1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /* $Id: polys.cc,v 1.50 1999-10-19 12:42:47 obachman Exp $ */ |
---|
5 | |
---|
6 | /* |
---|
7 | * ABSTRACT - all basic methods to manipulate polynomials |
---|
8 | */ |
---|
9 | |
---|
10 | /* includes */ |
---|
11 | #include <stdio.h> |
---|
12 | #include <string.h> |
---|
13 | #include <ctype.h> |
---|
14 | #include "mod2.h" |
---|
15 | #include "tok.h" |
---|
16 | #include "mmemory.h" |
---|
17 | #include "febase.h" |
---|
18 | #include "numbers.h" |
---|
19 | #include "polys.h" |
---|
20 | #include "ring.h" |
---|
21 | #include "binom.h" |
---|
22 | #include "polys-comp.h" |
---|
23 | |
---|
24 | /* ----------- global variables, set by pSetGlobals --------------------- */ |
---|
25 | /* initializes the internal data from the exp vector */ |
---|
26 | pSetmProc pSetm; |
---|
27 | /* computes length and maximal degree of a POLYnomial */ |
---|
28 | pLDegProc pLDeg; |
---|
29 | /* computes the degree of the initial term, used for std */ |
---|
30 | pFDegProc pFDeg; |
---|
31 | /* the monomial ordering of the head monomials a and b */ |
---|
32 | /* returns -1 if a comes before b, 0 if a=b, 1 otherwise */ |
---|
33 | pCompProc pComp0; |
---|
34 | |
---|
35 | int pVariables; // number of variables |
---|
36 | //int pVariablesW; // number of words of pVariables exponents |
---|
37 | //int pVariables1W; // number of words of (pVariables+1) exponents |
---|
38 | int pMonomSize; // size of monom (in bytes) |
---|
39 | int pMonomSizeW; // size of monom (in words) |
---|
40 | int *pVarOffset; // controls the way exponents are stored in a vector |
---|
41 | //int pVarLowIndex; // lowest exponent index |
---|
42 | //int pVarHighIndex; // highest exponent index |
---|
43 | //int pVarCompIndex; // Location of component in exponent vector |
---|
44 | |
---|
45 | /* 1 for polynomial ring, -1 otherwise */ |
---|
46 | int pOrdSgn; |
---|
47 | /* TRUE for momomial output as x2y, FALSE for x^2*y */ |
---|
48 | int pShortOut = (int)TRUE; |
---|
49 | // it is of type int, not BOOLEAN because it is also in ip |
---|
50 | /* TRUE if the monomial ordering is not compatible with pFDeg */ |
---|
51 | BOOLEAN pLexOrder; |
---|
52 | /* TRUE if the monomial ordering has polynomial and power series blocks */ |
---|
53 | BOOLEAN pMixedOrder; |
---|
54 | /* 1 for c ordering, -1 otherwise (i.e. for C ordering) */ |
---|
55 | int pComponentOrder; |
---|
56 | |
---|
57 | /* ----------- global variables, set by procedures from hecke/kstd1 ----- */ |
---|
58 | /* the highest monomial below pHEdge */ |
---|
59 | poly ppNoether = NULL; |
---|
60 | |
---|
61 | /* -------------- static variables --------------------------------------- */ |
---|
62 | /*is the basic comparing procedure during a computation of syzygies*/ |
---|
63 | static pCompProc pCompOld; |
---|
64 | /*for grouping module indicies during computations*/ |
---|
65 | int pMaxBound = 0; |
---|
66 | |
---|
67 | /*contains the headterms for the Schreyer orderings*/ |
---|
68 | static int* SchreyerOrd; |
---|
69 | static int maxSchreyer=0; |
---|
70 | static int indexShift=0; |
---|
71 | static pLDegProc pLDegOld; |
---|
72 | |
---|
73 | static int** polys_wv; |
---|
74 | static short * firstwv; |
---|
75 | static int * block0; |
---|
76 | static int * block1; |
---|
77 | static int firstBlockEnds; |
---|
78 | static int * order; |
---|
79 | |
---|
80 | /*0 implementation*/ |
---|
81 | /*-------- the several possibilities for pSetm:-----------------------*/ |
---|
82 | |
---|
83 | void rSetm(poly p) |
---|
84 | { |
---|
85 | int pos=0; |
---|
86 | if (currRing->typ!=NULL) |
---|
87 | { |
---|
88 | loop |
---|
89 | { |
---|
90 | sro_ord* o=&(currRing->typ[pos]); |
---|
91 | switch(o->ord_typ) |
---|
92 | { |
---|
93 | case ro_dp: |
---|
94 | { |
---|
95 | int a,e; |
---|
96 | a=o->data.dp.start; |
---|
97 | e=o->data.dp.end; |
---|
98 | long ord=0; |
---|
99 | for(int i=a;i<=e;i++) ord+=pGetExp(p,i); |
---|
100 | p->exp.l[o->data.dp.place]=ord; |
---|
101 | break; |
---|
102 | } |
---|
103 | case ro_wp: |
---|
104 | { |
---|
105 | int a,e; |
---|
106 | a=o->data.wp.start; |
---|
107 | e=o->data.wp.end; |
---|
108 | int *w=o->data.wp.weights; |
---|
109 | long ord=0; |
---|
110 | for(int i=a;i<=e;i++) ord+=pGetExp(p,i)*w[i-a]; |
---|
111 | p->exp.l[o->data.wp.place]=ord; |
---|
112 | break; |
---|
113 | } |
---|
114 | case ro_cp: |
---|
115 | { |
---|
116 | int a,e; |
---|
117 | a=o->data.cp.start; |
---|
118 | e=o->data.cp.end; |
---|
119 | int pl=o->data.cp.place; |
---|
120 | for(int i=a;i<=e;i++) { p->exp.e[pl]=pGetExp(p,i); pl++; } |
---|
121 | break; |
---|
122 | } |
---|
123 | case ro_syzcomp: |
---|
124 | { |
---|
125 | int c=pGetComp(p); |
---|
126 | long sc = c; |
---|
127 | #if 1 |
---|
128 | if (o->data.syzcomp.ShiftedComponents != NULL) |
---|
129 | { |
---|
130 | assume(o->data.syzcomp.Components != NULL); |
---|
131 | assume(c == 0 || o->data.syzcomp.Components[c] != 0); |
---|
132 | sc = |
---|
133 | o->data.syzcomp.ShiftedComponents[o->data.syzcomp.Components[c]]; |
---|
134 | assume(c == 0 || sc != 0); |
---|
135 | } |
---|
136 | p->exp.l[o->data.syzcomp.place]=sc; |
---|
137 | #endif |
---|
138 | break; |
---|
139 | } |
---|
140 | case ro_syz: |
---|
141 | { |
---|
142 | int c=pGetComp(p); |
---|
143 | if (c > o->data.syz.limit) |
---|
144 | p->exp.l[o->data.syz.place]= 1; |
---|
145 | else |
---|
146 | p->exp.l[o->data.syz.place]= 0; |
---|
147 | break; |
---|
148 | } |
---|
149 | default: |
---|
150 | Print("wrong ord in rSetm:%d\n",o->ord_typ); |
---|
151 | return; |
---|
152 | } |
---|
153 | pos++; |
---|
154 | if(pos==currRing->OrdSize) return; |
---|
155 | } |
---|
156 | } |
---|
157 | } |
---|
158 | |
---|
159 | void rSetmS(poly p, int* Components, long* ShiftedComponents) |
---|
160 | { |
---|
161 | int pos=0; |
---|
162 | assume(Components != NULL && ShiftedComponents != NULL); |
---|
163 | if (currRing->typ!=NULL) |
---|
164 | { |
---|
165 | loop |
---|
166 | { |
---|
167 | sro_ord* o=&(currRing->typ[pos]); |
---|
168 | switch(o->ord_typ) |
---|
169 | { |
---|
170 | case ro_dp: |
---|
171 | { |
---|
172 | int a,e; |
---|
173 | a=o->data.dp.start; |
---|
174 | e=o->data.dp.end; |
---|
175 | long ord=0; |
---|
176 | for(int i=a;i<=e;i++) ord+=pGetExp(p,i); |
---|
177 | p->exp.l[o->data.dp.place]=ord; |
---|
178 | break; |
---|
179 | } |
---|
180 | case ro_wp: |
---|
181 | { |
---|
182 | int a,e; |
---|
183 | a=o->data.wp.start; |
---|
184 | e=o->data.wp.end; |
---|
185 | int *w=o->data.wp.weights; |
---|
186 | long ord=0; |
---|
187 | for(int i=a;i<=e;i++) ord+=pGetExp(p,i)*w[i-a]; |
---|
188 | p->exp.l[o->data.wp.place]=ord; |
---|
189 | break; |
---|
190 | } |
---|
191 | case ro_cp: |
---|
192 | { |
---|
193 | int a,e; |
---|
194 | a=o->data.cp.start; |
---|
195 | e=o->data.cp.end; |
---|
196 | int pl=o->data.cp.place; |
---|
197 | for(int i=a;i<=e;i++) { p->exp.e[pl]=pGetExp(p,i); pl++; } |
---|
198 | break; |
---|
199 | } |
---|
200 | case ro_syzcomp: |
---|
201 | { |
---|
202 | #if 1 |
---|
203 | int c=pGetComp(p); |
---|
204 | long sc = ShiftedComponents[Components[c]]; |
---|
205 | assume(c == 0 || Components[c] != 0); |
---|
206 | assume(c == 0 || sc != 0); |
---|
207 | p->exp.l[o->data.syzcomp.place]=sc; |
---|
208 | #endif |
---|
209 | break; |
---|
210 | } |
---|
211 | default: |
---|
212 | Print("wrong ord in rSetm:%d\n",o->ord_typ); |
---|
213 | return; |
---|
214 | } |
---|
215 | pos++; |
---|
216 | if(pos==currRing->OrdSize) return; |
---|
217 | } |
---|
218 | } |
---|
219 | } |
---|
220 | |
---|
221 | /*-------- IMPLEMENTATION OF MONOMIAL COMPARISONS ---------------------*/ |
---|
222 | |
---|
223 | |
---|
224 | #define NonZeroR(l, actionG, actionS) \ |
---|
225 | do \ |
---|
226 | { \ |
---|
227 | long _l = l; \ |
---|
228 | if (_l) \ |
---|
229 | { \ |
---|
230 | if (_l > 0) actionG; \ |
---|
231 | actionS; \ |
---|
232 | } \ |
---|
233 | } \ |
---|
234 | while(0) |
---|
235 | |
---|
236 | #define Mreturn(d, multiplier) \ |
---|
237 | { \ |
---|
238 | if (d > 0) return multiplier; \ |
---|
239 | return -multiplier; \ |
---|
240 | } |
---|
241 | |
---|
242 | |
---|
243 | /*---------------------------------------------------*/ |
---|
244 | |
---|
245 | int pComp(poly p1, poly p2) |
---|
246 | { |
---|
247 | if (p2==NULL) |
---|
248 | return 1; |
---|
249 | if (p1==NULL) |
---|
250 | return -1; |
---|
251 | return pComp0(p1,p2); |
---|
252 | } |
---|
253 | |
---|
254 | |
---|
255 | /*----------pComp handling for syzygies---------------------*/ |
---|
256 | static void newHeadsB(polyset actHeads,int length) |
---|
257 | { |
---|
258 | int i; |
---|
259 | int* newOrder=(int*)Alloc(length*sizeof(int)); |
---|
260 | |
---|
261 | for (i=0;i<length;i++) |
---|
262 | { |
---|
263 | if (actHeads[i]!=NULL) |
---|
264 | { |
---|
265 | newOrder[i] = SchreyerOrd[pGetComp(actHeads[i])-1]; |
---|
266 | } |
---|
267 | else |
---|
268 | { |
---|
269 | newOrder[i]=0; |
---|
270 | } |
---|
271 | } |
---|
272 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
---|
273 | SchreyerOrd = newOrder; |
---|
274 | maxSchreyer = length; |
---|
275 | /* |
---|
276 | *for (i=0;i<maxSchreyer;i++); Print("%d ",SchreyerOrd[i]); |
---|
277 | *PrintLn(); |
---|
278 | */ |
---|
279 | } |
---|
280 | |
---|
281 | int mcompSchrB(poly p1,poly p2) |
---|
282 | { |
---|
283 | int CompP1=pGetComp(p1),CompP2=pGetComp(p2),result, |
---|
284 | cP1=SchreyerOrd[CompP1-1],cP2=SchreyerOrd[CompP2-1]; |
---|
285 | |
---|
286 | if (CompP1==CompP2) return pCompOld(p1,p2); |
---|
287 | pSetComp(p1,cP1); |
---|
288 | pSetComp(p2,cP2); |
---|
289 | result = pCompOld(p1,p2); |
---|
290 | pSetComp(p1,CompP1); |
---|
291 | pSetComp(p2,CompP2); |
---|
292 | if (!result) |
---|
293 | { |
---|
294 | if (CompP1>CompP2) |
---|
295 | return -1; |
---|
296 | else if (CompP1<CompP2) |
---|
297 | return 1; |
---|
298 | } |
---|
299 | return result; |
---|
300 | } |
---|
301 | |
---|
302 | |
---|
303 | static void newHeadsM(polyset actHeads,int length) |
---|
304 | { |
---|
305 | int i; |
---|
306 | int* newOrder= |
---|
307 | (int*)Alloc0((length+maxSchreyer-indexShift)*sizeof(int)); |
---|
308 | |
---|
309 | //for (i=0;i<length+maxSchreyer-indexShift;i++) |
---|
310 | // newOrder[i]=0; |
---|
311 | for (i=indexShift;i<maxSchreyer;i++) |
---|
312 | { |
---|
313 | newOrder[i-indexShift] = SchreyerOrd[i]; |
---|
314 | SchreyerOrd[i] = 0; |
---|
315 | } |
---|
316 | for (i=maxSchreyer-indexShift;i<length+maxSchreyer-indexShift;i++) |
---|
317 | newOrder[i] = newOrder[pGetComp(actHeads[i-maxSchreyer+indexShift])-1]; |
---|
318 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
---|
319 | SchreyerOrd = newOrder; |
---|
320 | indexShift = maxSchreyer-indexShift; |
---|
321 | maxSchreyer = length+indexShift; |
---|
322 | } |
---|
323 | |
---|
324 | /*2 |
---|
325 | * compute the length of a polynomial (in l) |
---|
326 | * and the degree of the monomial with maximal degree: |
---|
327 | * this is NOT the last one and the module component |
---|
328 | * has to be <= indexShift |
---|
329 | */ |
---|
330 | static int ldegSchrM(poly p,int *l) |
---|
331 | { |
---|
332 | int t,max; |
---|
333 | |
---|
334 | (*l)=1; |
---|
335 | max=pFDeg(p); |
---|
336 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=indexShift)) |
---|
337 | { |
---|
338 | pIter(p); |
---|
339 | t=pFDeg(p); |
---|
340 | if (t>max) max=t; |
---|
341 | (*l)++; |
---|
342 | } |
---|
343 | return max; |
---|
344 | } |
---|
345 | |
---|
346 | int mcompSchrM(poly p1,poly p2) |
---|
347 | { |
---|
348 | if ( pGetComp(p1)<=indexShift) |
---|
349 | { |
---|
350 | if ( pGetComp(p2)>indexShift) return 1; |
---|
351 | } |
---|
352 | else if ( pGetComp(p2)<=indexShift) return -1; |
---|
353 | return mcompSchrB(p1,p2); |
---|
354 | } |
---|
355 | |
---|
356 | void pSetSchreyerOrdM(polyset nextOrder, int length,int comps) |
---|
357 | { |
---|
358 | int i; |
---|
359 | |
---|
360 | if (length!=0) |
---|
361 | { |
---|
362 | if (maxSchreyer!=0) |
---|
363 | newHeadsM(nextOrder, length); |
---|
364 | else |
---|
365 | { |
---|
366 | indexShift = comps; |
---|
367 | if (indexShift==0) indexShift = 1; |
---|
368 | SchreyerOrd = (int*)Alloc((indexShift+length)*sizeof(int)); |
---|
369 | maxSchreyer = length+indexShift; |
---|
370 | for (i=0;i<indexShift;i++) |
---|
371 | SchreyerOrd[i] = i; |
---|
372 | for (i=indexShift;i<maxSchreyer;i++) |
---|
373 | SchreyerOrd[i] = pGetComp(nextOrder[i-indexShift]); |
---|
374 | pCompOld = pComp0; |
---|
375 | pComp0 = mcompSchrM; |
---|
376 | pLDegOld = pLDeg; |
---|
377 | pLDeg = ldegSchrM; |
---|
378 | } |
---|
379 | } |
---|
380 | else |
---|
381 | { |
---|
382 | if (maxSchreyer!=0) |
---|
383 | { |
---|
384 | Free((ADDRESS)SchreyerOrd,maxSchreyer*sizeof(int)); |
---|
385 | maxSchreyer = 0; |
---|
386 | indexShift = 0; |
---|
387 | pComp0 = pCompOld; |
---|
388 | pLDeg = pLDegOld; |
---|
389 | } |
---|
390 | } |
---|
391 | } |
---|
392 | |
---|
393 | void pSetSyzComp(int k) |
---|
394 | { |
---|
395 | pMaxBound=k; |
---|
396 | if((currRing->typ!=NULL) && (currRing->typ[0].ord_typ==ro_syz)) |
---|
397 | { |
---|
398 | if (currRing->typ!=NULL) |
---|
399 | currRing->typ[0].data.syz.limit=k; |
---|
400 | } |
---|
401 | else if ((currRing->order[0]!=ringorder_c) && (k!=0)) |
---|
402 | { |
---|
403 | WarnS("syzcomp in incompatible ring"); |
---|
404 | } |
---|
405 | } |
---|
406 | |
---|
407 | /*2 |
---|
408 | * the type of the module ordering: C: -1, c: 1 |
---|
409 | */ |
---|
410 | int pModuleOrder() |
---|
411 | { |
---|
412 | return pComponentOrder; |
---|
413 | } |
---|
414 | |
---|
415 | /* -------------------------------------------------------------------*/ |
---|
416 | /* several possibilities for pFDeg: the degree of the head term */ |
---|
417 | /*2 |
---|
418 | * compute the degree of the leading monomial of p |
---|
419 | * the ordering is compatible with degree, use a->order |
---|
420 | */ |
---|
421 | int pDeg(poly a) |
---|
422 | { |
---|
423 | return pGetOrder(a); |
---|
424 | } |
---|
425 | |
---|
426 | /*2 |
---|
427 | * compute the degree of the leading monomial of p |
---|
428 | * with respect to weigths 1 |
---|
429 | * (all are 1 so save multiplications or they are of different signs) |
---|
430 | * the ordering is not compatible with degree so do not use p->Order |
---|
431 | */ |
---|
432 | int pTotaldegree(poly p) |
---|
433 | { |
---|
434 | return pExpQuerSum(p); |
---|
435 | } |
---|
436 | |
---|
437 | /*2 |
---|
438 | * compute the degree of the leading monomial of p |
---|
439 | * with respect to weigths from the ordering |
---|
440 | * the ordering is not compatible with degree so do not use p->Order |
---|
441 | */ |
---|
442 | int pWTotaldegree(poly p) |
---|
443 | { |
---|
444 | assume(p != NULL); |
---|
445 | int i, k; |
---|
446 | int j =0; |
---|
447 | |
---|
448 | // iterate through each block: |
---|
449 | for (i=0;order[i]!=0;i++) |
---|
450 | { |
---|
451 | switch(order[i]) |
---|
452 | { |
---|
453 | case ringorder_wp: |
---|
454 | case ringorder_ws: |
---|
455 | case ringorder_Wp: |
---|
456 | case ringorder_Ws: |
---|
457 | for (k=block0[i];k<=block1[i];k++) |
---|
458 | { // in jedem block: |
---|
459 | j+= pGetExp(p,k)*polys_wv[i][k-block0[i]]; |
---|
460 | } |
---|
461 | break; |
---|
462 | case ringorder_M: |
---|
463 | case ringorder_lp: |
---|
464 | case ringorder_dp: |
---|
465 | case ringorder_ds: |
---|
466 | case ringorder_Dp: |
---|
467 | case ringorder_Ds: |
---|
468 | for (k=block0[i];k<=block1[i];k++) |
---|
469 | { |
---|
470 | j+= pGetExp(p,k); |
---|
471 | } |
---|
472 | break; |
---|
473 | case ringorder_c: |
---|
474 | case ringorder_C: |
---|
475 | case ringorder_S: |
---|
476 | break; |
---|
477 | case ringorder_a: |
---|
478 | for (k=block0[i];k<=block1[i];k++) |
---|
479 | { // only one line |
---|
480 | j+= pGetExp(p,k)*polys_wv[i][k-block0[i]]; |
---|
481 | } |
---|
482 | return j; |
---|
483 | } |
---|
484 | } |
---|
485 | return j; |
---|
486 | } |
---|
487 | int pWDegree(poly p) |
---|
488 | { |
---|
489 | int i, k; |
---|
490 | int j =0; |
---|
491 | |
---|
492 | for(i=1;i<=pVariables;i++) |
---|
493 | j+=pGetExp(p,i)*pWeight(i); |
---|
494 | return j; |
---|
495 | } |
---|
496 | |
---|
497 | /* ---------------------------------------------------------------------*/ |
---|
498 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
499 | /* compute in l also the pLength of p */ |
---|
500 | |
---|
501 | /*2 |
---|
502 | * compute the length of a polynomial (in l) |
---|
503 | * and the degree of the monomial with maximal degree: the last one |
---|
504 | */ |
---|
505 | static int ldeg0(poly p,int *l) |
---|
506 | { |
---|
507 | Exponent_t k= pGetComp(p); |
---|
508 | int ll=1; |
---|
509 | |
---|
510 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))==k)) |
---|
511 | { |
---|
512 | pIter(p); |
---|
513 | ll++; |
---|
514 | } |
---|
515 | *l=ll; |
---|
516 | return pGetOrder(p); |
---|
517 | } |
---|
518 | |
---|
519 | /*2 |
---|
520 | * compute the length of a polynomial (in l) |
---|
521 | * and the degree of the monomial with maximal degree: the last one |
---|
522 | * but search in all components before syzcomp |
---|
523 | */ |
---|
524 | static int ldeg0c(poly p,int *l) |
---|
525 | { |
---|
526 | int o=pFDeg(p); |
---|
527 | int ll=1; |
---|
528 | |
---|
529 | if (pMaxBound/*syzComp*/==0) |
---|
530 | { |
---|
531 | while ((p=pNext(p))!=NULL) |
---|
532 | { |
---|
533 | o=pFDeg(p); |
---|
534 | ll++; |
---|
535 | } |
---|
536 | } |
---|
537 | else |
---|
538 | { |
---|
539 | while ((p=pNext(p))!=NULL) |
---|
540 | { |
---|
541 | if (pGetComp(p)<=pMaxBound/*syzComp*/) |
---|
542 | { |
---|
543 | o=pFDeg(p); |
---|
544 | ll++; |
---|
545 | } |
---|
546 | else break; |
---|
547 | } |
---|
548 | } |
---|
549 | *l=ll; |
---|
550 | return o; |
---|
551 | } |
---|
552 | |
---|
553 | /*2 |
---|
554 | * compute the length of a polynomial (in l) |
---|
555 | * and the degree of the monomial with maximal degree: the first one |
---|
556 | * this works for the polynomial case with degree orderings |
---|
557 | * (both c,dp and dp,c) |
---|
558 | */ |
---|
559 | static int ldegb(poly p,int *l) |
---|
560 | { |
---|
561 | Exponent_t k= pGetComp(p); |
---|
562 | int o = pFDeg(p); |
---|
563 | int ll=1; |
---|
564 | |
---|
565 | while (((p=pNext(p))!=NULL) && (pGetComp(p)==k)) |
---|
566 | { |
---|
567 | ll++; |
---|
568 | } |
---|
569 | *l=ll; |
---|
570 | return o; |
---|
571 | } |
---|
572 | |
---|
573 | /*2 |
---|
574 | * compute the length of a polynomial (in l) |
---|
575 | * and the degree of the monomial with maximal degree: |
---|
576 | * this is NOT the last one, we have to look for it |
---|
577 | */ |
---|
578 | static int ldeg1(poly p,int *l) |
---|
579 | { |
---|
580 | Exponent_t k= pGetComp(p); |
---|
581 | int ll=1; |
---|
582 | int t,max; |
---|
583 | |
---|
584 | max=pFDeg(p); |
---|
585 | while (((p=pNext(p))!=NULL) && (pGetComp(p)==k)) |
---|
586 | { |
---|
587 | t=pFDeg(p); |
---|
588 | if (t>max) max=t; |
---|
589 | ll++; |
---|
590 | } |
---|
591 | *l=ll; |
---|
592 | return max; |
---|
593 | } |
---|
594 | |
---|
595 | /*2 |
---|
596 | * compute the length of a polynomial (in l) |
---|
597 | * and the degree of the monomial with maximal degree: |
---|
598 | * this is NOT the last one, we have to look for it |
---|
599 | * in all components |
---|
600 | */ |
---|
601 | static int ldeg1c(poly p,int *l) |
---|
602 | { |
---|
603 | int ll=1; |
---|
604 | int t,max; |
---|
605 | |
---|
606 | max=pFDeg(p); |
---|
607 | while ((p=pNext(p))!=NULL) |
---|
608 | { |
---|
609 | if ((pMaxBound/*syzComp*/==0) || (pGetComp(p)<=pMaxBound/*syzComp*/)) |
---|
610 | { |
---|
611 | if ((t=pFDeg(p))>max) max=t; |
---|
612 | ll++; |
---|
613 | } |
---|
614 | else break; |
---|
615 | } |
---|
616 | *l=ll; |
---|
617 | return max; |
---|
618 | } |
---|
619 | |
---|
620 | /* -------------------------------------------------------- */ |
---|
621 | /* set the variables for a choosen ordering */ |
---|
622 | |
---|
623 | |
---|
624 | /*2 |
---|
625 | * sets the comparision routine for monomials: for all but the first |
---|
626 | * block of variables (ip is the block number, o_r the number of the ordering) |
---|
627 | */ |
---|
628 | static void HighSet(int ip, int o_r) |
---|
629 | { |
---|
630 | switch(o_r) |
---|
631 | { |
---|
632 | case ringorder_lp: |
---|
633 | case ringorder_dp: |
---|
634 | case ringorder_Dp: |
---|
635 | case ringorder_wp: |
---|
636 | case ringorder_Wp: |
---|
637 | case ringorder_a: |
---|
638 | if (pOrdSgn==-1) pMixedOrder=TRUE; |
---|
639 | break; |
---|
640 | case ringorder_ls: |
---|
641 | case ringorder_ds: |
---|
642 | case ringorder_Ds: |
---|
643 | case ringorder_ws: |
---|
644 | case ringorder_Ws: |
---|
645 | case ringorder_s: |
---|
646 | break; |
---|
647 | case ringorder_c: |
---|
648 | pComponentOrder=1; |
---|
649 | break; |
---|
650 | case ringorder_C: |
---|
651 | case ringorder_S: |
---|
652 | pComponentOrder=-1; |
---|
653 | break; |
---|
654 | case ringorder_M: |
---|
655 | pMixedOrder=TRUE; |
---|
656 | break; |
---|
657 | #ifdef TEST |
---|
658 | default: |
---|
659 | Werror("wrong internal ordering:%d at %s, l:%d\n",o_r,__FILE__,__LINE__); |
---|
660 | #endif |
---|
661 | } |
---|
662 | } |
---|
663 | |
---|
664 | /* -------------------------------------------------------- */ |
---|
665 | /*2 |
---|
666 | * change all variables to fit the description of the new ring |
---|
667 | */ |
---|
668 | |
---|
669 | //void pChangeRing(ring newRing) |
---|
670 | //{ |
---|
671 | // rComplete(newRing); |
---|
672 | // pSetGlobals(newRing); |
---|
673 | //} |
---|
674 | |
---|
675 | void pSetGlobals(ring r, BOOLEAN complete) |
---|
676 | { |
---|
677 | int i; |
---|
678 | pComponentOrder=1; |
---|
679 | if (ppNoether!=NULL) pDelete(&ppNoether); |
---|
680 | pVariables = r->N; |
---|
681 | |
---|
682 | // set the various size parameters and initialize memory |
---|
683 | pMonomSize = POLYSIZE + r->ExpLSize * sizeof(long); |
---|
684 | pMonomSizeW = pMonomSize/sizeof(void*); |
---|
685 | |
---|
686 | // Initialize memory management |
---|
687 | mm_specHeap = r->mm_specHeap; |
---|
688 | |
---|
689 | pVarOffset = r->VarOffset; |
---|
690 | |
---|
691 | pOrdSgn = r->OrdSgn; |
---|
692 | pVectorOut=(r->order[0]==ringorder_c); |
---|
693 | order=r->order; |
---|
694 | block0=r->block0; |
---|
695 | block1=r->block1; |
---|
696 | firstwv=NULL; |
---|
697 | polys_wv=r->wvhdl; |
---|
698 | if (order[0]==ringorder_S) |
---|
699 | { |
---|
700 | order++; |
---|
701 | block0++; |
---|
702 | block1++; |
---|
703 | polys_wv++; |
---|
704 | } |
---|
705 | pFDeg=pTotaldegree; |
---|
706 | /*------- only one real block ----------------------*/ |
---|
707 | pLexOrder=FALSE; |
---|
708 | pMixedOrder=FALSE; |
---|
709 | if (pOrdSgn == 1) pLDeg = ldegb; |
---|
710 | else pLDeg = ldeg0; |
---|
711 | /*======== ordering type is (_,c) =========================*/ |
---|
712 | if ((order[0]==ringorder_unspec) |
---|
713 | ||( |
---|
714 | ((order[1]==ringorder_c)||(order[1]==ringorder_C)||(order[1]==ringorder_S)) |
---|
715 | && (order[0]!=ringorder_M) |
---|
716 | && (order[2]==0)) |
---|
717 | ) |
---|
718 | { |
---|
719 | if ((order[0]!=ringorder_unspec) |
---|
720 | && ((order[1]==ringorder_C)||(order[1]==ringorder_S))) |
---|
721 | pComponentOrder=-1; |
---|
722 | if (pOrdSgn == -1) pLDeg = ldeg0c; |
---|
723 | if ((order[0] == ringorder_lp) || (order[0] == ringorder_ls)) |
---|
724 | { |
---|
725 | pLexOrder=TRUE; |
---|
726 | pLDeg = ldeg1c; |
---|
727 | } |
---|
728 | if (order[0] == ringorder_wp || order[0] == ringorder_Wp || |
---|
729 | order[0] == ringorder_ws || order[0] == ringorder_Ws) |
---|
730 | pFDeg = pWTotaldegree; |
---|
731 | firstBlockEnds=block1[0]; |
---|
732 | } |
---|
733 | /*======== ordering type is (c,_) =========================*/ |
---|
734 | else if (((order[0]==ringorder_c) |
---|
735 | ||(order[0]==ringorder_C) |
---|
736 | ||(order[0]==ringorder_S)) |
---|
737 | && (order[1]!=ringorder_M) |
---|
738 | && (order[2]==0)) |
---|
739 | { |
---|
740 | /* pLDeg = ldeg0; is standard*/ |
---|
741 | if ((order[0]==ringorder_C)||(order[0]==ringorder_S)) |
---|
742 | pComponentOrder=-1; |
---|
743 | if ((order[1] == ringorder_lp) || (order[1] == ringorder_ls)) |
---|
744 | { |
---|
745 | pLexOrder=TRUE; |
---|
746 | pLDeg = ldeg1c; |
---|
747 | } |
---|
748 | firstBlockEnds=block1[1]; |
---|
749 | if (order[1] == ringorder_wp || order[1] == ringorder_Wp || |
---|
750 | order[1] == ringorder_ws || order[1] == ringorder_Ws) |
---|
751 | pFDeg = pWTotaldegree; |
---|
752 | } |
---|
753 | /*------- more than one block ----------------------*/ |
---|
754 | else |
---|
755 | { |
---|
756 | //pGetVarIndicies(pVariables, pVarOffset, pVarCompIndex, pVarLowIndex, |
---|
757 | // pVarHighIndex); |
---|
758 | //pLexOrder=TRUE; |
---|
759 | pVectorOut=order[0]==ringorder_c; |
---|
760 | if ((pVectorOut)||(order[0]==ringorder_C)||(order[0]==ringorder_S)) |
---|
761 | { |
---|
762 | if(block1[1]!=pVariables) pLexOrder=TRUE; |
---|
763 | firstBlockEnds=block1[1]; |
---|
764 | } |
---|
765 | else |
---|
766 | { |
---|
767 | if(block1[0]!=pVariables) pLexOrder=TRUE; |
---|
768 | firstBlockEnds=block1[0]; |
---|
769 | } |
---|
770 | /*the number of orderings:*/ |
---|
771 | i = 0; |
---|
772 | while (order[++i] != 0); |
---|
773 | do |
---|
774 | { |
---|
775 | i--; |
---|
776 | HighSet(i, order[i]);/*sets also pMixedOrder to TRUE, if...*/ |
---|
777 | } |
---|
778 | while (i != 0); |
---|
779 | |
---|
780 | if ((order[0]!=ringorder_c) |
---|
781 | &&(order[0]!=ringorder_C) |
---|
782 | &&(order[0]!=ringorder_S)) |
---|
783 | { |
---|
784 | pLDeg = ldeg1c; |
---|
785 | } |
---|
786 | else |
---|
787 | { |
---|
788 | pLDeg = ldeg1; |
---|
789 | } |
---|
790 | pFDeg = pWTotaldegree; // may be improved: pTotaldegree for lp/dp/ls/.. blocks |
---|
791 | } |
---|
792 | if (complete) |
---|
793 | { |
---|
794 | if ((pLexOrder) || (pOrdSgn==-1)) |
---|
795 | { |
---|
796 | test &= ~Sy_bit(OPT_REDTAIL); /* noredTail */ |
---|
797 | } |
---|
798 | pSetm=rSetm; |
---|
799 | pComp0=rComp0; |
---|
800 | } |
---|
801 | if (pFDeg!=pWTotaldegree) pFDeg=pTotaldegree; |
---|
802 | } |
---|
803 | |
---|
804 | /* -------------------------------------------------------- */ |
---|
805 | |
---|
806 | static Exponent_t pMultT_nok; |
---|
807 | /*2 |
---|
808 | * update the polynomial a by multipying it by |
---|
809 | * the (number) coefficient |
---|
810 | * and the exponent vector (of) exp (a well initialized polynomial) |
---|
811 | */ |
---|
812 | poly pMultT(poly a, poly exp ) |
---|
813 | { |
---|
814 | int i; |
---|
815 | number t,x,y=pGetCoeff(exp); |
---|
816 | poly aa=a; |
---|
817 | poly prev=NULL; |
---|
818 | |
---|
819 | pMultT_nok = pGetComp(exp); |
---|
820 | #ifdef PDEBUG |
---|
821 | pTest(a); |
---|
822 | pTest(exp); |
---|
823 | #endif |
---|
824 | while (a !=NULL) |
---|
825 | { |
---|
826 | x=pGetCoeff(a); |
---|
827 | t=nMult(x/*pGetCoeff(a)*/,y/*pGetCoeff(exp)*/); |
---|
828 | nDelete(&x/*pGetCoeff(a)*/); |
---|
829 | pSetCoeff0(a,t); |
---|
830 | if (nIsZero(t)) |
---|
831 | { |
---|
832 | if (prev==NULL) { pDelete1(&a); aa=a; } |
---|
833 | else { pDelete1(&prev->next); a=prev->next;} |
---|
834 | } |
---|
835 | else |
---|
836 | { |
---|
837 | { |
---|
838 | if (pMultT_nok) /* comp of exp != 0 */ |
---|
839 | { |
---|
840 | if (pGetComp(a) != 0) |
---|
841 | { |
---|
842 | return NULL /*FALSE*/; |
---|
843 | } |
---|
844 | } |
---|
845 | pMonAddOn(a,exp); |
---|
846 | } |
---|
847 | prev=a; |
---|
848 | pIter(a); |
---|
849 | } |
---|
850 | } |
---|
851 | pMultT_nok=0; |
---|
852 | pTest(aa); |
---|
853 | return aa; /*TRUE*/ |
---|
854 | } |
---|
855 | |
---|
856 | /*2 |
---|
857 | * multiply p1 with p2, p1 and p2 are destroyed |
---|
858 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
859 | */ |
---|
860 | poly pMult(poly p1, poly p2) |
---|
861 | { |
---|
862 | poly res, r, rn, a; |
---|
863 | BOOLEAN cont; |
---|
864 | |
---|
865 | if ((p1!=NULL) && (p2!=NULL)) |
---|
866 | { |
---|
867 | #ifdef PDEBUG |
---|
868 | pTest(p1); |
---|
869 | pTest(p2); |
---|
870 | #endif |
---|
871 | cont = TRUE; |
---|
872 | a = p1; |
---|
873 | if (pNext(p2)!=NULL) |
---|
874 | a = pCopy(a); |
---|
875 | else |
---|
876 | cont = FALSE; |
---|
877 | res = pMultT(a, p2); |
---|
878 | if (pMultT_nok) |
---|
879 | { |
---|
880 | if (cont) pDelete(&p1); |
---|
881 | pDelete(&res); |
---|
882 | pDelete(&p2); |
---|
883 | return NULL; |
---|
884 | } |
---|
885 | pTest(res); |
---|
886 | pDelete1(&p2); |
---|
887 | r = res; |
---|
888 | if (r!=NULL) rn = pNext(r); |
---|
889 | else rn=NULL; |
---|
890 | while (cont) |
---|
891 | { |
---|
892 | if (pNext(p2)==NULL) |
---|
893 | { |
---|
894 | a = p1; |
---|
895 | cont = FALSE; |
---|
896 | } |
---|
897 | else |
---|
898 | { |
---|
899 | a = pCopy(p1); |
---|
900 | } |
---|
901 | a=pMultT(a, p2); //sets pMultT_nok |
---|
902 | pTest(a); |
---|
903 | if (pMultT_nok) |
---|
904 | { |
---|
905 | if (cont) pDelete(&p1); |
---|
906 | pDelete(&a); |
---|
907 | pDelete(&res); |
---|
908 | pDelete(&p2); |
---|
909 | return NULL; |
---|
910 | } |
---|
911 | while ((rn!=NULL) && (pComp0(rn,a)>0)) |
---|
912 | { |
---|
913 | r = rn; |
---|
914 | pIter(rn); |
---|
915 | } |
---|
916 | if (r!=NULL) pNext(r) = rn = pAdd(a, rn); |
---|
917 | else res=r=a; |
---|
918 | pDelete1(&p2); |
---|
919 | } |
---|
920 | pTest(res); |
---|
921 | return res; |
---|
922 | } |
---|
923 | pDelete(&p1); |
---|
924 | pDelete(&p2); |
---|
925 | return NULL; |
---|
926 | } |
---|
927 | |
---|
928 | /*2 |
---|
929 | * update a by multiplying it with c (c will not be destroyed) |
---|
930 | */ |
---|
931 | void pMultN(poly a, number c) |
---|
932 | { |
---|
933 | number t; |
---|
934 | |
---|
935 | while (a!=NULL) |
---|
936 | { |
---|
937 | t=nMult(pGetCoeff(a), c); |
---|
938 | //nNormalize(t); |
---|
939 | pSetCoeff(a,t); |
---|
940 | pIter(a); |
---|
941 | } |
---|
942 | } |
---|
943 | |
---|
944 | /*2 |
---|
945 | * return a copy of the poly a times the number c (a,c will not be destroyed) |
---|
946 | */ |
---|
947 | poly pMultCopyN(poly a, number c) |
---|
948 | { |
---|
949 | poly result=NULL,hp; |
---|
950 | |
---|
951 | if (a != NULL) |
---|
952 | { |
---|
953 | result=pNew(); |
---|
954 | pCopy2(result,a); |
---|
955 | pNext(result)=NULL; |
---|
956 | pGetCoeff(result)=nMult(pGetCoeff(a),c); |
---|
957 | pIter(a); |
---|
958 | hp=result; |
---|
959 | while (a!=NULL) |
---|
960 | { |
---|
961 | hp=pNext(hp)=pNew(); |
---|
962 | pCopy2(hp,a); |
---|
963 | pSetCoeff0(hp,nMult(pGetCoeff(a), c)); |
---|
964 | pIter(a); |
---|
965 | } |
---|
966 | pNext(hp)=NULL; |
---|
967 | } |
---|
968 | return result; |
---|
969 | } |
---|
970 | |
---|
971 | /*2 |
---|
972 | * assumes that the head term of b is a multiple of the head term of a |
---|
973 | * and return the multiplicant *m |
---|
974 | */ |
---|
975 | poly pDivide(poly a, poly b) |
---|
976 | { |
---|
977 | int i; |
---|
978 | poly result=pInit(); |
---|
979 | |
---|
980 | for(i=(int)pVariables; i; i--) |
---|
981 | pSetExp(result,i, pGetExp(a,i)- pGetExp(b,i)); |
---|
982 | pSetComp(result, pGetComp(a) - pGetComp(b)); |
---|
983 | pSetm(result); |
---|
984 | return result; |
---|
985 | } |
---|
986 | |
---|
987 | /*2 |
---|
988 | * divides a by the monomial b, ignores monomials wihich are not divisible |
---|
989 | * assumes that b is not NULL |
---|
990 | */ |
---|
991 | poly pDivideM(poly a, poly b) |
---|
992 | { |
---|
993 | if (a==NULL) return NULL; |
---|
994 | poly result=a; |
---|
995 | poly prev=NULL; |
---|
996 | int i; |
---|
997 | number inv=nInvers(pGetCoeff(b)); |
---|
998 | |
---|
999 | while (a!=NULL) |
---|
1000 | { |
---|
1001 | if (pDivisibleBy(b,a)) |
---|
1002 | { |
---|
1003 | for(i=(int)pVariables; i; i--) |
---|
1004 | pSubExp(a,i, pGetExp(b,i)); |
---|
1005 | pSubComp(a, pGetComp(b)); |
---|
1006 | pSetm(a); |
---|
1007 | prev=a; |
---|
1008 | pIter(a); |
---|
1009 | } |
---|
1010 | else |
---|
1011 | { |
---|
1012 | if (prev==NULL) |
---|
1013 | { |
---|
1014 | pDelete1(&result); |
---|
1015 | a=result; |
---|
1016 | } |
---|
1017 | else |
---|
1018 | { |
---|
1019 | pDelete1(&pNext(prev)); |
---|
1020 | a=pNext(prev); |
---|
1021 | } |
---|
1022 | } |
---|
1023 | } |
---|
1024 | pMultN(result,inv); |
---|
1025 | nDelete(&inv); |
---|
1026 | pDelete(&b); |
---|
1027 | return result; |
---|
1028 | } |
---|
1029 | |
---|
1030 | /*2 |
---|
1031 | * returns the LCM of the head terms of a and b in *m |
---|
1032 | */ |
---|
1033 | void pLcm(poly a, poly b, poly m) |
---|
1034 | { |
---|
1035 | int i; |
---|
1036 | for (i=pVariables; i; i--) |
---|
1037 | { |
---|
1038 | pSetExp(m,i, max( pGetExp(a,i), pGetExp(b,i))); |
---|
1039 | } |
---|
1040 | pSetComp(m, max(pGetComp(a), pGetComp(b))); |
---|
1041 | } |
---|
1042 | |
---|
1043 | /*2 |
---|
1044 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
1045 | */ |
---|
1046 | poly pmInit(char *st, BOOLEAN &ok) |
---|
1047 | { |
---|
1048 | int i,j; |
---|
1049 | ok=FALSE; |
---|
1050 | BOOLEAN b=FALSE; |
---|
1051 | poly rc = pInit(); |
---|
1052 | char *s = nRead(st,&(rc->coef)); |
---|
1053 | if (s==st) |
---|
1054 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
1055 | { |
---|
1056 | j = rIsRingVar(s); |
---|
1057 | if (j >= 0) |
---|
1058 | { |
---|
1059 | pIncrExp(rc,1+j); |
---|
1060 | goto done; |
---|
1061 | } |
---|
1062 | } |
---|
1063 | else |
---|
1064 | b=TRUE; |
---|
1065 | while (*s!='\0') |
---|
1066 | { |
---|
1067 | char ss[2]; |
---|
1068 | ss[0] = *s++; |
---|
1069 | ss[1] = '\0'; |
---|
1070 | j = rIsRingVar(ss); |
---|
1071 | if (j >= 0) |
---|
1072 | { |
---|
1073 | s = eati(s,&i); |
---|
1074 | pAddExp(rc,1+j, (Exponent_t)i); |
---|
1075 | } |
---|
1076 | else |
---|
1077 | { |
---|
1078 | if ((s!=st)&&isdigit(st[0])) |
---|
1079 | { |
---|
1080 | errorreported=TRUE; |
---|
1081 | } |
---|
1082 | pDelete(&rc); |
---|
1083 | return NULL; |
---|
1084 | } |
---|
1085 | } |
---|
1086 | done: |
---|
1087 | ok=!errorreported; |
---|
1088 | if (nIsZero(pGetCoeff(rc))) pDelete1(&rc); |
---|
1089 | else |
---|
1090 | { |
---|
1091 | pSetm(rc); |
---|
1092 | } |
---|
1093 | return rc; |
---|
1094 | } |
---|
1095 | |
---|
1096 | /*2 |
---|
1097 | *make p homgeneous by multiplying the monomials by powers of x_varnum |
---|
1098 | */ |
---|
1099 | poly pHomogen (poly p, int varnum) |
---|
1100 | { |
---|
1101 | poly q=NULL; |
---|
1102 | poly res; |
---|
1103 | int o,ii; |
---|
1104 | |
---|
1105 | if (p!=NULL) |
---|
1106 | { |
---|
1107 | if ((varnum < 1) || (varnum > pVariables)) |
---|
1108 | { |
---|
1109 | return NULL; |
---|
1110 | } |
---|
1111 | o=pWTotaldegree(p); |
---|
1112 | q=pNext(p); |
---|
1113 | while (q != NULL) |
---|
1114 | { |
---|
1115 | ii=pWTotaldegree(q); |
---|
1116 | if (ii>o) o=ii; |
---|
1117 | pIter(q); |
---|
1118 | } |
---|
1119 | q = pCopy(p); |
---|
1120 | res = q; |
---|
1121 | while (q != NULL) |
---|
1122 | { |
---|
1123 | ii = o-pWTotaldegree(q); |
---|
1124 | if (ii!=0) |
---|
1125 | { |
---|
1126 | pAddExp(q,varnum, (Exponent_t)ii); |
---|
1127 | pSetm(q); |
---|
1128 | } |
---|
1129 | pIter(q); |
---|
1130 | } |
---|
1131 | q = pOrdPolyInsertSetm(res); |
---|
1132 | } |
---|
1133 | return q; |
---|
1134 | } |
---|
1135 | |
---|
1136 | |
---|
1137 | /*2 |
---|
1138 | *replaces the maximal powers of the leading monomial of p2 in p1 by |
---|
1139 | *the same powers of n, utility for dehomogenization |
---|
1140 | */ |
---|
1141 | poly pDehomogen (poly p1,poly p2,number n) |
---|
1142 | { |
---|
1143 | polyset P; |
---|
1144 | int SizeOfSet=5; |
---|
1145 | int i; |
---|
1146 | poly p; |
---|
1147 | number nn; |
---|
1148 | |
---|
1149 | P = (polyset)Alloc0(5*sizeof(poly)); |
---|
1150 | //for (i=0; i<5; i++) |
---|
1151 | //{ |
---|
1152 | // P[i] = NULL; |
---|
1153 | //} |
---|
1154 | pCancelPolyByMonom(p1,p2,&P,&SizeOfSet); |
---|
1155 | p = P[0]; |
---|
1156 | //P[0] = NULL ;// for safety, may be remoeved later |
---|
1157 | for (i=1; i<SizeOfSet; i++) |
---|
1158 | { |
---|
1159 | if (P[i] != NULL) |
---|
1160 | { |
---|
1161 | nPower(n,i,&nn); |
---|
1162 | pMultN(P[i],nn); |
---|
1163 | p = pAdd(p,P[i]); |
---|
1164 | //P[i] =NULL; // for safety, may be removed later |
---|
1165 | nDelete(&nn); |
---|
1166 | } |
---|
1167 | } |
---|
1168 | Free((ADDRESS)P,SizeOfSet*sizeof(poly)); |
---|
1169 | return p; |
---|
1170 | } |
---|
1171 | |
---|
1172 | /*4 |
---|
1173 | *Returns the exponent of the maximal power of the leading monomial of |
---|
1174 | *p2 in that of p1 |
---|
1175 | */ |
---|
1176 | static int pGetMaxPower (poly p1,poly p2) |
---|
1177 | { |
---|
1178 | int i,k,res = 32000; /*a very large integer*/ |
---|
1179 | |
---|
1180 | if (p1 == NULL) return 0; |
---|
1181 | for (i=1; i<=pVariables; i++) |
---|
1182 | { |
---|
1183 | if ( pGetExp(p2,i) != 0) |
---|
1184 | { |
---|
1185 | k = pGetExp(p1,i) / pGetExp(p2,i); |
---|
1186 | if (k < res) res = k; |
---|
1187 | } |
---|
1188 | } |
---|
1189 | return res; |
---|
1190 | } |
---|
1191 | |
---|
1192 | /*2 |
---|
1193 | *Returns as i-th entry of P the coefficient of the (i-1) power of |
---|
1194 | *the leading monomial of p2 in p1 |
---|
1195 | */ |
---|
1196 | void pCancelPolyByMonom (poly p1,poly p2,polyset * P,int * SizeOfSet) |
---|
1197 | { |
---|
1198 | int maxPow; |
---|
1199 | poly p,qp,Coeff; |
---|
1200 | |
---|
1201 | if (*P == NULL) |
---|
1202 | { |
---|
1203 | *P = (polyset) Alloc(5*sizeof(poly)); |
---|
1204 | *SizeOfSet = 5; |
---|
1205 | } |
---|
1206 | p = pCopy(p1); |
---|
1207 | while (p != NULL) |
---|
1208 | { |
---|
1209 | qp = p->next; |
---|
1210 | p->next = NULL; |
---|
1211 | maxPow = pGetMaxPower(p,p2); |
---|
1212 | Coeff = pDivByMonom(p,p2); |
---|
1213 | if (maxPow > *SizeOfSet) |
---|
1214 | { |
---|
1215 | pEnlargeSet(P,*SizeOfSet,maxPow+1-*SizeOfSet); |
---|
1216 | *SizeOfSet = maxPow+1; |
---|
1217 | } |
---|
1218 | (*P)[maxPow] = pAdd((*P)[maxPow],Coeff); |
---|
1219 | pDelete(&p); |
---|
1220 | p = qp; |
---|
1221 | } |
---|
1222 | } |
---|
1223 | |
---|
1224 | /*2 |
---|
1225 | *returns the leading monomial of p1 divided by the maximal power of that |
---|
1226 | *of p2 |
---|
1227 | */ |
---|
1228 | poly pDivByMonom (poly p1,poly p2) |
---|
1229 | { |
---|
1230 | int k, i; |
---|
1231 | |
---|
1232 | if (p1 == NULL) return NULL; |
---|
1233 | k = pGetMaxPower(p1,p2); |
---|
1234 | if (k == 0) |
---|
1235 | return pHead(p1); |
---|
1236 | else |
---|
1237 | { |
---|
1238 | number n; |
---|
1239 | poly p = pInit(); |
---|
1240 | |
---|
1241 | p->next = NULL; |
---|
1242 | for (i=1; i<=pVariables; i++) |
---|
1243 | { |
---|
1244 | pSetExp(p,i, pGetExp(p1,i)-k* pGetExp(p2,i)); |
---|
1245 | } |
---|
1246 | nPower(p2->coef,k,&n); |
---|
1247 | pSetCoeff0(p,nDiv(p1->coef,n)); |
---|
1248 | nDelete(&n); |
---|
1249 | pSetm(p); |
---|
1250 | return p; |
---|
1251 | } |
---|
1252 | } |
---|
1253 | /*----------utilities for syzygies--------------*/ |
---|
1254 | poly pTakeOutComp(poly * p, int k) |
---|
1255 | { |
---|
1256 | poly q = *p,qq=NULL,result = NULL; |
---|
1257 | |
---|
1258 | if (q==NULL) return NULL; |
---|
1259 | if (pGetComp(q)==k) |
---|
1260 | { |
---|
1261 | result = q; |
---|
1262 | while ((q!=NULL) && (pGetComp(q)==k)) |
---|
1263 | { |
---|
1264 | pSetComp(q,0); |
---|
1265 | qq = q; |
---|
1266 | pIter(q); |
---|
1267 | } |
---|
1268 | *p = q; |
---|
1269 | pNext(qq) = NULL; |
---|
1270 | } |
---|
1271 | if (q==NULL) return result; |
---|
1272 | if (pGetComp(q) > k) pDecrComp(q); |
---|
1273 | poly pNext_q; |
---|
1274 | while ((pNext_q=pNext(q))!=NULL) |
---|
1275 | { |
---|
1276 | if (pGetComp(pNext_q)==k) |
---|
1277 | { |
---|
1278 | if (result==NULL) |
---|
1279 | { |
---|
1280 | result = pNext_q; |
---|
1281 | qq = result; |
---|
1282 | } |
---|
1283 | else |
---|
1284 | { |
---|
1285 | pNext(qq) = pNext_q; |
---|
1286 | pIter(qq); |
---|
1287 | } |
---|
1288 | pNext(q) = pNext(pNext_q); |
---|
1289 | pNext(qq) =NULL; |
---|
1290 | pSetComp(qq,0); |
---|
1291 | } |
---|
1292 | else |
---|
1293 | { |
---|
1294 | /*pIter(q);*/ q=pNext_q; |
---|
1295 | if (pGetComp(q) > k) pDecrComp(q); |
---|
1296 | } |
---|
1297 | } |
---|
1298 | return result; |
---|
1299 | } |
---|
1300 | |
---|
1301 | // Splits *p into two polys: *q which consists of all monoms with |
---|
1302 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
1303 | void pTakeOutComp(poly *r_p, Exponent_t comp, poly *r_q, int *lq) |
---|
1304 | { |
---|
1305 | spolyrec pp, qq; |
---|
1306 | poly p, q, p_prev; |
---|
1307 | int l = 0; |
---|
1308 | |
---|
1309 | #ifdef HAVE_ASSUME |
---|
1310 | int lp = pLength(*r_p); |
---|
1311 | #endif |
---|
1312 | |
---|
1313 | pNext(&pp) = *r_p; |
---|
1314 | p = *r_p; |
---|
1315 | p_prev = &pp; |
---|
1316 | q = &qq; |
---|
1317 | |
---|
1318 | while(p != NULL) |
---|
1319 | { |
---|
1320 | while (pGetComp(p) == comp) |
---|
1321 | { |
---|
1322 | pNext(q) = p; |
---|
1323 | pIter(q); |
---|
1324 | pSetComp(p, 0); |
---|
1325 | pIter(p); |
---|
1326 | l++; |
---|
1327 | if (p == NULL) |
---|
1328 | { |
---|
1329 | pNext(p_prev) = NULL; |
---|
1330 | goto Finish; |
---|
1331 | } |
---|
1332 | } |
---|
1333 | pNext(p_prev) = p; |
---|
1334 | p_prev = p; |
---|
1335 | pIter(p); |
---|
1336 | } |
---|
1337 | |
---|
1338 | Finish: |
---|
1339 | pNext(q) = NULL; |
---|
1340 | *r_p = pNext(&pp); |
---|
1341 | *r_q = pNext(&qq); |
---|
1342 | *lq = l; |
---|
1343 | #ifdef HAVE_ASSUME |
---|
1344 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
1345 | #endif |
---|
1346 | pTest(*r_p); |
---|
1347 | pTest(*r_q); |
---|
1348 | } |
---|
1349 | |
---|
1350 | void pDecrOrdTakeOutComp(poly *r_p, Exponent_t comp, Order_t order, |
---|
1351 | poly *r_q, int *lq) |
---|
1352 | { |
---|
1353 | spolyrec pp, qq; |
---|
1354 | poly p, q, p_prev; |
---|
1355 | int l = 0; |
---|
1356 | |
---|
1357 | pNext(&pp) = *r_p; |
---|
1358 | p = *r_p; |
---|
1359 | p_prev = &pp; |
---|
1360 | q = &qq; |
---|
1361 | |
---|
1362 | #ifdef HAVE_ASSUME |
---|
1363 | if (p != NULL) |
---|
1364 | { |
---|
1365 | while (pNext(p) != NULL) |
---|
1366 | { |
---|
1367 | assume(pGetOrder(p) >= pGetOrder(pNext(p))); |
---|
1368 | pIter(p); |
---|
1369 | } |
---|
1370 | } |
---|
1371 | p = *r_p; |
---|
1372 | #endif |
---|
1373 | |
---|
1374 | while (p != NULL && pGetOrder(p) > order) pIter(p); |
---|
1375 | |
---|
1376 | while(p != NULL && pGetOrder(p) == order) |
---|
1377 | { |
---|
1378 | while (pGetComp(p) == comp) |
---|
1379 | { |
---|
1380 | pNext(q) = p; |
---|
1381 | pIter(q); |
---|
1382 | pIter(p); |
---|
1383 | pSetComp(p, 0); |
---|
1384 | l++; |
---|
1385 | if (p == NULL || pGetOrder(p) != order) |
---|
1386 | { |
---|
1387 | pNext(p_prev) = p; |
---|
1388 | goto Finish; |
---|
1389 | } |
---|
1390 | } |
---|
1391 | pNext(p_prev) = p; |
---|
1392 | p_prev = p; |
---|
1393 | pIter(p); |
---|
1394 | } |
---|
1395 | |
---|
1396 | Finish: |
---|
1397 | pNext(q) = NULL; |
---|
1398 | *r_p = pNext(&pp); |
---|
1399 | *r_q = pNext(&qq); |
---|
1400 | *lq = l; |
---|
1401 | } |
---|
1402 | |
---|
1403 | #if 1 |
---|
1404 | poly pTakeOutComp1(poly * p, int k) |
---|
1405 | { |
---|
1406 | poly q = *p; |
---|
1407 | |
---|
1408 | if (q==NULL) return NULL; |
---|
1409 | |
---|
1410 | poly qq=NULL,result = NULL; |
---|
1411 | |
---|
1412 | if (pGetComp(q)==k) |
---|
1413 | { |
---|
1414 | result = q; /* *p */ |
---|
1415 | while ((q!=NULL) && (pGetComp(q)==k)) |
---|
1416 | { |
---|
1417 | pSetComp(q,0); |
---|
1418 | qq = q; |
---|
1419 | pIter(q); |
---|
1420 | } |
---|
1421 | *p = q; |
---|
1422 | pNext(qq) = NULL; |
---|
1423 | } |
---|
1424 | if (q==NULL) return result; |
---|
1425 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
1426 | while (pNext(q)!=NULL) |
---|
1427 | { |
---|
1428 | if (pGetComp(pNext(q))==k) |
---|
1429 | { |
---|
1430 | if (result==NULL) |
---|
1431 | { |
---|
1432 | result = pNext(q); |
---|
1433 | qq = result; |
---|
1434 | } |
---|
1435 | else |
---|
1436 | { |
---|
1437 | pNext(qq) = pNext(q); |
---|
1438 | pIter(qq); |
---|
1439 | } |
---|
1440 | pNext(q) = pNext(pNext(q)); |
---|
1441 | pNext(qq) =NULL; |
---|
1442 | pSetComp(qq,0); |
---|
1443 | } |
---|
1444 | else |
---|
1445 | { |
---|
1446 | pIter(q); |
---|
1447 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
1448 | } |
---|
1449 | } |
---|
1450 | return result; |
---|
1451 | } |
---|
1452 | #endif |
---|
1453 | |
---|
1454 | void pDeleteComp(poly * p,int k) |
---|
1455 | { |
---|
1456 | poly q; |
---|
1457 | |
---|
1458 | while ((*p!=NULL) && (pGetComp(*p)==k)) pDelete1(p); |
---|
1459 | if (*p==NULL) return; |
---|
1460 | q = *p; |
---|
1461 | if (pGetComp(q)>k) pDecrComp(q); |
---|
1462 | while (pNext(q)!=NULL) |
---|
1463 | { |
---|
1464 | if (pGetComp(pNext(q))==k) |
---|
1465 | pDelete1(&(pNext(q))); |
---|
1466 | else |
---|
1467 | { |
---|
1468 | pIter(q); |
---|
1469 | if (pGetComp(q)>k) pDecrComp(q); |
---|
1470 | } |
---|
1471 | } |
---|
1472 | } |
---|
1473 | /*----------end of utilities for syzygies--------------*/ |
---|
1474 | |
---|
1475 | /*2 |
---|
1476 | * pair has no common factor ? or is no polynomial |
---|
1477 | */ |
---|
1478 | BOOLEAN pHasNotCF(poly p1, poly p2) |
---|
1479 | { |
---|
1480 | |
---|
1481 | if (pGetComp(p1) > 0 || pGetComp(p2) > 0) |
---|
1482 | return FALSE; |
---|
1483 | int i = 1; |
---|
1484 | loop |
---|
1485 | { |
---|
1486 | if ((pGetExp(p1, i) > 0) && (pGetExp(p2, i) > 0)) return FALSE; |
---|
1487 | if (i == pVariables) return TRUE; |
---|
1488 | i++; |
---|
1489 | } |
---|
1490 | } |
---|
1491 | |
---|
1492 | |
---|
1493 | /*2 |
---|
1494 | *should return 1 if p divides q and p<q, |
---|
1495 | * -1 if q divides p and q<p |
---|
1496 | * 0 otherwise |
---|
1497 | */ |
---|
1498 | int pDivComp(poly p, poly q) |
---|
1499 | { |
---|
1500 | if (pGetComp(p) == pGetComp(q)) |
---|
1501 | { |
---|
1502 | int i=pVariables; |
---|
1503 | long d; |
---|
1504 | BOOLEAN a=FALSE, b=FALSE; |
---|
1505 | for (; i>0; i--) |
---|
1506 | { |
---|
1507 | d = pGetExpDiff(p, q, i); |
---|
1508 | if (d) |
---|
1509 | { |
---|
1510 | if (d < 0) |
---|
1511 | { |
---|
1512 | if (b) return 0; |
---|
1513 | a =TRUE; |
---|
1514 | } |
---|
1515 | else |
---|
1516 | { |
---|
1517 | if (a) return 0; |
---|
1518 | b = TRUE; |
---|
1519 | } |
---|
1520 | } |
---|
1521 | } |
---|
1522 | if (a) return 1; |
---|
1523 | else if (b) return -1; |
---|
1524 | } |
---|
1525 | return 0; |
---|
1526 | } |
---|
1527 | /*2 |
---|
1528 | *divides p1 by its leading monomial |
---|
1529 | */ |
---|
1530 | void pNorm(poly p1) |
---|
1531 | { |
---|
1532 | poly h; |
---|
1533 | number k, c; |
---|
1534 | |
---|
1535 | if (p1!=NULL) |
---|
1536 | { |
---|
1537 | if (!nIsOne(pGetCoeff(p1))) |
---|
1538 | { |
---|
1539 | nNormalize(pGetCoeff(p1)); |
---|
1540 | k=pGetCoeff(p1); |
---|
1541 | c = nInit(1); |
---|
1542 | pSetCoeff0(p1,c); |
---|
1543 | h = pNext(p1); |
---|
1544 | while (h!=NULL) |
---|
1545 | { |
---|
1546 | c=nDiv(pGetCoeff(h),k); |
---|
1547 | if (!nIsOne(c)) nNormalize(c); |
---|
1548 | pSetCoeff(h,c); |
---|
1549 | pIter(h); |
---|
1550 | } |
---|
1551 | nDelete(&k); |
---|
1552 | } |
---|
1553 | else |
---|
1554 | { |
---|
1555 | h = pNext(p1); |
---|
1556 | while (h!=NULL) |
---|
1557 | { |
---|
1558 | nNormalize(pGetCoeff(h)); |
---|
1559 | pIter(h); |
---|
1560 | } |
---|
1561 | } |
---|
1562 | } |
---|
1563 | } |
---|
1564 | |
---|
1565 | /*2 |
---|
1566 | *normalize all coeffizients |
---|
1567 | */ |
---|
1568 | void pNormalize(poly p) |
---|
1569 | { |
---|
1570 | while (p!=NULL) |
---|
1571 | { |
---|
1572 | nTest(pGetCoeff(p)); |
---|
1573 | nNormalize(pGetCoeff(p)); |
---|
1574 | pIter(p); |
---|
1575 | } |
---|
1576 | } |
---|
1577 | |
---|
1578 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
1579 | // Poly with Exp(n) != 0 is reversed |
---|
1580 | static void pSplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero) |
---|
1581 | { |
---|
1582 | if (p == NULL) |
---|
1583 | { |
---|
1584 | *non_zero = NULL; |
---|
1585 | *zero = NULL; |
---|
1586 | return; |
---|
1587 | } |
---|
1588 | spolyrec sz; |
---|
1589 | poly z, n_z, next; |
---|
1590 | z = &sz; |
---|
1591 | n_z = NULL; |
---|
1592 | |
---|
1593 | while(p != NULL) |
---|
1594 | { |
---|
1595 | next = pNext(p); |
---|
1596 | if (pGetExp(p, n) == 0) |
---|
1597 | { |
---|
1598 | pNext(z) = p; |
---|
1599 | pIter(z); |
---|
1600 | } |
---|
1601 | else |
---|
1602 | { |
---|
1603 | pNext(p) = n_z; |
---|
1604 | n_z = p; |
---|
1605 | } |
---|
1606 | p = next; |
---|
1607 | } |
---|
1608 | pNext(z) = NULL; |
---|
1609 | *zero = pNext(&sz); |
---|
1610 | *non_zero = n_z; |
---|
1611 | return; |
---|
1612 | } |
---|
1613 | |
---|
1614 | /*3 |
---|
1615 | * substitute the n-th variable by 1 in p |
---|
1616 | * destroy p |
---|
1617 | */ |
---|
1618 | static poly pSubst1 (poly p,int n) |
---|
1619 | { |
---|
1620 | poly qq,result = NULL; |
---|
1621 | poly zero, non_zero; |
---|
1622 | |
---|
1623 | // reverse, so that add is likely to be linear |
---|
1624 | pSplitAndReversePoly(p, n, &non_zero, &zero); |
---|
1625 | |
---|
1626 | while (non_zero != NULL) |
---|
1627 | { |
---|
1628 | assume(pGetExp(non_zero, n) != 0); |
---|
1629 | qq = non_zero; |
---|
1630 | pIter(non_zero); |
---|
1631 | qq->next = NULL; |
---|
1632 | pSetExp(qq,n,0); |
---|
1633 | pSetm(qq); |
---|
1634 | result = pAdd(result,qq); |
---|
1635 | } |
---|
1636 | p = pAdd(result, zero); |
---|
1637 | pTest(p); |
---|
1638 | return p; |
---|
1639 | } |
---|
1640 | |
---|
1641 | /*3 |
---|
1642 | * substitute the n-th variable by number e in p |
---|
1643 | * destroy p |
---|
1644 | */ |
---|
1645 | static poly pSubst2 (poly p,int n, number e) |
---|
1646 | { |
---|
1647 | assume( ! nIsZero(e) ); |
---|
1648 | poly qq,result = NULL; |
---|
1649 | number nn, nm; |
---|
1650 | poly zero, non_zero; |
---|
1651 | |
---|
1652 | // reverse, so that add is likely to be linear |
---|
1653 | pSplitAndReversePoly(p, n, &non_zero, &zero); |
---|
1654 | |
---|
1655 | while (non_zero != NULL) |
---|
1656 | { |
---|
1657 | assume(pGetExp(non_zero, n) != 0); |
---|
1658 | qq = non_zero; |
---|
1659 | pIter(non_zero); |
---|
1660 | qq->next = NULL; |
---|
1661 | nPower(e, pGetExp(qq, n), &nn); |
---|
1662 | nm = nMult(nn, pGetCoeff(qq)); |
---|
1663 | pSetCoeff(qq, nm); |
---|
1664 | nDelete(&nn); |
---|
1665 | pSetExp(qq, n, 0); |
---|
1666 | pSetm(qq); |
---|
1667 | result = pAdd(result,qq); |
---|
1668 | } |
---|
1669 | p = pAdd(result, zero); |
---|
1670 | pTest(p); |
---|
1671 | return p; |
---|
1672 | } |
---|
1673 | |
---|
1674 | |
---|
1675 | /* delete monoms whose n-th exponent is different from zero */ |
---|
1676 | poly pSubst0(poly p, int n) |
---|
1677 | { |
---|
1678 | spolyrec res; |
---|
1679 | poly h = &res; |
---|
1680 | pNext(h) = p; |
---|
1681 | |
---|
1682 | while (pNext(h)!=NULL) |
---|
1683 | { |
---|
1684 | if (pGetExp(pNext(h),n)!=0) |
---|
1685 | { |
---|
1686 | pDelete1(&pNext(h)); |
---|
1687 | } |
---|
1688 | else |
---|
1689 | { |
---|
1690 | pIter(h); |
---|
1691 | } |
---|
1692 | } |
---|
1693 | pTest(pNext(&res)); |
---|
1694 | return pNext(&res); |
---|
1695 | } |
---|
1696 | |
---|
1697 | /*2 |
---|
1698 | * substitute the n-th variable by e in p |
---|
1699 | * destroy p |
---|
1700 | */ |
---|
1701 | poly pSubst(poly p, int n, poly e) |
---|
1702 | { |
---|
1703 | if (e == NULL) return pSubst0(p, n); |
---|
1704 | |
---|
1705 | if (pIsConstant(e)) |
---|
1706 | { |
---|
1707 | if (nIsOne(pGetCoeff(e))) return pSubst1(p,n); |
---|
1708 | else return pSubst2(p, n, pGetCoeff(e)); |
---|
1709 | } |
---|
1710 | |
---|
1711 | int exponent,i; |
---|
1712 | poly h, res, m; |
---|
1713 | Exponent_t *me,*ee; |
---|
1714 | number nu,nu1; |
---|
1715 | |
---|
1716 | me=(Exponent_t *)Alloc((pVariables+1)*sizeof(Exponent_t)); |
---|
1717 | ee=(Exponent_t *)Alloc((pVariables+1)*sizeof(Exponent_t)); |
---|
1718 | if (e!=NULL) pGetExpV(e,ee); |
---|
1719 | res=NULL; |
---|
1720 | h=p; |
---|
1721 | while (h!=NULL) |
---|
1722 | { |
---|
1723 | if ((e!=NULL) || (pGetExp(h,n)==0)) |
---|
1724 | { |
---|
1725 | m=pHead(h); |
---|
1726 | pGetExpV(m,me); |
---|
1727 | exponent=me[n]; |
---|
1728 | me[n]=0; |
---|
1729 | for(i=pVariables;i>0;i--) |
---|
1730 | me[i]+=exponent*ee[i]; |
---|
1731 | pSetExpV(m,me); |
---|
1732 | if (e!=NULL) |
---|
1733 | { |
---|
1734 | nPower(pGetCoeff(e),exponent,&nu); |
---|
1735 | nu1=nMult(pGetCoeff(m),nu); |
---|
1736 | nDelete(&nu); |
---|
1737 | pSetCoeff(m,nu1); |
---|
1738 | } |
---|
1739 | res=pAdd(res,m); |
---|
1740 | } |
---|
1741 | pDelete1(&h); |
---|
1742 | } |
---|
1743 | Free((ADDRESS)me,(pVariables+1)*sizeof(Exponent_t)); |
---|
1744 | Free((ADDRESS)ee,(pVariables+1)*sizeof(Exponent_t)); |
---|
1745 | return res; |
---|
1746 | } |
---|
1747 | |
---|
1748 | BOOLEAN pCompareChain (poly p,poly p1,poly p2,poly lcm) |
---|
1749 | { |
---|
1750 | int k, j; |
---|
1751 | |
---|
1752 | if (lcm==NULL) return FALSE; |
---|
1753 | |
---|
1754 | for (j=pVariables; j; j--) |
---|
1755 | if ( pGetExp(p,j) > pGetExp(lcm,j)) return FALSE; |
---|
1756 | if ( pGetComp(p) != pGetComp(lcm)) return FALSE; |
---|
1757 | for (j=pVariables; j; j--) |
---|
1758 | { |
---|
1759 | if (pGetExp(p1,j)!=pGetExp(lcm,j)) |
---|
1760 | { |
---|
1761 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
1762 | { |
---|
1763 | for (k=pVariables; k>j; k--) |
---|
1764 | { |
---|
1765 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1766 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
1767 | return TRUE; |
---|
1768 | } |
---|
1769 | for (k=j-1; k; k--) |
---|
1770 | { |
---|
1771 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1772 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
1773 | return TRUE; |
---|
1774 | } |
---|
1775 | return FALSE; |
---|
1776 | } |
---|
1777 | } |
---|
1778 | else if (pGetExp(p2,j)!=pGetExp(lcm,j)) |
---|
1779 | { |
---|
1780 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
1781 | { |
---|
1782 | for (k=pVariables; k>j; k--) |
---|
1783 | { |
---|
1784 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1785 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
1786 | return TRUE; |
---|
1787 | } |
---|
1788 | for (k=j-1; k!=0 ; k--) |
---|
1789 | { |
---|
1790 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1791 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
1792 | return TRUE; |
---|
1793 | } |
---|
1794 | return FALSE; |
---|
1795 | } |
---|
1796 | } |
---|
1797 | } |
---|
1798 | return FALSE; |
---|
1799 | } |
---|
1800 | |
---|
1801 | int pWeight(int i) |
---|
1802 | { |
---|
1803 | if ((firstwv==NULL) || (i>firstBlockEnds)) |
---|
1804 | { |
---|
1805 | return 1; |
---|
1806 | } |
---|
1807 | return firstwv[i-1]; |
---|
1808 | } |
---|
1809 | |
---|