|
2950 | M1 = idrMoveR(M, newRing); |
---|
2951 | Gomega2 = idrMoveR(Gomega1, newRing); |
---|
2952 | |
---|
2953 | to=clock(); |
---|
2954 | /* compute a reduced Groebner basis of <G> w.r.t. "newRing" by the |
---|
2955 | lifting process*/ |
---|
2956 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
2957 | xtlift=xtlift+clock()-to; |
---|
2958 | idDelete(&M1); |
---|
2959 | idDelete(&Gomega2); |
---|
2960 | idDelete(&G); |
---|
2961 | |
---|
2962 | /* change the ring to newRing */ |
---|
2963 | rChangeCurrRing(newRing); |
---|
2964 | F1 = idrMoveR(F, oldRing); |
---|
2965 | |
---|
2966 | to=clock(); |
---|
2967 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
2968 | G = kInterRedCC(F1, NULL); |
---|
2969 | xtred=xtred+clock()-to; |
---|
2970 | idDelete(&F1); |
---|
2971 | |
---|
2972 | if(endwalks == 1) |
---|
2973 | break; |
---|
2974 | |
---|
2975 | FIRST_STEP: |
---|
2976 | to=clock(); |
---|
2977 | Overflow_Error = FALSE; |
---|
2978 | /* compute a next weight vector */ |
---|
2979 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
2980 | xtnw=xtnw+clock()-to; |
---|
2981 | #ifdef PRINT_VECTORS |
---|
2982 | MivString(curr_weight, target_weight, next_weight); |
---|
2983 | #endif |
---|
2984 | |
---|
2985 | if(Overflow_Error == TRUE) { |
---|
2986 | //PrintS("\n// ** The next vector does NOT stay in Cone!!\n"); |
---|
2987 | #ifdef TEST_OVERFLOW |
---|
2988 | goto LastGB_Finish; |
---|
2989 | #endif |
---|
2990 | |
---|
2991 | nnwinC = 0; |
---|
2992 | if(tp_deg == nV) |
---|
2993 | nlast = 1; |
---|
2994 | |
---|
2995 | delete next_weight; |
---|
2996 | break; |
---|
2997 | } |
---|
2998 | |
---|
2999 | if(MivComp(next_weight, ivNull) == 1) { |
---|
3000 | //newRing = currRing; |
---|
3001 | delete next_weight; |
---|
3002 | break; |
---|
3003 | } |
---|
3004 | |
---|
3005 | if(MivComp(next_weight, target_weight) == 1) { |
---|
3006 | if(tp_deg == nV) |
---|
3007 | endwalks = 1; |
---|
3008 | else { |
---|
3009 | REC_LAST_GB_ALT2: |
---|
3010 | nOverflow_Error = Overflow_Error; |
---|
3011 | tproc=tproc+clock()-tinput; |
---|
3012 | /* |
---|
3013 | Print("\n// takes %d steps and calls \"Rec_LastGB\" (%d):", |
---|
3014 | nwalk, tp_deg+1); |
---|
3015 | */ |
---|
3016 | G = Rec_LastGB(G,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
3017 | newRing = currRing; |
---|
3018 | delete next_weight; |
---|
3019 | break; |
---|
3020 | } |
---|
3021 | } |
---|
3022 | |
---|
3023 | for(i=nV-1; i>=0; i--) { |
---|
3024 | //(*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
3025 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
3026 | } |
---|
3027 | delete next_weight; |
---|
3028 | }//while |
---|
3029 | |
---|
3030 | delete ivNull; |
---|
3031 | |
---|
3032 | if(tp_deg != nV) { |
---|
3033 | newRing = currRing; |
---|
3034 | |
---|
3035 | if (currRing->parameter != NULL) |
---|
3036 | DefRingParlp(); |
---|
3037 | else |
---|
3038 | VMrDefaultlp(); |
---|
3039 | |
---|
3040 | F1 = idrMoveR(G, newRing); |
---|
3041 | |
---|
3042 | if(nnwinC == 0 || test_w_in_ConeCC(F1, target_weight) != 1 ) { |
---|
3043 | nOverflow_Error = Overflow_Error; |
---|
3044 | //Print("\n// takes %d steps and calls \"Rec_LastGB (%d):", tp_deg+1); |
---|
3045 | tproc=tproc+clock()-tinput; |
---|
3046 | F1 = Rec_LastGB(F1,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
3047 | } |
---|
3048 | delete target_weight; |
---|
3049 | |
---|
3050 | TargetRing = currRing; |
---|
3051 | rChangeCurrRing(EXXRing); |
---|
3052 | result = idrMoveR(F1, TargetRing); |
---|
3053 | } |
---|
3054 | else { |
---|
3055 | if(nlast == 1) { |
---|
3056 | JUNI_STD: |
---|
3057 | |
---|
3058 | newRing = currRing; |
---|
3059 | if (currRing->parameter != NULL) |
---|
3060 | DefRingParlp(); |
---|
3061 | else |
---|
3062 | VMrDefaultlp(); |
---|
3063 | |
---|
3064 | KSTD_Finish: |
---|
3065 | if(isGB == FALSE) |
---|
3066 | F1 = idrMoveR(G, newRing); |
---|
3067 | else |
---|
3068 | F1 = G; |
---|
3069 | to=clock(); |
---|
3070 | // Print("\n// apply the Buchberger's alg in ring = %s",rString(currRing)); |
---|
3071 | // idElements(F1, "F1"); |
---|
3072 | G = MstdCC(F1); |
---|
3073 | xtextra=xtextra+clock()-to; |
---|
3074 | |
---|
3075 | |
---|
3076 | idDelete(&F1); |
---|
3077 | newRing = currRing; |
---|
3078 | } |
---|
3079 | |
---|
3080 | LastGB_Finish: |
---|
3081 | rChangeCurrRing(EXXRing); |
---|
3082 | result = idrMoveR(G, newRing); |
---|
3083 | } |
---|
3084 | |
---|
3085 | if(Overflow_Error == FALSE) |
---|
3086 | Overflow_Error=nError; |
---|
3087 | /* |
---|
3088 | Print("\n// \"Rec_LastGB\" (%d) took %d steps and %.2f sec.Overflow_Error (%d)", tp_deg, |
---|
3089 | nwalk, ((double) tproc)/1000000, nOverflow_Error); |
---|
3090 | */ |
---|
3091 | return(result); |
---|
3092 | } |
---|
3093 | |
---|
3094 | /* The following subroutine is the implementation of our second improved |
---|
3095 | Groebner walk algorithm, i.e. the second altervative algorithm. |
---|
3096 | First we use the Grobner walk algorithm and then we call the changed |
---|
3097 | perturbation walk algorithm with increased degree, if an intermediate |
---|
3098 | weight vector is equal to the current target weight vector. |
---|
3099 | This call will be only repeated until we get the wanted reduced Groebner |
---|
3100 | basis or n times, where n is the numbers of variables. |
---|
3101 | */ |
---|
3102 | /* walk + recursive LastGB */ |
---|
3103 | ideal MAltwalk2(ideal Go, intvec* curr_weight, intvec* target_weight) |
---|
3104 | { |
---|
3105 | Set_Error(FALSE); |
---|
3106 | Overflow_Error = FALSE; |
---|
3107 | BOOLEAN nOverflow_Error = FALSE; |
---|
3108 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
3109 | |
---|
3110 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
3111 | xftinput = clock(); |
---|
3112 | clock_t tostd, tproc; |
---|
3113 | |
---|
3114 | nstep = 0; |
---|
3115 | int i, nV = currRing->N; |
---|
3116 | int nwalk=0, endwalks=0, nhilb=1; |
---|
3117 | |
---|
3118 | ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G, G1; |
---|
3119 | ring endRing, newRing, oldRing; |
---|
3120 | intvec* ivNull = new intvec(nV); |
---|
3121 | intvec* next_weight; |
---|
3122 | intvec* extra_curr_weight = new intvec(nV); |
---|
3123 | intvec* hilb_func; |
---|
3124 | intvec* exivlp = Mivlp(nV); |
---|
3125 | |
---|
3126 | ring XXRing = currRing; |
---|
3127 | |
---|
3128 | //Print("\n// ring r_input = %s;", rString(currRing)); |
---|
3129 | to = clock(); |
---|
3130 | /* compute the reduced Groebner basis of the given ideal w.r.t. |
---|
3131 | a "fast" monomial order, e.g. degree reverse lex. order (dp) */ |
---|
3132 | G = MstdCC(Go); |
---|
3133 | tostd=clock()-to; |
---|
3134 | |
---|
3135 | /* |
---|
3136 | Print("\n// Computation of the first std took = %.2f sec", |
---|
3137 | ((double) tostd)/1000000); |
---|
3138 | */ |
---|
3139 | if(currRing->order[0] == ringorder_a) |
---|
3140 | goto NEXT_VECTOR; |
---|
3141 | |
---|
3142 | while(1) |
---|
3143 | { |
---|
3144 | nwalk ++; |
---|
3145 | nstep ++; |
---|
3146 | to = clock(); |
---|
3147 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
3148 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
3149 | xtif=xtif+clock()-to; |
---|
3150 | #if 0 |
---|
3151 | if(Overflow_Error == TRUE) |
---|
3152 | { |
---|
3153 | for(i=nV-1; i>=0; i--) |
---|
3154 | (*curr_weight)[i] = (*extra_curr_weight)[i]; |
---|
3155 | delete extra_curr_weight; |
---|
3156 | goto LAST_GB_ALT2; |
---|
3157 | } |
---|
3158 | #endif |
---|
3159 | oldRing = currRing; |
---|
3160 | |
---|
3161 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
3162 | if (currRing->parameter != NULL) |
---|
3163 | DefRingPar(curr_weight); |
---|
3164 | else |
---|
3165 | VMrDefault(curr_weight); |
---|
3166 | |
---|
3167 | newRing = currRing; |
---|
3168 | Gomega1 = idrMoveR(Gomega, oldRing); |
---|
3169 | to = clock(); |
---|
3170 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
3171 | M = MstdhomCC(Gomega1); |
---|
3172 | xtstd=xtstd+clock()-to; |
---|
3173 | /* change the ring to oldRing */ |
---|
3174 | rChangeCurrRing(oldRing); |
---|
3175 | M1 = idrMoveR(M, newRing); |
---|
3176 | Gomega2 = idrMoveR(Gomega1, newRing); |
---|
3177 | |
---|
3178 | to = clock(); |
---|
3179 | /* compute the reduced Groebner basis of <G> w.r.t. "newRing" |
---|
3180 | by the liftig process */ |
---|
3181 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
3182 | xtlift=xtlift+clock()-to; |
---|
3183 | idDelete(&M1); |
---|
3184 | idDelete(&Gomega2); |
---|
3185 | idDelete(&G); |
---|
3186 | |
---|
3187 | /* change the ring to newRing */ |
---|
3188 | rChangeCurrRing(newRing); |
---|
3189 | F1 = idrMoveR(F, oldRing); |
---|
3190 | |
---|
3191 | to = clock(); |
---|
3192 | /* reduce the Groebner basis <G> w.r.t. newRing */ |
---|
3193 | G = kInterRedCC(F1, NULL); |
---|
3194 | xtred=xtred+clock()-to; |
---|
3195 | idDelete(&F1); |
---|
3196 | |
---|
3197 | if(endwalks == 1) |
---|
3198 | break; |
---|
3199 | |
---|
3200 | NEXT_VECTOR: |
---|
3201 | to = clock(); |
---|
3202 | /* compute a next weight vector */ |
---|
3203 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
3204 | xtnw=xtnw+clock()-to; |
---|
3205 | #ifdef PRINT_VECTORS |
---|
3206 | MivString(curr_weight, target_weight, next_weight); |
---|
3207 | #endif |
---|
3208 | |
---|
3209 | if(Overflow_Error == TRUE) |
---|
3210 | { |
---|
3211 | /* |
---|
3212 | ivString(next_weight, "omega"); |
---|
3213 | PrintS("\n// ** The weight vector does NOT stay in Cone!!\n"); |
---|
3214 | */ |
---|
3215 | #ifdef TEST_OVERFLOW |
---|
3216 | goto TEST_OVERFLOW_OI; |
---|
3217 | #endif |
---|
3218 | |
---|
3219 | |
---|
3220 | newRing = currRing; |
---|
3221 | if (currRing->parameter != NULL) |
---|
3222 | DefRingPar(target_weight); |
---|
3223 | else |
---|
3224 | VMrDefault(target_weight); |
---|
3225 | |
---|
3226 | F1 = idrMoveR(G, newRing); |
---|
3227 | G = MstdCC(F1); |
---|
3228 | idDelete(&F1); |
---|
3229 | newRing = currRing; |
---|
3230 | break; |
---|
3231 | } |
---|
3232 | |
---|
3233 | if(MivComp(next_weight, ivNull) == 1) |
---|
3234 | { |
---|
3235 | newRing = currRing; |
---|
3236 | delete next_weight; |
---|
3237 | break; |
---|
3238 | } |
---|
3239 | |
---|
3240 | if(MivComp(next_weight, target_weight) == 1) |
---|
3241 | { |
---|
3242 | if(MivSame(target_weight, exivlp)==1) |
---|
3243 | { |
---|
3244 | LAST_GB_ALT2: |
---|
3245 | nOverflow_Error = Overflow_Error; |
---|
3246 | tproc = clock()-xftinput; |
---|
3247 | //Print("\n// takes %d steps and calls the recursion of level 2:", nwalk); |
---|
3248 | /* call the changed perturbation walk algorithm with degree 2 */ |
---|
3249 | G = Rec_LastGB(G, curr_weight, target_weight, 2,1); |
---|
3250 | newRing = currRing; |
---|
3251 | delete next_weight; |
---|
3252 | break; |
---|
3253 | } |
---|
3254 | endwalks = 1; |
---|
3255 | } |
---|
3256 | |
---|
3257 | for(i=nV-1; i>=0; i--) |
---|
3258 | { |
---|
3259 | //(*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
3260 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
3261 | } |
---|
3262 | delete next_weight; |
---|
3263 | } |
---|
3264 | TEST_OVERFLOW_OI: |
---|
3265 | rChangeCurrRing(XXRing); |
---|
3266 | G = idrMoveR(G, newRing); |
---|
3267 | delete ivNull; |
---|
3268 | delete exivlp; |
---|
3269 | |
---|
3270 | #ifdef TIME_TEST |
---|
3271 | Print("\n// \"Main procedure\" took %d steps dnd %.2f sec. Overflow_Error (%d)", nwalk, |
---|
3272 | ((double) tproc)/1000000, nOverflow_Error); |
---|
3273 | |
---|
3274 | TimeStringFractal(xftinput, tostd, xtif, xtstd, xtextra,xtlift, xtred,xtnw); |
---|
3275 | |
---|
3276 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
3277 | //Print("\n// Overflow_Error? (%d)", nOverflow_Error); |
---|
3278 | Print("\n// Awalk2 took %d steps!!", nstep); |
---|
3279 | #endif |
---|
3280 | |
---|
3281 | return(G); |
---|
3282 | } |
---|
3283 | |
---|
3284 | |
---|
3285 | /* 5.5.02 */ |
---|
3286 | /* The implementation of the fractal walk algorithmus */ |
---|
3287 | |
---|
3288 | /* The main procedur Mfwalk calls the recursive Subroutine |
---|
3289 | rec_fractal_call to compute the wanted Gröbner basis. |
---|
3290 | At the main procedur we compute the reduced Gröbner basis w.r.t. a "fast" |
---|
3291 | order, e.g. "dp" and a sequence of weight vectors which are row vectors |
---|
3292 | of a matrix. This matrix defines the given monomial order, e.g. "lp" |
---|
3293 | */ |
---|
3294 | |
---|
3295 | |
---|
3296 | |
---|
3297 | |
---|
3298 | /* perturb the matrix order of "lex" */ |
---|
3299 | static intvec* NewVectorlp(ideal I) |
---|
3300 | { |
---|
3301 | int nV = currRing->N; |
---|
3302 | intvec* iv_wlp = MivMatrixOrderlp(nV); |
---|
3303 | intvec* result = Mfpertvector(I, iv_wlp); |
---|
3304 | delete iv_wlp; |
---|
3305 | return result; |
---|
3306 | } |
---|
3307 | |
---|
3308 | int ngleich; |
---|
3309 | intvec* Xsigma; |
---|
3310 | intvec* Xtau; |
---|
3311 | int xn; |
---|
3312 | intvec* Xivinput; |
---|
3313 | intvec* Xivlp; |
---|
3314 | |
---|
3315 | |
---|
3316 | |
---|
3317 | /*********************************************************************** |
---|
3318 | The procedur REC_GB_Mwalk computes a GB for <G> w.r.t. the weight order |
---|
3319 | otw, where G is a reduced GB w.r.t. the weight order cw. |
---|
3320 | The new procedur Mwalk calls REC_GB. |
---|
3321 | ************************************************************************/ |
---|
3322 | static ideal REC_GB_Mwalk(ideal G, intvec* curr_weight, intvec* orig_target_weight, |
---|
3323 | int tp_deg, int npwinc) |
---|
3324 | { |
---|
3325 | BOOLEAN nError = Overflow_Error; |
---|
3326 | Overflow_Error = FALSE; |
---|
3327 | |
---|
3328 | int i, nV = currRing->N, ntwC, npwinC; |
---|
3329 | int nwalk=0, endwalks=0, nnwinC=1, nlast = 0; |
---|
3330 | ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG; |
---|
3331 | ring newRing, oldRing, TargetRing; |
---|
3332 | intvec* iv_M_lp; |
---|
3333 | intvec* target_weight; |
---|
3334 | intvec* ivNull = new intvec(nV); |
---|
3335 | intvec* hilb_func; |
---|
3336 | BOOLEAN isGB = FALSE; |
---|
3337 | |
---|
3338 | /* to avoid (1,0,...,0) as the target vector */ |
---|
3339 | intvec* last_omega = new intvec(nV); |
---|
3340 | for(i=nV-1; i>0; i--) |
---|
3341 | (*last_omega)[i] = 1; |
---|
3342 | (*last_omega)[0] = 10000; |
---|
3343 | |
---|
3344 | ring EXXRing = currRing; |
---|
3345 | |
---|
3346 | /* compute a pertubed weight vector of the target weight vector */ |
---|
3347 | if(tp_deg > 1 && tp_deg <= nV) |
---|
3348 | { |
---|
3349 | ideal H0 = idHeadCC(G); |
---|
3350 | if (currRing->parameter != NULL) |
---|
3351 | DefRingPar(orig_target_weight); |
---|
3352 | else |
---|
3353 | VMrDefault(orig_target_weight); |
---|
3354 | |
---|
3355 | TargetRing = currRing; |
---|
3356 | ssG = idrMoveR(G,EXXRing); |
---|
3357 | |
---|
3358 | ideal H0_tmp = idrMoveR(H0,EXXRing); |
---|
3359 | ideal H1 = idHeadCC(ssG); |
---|
3360 | id_Delete(&H0,EXXRing); |
---|
3361 | |
---|
3362 | if(test_G_GB_walk(H0_tmp,H1)==1) |
---|
3363 | { |
---|
3364 | //Print("//input in %d-th recursive is a GB",tp_deg); |
---|
3365 | idDelete(&H0_tmp);idDelete(&H1); |
---|
3366 | G = ssG; |
---|
3367 | ssG = NULL; |
---|
3368 | newRing = currRing; |
---|
3369 | delete ivNull; |
---|
3370 | if(npwinc == 0) |
---|
3371 | { |
---|
3372 | isGB = TRUE; |
---|
3373 | goto KSTD_Finish; |
---|
3374 | } |
---|
3375 | else |
---|
3376 | goto LastGB_Finish; |
---|
3377 | } |
---|
3378 | idDelete(&H0_tmp); idDelete(&H1); |
---|
3379 | |
---|
3380 | intvec* ivlp = Mivlp(nV); |
---|
3381 | if( MivSame(orig_target_weight, ivlp)==1 ) |
---|
3382 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
3383 | else |
---|
3384 | iv_M_lp = MivMatrixOrder(orig_target_weight); |
---|
3385 | |
---|
3386 | //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg); |
---|
3387 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
3388 | |
---|
3389 | delete ivlp; |
---|
3390 | delete iv_M_lp; |
---|
3391 | |
---|
3392 | rChangeCurrRing(EXXRing); |
---|
3393 | G = idrMoveR(ssG, TargetRing); |
---|
3394 | } |
---|
3395 | |
---|
3396 | while(1) |
---|
3397 | { |
---|
3398 | nwalk ++; |
---|
3399 | nstep++; |
---|
3400 | if(nwalk == 1) |
---|
3401 | goto NEXT_STEP; |
---|
3402 | |
---|
3403 | //Print("\n// Entering the %d-th step in the %d-th recursive:",nwalk,tp_deg); |
---|
3404 | to = clock(); |
---|
3405 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
3406 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
3407 | xtif = xtif + clock()-to; |
---|
3408 | |
---|
3409 | #ifndef BUCHBERGER_ALG |
---|
3410 | if(isNolVector(curr_weight) == 0) |
---|
3411 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
3412 | else |
---|
3413 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
3414 | #endif // BUCHBERGER_ALG |
---|
3415 | |
---|
3416 | oldRing = currRing; |
---|
3417 | |
---|
3418 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
3419 | if (currRing->parameter != NULL) |
---|
3420 | DefRingPar(curr_weight); |
---|
3421 | else |
---|
3422 | VMrDefault(curr_weight); |
---|
3423 | |
---|
3424 | newRing = currRing; |
---|
3425 | Gomega1 = idrMoveR(Gomega, oldRing); |
---|
3426 | |
---|
3427 | to = clock(); |
---|
3428 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
3429 | #ifdef BUCHBERGER_ALG |
---|
3430 | M = MstdhomCC(Gomega1); |
---|
3431 | #else |
---|
3432 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
3433 | delete hilb_func; |
---|
3434 | #endif // BUCHBERGER_ALG |
---|
3435 | xtstd = xtstd + clock() - to; |
---|
3436 | |
---|
3437 | /* change the ring to oldRing */ |
---|
3438 | rChangeCurrRing(oldRing); |
---|
3439 | |
---|
3440 | M1 = idrMoveR(M, newRing); |
---|
3441 | Gomega2 = idrMoveR(Gomega1, newRing); |
---|
3442 | |
---|
3443 | to = clock(); |
---|
3444 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
3445 | xtlift = xtlift + clock() -to; |
---|
3446 | |
---|
3447 | idDelete(&M1); |
---|
3448 | idDelete(&Gomega2); |
---|
3449 | idDelete(&G); |
---|
3450 | |
---|
3451 | |
---|
3452 | /* change the ring to newRing */ |
---|
3453 | rChangeCurrRing(newRing); |
---|
3454 | F1 = idrMoveR(F, oldRing); |
---|
3455 | |
---|
3456 | to = clock(); |
---|
3457 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
3458 | G = kInterRedCC(F1, NULL); |
---|
3459 | xtred = xtred + clock() -to; |
---|
3460 | |
---|
3461 | idDelete(&F1); |
---|
3462 | |
---|
3463 | if(endwalks == 1) |
---|
3464 | break; |
---|
3465 | |
---|
3466 | NEXT_STEP: |
---|
3467 | to = clock(); |
---|
3468 | /* compute a next weight vector */ |
---|
3469 | intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
3470 | xtnw = xtnw + clock() - to; |
---|
3471 | |
---|
3472 | #ifdef PRINT_VECTORS |
---|
3473 | MivString(curr_weight, target_weight, next_weight); |
---|
3474 | #endif |
---|
3475 | |
---|
3476 | /*check whether the computed vector does in the correct cone */ |
---|
3477 | //ntwC = test_w_in_ConeCC(G, next_weight); |
---|
3478 | //if(ntwC != 1) |
---|
3479 | if(Overflow_Error == TRUE) |
---|
3480 | { |
---|
3481 | PrintS("\n// ** The computed vector does NOT stay in Cone!!\n"); |
---|
3482 | nnwinC = 0; |
---|
3483 | if(tp_deg == nV) |
---|
3484 | nlast = 1; |
---|
3485 | delete next_weight; |
---|
3486 | break; |
---|
3487 | } |
---|
3488 | if(MivComp(next_weight, ivNull) == 1) |
---|
3489 | { |
---|
3490 | newRing = currRing; |
---|
3491 | delete next_weight; |
---|
3492 | break; |
---|
3493 | } |
---|
3494 | |
---|
3495 | if(MivComp(next_weight, target_weight) == 1) |
---|
3496 | { |
---|
3497 | if(tp_deg == nV) |
---|
3498 | endwalks = 1; |
---|
3499 | else { |
---|
3500 | G = REC_GB_Mwalk(G,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
3501 | newRing = currRing; |
---|
3502 | delete next_weight; |
---|
3503 | break; |
---|
3504 | } |
---|
3505 | } |
---|
3506 | |
---|
3507 | /* 06.11.01 NOT Changed */ |
---|
3508 | for(i=nV-1; i>=0; i--) |
---|
3509 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
3510 | |
---|
3511 | delete next_weight; |
---|
3512 | }//while |
---|
3513 | |
---|
3514 | delete ivNull; |
---|
3515 | |
---|
3516 | if(tp_deg != nV) |
---|
3517 | { |
---|
3518 | //28.07.03 |
---|
3519 | newRing = currRing; |
---|
3520 | |
---|
3521 | if (currRing->parameter != NULL) |
---|
3522 | // DefRingParlp(); // |
---|
3523 | DefRingPar(orig_target_weight); |
---|
3524 | else |
---|
3525 | VMrDefault(orig_target_weight); |
---|
3526 | |
---|
3527 | |
---|
3528 | F1 = idrMoveR(G, newRing); |
---|
3529 | |
---|
3530 | if(nnwinC == 0) |
---|
3531 | F1 = REC_GB_Mwalk(F1,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
3532 | else |
---|
3533 | if(test_w_in_ConeCC(F1, target_weight) != 1) |
---|
3534 | F1 = REC_GB_Mwalk(F1,curr_weight, orig_target_weight,tp_deg+1,nnwinC); |
---|
3535 | |
---|
3536 | delete target_weight; |
---|
3537 | |
---|
3538 | TargetRing = currRing; |
---|
3539 | rChangeCurrRing(EXXRing); |
---|
3540 | result = idrMoveR(F1, TargetRing); |
---|
3541 | } |
---|
3542 | else |
---|
3543 | { |
---|
3544 | if(nlast == 1) |
---|
3545 | { |
---|
3546 | if (currRing->parameter != NULL) |
---|
3547 | DefRingPar(orig_target_weight); |
---|
3548 | else |
---|
3549 | VMrDefault(orig_target_weight); |
---|
3550 | |
---|
3551 | |
---|
3552 | KSTD_Finish: |
---|
3553 | if(isGB == FALSE) |
---|
3554 | F1 = idrMoveR(G, newRing); |
---|
3555 | else |
---|
3556 | F1 = G; |
---|
3557 | to=clock(); |
---|
3558 | /* apply Buchberger alg to compute a red. GB of F1 */ |
---|
3559 | G = MstdCC(F1); |
---|
3560 | xtextra=clock()-to; |
---|
3561 | idDelete(&F1); |
---|
3562 | newRing = currRing; |
---|
3563 | } |
---|
3564 | |
---|
3565 | LastGB_Finish: |
---|
3566 | rChangeCurrRing(EXXRing); |
---|
3567 | result = idrMoveR(G, newRing); |
---|
3568 | } |
---|
3569 | |
---|
3570 | if(Overflow_Error == FALSE) |
---|
3571 | Overflow_Error = nError; |
---|
3572 | |
---|
3573 | return(result); |
---|
3574 | } |
---|
3575 | |
---|
3576 | |
---|
3577 | /* 08.09.02 */ |
---|
3578 | /******** THE NEW GRÖBNER WALK ALGORITHM **********/ |
---|
3579 | /* Gröbnerwalk with a recursive "second" alternative GW, REC_GB_Mwalk |
---|
3580 | that only computes the last reduced GB */ |
---|
3581 | ideal Mwalk(ideal Go, intvec* curr_weight, intvec* target_weight) |
---|
3582 | { |
---|
3583 | Set_Error(FALSE); |
---|
3584 | Overflow_Error = FALSE; |
---|
3585 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
3586 | |
---|
3587 | clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0; |
---|
3588 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; |
---|
3589 | tinput = clock(); |
---|
3590 | clock_t tim; |
---|
3591 | nstep=0; |
---|
3592 | int i, nV = currRing->N; |
---|
3593 | int nwalk=0, endwalks=0; |
---|
3594 | |
---|
3595 | ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G, G1; |
---|
3596 | ring endRing, newRing, oldRing; |
---|
3597 | intvec* ivNull = new intvec(nV); |
---|
3598 | intvec* exivlp = Mivlp(nV); |
---|
3599 | intvec* hilb_func; |
---|
3600 | |
---|
3601 | intvec* tmp_weight = new intvec(nV); |
---|
3602 | for(i=nV-1; i>=0; i--) |
---|
3603 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
3604 | |
---|
3605 | /* to avoid (1,0,...,0) as the target vector */ |
---|
3606 | intvec* last_omega = new intvec(nV); |
---|
3607 | for(i=nV-1; i>0; i--) |
---|
3608 | (*last_omega)[i] = 1; |
---|
3609 | (*last_omega)[0] = 10000; |
---|
3610 | |
---|
3611 | ring XXRing = currRing; |
---|
3612 | |
---|
3613 | to = clock(); |
---|
3614 | /* the monomial ordering of this current ring would be "dp" */ |
---|
3615 | G = MstdCC(Go); |
---|
3616 | tostd = clock()-to; |
---|
3617 | |
---|
3618 | if(currRing->order[0] == ringorder_a) |
---|
3619 | goto NEXT_VECTOR; |
---|
3620 | |
---|
3621 | while(1) |
---|
3622 | { |
---|
3623 | nwalk ++; |
---|
3624 | nstep ++; |
---|
3625 | to = clock(); |
---|
3626 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
3627 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
3628 | tif = tif + clock()-to; |
---|
3629 | oldRing = currRing; |
---|
3630 | |
---|
3631 | if(endwalks == 1) |
---|
3632 | { |
---|
3633 | /* compute a reduced Groebner basis of Gomega w.r.t. >>_cw by |
---|
3634 | the recursive changed perturbation walk alg. */ |
---|
3635 | tim = clock(); |
---|
3636 | /* |
---|
3637 | Print("\n// **** Gröbnerwalk took %d steps and ", nwalk); |
---|
3638 | PrintS("\n// **** call the rec. Pert. Walk to compute a red GB of:"); |
---|
3639 | idElements(Gomega, "G_omega"); |
---|
3640 | */ |
---|
3641 | |
---|
3642 | if(MivSame(exivlp, target_weight)==1) |
---|
3643 | M = REC_GB_Mwalk(idCopy(Gomega), tmp_weight, curr_weight, 2,1); |
---|
3644 | else |
---|
3645 | goto NORMAL_GW; |
---|
3646 | /* |
---|
3647 | Print("\n// time for the last std(Gw) = %.2f sec", |
---|
3648 | ((double) (clock()-tim)/1000000)); |
---|
3649 | PrintS("\n// ***************************************************\n"); |
---|
3650 | */ |
---|
3651 | #ifdef CHECK_IDEAL_MWALK |
---|
3652 | idElements(Gomega, "G_omega"); |
---|
3653 | headidString(Gomega, "Gw"); |
---|
3654 | idElements(M, "M"); |
---|
3655 | //headidString(M, "M"); |
---|
3656 | #endif |
---|
3657 | to = clock(); |
---|
3658 | F = MLifttwoIdeal(Gomega, M, G); |
---|
3659 | xtlift = xtlift + clock() - to; |
---|
3660 | |
---|
3661 | idDelete(&Gomega); |
---|
3662 | idDelete(&M); |
---|
3663 | idDelete(&G); |
---|
3664 | |
---|
3665 | oldRing = currRing; |
---|
3666 | |
---|
3667 | /* create a new ring newRing */ |
---|
3668 | if (currRing->parameter != NULL) |
---|
3669 | DefRingPar(curr_weight); |
---|
3670 | else |
---|
3671 | VMrDefault(curr_weight); |
---|
3672 | |
---|
3673 | newRing = currRing; |
---|
3674 | F1 = idrMoveR(F, oldRing); |
---|
3675 | } |
---|
3676 | else |
---|
3677 | { |
---|
3678 | NORMAL_GW: |
---|
3679 | #ifndef BUCHBERGER_ALG |
---|
3680 | if(isNolVector(curr_weight) == 0) |
---|
3681 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
3682 | else |
---|
3683 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
3684 | #endif // BUCHBERGER_ALG |
---|
3685 | |
---|
3686 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
3687 | if (currRing->parameter != NULL) |
---|
3688 | DefRingPar(curr_weight); |
---|
3689 | else |
---|
3690 | VMrDefault(curr_weight); |
---|
3691 | |
---|
3692 | newRing = currRing; |
---|
3693 | Gomega1 = idrMoveR(Gomega, oldRing); |
---|
3694 | |
---|
3695 | to = clock(); |
---|
3696 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
3697 | #ifdef BUCHBERGER_ALG |
---|
3698 | M = MstdhomCC(Gomega1); |
---|
3699 | #else |
---|
3700 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
3701 | delete hilb_func; |
---|
3702 | #endif // BUCHBERGER_ALG |
---|
3703 | tstd = tstd + clock() - to; |
---|
3704 | |
---|
3705 | /* change the ring to oldRing */ |
---|
3706 | rChangeCurrRing(oldRing); |
---|
3707 | M1 = idrMoveR(M, newRing); |
---|
3708 | Gomega2 = idrMoveR(Gomega1, newRing); |
---|
3709 | |
---|
3710 | to = clock(); |
---|
3711 | /* compute a representation of the generators of submod (M) |
---|
3712 | with respect to those of mod (Gomega). |
---|
3713 | Gomega is a reduced Groebner basis w.r.t. the current ring */ |
---|
3714 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
3715 | tlift = tlift + clock() - to; |
---|
3716 | |
---|
3717 | idDelete(&M1); |
---|
3718 | idDelete(&Gomega2); |
---|
3719 | idDelete(&G); |
---|
3720 | |
---|
3721 | /* change the ring to newRing */ |
---|
3722 | rChangeCurrRing(newRing); |
---|
3723 | F1 = idrMoveR(F, oldRing); |
---|
3724 | } |
---|
3725 | |
---|
3726 | to = clock(); |
---|
3727 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
3728 | G = kInterRedCC(F1, NULL); |
---|
3729 | if(endwalks != 1) |
---|
3730 | tred = tred + clock() - to; |
---|
3731 | else |
---|
3732 | xtred = xtred + clock() - to; |
---|
3733 | |
---|
3734 | idDelete(&F1); |
---|
3735 | if(endwalks == 1) |
---|
3736 | break; |
---|
3737 | |
---|
3738 | NEXT_VECTOR: |
---|
3739 | to = clock(); |
---|
3740 | /* compute a next weight vector */ |
---|
3741 | intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
3742 | tnw = tnw + clock() - to; |
---|
3743 | #ifdef PRINT_VECTORS |
---|
3744 | MivString(curr_weight, target_weight, next_weight); |
---|
3745 | #endif |
---|
3746 | |
---|
3747 | //if(test_w_in_ConeCC(G, next_weight) != 1) |
---|
3748 | if(Overflow_Error == TRUE) |
---|
3749 | { |
---|
3750 | newRing = currRing; |
---|
3751 | PrintS("\n// ** The computed vector does NOT stay in Cone!!\n"); |
---|
3752 | |
---|
3753 | if (currRing->parameter != NULL) |
---|
3754 | DefRingPar(target_weight); |
---|
3755 | else |
---|
3756 | VMrDefault(target_weight); |
---|
3757 | |
---|
3758 | F1 = idrMoveR(G, newRing); |
---|
3759 | G = MstdCC(F1); |
---|
3760 | idDelete(&F1); |
---|
3761 | |
---|
3762 | newRing = currRing; |
---|
3763 | break; |
---|
3764 | } |
---|
3765 | |
---|
3766 | if(MivComp(next_weight, ivNull) == 1) |
---|
3767 | { |
---|
3768 | newRing = currRing; |
---|
3769 | delete next_weight; |
---|
3770 | break; |
---|
3771 | } |
---|
3772 | if(MivComp(next_weight, target_weight) == 1) |
---|
3773 | endwalks = 1; |
---|
3774 | |
---|
3775 | for(i=nV-1; i>=0; i--) { |
---|
3776 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
3777 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
3778 | } |
---|
3779 | delete next_weight; |
---|
3780 | } |
---|
3781 | rChangeCurrRing(XXRing); |
---|
3782 | G = idrMoveR(G, newRing); |
---|
3783 | |
---|
3784 | delete tmp_weight; |
---|
3785 | delete ivNull; |
---|
3786 | delete exivlp; |
---|
3787 | |
---|
3788 | #ifdef TIME_TEST |
---|
3789 | TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep); |
---|
3790 | |
---|
3791 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
3792 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
3793 | #endif |
---|
3794 | return(G); |
---|
3795 | } |
---|
3796 | |
---|
3797 | /* 2.12.02*/ |
---|
3798 | ideal Mwalk_tst(ideal Go, intvec* curr_weight, intvec* target_weight) |
---|
3799 | { |
---|
3800 | clock_t tinput=clock(); |
---|
3801 | //idString(Go,"Ginp"); |
---|
3802 | int i, nV = currRing->N; |
---|
3803 | int nwalk=0, endwalks=0; |
---|
3804 | |
---|
3805 | ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G, G1; |
---|
3806 | ring endRing, newRing, oldRing; |
---|
3807 | intvec* ivNull = new intvec(nV); |
---|
3808 | ring XXRing = currRing; |
---|
3809 | |
---|
3810 | intvec* tmp_weight = new intvec(nV); |
---|
3811 | for(i=nV-1; i>=0; i--) |
---|
3812 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
3813 | |
---|
3814 | /* the monomial ordering of this current ring would be "dp" */ |
---|
3815 | G = MstdCC(Go); |
---|
3816 | |
---|
3817 | intvec* hilb_func; |
---|
3818 | |
---|
3819 | /* to avoid (1,0,...,0) as the target vector */ |
---|
3820 | intvec* last_omega = new intvec(nV); |
---|
3821 | for(i=nV-1; i>0; i--) |
---|
3822 | (*last_omega)[i] = 1; |
---|
3823 | (*last_omega)[0] = 10000; |
---|
3824 | |
---|
3825 | while(1) |
---|
3826 | { |
---|
3827 | nwalk ++; |
---|
3828 | //Print("\n// Entering the %d-th step:", nwalk); |
---|
3829 | //Print("\n// ring r[%d] = %s;", nwalk, rString(currRing)); |
---|
3830 | idString(G,"G"); |
---|
3831 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
3832 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
3833 | //ivString(curr_weight, "omega"); |
---|
3834 | idString(Gomega,"Gw"); |
---|
3835 | |
---|
3836 | #ifndef BUCHBERGER_ALG |
---|
3837 | if(isNolVector(curr_weight) == 0) |
---|
3838 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
3839 | else |
---|
3840 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
3841 | #endif // BUCHBERGER_ALG |
---|
3842 | |
---|
3843 | |
---|
3844 | oldRing = currRing; |
---|
3845 | |
---|
3846 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
3847 | VMrDefault(curr_weight); |
---|
3848 | newRing = currRing; |
---|
3849 | |
---|
3850 | Gomega1 = idrMoveR(Gomega, oldRing); |
---|
3851 | |
---|
3852 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
3853 | #ifdef BUCHBERGER_ALG |
---|
3854 | M = MstdhomCC(Gomega1); |
---|
3855 | #else |
---|
3856 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
3857 | delete hilb_func; |
---|
3858 | #endif // BUCHBERGER_ALG |
---|
3859 | |
---|
3860 | idString(M,"M"); |
---|
3861 | |
---|
3862 | /* change the ring to oldRing */ |
---|
3863 | rChangeCurrRing(oldRing); |
---|
3864 | M1 = idrMoveR(M, newRing); |
---|
3865 | Gomega2 = idrMoveR(Gomega1, newRing); |
---|
3866 | |
---|
3867 | /* compute a representation of the generators of submod (M) |
---|
3868 | with respect to those of mod (Gomega). |
---|
3869 | Gomega is a reduced Groebner basis w.r.t. the current ring */ |
---|
3870 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
3871 | idDelete(&M1); |
---|
3872 | idDelete(&Gomega2); |
---|
3873 | idDelete(&G); |
---|
3874 | idString(F,"F"); |
---|
3875 | |
---|
3876 | /* change the ring to newRing */ |
---|
3877 | rChangeCurrRing(newRing); |
---|
3878 | F1 = idrMoveR(F, oldRing); |
---|
3879 | |
---|
3880 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
3881 | G = kInterRedCC(F1, NULL); |
---|
3882 | //idSkipZeroes(G);//done by kInterRed |
---|
3883 | idDelete(&F1); |
---|
3884 | idString(G,"G"); |
---|
3885 | if(endwalks == 1) |
---|
3886 | break; |
---|
3887 | |
---|
3888 | /* compute a next weight vector */ |
---|
3889 | intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
3890 | #ifdef PRINT_VECTORS |
---|
3891 | MivString(curr_weight, target_weight, next_weight); |
---|
3892 | #endif |
---|
3893 | |
---|
3894 | if(MivComp(next_weight, ivNull) == 1) |
---|
3895 | { |
---|
3896 | delete next_weight; |
---|
3897 | break; |
---|
3898 | } |
---|
3899 | if(MivComp(next_weight, target_weight) == 1) |
---|
3900 | endwalks = 1; |
---|
3901 | |
---|
3902 | for(i=nV-1; i>=0; i--) |
---|
3903 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
3904 | |
---|
3905 | /* 06.11.01 to free the memory: NOT Changed!!*/ |
---|
3906 | for(i=nV-1; i>=0; i--) |
---|
3907 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
3908 | delete next_weight; |
---|
3909 | } |
---|
3910 | rChangeCurrRing(XXRing); |
---|
3911 | G = idrMoveR(G, newRing); |
---|
3912 | |
---|
3913 | delete tmp_weight; |
---|
3914 | delete ivNull; |
---|
3915 | PrintLn(); |
---|
3916 | return(G); |
---|
3917 | } |
---|
3918 | |
---|
3919 | |
---|
3920 | |
---|
3921 | /**************************************************************/ |
---|
3922 | /* Implementation of the perturbation walk algorithm */ |
---|
3923 | /**************************************************************/ |
---|
3924 | /* If the perturbed target weight vector or an intermediate weight vector |
---|
3925 | doesn't stay in the correct Groebner cone, we have only |
---|
3926 | a reduced Groebner basis for the given ideal with respect to |
---|
3927 | a monomial order which differs to the given order. |
---|
3928 | Then we have to compute the wanted reduced Groebner basis for it. |
---|
3929 | For this, we can use |
---|
3930 | 1) the improved Buchberger algorithm or |
---|
3931 | 2) the changed perturbation walk algorithm with a decreased degree. |
---|
3932 | */ |
---|
3933 | /* use kStd, if nP = 0, else call LastGB */ |
---|
3934 | ideal Mpwalk(ideal Go, int op_deg, int tp_deg,intvec* curr_weight, |
---|
3935 | intvec* target_weight, int nP) |
---|
3936 | { |
---|
3937 | Set_Error(FALSE ); |
---|
3938 | Overflow_Error = FALSE; |
---|
3939 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
3940 | |
---|
3941 | clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0; |
---|
3942 | xtextra=0; |
---|
3943 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; |
---|
3944 | tinput = clock(); |
---|
3945 | |
---|
3946 | clock_t tim; |
---|
3947 | |
---|
3948 | nstep = 0; |
---|
3949 | int i, ntwC=1, ntestw=1, nV = currRing->N, op_tmp = op_deg; |
---|
3950 | int endwalks=0, nhilb=0, ntestomega=0; |
---|
3951 | |
---|
3952 | ideal Gomega, M, F, G, Gomega1, Gomega2, M1,F1,Eresult,ssG; |
---|
3953 | ring newRing, oldRing, TargetRing; |
---|
3954 | intvec* iv_M_dp; |
---|
3955 | intvec* iv_M_lp; |
---|
3956 | intvec* exivlp = Mivlp(nV); |
---|
3957 | intvec* orig_target = target_weight; |
---|
3958 | intvec* pert_target_vector = target_weight; |
---|
3959 | intvec* ivNull = new intvec(nV); |
---|
3960 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
3961 | intvec* cw_tmp = curr_weight; |
---|
3962 | intvec* hilb_func; |
---|
3963 | intvec* next_weight; |
---|
3964 | intvec* extra_curr_weight = new intvec(nV); |
---|
3965 | |
---|
3966 | /* to avoid (1,0,...,0) as the target vector */ |
---|
3967 | intvec* last_omega = new intvec(nV); |
---|
3968 | for(i=nV-1; i>0; i--) |
---|
3969 | (*last_omega)[i] = 1; |
---|
3970 | (*last_omega)[0] = 10000; |
---|
3971 | |
---|
3972 | ring XXRing = currRing; |
---|
3973 | |
---|
3974 | |
---|
3975 | to = clock(); |
---|
3976 | /* perturbs the original vector */ |
---|
3977 | if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) := "dp" |
---|
3978 | { |
---|
3979 | G = MstdCC(Go); |
---|
3980 | tostd = clock()-to; |
---|
3981 | if(op_deg != 1){ |
---|
3982 | iv_M_dp = MivMatrixOrderdp(nV); |
---|
3983 | //ivString(iv_M_dp, "iv_M_dp"); |
---|
3984 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
3985 | } |
---|
3986 | } |
---|
3987 | else |
---|
3988 | { |
---|
3989 | //ring order := (a(curr_weight),lp); |
---|
3990 | if (currRing->parameter != NULL) |
---|
3991 | DefRingPar(curr_weight); |
---|
3992 | else |
---|
3993 | VMrDefault(curr_weight); |
---|
3994 | |
---|
3995 | G = idrMoveR(Go, XXRing); |
---|
3996 | G = MstdCC(G); |
---|
3997 | tostd = clock()-to; |
---|
3998 | if(op_deg != 1){ |
---|
3999 | iv_M_dp = MivMatrixOrder(curr_weight); |
---|
4000 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
4001 | } |
---|
4002 | } |
---|
4003 | delete iv_dp; |
---|
4004 | if(op_deg != 1) delete iv_M_dp; |
---|
4005 | |
---|
4006 | ring HelpRing = currRing; |
---|
4007 | |
---|
4008 | /* perturbs the target weight vector */ |
---|
4009 | if(tp_deg > 1 && tp_deg <= nV) |
---|
4010 | { |
---|
4011 | if (currRing->parameter != NULL) |
---|
4012 | DefRingPar(target_weight); |
---|
4013 | else |
---|
4014 | VMrDefault(target_weight); |
---|
4015 | |
---|
4016 | TargetRing = currRing; |
---|
4017 | ssG = idrMoveR(G,HelpRing); |
---|
4018 | if(MivSame(target_weight, exivlp) == 1) |
---|
4019 | { |
---|
4020 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
4021 | //ivString(iv_M_lp, "iv_M_lp"); |
---|
4022 | //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg); |
---|
4023 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
4024 | } |
---|
4025 | else |
---|
4026 | { |
---|
4027 | iv_M_lp = MivMatrixOrder(target_weight); |
---|
4028 | //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg); |
---|
4029 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
4030 | } |
---|
4031 | delete iv_M_lp; |
---|
4032 | pert_target_vector = target_weight; //vor 19. mai 2003//test 19 Junu 03 |
---|
4033 | rChangeCurrRing(HelpRing); |
---|
4034 | G = idrMoveR(ssG, TargetRing); |
---|
4035 | } |
---|
4036 | /* |
---|
4037 | Print("\n// Perturbationwalkalg. vom Gradpaar (%d,%d):",op_deg,tp_deg); |
---|
4038 | ivString(curr_weight, "new sigma"); |
---|
4039 | ivString(target_weight, "new tau"); |
---|
4040 | */ |
---|
4041 | while(1) |
---|
4042 | { |
---|
4043 | nstep ++; |
---|
4044 | to = clock(); |
---|
4045 | /* compute an initial form ideal of <G> w.r.t. the weight vector |
---|
4046 | "curr_weight" */ |
---|
4047 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
4048 | |
---|
4049 | |
---|
4050 | #ifdef ENDWALKS |
---|
4051 | if(endwalks == 1){ |
---|
4052 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
4053 | idElements(G, "G"); |
---|
4054 | // idElements(Gomega, "Gw"); |
---|
4055 | headidString(G, "G"); |
---|
4056 | //headidString(Gomega, "Gw"); |
---|
4057 | } |
---|
4058 | #endif |
---|
4059 | |
---|
4060 | tif = tif + clock()-to; |
---|
4061 | |
---|
4062 | #ifndef BUCHBERGER_ALG |
---|
4063 | if(isNolVector(curr_weight) == 0) |
---|
4064 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
4065 | else |
---|
4066 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
4067 | #endif // BUCHBERGER_ALG |
---|
4068 | |
---|
4069 | oldRing = currRing; |
---|
4070 | |
---|
4071 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
4072 | if (currRing->parameter != NULL) |
---|
4073 | DefRingPar(curr_weight); |
---|
4074 | else |
---|
4075 | VMrDefault(curr_weight); |
---|
4076 | |
---|
4077 | newRing = currRing; |
---|
4078 | Gomega1 = idrMoveR(Gomega, oldRing); |
---|
4079 | |
---|
4080 | #ifdef ENDWALKS |
---|
4081 | if(endwalks==1) |
---|
4082 | { |
---|
4083 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
4084 | idElements(Gomega1, "Gw"); |
---|
4085 | headidString(Gomega1, "headGw"); |
---|
4086 | PrintS("\n// compute a rGB of Gw:\n"); |
---|
4087 | |
---|
4088 | #ifndef BUCHBERGER_ALG |
---|
4089 | ivString(hilb_func, "w"); |
---|
4090 | #endif |
---|
4091 | } |
---|
4092 | #endif |
---|
4093 | |
---|
4094 | tim = clock(); |
---|
4095 | to = clock(); |
---|
4096 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
4097 | #ifdef BUCHBERGER_ALG |
---|
4098 | M = MstdhomCC(Gomega1); |
---|
4099 | #else |
---|
4100 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
4101 | delete hilb_func; |
---|
4102 | #endif // BUCHBERGER_ALG |
---|
4103 | |
---|
4104 | if(endwalks == 1){ |
---|
4105 | xtstd = xtstd+clock()-to; |
---|
4106 | #ifdef ENDWALKS |
---|
4107 | Print("\n// time for the last std(Gw) = %.2f sec\n", |
---|
4108 | ((double) clock())/1000000 -((double)tim) /1000000); |
---|
4109 | #endif |
---|
4110 | } |
---|
4111 | else |
---|
4112 | tstd=tstd+clock()-to; |
---|
4113 | |
---|
4114 | /* change the ring to oldRing */ |
---|
4115 | rChangeCurrRing(oldRing); |
---|
4116 | M1 = idrMoveR(M, newRing); |
---|
4117 | Gomega2 = idrMoveR(Gomega1, newRing); |
---|
4118 | |
---|
4119 | //if(endwalks==1) PrintS("\n// Lifting is working:.."); |
---|
4120 | |
---|
4121 | to=clock(); |
---|
4122 | /* compute a representation of the generators of submod (M) |
---|
4123 | with respect to those of mod (Gomega). |
---|
4124 | Gomega is a reduced Groebner basis w.r.t. the current ring */ |
---|
4125 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
4126 | if(endwalks != 1) |
---|
4127 | tlift = tlift+clock()-to; |
---|
4128 | else |
---|
4129 | xtlift=clock()-to; |
---|
4130 | |
---|
4131 | idDelete(&M1); |
---|
4132 | idDelete(&Gomega2); |
---|
4133 | idDelete(&G); |
---|
4134 | |
---|
4135 | /* change the ring to newRing */ |
---|
4136 | rChangeCurrRing(newRing); |
---|
4137 | F1 = idrMoveR(F, oldRing); |
---|
4138 | |
---|
4139 | //if(endwalks==1)PrintS("\n// InterRed is working now:"); |
---|
4140 | |
---|
4141 | to=clock(); |
---|
4142 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
4143 | G = kInterRedCC(F1, NULL); |
---|
4144 | if(endwalks != 1) |
---|
4145 | tred = tred+clock()-to; |
---|
4146 | else |
---|
4147 | xtred=clock()-to; |
---|
4148 | |
---|
4149 | idDelete(&F1); |
---|
4150 | |
---|
4151 | if(endwalks == 1) |
---|
4152 | break; |
---|
4153 | |
---|
4154 | to=clock(); |
---|
4155 | /* compute a next weight vector */ |
---|
4156 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
4157 | tnw=tnw+clock()-to; |
---|
4158 | #ifdef PRINT_VECTORS |
---|
4159 | MivString(curr_weight, target_weight, next_weight); |
---|
4160 | #endif |
---|
4161 | |
---|
4162 | if(Overflow_Error == TRUE) |
---|
4163 | { |
---|
4164 | ntwC = 0; |
---|
4165 | ntestomega = 1; |
---|
4166 | //Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
4167 | //idElements(G, "G"); |
---|
4168 | delete next_weight; |
---|
4169 | goto FINISH_160302; |
---|
4170 | } |
---|
4171 | if(MivComp(next_weight, ivNull) == 1){ |
---|
4172 | newRing = currRing; |
---|
4173 | delete next_weight;//16.03.02 |
---|
4174 | //Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
4175 | break; |
---|
4176 | } |
---|
4177 | if(MivComp(next_weight, target_weight) == 1) |
---|
4178 | endwalks = 1; |
---|
4179 | |
---|
4180 | for(i=nV-1; i>=0; i--) |
---|
4181 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
4182 | |
---|
4183 | delete next_weight; |
---|
4184 | }//while |
---|
4185 | |
---|
4186 | if(tp_deg != 1) |
---|
4187 | { |
---|
4188 | FINISH_160302://16.03.02 |
---|
4189 | if(MivSame(orig_target, exivlp) == 1) |
---|
4190 | if (currRing->parameter != NULL) |
---|
4191 | DefRingParlp(); |
---|
4192 | else |
---|
4193 | VMrDefaultlp(); |
---|
4194 | else |
---|
4195 | if (currRing->parameter != NULL) |
---|
4196 | DefRingPar(orig_target); |
---|
4197 | else |
---|
4198 | VMrDefault(orig_target); |
---|
4199 | |
---|
4200 | TargetRing=currRing; |
---|
4201 | F1 = idrMoveR(G, newRing); |
---|
4202 | #ifdef CHECK_IDEAL |
---|
4203 | headidString(G, "G"); |
---|
4204 | #endif |
---|
4205 | |
---|
4206 | |
---|
4207 | // check whether the pertubed target vector stays in the correct cone |
---|
4208 | if(ntwC != 0){ |
---|
4209 | ntestw = test_w_in_ConeCC(F1, pert_target_vector); |
---|
4210 | } |
---|
4211 | |
---|
4212 | if( ntestw != 1 || ntwC == 0) |
---|
4213 | { |
---|
4214 | /* |
---|
4215 | if(ntestw != 1){ |
---|
4216 | ivString(pert_target_vector, "tau"); |
---|
4217 | PrintS("\n// ** perturbed target vector doesn't stay in cone!!"); |
---|
4218 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
4219 | idElements(F1, "G"); |
---|
4220 | } |
---|
4221 | */ |
---|
4222 | /* LastGB is "better" than the kStd subroutine */ |
---|
4223 | to=clock(); |
---|
4224 | ideal eF1; |
---|
4225 | if(nP == 0 || tp_deg == 1 || MivSame(orig_target, exivlp) != 1){ |
---|
4226 | // PrintS("\n// ** calls \"std\" to compute a GB"); |
---|
4227 | eF1 = MstdCC(F1); |
---|
4228 | idDelete(&F1); |
---|
4229 | } |
---|
4230 | else { |
---|
4231 | // PrintS("\n// ** calls \"LastGB\" to compute a GB"); |
---|
4232 | rChangeCurrRing(newRing); |
---|
4233 | ideal F2 = idrMoveR(F1, TargetRing); |
---|
4234 | eF1 = LastGB(F2, curr_weight, tp_deg-1); |
---|
4235 | F2=NULL; |
---|
4236 | } |
---|
4237 | xtextra=clock()-to; |
---|
4238 | ring exTargetRing = currRing; |
---|
4239 | |
---|
4240 | rChangeCurrRing(XXRing); |
---|
4241 | Eresult = idrMoveR(eF1, exTargetRing); |
---|
4242 | } |
---|
4243 | else{ |
---|
4244 | rChangeCurrRing(XXRing); |
---|
4245 | Eresult = idrMoveR(F1, TargetRing); |
---|
4246 | } |
---|
4247 | } |
---|
4248 | else { |
---|
4249 | rChangeCurrRing(XXRing); |
---|
4250 | Eresult = idrMoveR(G, newRing); |
---|
4251 | } |
---|
4252 | delete ivNull; |
---|
4253 | if(tp_deg != 1) |
---|
4254 | delete target_weight; |
---|
4255 | |
---|
4256 | if(op_deg != 1 ) |
---|
4257 | delete curr_weight; |
---|
4258 | |
---|
4259 | delete exivlp; |
---|
4260 | delete last_omega; |
---|
4261 | |
---|
4262 | #ifdef TIME_TEST |
---|
4263 | TimeStringFractal(tinput, tostd, tif+xtif, tstd+xtstd,0, tlift+xtlift, tred+xtred, |
---|
4264 | tnw+xtnw); |
---|
4265 | |
---|
4266 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
4267 | Print("\n// It took %d steps and Overflow_Error? (%d)\n", nstep, Overflow_Error); |
---|
4268 | #endif |
---|
4269 | return(Eresult); |
---|
4270 | } |
---|
4271 | |
---|
4272 | intvec* XivNull; |
---|
4273 | |
---|
4274 | /* define a matrix (1 ... 1) */ |
---|
4275 | intvec* MMatrixone(int nV) |
---|
4276 | { |
---|
4277 | int i,j; |
---|
4278 | intvec* ivM = new intvec(nV*nV); |
---|
4279 | |
---|
4280 | for(i=0; i<nV; i++) |
---|
4281 | for(j=0; j<nV; j++) |
---|
4282 | (*ivM)[i*nV + j] = 1; |
---|
4283 | |
---|
4284 | return(ivM); |
---|
4285 | } |
---|
4286 | |
---|
4287 | int nnflow; |
---|
4288 | int Xcall; |
---|
4289 | int Xngleich; |
---|
4290 | |
---|
4291 | /* 27.07.03 */ |
---|
4292 | /* Perturb the start weight vector at the top level, i.e. nlev = 1 */ |
---|
4293 | static ideal rec_fractal_call(ideal G, int nlev, intvec* omtmp) |
---|
4294 | { |
---|
4295 | Overflow_Error = FALSE; |
---|
4296 | //Print("\n\n// Entering the %d-th recursion:", nlev); |
---|
4297 | |
---|
4298 | int i, nV = currRing->N; |
---|
4299 | ring new_ring, testring, extoRing; |
---|
4300 | ideal Gomega, Gomega1, Gomega2, F, F1, Gresult, Gresult1, G1, Gt; |
---|
4301 | int nwalks = 0; |
---|
4302 | intvec* Mwlp; |
---|
4303 | intvec* hilb_func; |
---|
4304 | intvec* extXtau; |
---|
4305 | intvec* next_vect; |
---|
4306 | intvec* omega2 = new intvec(nV); |
---|
4307 | intvec* altomega = new intvec(nV); |
---|
4308 | |
---|
4309 | BOOLEAN isnewtarget = FALSE; |
---|
4310 | |
---|
4311 | /* to avoid (1,0,...,0) as the target vector (Hans) */ |
---|
4312 | intvec* last_omega = new intvec(nV); |
---|
4313 | for(i=nV-1; i>0; i--) |
---|
4314 | (*last_omega)[i] = 1; |
---|
4315 | (*last_omega)[0] = 10000; |
---|
4316 | |
---|
4317 | intvec* omega = new intvec(nV); |
---|
4318 | for(i=0; i<nV; i++) { |
---|
4319 | if(Xsigma->length() == nV) |
---|
4320 | (*omega)[i] = (*Xsigma)[i]; |
---|
4321 | else |
---|
4322 | (*omega)[i] = (*Xsigma)[(nV*(nlev-1))+i]; |
---|
4323 | |
---|
4324 | (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i]; |
---|
4325 | } |
---|
4326 | |
---|
4327 | if(nlev == 1) Xcall = 1; |
---|
4328 | else Xcall = 0; |
---|
4329 | |
---|
4330 | ring oRing = currRing; |
---|
4331 | |
---|
4332 | while(1) |
---|
4333 | { |
---|
4334 | #ifdef FIRST_STEP_FRACTAL |
---|
4335 | // perturb the current weight vector only on the top level or |
---|
4336 | // after perturbation of the both vectors, nlev = 2 as the top level |
---|
4337 | if((nlev == 1 && Xcall == 0) || (nlev == 2 && Xngleich == 1)) |
---|
4338 | if(islengthpoly2(G) == 1) |
---|
4339 | { |
---|
4340 | Mwlp = MivWeightOrderlp(omega); |
---|
4341 | Xsigma = Mfpertvector(G, Mwlp); |
---|
4342 | delete Mwlp; |
---|
4343 | Overflow_Error = FALSE; |
---|
4344 | } |
---|
4345 | #endif |
---|
4346 | nwalks ++; |
---|
4347 | NEXT_VECTOR_FRACTAL: |
---|
4348 | to=clock(); |
---|
4349 | /* determine the next border */ |
---|
4350 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
4351 | xtnw=xtnw+clock()-to; |
---|
4352 | #ifdef PRINT_VECTORS |
---|
4353 | MivString(omega, omega2, next_vect); |
---|
4354 | #endif |
---|
4355 | oRing = currRing; |
---|
4356 | |
---|
4357 | /* We only perturb the current target vector at the recursion level 1 */ |
---|
4358 | if(Xngleich == 0 && nlev == 1) //(ngleich == 0) important, e.g. ex2, ex3 |
---|
4359 | if (MivComp(next_vect, omega2) == 1) |
---|
4360 | { |
---|
4361 | /* to dispense with taking initial (and lifting/interreducing |
---|
4362 | after the call of recursion */ |
---|
4363 | //Print("\n\n// ** Perturb the both vectors with degree %d with",nlev); |
---|
4364 | //idElements(G, "G"); |
---|
4365 | |
---|
4366 | Xngleich = 1; |
---|
4367 | nlev +=1; |
---|
4368 | |
---|
4369 | if (currRing->parameter != NULL) |
---|
4370 | DefRingPar(omtmp); |
---|
4371 | else |
---|
4372 | VMrDefault(omtmp); |
---|
4373 | |
---|
4374 | testring = currRing; |
---|
4375 | Gt = idrMoveR(G, oRing); |
---|
4376 | |
---|
4377 | /* perturb the original target vector w.r.t. the current GB */ |
---|
4378 | delete Xtau; |
---|
4379 | Xtau = NewVectorlp(Gt); |
---|
4380 | |
---|
4381 | rChangeCurrRing(oRing); |
---|
4382 | G = idrMoveR(Gt, testring); |
---|
4383 | |
---|
4384 | /* perturb the current vector w.r.t. the current GB */ |
---|
4385 | Mwlp = MivWeightOrderlp(omega); |
---|
4386 | Xsigma = Mfpertvector(G, Mwlp); |
---|
4387 | delete Mwlp; |
---|
4388 | |
---|
4389 | for(i=nV-1; i>=0; i--) { |
---|
4390 | (*omega2)[i] = (*Xtau)[nV+i]; |
---|
4391 | (*omega)[i] = (*Xsigma)[nV+i]; |
---|
4392 | } |
---|
4393 | |
---|
4394 | delete next_vect; |
---|
4395 | to=clock(); |
---|
4396 | |
---|
4397 | /* to avoid the value of Overflow_Error that occur in Mfpertvector*/ |
---|
4398 | Overflow_Error = FALSE; |
---|
4399 | |
---|
4400 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
4401 | xtnw=xtnw+clock()-to; |
---|
4402 | |
---|
4403 | #ifdef PRINT_VECTORS |
---|
4404 | MivString(omega, omega2, next_vect); |
---|
4405 | #endif |
---|
4406 | } |
---|
4407 | |
---|
4408 | |
---|
4409 | /* check whether the the computed vector is in the correct cone */ |
---|
4410 | /* If no, the reduced GB of an omega-homogeneous ideal will be |
---|
4411 | computed by Buchberger algorithm and stop this recursion step*/ |
---|
4412 | //if(test_w_in_ConeCC(G, next_vect) != 1) //e.g. Example s7, cyc6 |
---|
4413 | if(Overflow_Error == TRUE) |
---|
4414 | { |
---|
4415 | delete next_vect; |
---|
4416 | |
---|
4417 | OVERFLOW_IN_NEXT_VECTOR: |
---|
4418 | if (currRing->parameter != NULL) |
---|
4419 | DefRingPar(omtmp); |
---|
4420 | else |
---|
4421 | VMrDefault(omtmp); |
---|
4422 | |
---|
4423 | #ifdef TEST_OVERFLOW |
---|
4424 | Gt = idrMoveR(G, oRing); |
---|
4425 | Gt = NULL; return(Gt); |
---|
4426 | #endif |
---|
4427 | |
---|
4428 | //Print("\n\n// apply BB's alg. in ring r = %s;", rString(currRing)); |
---|
4429 | to=clock(); |
---|
4430 | Gt = idrMoveR(G, oRing); |
---|
4431 | G1 = MstdCC(Gt); |
---|
4432 | xtextra=xtextra+clock()-to; |
---|
4433 | Gt = NULL; |
---|
4434 | |
---|
4435 | delete omega2; |
---|
4436 | delete altomega; |
---|
4437 | |
---|
4438 | //Print("\n// Leaving the %d-th recursion with %d steps", nlev, nwalks); |
---|
4439 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
4440 | nnflow ++; |
---|
4441 | |
---|
4442 | Overflow_Error = FALSE; |
---|
4443 | return (G1); |
---|
4444 | } |
---|
4445 | |
---|
4446 | |
---|
4447 | /* If the perturbed target vector stays in the correct cone, |
---|
4448 | return the current GB, |
---|
4449 | otherwise, return the computed GB by the Buchberger-algorithm. |
---|
4450 | Then we update the perturbed target vectors w.r.t. this GB. */ |
---|
4451 | |
---|
4452 | /* the computed vector is equal to the origin vector, since |
---|
4453 | t is not defined */ |
---|
4454 | if (MivComp(next_vect, XivNull) == 1) |
---|
4455 | { |
---|
4456 | if (currRing->parameter != NULL) |
---|
4457 | DefRingPar(omtmp); |
---|
4458 | else |
---|
4459 | VMrDefault(omtmp); |
---|
4460 | |
---|
4461 | testring = currRing; |
---|
4462 | Gt = idrMoveR(G, oRing); |
---|
4463 | |
---|
4464 | if(test_w_in_ConeCC(Gt, omega2) == 1) { |
---|
4465 | delete omega2; |
---|
4466 | delete next_vect; |
---|
4467 | delete altomega; |
---|
4468 | //Print("\n// Leaving the %d-th recursion with %d steps ",nlev, nwalks); |
---|
4469 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
4470 | |
---|
4471 | return (Gt); |
---|
4472 | } |
---|
4473 | else |
---|
4474 | { |
---|
4475 | //ivString(omega2, "tau'"); |
---|
4476 | //Print("\n// tau' doesn't stay in the correct cone!!"); |
---|
4477 | |
---|
4478 | #ifndef MSTDCC_FRACTAL |
---|
4479 | //07.08.03 |
---|
4480 | //ivString(Xtau, "old Xtau"); |
---|
4481 | intvec* Xtautmp = Mfpertvector(Gt, MivMatrixOrder(omtmp)); |
---|
4482 | #ifdef TEST_OVERFLOW |
---|
4483 | if(Overflow_Error == TRUE) |
---|
4484 | Gt = NULL; return(Gt); |
---|
4485 | #endif |
---|
4486 | |
---|
4487 | if(MivSame(Xtau, Xtautmp) == 1) |
---|
4488 | { |
---|
4489 | //PrintS("\n// Update vectors are equal to the old vectors!!"); |
---|
4490 | delete Xtautmp; |
---|
4491 | goto FRACTAL_MSTDCC; |
---|
4492 | } |
---|
4493 | |
---|
4494 | Xtau = Xtautmp; |
---|
4495 | Xtautmp = NULL; |
---|
4496 | //ivString(Xtau, "new Xtau"); |
---|
4497 | |
---|
4498 | for(i=nV-1; i>=0; i--) |
---|
4499 | (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i]; |
---|
4500 | |
---|
4501 | //Print("\n// ring tau = %s;", rString(currRing)); |
---|
4502 | rChangeCurrRing(oRing); |
---|
4503 | G = idrMoveR(Gt, testring); |
---|
4504 | |
---|
4505 | goto NEXT_VECTOR_FRACTAL; |
---|
4506 | #endif |
---|
4507 | |
---|
4508 | FRACTAL_MSTDCC: |
---|
4509 | //Print("\n// apply BB-Alg in ring = %s;", rString(currRing)); |
---|
4510 | to=clock(); |
---|
4511 | G = MstdCC(Gt); |
---|
4512 | xtextra=xtextra+clock()-to; |
---|
4513 | |
---|
4514 | oRing = currRing; |
---|
4515 | |
---|
4516 | // update the original target vector w.r.t. the current GB |
---|
4517 | if(MivSame(Xivinput, Xivlp) == 1) |
---|
4518 | if (currRing->parameter != NULL) |
---|
4519 | DefRingParlp(); |
---|
4520 | else |
---|
4521 | VMrDefaultlp(); |
---|
4522 | else |
---|
4523 | if (currRing->parameter != NULL) |
---|
4524 | DefRingPar(Xivinput); |
---|
4525 | else |
---|
4526 | VMrDefault(Xivinput); |
---|
4527 | |
---|
4528 | testring = currRing; |
---|
4529 | Gt = idrMoveR(G, oRing); |
---|
4530 | |
---|
4531 | delete Xtau; |
---|
4532 | Xtau = NewVectorlp(Gt); |
---|
4533 | |
---|
4534 | rChangeCurrRing(oRing); |
---|
4535 | G = idrMoveR(Gt, testring); |
---|
4536 | |
---|
4537 | delete omega2; |
---|
4538 | delete next_vect; |
---|
4539 | delete altomega; |
---|
4540 | /* |
---|
4541 | Print("\n// Leaving the %d-th recursion with %d steps,", nlev,nwalks); |
---|
4542 | Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
4543 | */ |
---|
4544 | if(Overflow_Error == TRUE) |
---|
4545 | nnflow ++; |
---|
4546 | |
---|
4547 | Overflow_Error = FALSE; |
---|
4548 | return(G); |
---|
4549 | } |
---|
4550 | } |
---|
4551 | |
---|
4552 | for(i=nV-1; i>=0; i--) { |
---|
4553 | (*altomega)[i] = (*omega)[i]; |
---|
4554 | (*omega)[i] = (*next_vect)[i]; |
---|
4555 | } |
---|
4556 | delete next_vect; |
---|
4557 | |
---|
4558 | to=clock(); |
---|
4559 | /* Take the initial form of <G> w.r.t. omega */ |
---|
4560 | Gomega = MwalkInitialForm(G, omega); |
---|
4561 | xtif=xtif+clock()-to; |
---|
4562 | |
---|
4563 | #ifndef BUCHBERGER_ALG |
---|
4564 | if(isNolVector(omega) == 0) |
---|
4565 | hilb_func = hFirstSeries(Gomega,NULL,NULL,omega,currRing); |
---|
4566 | else |
---|
4567 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
4568 | #endif // BUCHBERGER_ALG |
---|
4569 | |
---|
4570 | if (currRing->parameter != NULL) |
---|
4571 | DefRingPar(omega); |
---|
4572 | else |
---|
4573 | VMrDefault(omega); |
---|
4574 | |
---|
4575 | Gomega1 = idrMoveR(Gomega, oRing); |
---|
4576 | |
---|
4577 | /* Maximal recursion depth, to compute a red. GB */ |
---|
4578 | /* Fractal walk with the alternative recursion */ |
---|
4579 | /* alternative recursion */ |
---|
4580 | // if(nlev == nV || lengthpoly(Gomega1) == 0) |
---|
4581 | if(nlev == Xnlev || lengthpoly(Gomega1) == 0) |
---|
4582 | //if(nlev == nV) // blind recursion |
---|
4583 | { |
---|
4584 | /* |
---|
4585 | if(Xnlev != nV) |
---|
4586 | { |
---|
4587 | Print("\n// ** Xnlev = %d", Xnlev); |
---|
4588 | ivString(Xtau, "Xtau"); |
---|
4589 | } |
---|
4590 | */ |
---|
4591 | to=clock(); |
---|
4592 | #ifdef BUCHBERGER_ALG |
---|
4593 | Gresult = MstdhomCC(Gomega1); |
---|
4594 | #else |
---|
4595 | Gresult =kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,omega); |
---|
4596 | delete hilb_func; |
---|
4597 | #endif // BUCHBERGER_ALG |
---|
4598 | xtstd=xtstd+clock()-to; |
---|
4599 | } |
---|
4600 | else { |
---|
4601 | rChangeCurrRing(oRing); |
---|
4602 | Gomega1 = idrMoveR(Gomega1, oRing); |
---|
4603 | Gresult = rec_fractal_call(idCopy(Gomega1),nlev+1,omega); |
---|
4604 | } |
---|
4605 | |
---|
4606 | //convert a Groebner basis from a ring to another ring, |
---|
4607 | new_ring = currRing; |
---|
4608 | |
---|
4609 | rChangeCurrRing(oRing); |
---|
4610 | Gresult1 = idrMoveR(Gresult, new_ring); |
---|
4611 | Gomega2 = idrMoveR(Gomega1, new_ring); |
---|
4612 | |
---|
4613 | to=clock(); |
---|
4614 | /* Lifting process */ |
---|
4615 | F = MLifttwoIdeal(Gomega2, Gresult1, G); |
---|
4616 | xtlift=xtlift+clock()-to; |
---|
4617 | idDelete(&Gresult1); |
---|
4618 | idDelete(&Gomega2); |
---|
4619 | idDelete(&G); |
---|
4620 | |
---|
4621 | rChangeCurrRing(new_ring); |
---|
4622 | F1 = idrMoveR(F, oRing); |
---|
4623 | |
---|
4624 | to=clock(); |
---|
4625 | /* Interreduce G */ |
---|
4626 | G = kInterRedCC(F1, NULL); |
---|
4627 | xtred=xtred+clock()-to; |
---|
4628 | idDelete(&F1); |
---|
4629 | } |
---|
4630 | } |
---|
4631 | |
---|
4632 | ideal Mfwalk(ideal G, intvec* ivstart, intvec* ivtarget) |
---|
4633 | { |
---|
4634 | Set_Error(FALSE); |
---|
4635 | Overflow_Error = FALSE; |
---|
4636 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
4637 | //Print("\n// ring ro = %s;", rString(currRing)); |
---|
4638 | |
---|
4639 | nnflow = 0; |
---|
4640 | Xngleich = 0; |
---|
4641 | Xcall = 0; |
---|
4642 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
4643 | xftinput = clock(); |
---|
4644 | |
---|
4645 | ring oldRing = currRing; |
---|
4646 | int i, nV = currRing->N; |
---|
4647 | XivNull = new intvec(nV); |
---|
4648 | Xivinput = ivtarget; |
---|
4649 | ngleich = 0; |
---|
4650 | to=clock(); |
---|
4651 | ideal I = MstdCC(G); |
---|
4652 | G = NULL; |
---|
4653 | xftostd=clock()-to; |
---|
4654 | Xsigma = ivstart; |
---|
4655 | |
---|
4656 | Xnlev=nV; |
---|
4657 | |
---|
4658 | #ifdef FIRST_STEP_FRACTAL |
---|
4659 | ideal Gw = MwalkInitialForm(I, ivstart); |
---|
4660 | for(i=IDELEMS(Gw)-1; i>=0; i--) |
---|
4661 | { |
---|
4662 | if((Gw->m[i]!=NULL) /* len >=0 */ |
---|
4663 | && (Gw->m[i]->next!=NULL) /* len >=1 */ |
---|
4664 | && (Gw->m[i]->next->next!=NULL)) /* len >=2 */ |
---|
4665 | { |
---|
4666 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
4667 | intvec* Mdp; |
---|
4668 | |
---|
4669 | if(MivSame(ivstart, iv_dp) != 1) |
---|
4670 | Mdp = MivWeightOrderdp(ivstart); |
---|
4671 | else |
---|
4672 | Mdp = MivMatrixOrderdp(nV); |
---|
4673 | |
---|
4674 | Xsigma = Mfpertvector(I, Mdp); |
---|
4675 | Overflow_Error = FALSE; |
---|
4676 | |
---|
4677 | delete Mdp; |
---|
4678 | delete iv_dp; |
---|
4679 | break; |
---|
4680 | } |
---|
4681 | } |
---|
4682 | idDelete(&Gw); |
---|
4683 | #endif |
---|
4684 | |
---|
4685 | ideal I1; |
---|
4686 | intvec* Mlp; |
---|
4687 | Xivlp = Mivlp(nV); |
---|
4688 | |
---|
4689 | if(MivComp(ivtarget, Xivlp) != 1) |
---|
4690 | { |
---|
4691 | if (currRing->parameter != NULL) |
---|
4692 | DefRingPar(ivtarget); |
---|
4693 | else |
---|
4694 | VMrDefault(ivtarget); |
---|
4695 | |
---|
4696 | I1 = idrMoveR(I, oldRing); |
---|
4697 | Mlp = MivWeightOrderlp(ivtarget); |
---|
4698 | Xtau = Mfpertvector(I1, Mlp); |
---|
4699 | } |
---|
4700 | else |
---|
4701 | { |
---|
4702 | if (currRing->parameter != NULL) |
---|
4703 | DefRingParlp(); |
---|
4704 | else |
---|
4705 | VMrDefaultlp(); |
---|
4706 | |
---|
4707 | I1 = idrMoveR(I, oldRing); |
---|
4708 | Mlp = MivMatrixOrderlp(nV); |
---|
4709 | Xtau = Mfpertvector(I1, Mlp); |
---|
4710 | } |
---|
4711 | delete Mlp; |
---|
4712 | Overflow_Error = FALSE; |
---|
4713 | |
---|
4714 | //ivString(Xsigma, "Xsigma"); |
---|
4715 | //ivString(Xtau, "Xtau"); |
---|
4716 | |
---|
4717 | id_Delete(&I, oldRing); |
---|
4718 | ring tRing = currRing; |
---|
4719 | |
---|
4720 | if (currRing->parameter != NULL) |
---|
4721 | DefRingPar(ivstart); |
---|
4722 | else |
---|
4723 | VMrDefault(ivstart); |
---|
4724 | |
---|
4725 | I = idrMoveR(I1,tRing); |
---|
4726 | to=clock(); |
---|
4727 | ideal J = MstdCC(I); |
---|
4728 | idDelete(&I); |
---|
4729 | xftostd=xftostd+clock()-to; |
---|
4730 | |
---|
4731 | ideal resF; |
---|
4732 | ring helpRing = currRing; |
---|
4733 | |
---|
4734 | J = rec_fractal_call(J, 1, ivtarget); |
---|
4735 | |
---|
4736 | rChangeCurrRing(oldRing); |
---|
4737 | resF = idrMoveR(J, helpRing); |
---|
4738 | idSkipZeroes(resF); |
---|
4739 | |
---|
4740 | delete Xivlp; |
---|
4741 | delete Xsigma; |
---|
4742 | delete Xtau; |
---|
4743 | delete XivNull; |
---|
4744 | |
---|
4745 | #ifdef TIME_TEST |
---|
4746 | TimeStringFractal(xftinput, xftostd, xtif, xtstd, xtextra, |
---|
4747 | xtlift, xtred, xtnw); |
---|
4748 | |
---|
4749 | |
---|
4750 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
4751 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
4752 | Print("\n// the numbers of Overflow_Error (%d)", nnflow); |
---|
4753 | #endif |
---|
4754 | |
---|
4755 | return(resF); |
---|
4756 | } |
---|
4757 | |
---|
4758 | /* Tran algorithm */ |
---|
4759 | /* use kStd, if nP = 0, else call Ab_Rec_Pert (LastGB) */ |
---|
4760 | ideal TranMImprovwalk(ideal G,intvec* curr_weight,intvec* target_tmp, int nP) |
---|
4761 | { |
---|
4762 | clock_t mtim = clock(); |
---|
4763 | Set_Error(FALSE ); |
---|
4764 | Overflow_Error = FALSE; |
---|
4765 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
4766 | //Print("\n// ring ro = %s;", rString(currRing)); |
---|
4767 | |
---|
4768 | clock_t tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0, textra=0; |
---|
4769 | clock_t tinput = clock(); |
---|
4770 | |
---|
4771 | int nsteppert=0, i, nV = currRing->N, nwalk=0, npert_tmp=0; |
---|
4772 | int *npert=(int*)omAlloc(2*nV*sizeof(int)); |
---|
4773 | ideal Gomega, M,F, G1, Gomega1, Gomega2, M1, F1; |
---|
4774 | ring endRing, newRing, oldRing, lpRing; |
---|
4775 | intvec* next_weight; |
---|
4776 | intvec* ivNull = new intvec(nV); //define (0,...,0) |
---|
4777 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
4778 | intvec* iv_lp = Mivlp(nV); //define (1,0,...,0) |
---|
4779 | ideal H0, H1, H2, Glp; |
---|
4780 | int nGB, endwalks = 0, nwalkpert=0, npertstep=0; |
---|
4781 | intvec* Mlp = MivMatrixOrderlp(nV); |
---|
4782 | intvec* vector_tmp = new intvec(nV); |
---|
4783 | intvec* hilb_func; |
---|
4784 | |
---|
4785 | /* to avoid (1,0,...,0) as the target vector */ |
---|
4786 | intvec* last_omega = new intvec(nV); |
---|
4787 | for(i=nV-1; i>0; i--) |
---|
4788 | (*last_omega)[i] = 1; |
---|
4789 | (*last_omega)[0] = 10000; |
---|
4790 | |
---|
4791 | // intvec* extra_curr_weight = new intvec(nV); |
---|
4792 | intvec* target_weight = new intvec(nV); |
---|
4793 | for(i=nV-1; i>=0; i--) |
---|
4794 | (*target_weight)[i] = (*target_tmp)[i]; |
---|
4795 | |
---|
4796 | ring XXRing = currRing; |
---|
4797 | newRing = currRing; |
---|
4798 | |
---|
4799 | to=clock(); |
---|
4800 | /* compute a red. GB w.r.t. the help ring */ |
---|
4801 | if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) = "dp" |
---|
4802 | G = MstdCC(G); |
---|
4803 | else |
---|
4804 | { |
---|
4805 | //rOrdStr(currRing) = (a(.c_w..),lp,C) |
---|
4806 | if (currRing->parameter != NULL) |
---|
4807 | DefRingPar(curr_weight); |
---|
4808 | else |
---|
4809 | VMrDefault(curr_weight); |
---|
4810 | G = idrMoveR(G, XXRing); |
---|
4811 | G = MstdCC(G); |
---|
4812 | } |
---|
4813 | tostd=clock()-to; |
---|
4814 | |
---|
4815 | #ifdef REPRESENTATION_OF_SIGMA |
---|
4816 | ideal Gw = MwalkInitialForm(G, curr_weight); |
---|
4817 | |
---|
4818 | if(islengthpoly2(Gw)==1) |
---|
4819 | { |
---|
4820 | intvec* MDp; |
---|
4821 | if(MivComp(curr_weight, iv_dp) == 1) |
---|
4822 | MDp = MatrixOrderdp(nV); //MivWeightOrderlp(iv_dp); |
---|
4823 | else |
---|
4824 | MDp = MivWeightOrderlp(curr_weight); |
---|
4825 | |
---|
4826 | curr_weight = RepresentationMatrix_Dp(G, MDp); |
---|
4827 | |
---|
4828 | delete MDp; |
---|
4829 | |
---|
4830 | ring exring = currRing; |
---|
4831 | |
---|
4832 | if (currRing->parameter != NULL) |
---|
4833 | DefRingPar(curr_weight); |
---|
4834 | else |
---|
4835 | VMrDefault(curr_weight); |
---|
4836 | to=clock(); |
---|
4837 | Gw = idrMoveR(G, exring); |
---|
4838 | G = MstdCC(Gw); |
---|
4839 | Gw = NULL; |
---|
4840 | tostd=tostd+clock()-to; |
---|
4841 | //ivString(curr_weight,"rep. sigma"); |
---|
4842 | goto COMPUTE_NEW_VECTOR; |
---|
4843 | } |
---|
4844 | |
---|
4845 | idDelete(&Gw); |
---|
4846 | delete iv_dp; |
---|
4847 | #endif |
---|
4848 | |
---|
4849 | |
---|
4850 | while(1) |
---|
4851 | { |
---|
4852 | to=clock(); |
---|
4853 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
4854 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
4855 | tif=tif+clock()-to; |
---|
4856 | |
---|
4857 | #ifndef BUCHBERGER_ALG |
---|
4858 | if(isNolVector(curr_weight) == 0) |
---|
4859 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
4860 | else |
---|
4861 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
4862 | #endif // BUCHBERGER_ALG |
---|
4863 | |
---|
4864 | oldRing = currRing; |
---|
4865 | |
---|
4866 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
4867 | if (currRing->parameter != NULL) |
---|
4868 | DefRingPar(curr_weight); |
---|
4869 | else |
---|
4870 | VMrDefault(curr_weight); |
---|
4871 | |
---|
4872 | newRing = currRing; |
---|
4873 | Gomega1 = idrMoveR(Gomega, oldRing); |
---|
4874 | |
---|
4875 | to=clock(); |
---|
4876 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
4877 | #ifdef BUCHBERGER_ALG |
---|
4878 | M = MstdhomCC(Gomega1); |
---|
4879 | #else |
---|
4880 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
4881 | delete hilb_func; |
---|
4882 | #endif // BUCHBERGER_ALG |
---|
4883 | tstd=tstd+clock()-to; |
---|
4884 | |
---|
4885 | /* change the ring to oldRing */ |
---|
4886 | rChangeCurrRing(oldRing); |
---|
4887 | M1 = idrMoveR(M, newRing); |
---|
4888 | Gomega2 = idrMoveR(Gomega1, newRing); |
---|
4889 | |
---|
4890 | to=clock(); |
---|
4891 | /* compute a representation of the generators of submod (M) |
---|
4892 | with respect to those of mod (Gomega). |
---|
4893 | Gomega is a reduced Groebner basis w.r.t. the current ring */ |
---|
4894 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
4895 | tlift=tlift+clock()-to; |
---|
4896 | |
---|
4897 | idDelete(&M1); |
---|
4898 | idDelete(&Gomega2); |
---|
4899 | idDelete(&G); |
---|
4900 | |
---|
4901 | /* change the ring to newRing */ |
---|
4902 | rChangeCurrRing(newRing); |
---|
4903 | F1 = idrMoveR(F, oldRing); |
---|
4904 | |
---|
4905 | to=clock(); |
---|
4906 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
4907 | G = kInterRedCC(F1, NULL); |
---|
4908 | tred=tred+clock()-to; |
---|
4909 | idDelete(&F1); |
---|
4910 | |
---|
4911 | |
---|
4912 | COMPUTE_NEW_VECTOR: |
---|
4913 | newRing = currRing; |
---|
4914 | nwalk++; |
---|
4915 | nwalkpert++; |
---|
4916 | to=clock(); |
---|
4917 | /* compute a next weight vector */ |
---|
4918 | next_weight = MwalkNextWeightCC(curr_weight,target_weight, G); |
---|
4919 | tnw=tnw+clock()-to; |
---|
4920 | #ifdef PRINT_VECTORS |
---|
4921 | MivString(curr_weight, target_weight, next_weight); |
---|
4922 | #endif |
---|
4923 | |
---|
4924 | |
---|
4925 | /* check whether the computed intermediate weight vector in |
---|
4926 | the correct cone is, since sometimes it is very big e.g. s7, cyc7. |
---|
4927 | If it is NOT in the cone, then one has directly to compute |
---|
4928 | a reduced Groebner basis with respect to the lexicographic ordering |
---|
4929 | for the known Groebner basis that it is computed in the last step. |
---|
4930 | */ |
---|
4931 | //if(test_w_in_ConeCC(G, next_weight) != 1) |
---|
4932 | if(Overflow_Error == TRUE) |
---|
4933 | { |
---|
4934 | OMEGA_OVERFLOW_TRAN_NEW: |
---|
4935 | //Print("\n// takes %d steps!", nwalk-1); |
---|
4936 | //Print("\n//ring lastRing = %s;", rString(currRing)); |
---|
4937 | #ifdef TEST_OVERFLOW |
---|
4938 | goto BE_FINISH; |
---|
4939 | #endif |
---|
4940 | |
---|
4941 | #ifdef CHECK_IDEAL_MWALK |
---|
4942 | idElements(G, "G"); |
---|
4943 | //headidString(G, "G"); |
---|
4944 | #endif |
---|
4945 | |
---|
4946 | if(MivSame(target_tmp, iv_lp) == 1) |
---|
4947 | if (currRing->parameter != NULL) |
---|
4948 | DefRingParlp(); |
---|
4949 | else |
---|
4950 | VMrDefaultlp(); |
---|
4951 | else |
---|
4952 | if (currRing->parameter != NULL) |
---|
4953 | DefRingPar(target_tmp); |
---|
4954 | else |
---|
4955 | VMrDefault(target_tmp); |
---|
4956 | |
---|
4957 | lpRing = currRing; |
---|
4958 | G1 = idrMoveR(G, newRing); |
---|
4959 | |
---|
4960 | to=clock(); |
---|
4961 | /*apply kStd or LastGB to compute a lex. red. Groebner basis of <G>*/ |
---|
4962 | if(nP == 0 || MivSame(target_tmp, iv_lp) == 0){ |
---|
4963 | //Print("\n\n// calls \"std in ring r_%d = %s;", nwalk, rString(currRing)); |
---|
4964 | G = MstdCC(G1);//no result for qnt1 |
---|
4965 | } |
---|
4966 | else { |
---|
4967 | rChangeCurrRing(newRing); |
---|
4968 | G1 = idrMoveR(G1, lpRing); |
---|
4969 | |
---|
4970 | //Print("\n\n// calls \"LastGB\" (%d) to compute a GB", nV-1); |
---|
4971 | G = LastGB(G1, curr_weight, nV-1); //no result for kats7 |
---|
4972 | |
---|
4973 | rChangeCurrRing(lpRing); |
---|
4974 | G = idrMoveR(G, newRing); |
---|
4975 | } |
---|
4976 | textra=clock()-to; |
---|
4977 | npert[endwalks]=nwalk-npert_tmp; |
---|
4978 | npert_tmp = nwalk; |
---|
4979 | endwalks ++; |
---|
4980 | break; |
---|
4981 | } |
---|
4982 | |
---|
4983 | /* check whether the computed Groebner basis a really Groebner basis is. |
---|
4984 | if no, we perturb the target vector with the maximal "perturbation" |
---|
4985 | degree.*/ |
---|
4986 | if(MivComp(next_weight, target_weight) == 1 || |
---|
4987 | MivComp(next_weight, curr_weight) == 1 ) |
---|
4988 | { |
---|
4989 | //Print("\n//ring r_%d = %s;", nwalk, rString(currRing)); |
---|
4990 | |
---|
4991 | |
---|
4992 | //compute the number of perturbations and its step |
---|
4993 | npert[endwalks]=nwalk-npert_tmp; |
---|
4994 | npert_tmp = nwalk; |
---|
4995 | |
---|
4996 | endwalks ++; |
---|
4997 | |
---|
4998 | /*it is very important if the walk only uses one step, e.g. Fate, liu*/ |
---|
4999 | if(endwalks == 1 && MivComp(next_weight, curr_weight) == 1){ |
---|
5000 | rChangeCurrRing(XXRing); |
---|
5001 | G = idrMoveR(G, newRing); |
---|
5002 | goto FINISH; |
---|
5003 | } |
---|
5004 | H0 = idHead(G); |
---|
5005 | |
---|
5006 | if(MivSame(target_tmp, iv_lp) == 1) |
---|
5007 | if (currRing->parameter != NULL) |
---|
5008 | DefRingParlp(); |
---|
5009 | else |
---|
5010 | VMrDefaultlp(); |
---|
5011 | else |
---|
5012 | if (currRing->parameter != NULL) |
---|
5013 | DefRingPar(target_tmp); |
---|
5014 | else |
---|
5015 | VMrDefault(target_tmp); |
---|
5016 | |
---|
5017 | lpRing = currRing; |
---|
5018 | Glp = idrMoveR(G, newRing); |
---|
5019 | H2 = idrMoveR(H0, newRing); |
---|
5020 | |
---|
5021 | /* Apply Lemma 2.2 in Collart et. al (1997) to check whether |
---|
5022 | cone(k-1) is equal to cone(k) */ |
---|
5023 | nGB = 1; |
---|
5024 | for(i=IDELEMS(Glp)-1; i>=0; i--) |
---|
5025 | { |
---|
5026 | poly t; |
---|
5027 | if((t=pSub(pHead(Glp->m[i]), pCopy(H2->m[i]))) != NULL) |
---|
5028 | { |
---|
5029 | pDelete(&t); |
---|
5030 | idDelete(&H2);//5.5.02 |
---|
5031 | nGB = 0; //i.e. Glp is no reduced Groebner basis |
---|
5032 | break; |
---|
5033 | } |
---|
5034 | pDelete(&t); |
---|
5035 | } |
---|
5036 | |
---|
5037 | idDelete(&H2);//5.5.02 |
---|
5038 | |
---|
5039 | if(nGB == 1) |
---|
5040 | { |
---|
5041 | G = Glp; |
---|
5042 | Glp = NULL; |
---|
5043 | break; |
---|
5044 | } |
---|
5045 | |
---|
5046 | /* perturb the target weight vector, if the vector target_tmp |
---|
5047 | stays in many cones */ |
---|
5048 | poly p; |
---|
5049 | BOOLEAN plength3 = FALSE; |
---|
5050 | for(i=IDELEMS(Glp)-1; i>=0; i--) |
---|
5051 | { |
---|
5052 | p = MpolyInitialForm(Glp->m[i], target_tmp); |
---|
5053 | if(p->next != NULL && |
---|
5054 | p->next->next != NULL && |
---|
5055 | p->next->next->next != NULL) |
---|
5056 | { |
---|
5057 | Overflow_Error = FALSE; |
---|
5058 | |
---|
5059 | for(i=0; i<nV; i++) |
---|
5060 | (*vector_tmp)[i] = (*target_weight)[i]; |
---|
5061 | |
---|
5062 | delete target_weight; |
---|
5063 | target_weight = MPertVectors(Glp, Mlp, nV); |
---|
5064 | |
---|
5065 | if(MivComp(vector_tmp, target_weight)==1) |
---|
5066 | { |
---|
5067 | //PrintS("\n// The old and new representaion vector are the same!!"); |
---|
5068 | G = Glp; |
---|
5069 | newRing = currRing; |
---|
5070 | goto OMEGA_OVERFLOW_TRAN_NEW; |
---|
5071 | } |
---|
5072 | |
---|
5073 | if(Overflow_Error == TRUE) |
---|
5074 | { |
---|
5075 | rChangeCurrRing(newRing); |
---|
5076 | G = idrMoveR(Glp, lpRing); |
---|
5077 | goto OMEGA_OVERFLOW_TRAN_NEW; |
---|
5078 | } |
---|
5079 | |
---|
5080 | plength3 = TRUE; |
---|
5081 | pDelete(&p); |
---|
5082 | break; |
---|
5083 | } |
---|
5084 | pDelete(&p); |
---|
5085 | } |
---|
5086 | |
---|
5087 | if(plength3 == FALSE) |
---|
5088 | { |
---|
5089 | rChangeCurrRing(newRing); |
---|
5090 | G = idrMoveR(Glp, lpRing); |
---|
5091 | goto TRAN_LIFTING; |
---|
5092 | } |
---|
5093 | |
---|
5094 | |
---|
5095 | npertstep = nwalk; |
---|
5096 | nwalkpert = 1; |
---|
5097 | nsteppert ++; |
---|
5098 | |
---|
5099 | /* |
---|
5100 | Print("\n// Subroutine needs (%d) steps.", nwalk); |
---|
5101 | idElements(Glp, "last G in walk:"); |
---|
5102 | PrintS("\n//****************************************"); |
---|
5103 | Print("\n// Perturb the original target vector (%d): ", nsteppert); |
---|
5104 | ivString(target_weight, "new target"); |
---|
5105 | PrintS("\n//****************************************\n"); |
---|
5106 | */ |
---|
5107 | rChangeCurrRing(newRing); |
---|
5108 | G = idrMoveR(Glp, lpRing); |
---|
5109 | |
---|
5110 | delete next_weight; |
---|
5111 | |
---|
5112 | //Print("\n// ring rNEW = %s;", rString(currRing)); |
---|
5113 | goto COMPUTE_NEW_VECTOR; |
---|
5114 | } |
---|
5115 | |
---|
5116 | TRAN_LIFTING: |
---|
5117 | for(i=nV-1; i>=0; i--) |
---|
5118 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
5119 | |
---|
5120 | delete next_weight; |
---|
5121 | }//while |
---|
5122 | |
---|
5123 | BE_FINISH: |
---|
5124 | rChangeCurrRing(XXRing); |
---|
5125 | G = idrMoveR(G, lpRing); |
---|
5126 | |
---|
5127 | FINISH: |
---|
5128 | delete ivNull; |
---|
5129 | delete next_weight; |
---|
5130 | delete iv_lp; |
---|
5131 | omFree(npert); |
---|
5132 | |
---|
5133 | #ifdef TIME_TEST |
---|
5134 | Print("\n// Computation took %d steps and %.2f sec", |
---|
5135 | nwalk, ((double) (clock()-mtim)/1000000)); |
---|
5136 | |
---|
5137 | TimeStringFractal(tinput, tostd, tif, tstd, textra, tlift, tred, tnw); |
---|
5138 | |
---|
5139 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
5140 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
5141 | #endif |
---|
5142 | |
---|
5143 | return(G); |
---|
5144 | } |
---|
5145 | |
---|
5146 | |
---|
5147 | /* compute the reduced Gröbner basis of an ideal <Go> w.r.t. lp */ |
---|
5148 | static ideal Mpwalk_MAltwalk1(ideal Go, intvec* curr_weight, int tp_deg) |
---|
5149 | { |
---|
5150 | Overflow_Error = FALSE; |
---|
5151 | BOOLEAN nOverflow_Error = FALSE; |
---|
5152 | clock_t tproc=0; |
---|
5153 | clock_t tinput=clock(); |
---|
5154 | int i, nV = currRing->N; |
---|
5155 | int nwalk=0, endwalks=0, ntestwinC=1; |
---|
5156 | int tp_deg_tmp = tp_deg; |
---|
5157 | ideal Gomega, M, F, G, M1, F1, Gomega1, Gomega2, G1; |
---|
5158 | ring endRing, newRing, oldRing, TargetRing; |
---|
5159 | intvec* next_weight; |
---|
5160 | intvec* ivNull = new intvec(nV); |
---|
5161 | intvec* extra_curr_weight = new intvec(nV); |
---|
5162 | |
---|
5163 | ring YXXRing = currRing; |
---|
5164 | |
---|
5165 | intvec* iv_M_dpp = MivMatrixOrderlp(nV); |
---|
5166 | intvec* target_weight;// = Mivlp(nV); |
---|
5167 | ideal ssG; |
---|
5168 | |
---|
5169 | /* perturb the target vector */ |
---|
5170 | while(1) |
---|
5171 | { |
---|
5172 | if(Overflow_Error == FALSE) |
---|
5173 | { |
---|
5174 | if (currRing->parameter != NULL) |
---|
5175 | DefRingParlp(); |
---|
5176 | else |
---|
5177 | VMrDefaultlp(); |
---|
5178 | |
---|
5179 | TargetRing = currRing; |
---|
5180 | ssG = idrMoveR(Go,YXXRing); |
---|
5181 | } |
---|
5182 | Overflow_Error = FALSE; |
---|
5183 | if(tp_deg != 1) |
---|
5184 | target_weight = MPertVectors(ssG, iv_M_dpp, tp_deg); |
---|
5185 | else |
---|
5186 | { |
---|
5187 | target_weight = Mivlp(nV); |
---|
5188 | break; |
---|
5189 | } |
---|
5190 | if(Overflow_Error == FALSE) |
---|
5191 | break; |
---|
5192 | |
---|
5193 | Overflow_Error = TRUE; |
---|
5194 | tp_deg --; |
---|
5195 | } |
---|
5196 | if(tp_deg != tp_deg_tmp) |
---|
5197 | { |
---|
5198 | Overflow_Error = TRUE; |
---|
5199 | nOverflow_Error = TRUE; |
---|
5200 | } |
---|
5201 | |
---|
5202 | // Print("\n// tp_deg = %d", tp_deg); |
---|
5203 | // ivString(target_weight, "pert target"); |
---|
5204 | |
---|
5205 | delete iv_M_dpp; |
---|
5206 | intvec* hilb_func; |
---|
5207 | |
---|
5208 | /* to avoid (1,0,...,0) as the target vector */ |
---|
5209 | intvec* last_omega = new intvec(nV); |
---|
5210 | for(i=nV-1; i>0; i--) |
---|
5211 | (*last_omega)[i] = 1; |
---|
5212 | (*last_omega)[0] = 10000; |
---|
5213 | |
---|
5214 | rChangeCurrRing(YXXRing); |
---|
5215 | G = idrMoveR(ssG, TargetRing); |
---|
5216 | |
---|
5217 | while(1) |
---|
5218 | { |
---|
5219 | nwalk ++; |
---|
5220 | nstep ++; |
---|
5221 | |
---|
5222 | if(nwalk==1) |
---|
5223 | goto FIRST_STEP; |
---|
5224 | |
---|
5225 | to=clock(); |
---|
5226 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
5227 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
5228 | xtif=xtif+clock()-to; |
---|
5229 | #if 0 |
---|
5230 | if(Overflow_Error == TRUE) |
---|
5231 | { |
---|
5232 | for(i=nV-1; i>=0; i--) |
---|
5233 | (*curr_weight)[i] = (*extra_curr_weight)[i]; |
---|
5234 | delete extra_curr_weight; |
---|
5235 | goto LASTGB_ALT1; |
---|
5236 | } |
---|
5237 | #endif |
---|
5238 | #ifndef BUCHBERGER_ALG |
---|
5239 | if(isNolVector(curr_weight) == 0) |
---|
5240 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
5241 | else |
---|
5242 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
5243 | #endif // BUCHBERGER_ALG |
---|
5244 | |
---|
5245 | oldRing = currRing; |
---|
5246 | |
---|
5247 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
5248 | if (currRing->parameter != NULL) |
---|
5249 | DefRingPar(curr_weight); |
---|
5250 | else |
---|
5251 | VMrDefault(curr_weight); |
---|
5252 | |
---|
5253 | newRing = currRing; |
---|
5254 | Gomega1 = idrMoveR(Gomega, oldRing); |
---|
5255 | |
---|
5256 | #ifdef ENDWALKS |
---|
5257 | if(endwalks == 1) |
---|
5258 | { |
---|
5259 | Print("\n// it is %d-th step!!", nwalk); |
---|
5260 | idElements(Gomega1, "Gw"); |
---|
5261 | PrintS("\n// compute a rGB of Gw:"); |
---|
5262 | } |
---|
5263 | #endif |
---|
5264 | |
---|
5265 | to=clock(); |
---|
5266 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
5267 | #ifdef BUCHBERGER_ALG |
---|
5268 | M = MstdhomCC(Gomega1); |
---|
5269 | #else |
---|
5270 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
5271 | delete hilb_func; |
---|
5272 | #endif // BUCHBERGER_ALG |
---|
5273 | xtstd=xtstd+clock()-to; |
---|
5274 | |
---|
5275 | /* change the ring to oldRing */ |
---|
5276 | rChangeCurrRing(oldRing); |
---|
5277 | M1 = idrMoveR(M, newRing); |
---|
5278 | Gomega2 = idrMoveR(Gomega1, newRing); |
---|
5279 | to=clock(); |
---|
5280 | |
---|
5281 | // if(endwalks == 1) PrintS("\n// Lifting is still working:"); |
---|
5282 | |
---|
5283 | /* compute a reduced Groebner basis of <G> w.r.t. "newRing" by the |
---|
5284 | lifting process */ |
---|
5285 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
5286 | xtlift=xtlift+clock()-to; |
---|
5287 | |
---|
5288 | idDelete(&M1); |
---|
5289 | idDelete(&Gomega2); |
---|
5290 | idDelete(&G); |
---|
5291 | |
---|
5292 | /* change the ring to newRing */ |
---|
5293 | rChangeCurrRing(newRing); |
---|
5294 | F1 = idrMoveR(F, oldRing); |
---|
5295 | to=clock(); |
---|
5296 | //if(endwalks == 1) PrintS("\n// InterRed is still working:"); |
---|
5297 | /* reduce the Groebner basis <G> w.r.t. the new ring */ |
---|
5298 | G = kInterRedCC(F1, NULL); |
---|
5299 | xtred=xtred+clock()-to; |
---|
5300 | idDelete(&F1); |
---|
5301 | |
---|
5302 | if(endwalks == 1) |
---|
5303 | break; |
---|
5304 | |
---|
5305 | FIRST_STEP: |
---|
5306 | Overflow_Error=FALSE; |
---|
5307 | to=clock(); |
---|
5308 | /* compute a next weight vector */ |
---|
5309 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
5310 | xtnw=xtnw+clock()-to; |
---|
5311 | #ifdef PRINT_VECTORS |
---|
5312 | MivString(curr_weight, target_weight, next_weight); |
---|
5313 | #endif |
---|
5314 | |
---|
5315 | if(Overflow_Error == TRUE) |
---|
5316 | { |
---|
5317 | delete next_weight; |
---|
5318 | |
---|
5319 | LASTGB_ALT1: |
---|
5320 | if(tp_deg > 1){ |
---|
5321 | nOverflow_Error = Overflow_Error; |
---|
5322 | tproc = tproc+clock()-tinput; |
---|
5323 | /* |
---|
5324 | Print("\n// A subroutine takes %d steps and calls \"Mpwalk\" (1,%d):", |
---|
5325 | nwalk, tp_deg-1); |
---|
5326 | */ |
---|
5327 | G1 = Mpwalk_MAltwalk1(G, curr_weight, tp_deg-1); |
---|
5328 | goto MPW_Finish; |
---|
5329 | } |
---|
5330 | else { |
---|
5331 | newRing = currRing; |
---|
5332 | ntestwinC = 0; |
---|
5333 | break; |
---|
5334 | } |
---|
5335 | } |
---|
5336 | |
---|
5337 | if(MivComp(next_weight, ivNull) == 1) |
---|
5338 | { |
---|
5339 | newRing = currRing; |
---|
5340 | delete next_weight; |
---|
5341 | break; |
---|
5342 | } |
---|
5343 | if(MivComp(next_weight, target_weight) == 1) |
---|
5344 | endwalks = 1; |
---|
5345 | |
---|
5346 | for(i=nV-1; i>=0; i--) |
---|
5347 | { |
---|
5348 | //(*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
5349 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
5350 | } |
---|
5351 | delete next_weight; |
---|
5352 | }//while |
---|
5353 | |
---|
5354 | /* check wheather the pertubed target vector is correct */ |
---|
5355 | |
---|
5356 | //define and execute ring with lex. order |
---|
5357 | if (currRing->parameter != NULL) |
---|
5358 | DefRingParlp(); |
---|
5359 | else |
---|
5360 | VMrDefaultlp(); |
---|
5361 | |
---|
5362 | G1 = idrMoveR(G, newRing); |
---|
5363 | |
---|
5364 | if( test_w_in_ConeCC(G1, target_weight) != 1 || ntestwinC == 0) |
---|
5365 | { |
---|
5366 | PrintS("\n// The perturbed target vector doesn't STAY in the correct cone!!"); |
---|
5367 | if(tp_deg == 1){ |
---|
5368 | //Print("\n// subroutine takes %d steps and applys \"std\"", nwalk); |
---|
5369 | to=clock(); |
---|
5370 | ideal G2 = MstdCC(G1); |
---|
5371 | xtextra=xtextra+clock()-to; |
---|
5372 | idDelete(&G1); |
---|
5373 | G1 = G2; |
---|
5374 | G2 = NULL; |
---|
5375 | } |
---|
5376 | else { |
---|
5377 | nOverflow_Error = Overflow_Error; |
---|
5378 | tproc = tproc+clock()-tinput; |
---|
5379 | /* |
---|
5380 | Print("\n// B subroutine takes %d steps and calls \"Mpwalk\" (1,%d) :", |
---|
5381 | nwalk, tp_deg-1); |
---|
5382 | */ |
---|
5383 | G1 = Mpwalk_MAltwalk1(G1, curr_weight, tp_deg-1); |
---|
5384 | } |
---|
5385 | } |
---|
5386 | |
---|
5387 | MPW_Finish: |
---|
5388 | newRing = currRing; |
---|
5389 | rChangeCurrRing(YXXRing); |
---|
5390 | ideal result = idrMoveR(G1, newRing); |
---|
5391 | |
---|
5392 | delete ivNull; |
---|
5393 | delete target_weight; |
---|
5394 | |
---|
5395 | /* |
---|
5396 | Print("\n// \"Mpwalk\" (1,%d) took %d steps and %.2f sec. Overflow_Error (%d)", tp_deg, |
---|
5397 | nwalk, ((double) clock()-tinput)/1000000, nOverflow_Error); |
---|
5398 | */ |
---|
5399 | |
---|
5400 | return(result); |
---|
5401 | } |
---|
5402 | |
---|
5403 | /* August 2003 */ |
---|
5404 | ideal MAltwalk1(ideal Go, int op_deg, int tp_deg, intvec* curr_weight, |
---|
5405 | intvec* target_weight) |
---|
5406 | { |
---|
5407 | Set_Error(FALSE ); |
---|
5408 | Overflow_Error = FALSE; |
---|
5409 | BOOLEAN nOverflow_Error = FALSE; |
---|
5410 | // Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
5411 | |
---|
5412 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
5413 | xftinput = clock(); |
---|
5414 | clock_t tostd, tproc; |
---|
5415 | |
---|
5416 | nstep = 0; |
---|
5417 | int i, nV = currRing->N; |
---|
5418 | int nwalk=0, endwalks=0; |
---|
5419 | int op_tmp = op_deg; |
---|
5420 | ideal Gomega, M, F, G, G1, Gomega1, Gomega2, M1, F1; |
---|
5421 | ring endRing, newRing, oldRing, TargetRing; |
---|
5422 | intvec* next_weight; |
---|
5423 | intvec* iv_M_dp; |
---|
5424 | intvec* ivNull = new intvec(nV); |
---|
5425 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
5426 | intvec* exivlp = Mivlp(nV); |
---|
5427 | intvec* extra_curr_weight = new intvec(nV); |
---|
5428 | intvec* hilb_func; |
---|
5429 | |
---|
5430 | intvec* cw_tmp = curr_weight; |
---|
5431 | |
---|
5432 | /* to avoid (1,0,...,0) as the target vector */ |
---|
5433 | intvec* last_omega = new intvec(nV); |
---|
5434 | for(i=nV-1; i>0; i--) |
---|
5435 | (*last_omega)[i] = 1; |
---|
5436 | (*last_omega)[0] = 10000; |
---|
5437 | |
---|
5438 | ring XXRing = currRing; |
---|
5439 | |
---|
5440 | to=clock(); |
---|
5441 | /* compute a pertubed weight vector of the original weight vector. |
---|
5442 | The perturbation degree is recursive decrease until that vector |
---|
5443 | stays inn the correct cone. */ |
---|
5444 | while(1) |
---|
5445 | { |
---|
5446 | if(Overflow_Error == FALSE) |
---|
5447 | { |
---|
5448 | if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) = "dp" |
---|
5449 | if(op_tmp == op_deg) { |
---|
5450 | G = MstdCC(Go); |
---|
5451 | if(op_deg != 1) |
---|
5452 | iv_M_dp = MivMatrixOrderdp(nV); |
---|
5453 | } |
---|
5454 | } |
---|
5455 | else |
---|
5456 | { |
---|
5457 | if(op_tmp == op_deg) { |
---|
5458 | //rOrdStr(currRing) = (a(...),lp,C) |
---|
5459 | if (currRing->parameter != NULL) |
---|
5460 | DefRingPar(cw_tmp); |
---|
5461 | else |
---|
5462 | VMrDefault(cw_tmp); |
---|
5463 | |
---|
5464 | G = idrMoveR(Go, XXRing); |
---|
5465 | G = MstdCC(G); |
---|
5466 | if(op_deg != 1) |
---|
5467 | iv_M_dp = MivMatrixOrder(cw_tmp); |
---|
5468 | } |
---|
5469 | } |
---|
5470 | Overflow_Error = FALSE; |
---|
5471 | if(op_deg != 1) |
---|
5472 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
5473 | else { |
---|
5474 | curr_weight = cw_tmp; |
---|
5475 | break; |
---|
5476 | } |
---|
5477 | if(Overflow_Error == FALSE) |
---|
5478 | break; |
---|
5479 | |
---|
5480 | Overflow_Error = TRUE; |
---|
5481 | op_deg --; |
---|
5482 | } |
---|
5483 | tostd=clock()-to; |
---|
5484 | |
---|
5485 | if(op_tmp != 1 ) |
---|
5486 | delete iv_M_dp; |
---|
5487 | delete iv_dp; |
---|
5488 | |
---|
5489 | if(currRing->order[0] == ringorder_a) |
---|
5490 | goto NEXT_VECTOR; |
---|
5491 | |
---|
5492 | while(1) |
---|
5493 | { |
---|
5494 | nwalk ++; |
---|
5495 | nstep ++; |
---|
5496 | |
---|
5497 | to = clock(); |
---|
5498 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
5499 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
5500 | xtif=xtif+clock()-to; |
---|
5501 | #if 0 |
---|
5502 | if(Overflow_Error == TRUE) |
---|
5503 | { |
---|
5504 | for(i=nV-1; i>=0; i--) |
---|
5505 | (*curr_weight)[i] = (*extra_curr_weight)[i]; |
---|
5506 | delete extra_curr_weight; |
---|
5507 | |
---|
5508 | newRing = currRing; |
---|
5509 | goto MSTD_ALT1; |
---|
5510 | } |
---|
5511 | #endif |
---|
5512 | #ifndef BUCHBERGER_ALG |
---|
5513 | if(isNolVector(curr_weight) == 0) |
---|
5514 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
5515 | else |
---|
5516 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
5517 | #endif // BUCHBERGER_ALG |
---|
5518 | |
---|
5519 | oldRing = currRing; |
---|
5520 | |
---|
5521 | /* define a new ring which ordering is "(a(curr_weight),lp) */ |
---|
5522 | if (currRing->parameter != NULL) |
---|
5523 | DefRingPar(curr_weight); |
---|
5524 | else |
---|
5525 | VMrDefault(curr_weight); |
---|
5526 | |
---|
5527 | newRing = currRing; |
---|
5528 | Gomega1 = idrMoveR(Gomega, oldRing); |
---|
5529 | |
---|
5530 | to=clock(); |
---|
5531 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
5532 | #ifdef BUCHBERGER_ALG |
---|
5533 | M = MstdhomCC(Gomega1); |
---|
5534 | #else |
---|
5535 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
5536 | delete hilb_func; |
---|
5537 | #endif // BUCHBERGER_ALG |
---|
5538 | xtstd=xtstd+clock()-to; |
---|
5539 | |
---|
5540 | /* change the ring to oldRing */ |
---|
5541 | rChangeCurrRing(oldRing); |
---|
5542 | M1 = idrMoveR(M, newRing); |
---|
5543 | Gomega2 = idrMoveR(Gomega1, newRing); |
---|
5544 | |
---|
5545 | to=clock(); |
---|
5546 | /* compute a reduced Groebner basis of <G> w.r.t. "newRing" by the |
---|
5547 | lifting process */ |
---|
5548 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
5549 | xtlift=xtlift+clock()-to; |
---|
5550 | |
---|
5551 | idDelete(&M1); |
---|
5552 | idDelete(&Gomega2); |
---|
5553 | idDelete(&G); |
---|
5554 | |
---|
5555 | /* change the ring to newRing */ |
---|
5556 | rChangeCurrRing(newRing); |
---|
5557 | F1 = idrMoveR(F, oldRing); |
---|
5558 | |
---|
5559 | to=clock(); |
---|
5560 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
5561 | G = kInterRedCC(F1, NULL); |
---|
5562 | xtred=xtred+clock()-to; |
---|
5563 | idDelete(&F1); |
---|
5564 | |
---|
5565 | if(endwalks == 1) |
---|
5566 | break; |
---|
5567 | |
---|
5568 | NEXT_VECTOR: |
---|
5569 | to=clock(); |
---|
5570 | /* compute a next weight vector */ |
---|
5571 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
5572 | xtnw=xtnw+clock()-to; |
---|
5573 | #ifdef PRINT_VECTORS |
---|
5574 | MivString(curr_weight, target_weight, next_weight); |
---|
5575 | #endif |
---|
5576 | |
---|
5577 | if(Overflow_Error == TRUE) |
---|
5578 | { |
---|
5579 | newRing = currRing; |
---|
5580 | |
---|
5581 | if (currRing->parameter != NULL) |
---|
5582 | DefRingPar(target_weight); |
---|
5583 | else |
---|
5584 | VMrDefault(target_weight); |
---|
5585 | |
---|
5586 | F1 = idrMoveR(G, newRing); |
---|
5587 | G = MstdCC(F1); |
---|
5588 | idDelete(&F1); |
---|
5589 | newRing = currRing; |
---|
5590 | break; //for while |
---|
5591 | } |
---|
5592 | |
---|
5593 | |
---|
5594 | /* G is the wanted Groebner basis if next_weight == curr_weight */ |
---|
5595 | if(MivComp(next_weight, ivNull) == 1) |
---|
5596 | { |
---|
5597 | newRing = currRing; |
---|
5598 | delete next_weight; |
---|
5599 | break; //for while |
---|
5600 | } |
---|
5601 | |
---|
5602 | if(MivComp(next_weight, target_weight) == 1) |
---|
5603 | { |
---|
5604 | if(tp_deg == 1 || MivSame(target_weight, exivlp) == 0) |
---|
5605 | endwalks = 1; |
---|
5606 | else |
---|
5607 | { |
---|
5608 | MSTD_ALT1: |
---|
5609 | nOverflow_Error = Overflow_Error; |
---|
5610 | tproc = clock()-xftinput; |
---|
5611 | /* |
---|
5612 | Print("\n// main routine takes %d steps and calls \"Mpwalk\" (1,%d):", |
---|
5613 | nwalk, tp_deg); |
---|
5614 | */ |
---|
5615 | // compute the red. GB of <G> w.r.t. the lex order by |
---|
5616 | // the "recursive-modified" perturbation walk alg (1,tp_deg) |
---|
5617 | G = Mpwalk_MAltwalk1(G, curr_weight, tp_deg); |
---|
5618 | delete next_weight; |
---|
5619 | break; // for while |
---|
5620 | } |
---|
5621 | } |
---|
5622 | |
---|
5623 | /* 06.11.01 NOT Changed, to free memory*/ |
---|
5624 | for(i=nV-1; i>=0; i--) |
---|
5625 | { |
---|
5626 | //(*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
5627 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
5628 | } |
---|
5629 | delete next_weight; |
---|
5630 | }//while |
---|
5631 | |
---|
5632 | rChangeCurrRing(XXRing); |
---|
5633 | ideal result = idrMoveR(G, newRing); |
---|
5634 | id_Delete(&G, newRing); |
---|
5635 | |
---|
5636 | delete ivNull; |
---|
5637 | if(op_deg != 1 ) |
---|
5638 | delete curr_weight; |
---|
5639 | |
---|
5640 | delete exivlp; |
---|
5641 | #ifdef TIME_TEST |
---|
5642 | |
---|
5643 | Print("\n// \"Main procedure\" took %d steps, %.2f sec. and Overflow_Error(%d)", |
---|
5644 | nwalk, ((double) tproc)/1000000, nOverflow_Error); |
---|
5645 | |
---|
5646 | TimeStringFractal(xftinput, tostd, xtif, xtstd,xtextra, xtlift, xtred, xtnw); |
---|
5647 | |
---|
5648 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
5649 | Print("\n// Overflow_Error? (%d)", Overflow_Error); |
---|
5650 | Print("\n// Awalk1 took %d steps.\n", nstep); |
---|
5651 | #endif |
---|
5652 | return(result); |
---|
5653 | } |
---|
5654 | |
---|