1 | // emacs edit mode for this file is -*- C++ -*- |
---|
2 | /**************************************** |
---|
3 | * Computer Algebra System SINGULAR * |
---|
4 | ****************************************/ |
---|
5 | /* |
---|
6 | * ABSTRACT: interface between Singular and factory |
---|
7 | */ |
---|
8 | |
---|
9 | //#define FACTORIZE2_DEBUG |
---|
10 | |
---|
11 | #include "misc/auxiliary.h" |
---|
12 | #include "clapsing.h" |
---|
13 | |
---|
14 | #include "factory/factory.h" |
---|
15 | #include "factory/cf_roots.h" |
---|
16 | |
---|
17 | #include "coeffs/numbers.h" |
---|
18 | #include "coeffs/coeffs.h" |
---|
19 | #include "coeffs/bigintmat.h" |
---|
20 | |
---|
21 | #include "monomials/ring.h" |
---|
22 | #include "simpleideals.h" |
---|
23 | #include "polys/flintconv.h" |
---|
24 | #include "polys/flint_mpoly.h" |
---|
25 | |
---|
26 | #ifdef HAVE_NTL |
---|
27 | #include <NTL/config.h> |
---|
28 | #ifdef NTL_STD_CXX |
---|
29 | #ifdef NOSTREAMIO |
---|
30 | # ifdef HAVE_IOSTREAM |
---|
31 | # include <iostream> |
---|
32 | # define OSTREAM std::ostream |
---|
33 | # define ISTREAM std::istream |
---|
34 | # elif defined(HAVE_IOSTREAM_H) |
---|
35 | # include <iostream.h> |
---|
36 | # define OSTREAM ostream |
---|
37 | # define ISTREAM istream |
---|
38 | # endif |
---|
39 | #endif /* ! NOSTREAMIO */ |
---|
40 | #endif |
---|
41 | #include <NTL/mat_ZZ.h> |
---|
42 | #include <NTL/mat_lzz_p.h> |
---|
43 | |
---|
44 | #ifdef NTL_CLIENT // in <NTL/tools.h>: using of name space NTL |
---|
45 | NTL_CLIENT |
---|
46 | #endif |
---|
47 | |
---|
48 | #endif |
---|
49 | |
---|
50 | //#include "polys.h" |
---|
51 | #define TRANSEXT_PRIVATES |
---|
52 | |
---|
53 | #include "ext_fields/transext.h" |
---|
54 | |
---|
55 | |
---|
56 | #include "clapconv.h" |
---|
57 | |
---|
58 | #include "polys/monomials/p_polys.h" |
---|
59 | #include "polys/monomials/ring.h" |
---|
60 | #include "polys/simpleideals.h" |
---|
61 | #include "misc/intvec.h" |
---|
62 | #include "polys/matpol.h" |
---|
63 | #include "coeffs/bigintmat.h" |
---|
64 | |
---|
65 | |
---|
66 | void out_cf(const char *s1,const CanonicalForm &f,const char *s2); |
---|
67 | |
---|
68 | poly singclap_gcd_r ( poly f, poly g, const ring r ) |
---|
69 | { |
---|
70 | poly res=NULL; |
---|
71 | |
---|
72 | assume(f!=NULL); |
---|
73 | assume(g!=NULL); |
---|
74 | |
---|
75 | if(pNext(f)==NULL) |
---|
76 | { |
---|
77 | return p_GcdMon(f,g,r); |
---|
78 | } |
---|
79 | else if(pNext(g)==NULL) |
---|
80 | { |
---|
81 | return p_GcdMon(g,f,r); |
---|
82 | } |
---|
83 | #ifdef HAVE_FLINT |
---|
84 | #if __FLINT_RELEASE >= 20503 |
---|
85 | if (rField_is_Zp(r) && (r->cf->ch>10)) |
---|
86 | { |
---|
87 | nmod_mpoly_ctx_t ctx; |
---|
88 | if (!convSingRFlintR(ctx,r)) |
---|
89 | { |
---|
90 | // leading coef. 1 |
---|
91 | return Flint_GCD_MP(f,pLength(f),g,pLength(g),ctx,r); |
---|
92 | } |
---|
93 | } |
---|
94 | else |
---|
95 | if (rField_is_Q(r)) |
---|
96 | { |
---|
97 | fmpq_mpoly_ctx_t ctx; |
---|
98 | if (!convSingRFlintR(ctx,r)) |
---|
99 | { |
---|
100 | // leading coef. positive, all coeffs in Z |
---|
101 | poly res=Flint_GCD_MP(f,pLength(f),g,pLength(g),ctx,r); |
---|
102 | res=p_Cleardenom(res,r); |
---|
103 | return res; |
---|
104 | } |
---|
105 | } |
---|
106 | else |
---|
107 | if (rField_is_Z(r)) |
---|
108 | { |
---|
109 | fmpz_mpoly_ctx_t ctx; |
---|
110 | if (!convSingRFlintR(ctx,r)) |
---|
111 | { |
---|
112 | // leading coef. positive, all coeffs in Z |
---|
113 | poly res=Flint_GCD_MP(f,pLength(f),g,pLength(g),ctx,r); |
---|
114 | return res; |
---|
115 | } |
---|
116 | } |
---|
117 | #endif |
---|
118 | #endif |
---|
119 | Off(SW_RATIONAL); |
---|
120 | if (rField_is_Q(r) || rField_is_Zp(r) || rField_is_Z(r) |
---|
121 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
122 | { |
---|
123 | setCharacteristic( rInternalChar(r) ); |
---|
124 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g, r ) ); |
---|
125 | res=convFactoryPSingP( gcd( F, G ) , r); |
---|
126 | if ( rField_is_Zp(r)) |
---|
127 | p_Norm(res,r); // leading coef. 1 |
---|
128 | else if (rField_is_Q(r) && (!n_GreaterZero(pGetCoeff(res),r->cf))) |
---|
129 | res = p_Neg(res,r); // leading coef. positive, all coeffs in Z |
---|
130 | } |
---|
131 | // and over Q(a) / Fp(a) |
---|
132 | else if ( r->cf->extRing!=NULL ) |
---|
133 | { |
---|
134 | if ( rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
135 | else setCharacteristic( rInternalChar(r) ); |
---|
136 | if (r->cf->extRing->qideal!=NULL) |
---|
137 | { |
---|
138 | bool b1=isOn(SW_USE_QGCD); |
---|
139 | if ( rField_is_Q_a(r) ) On(SW_USE_QGCD); |
---|
140 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
141 | r->cf->extRing); |
---|
142 | Variable a=rootOf(mipo); |
---|
143 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
144 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
145 | res= convFactoryAPSingAP( gcd( F, G ),r ); |
---|
146 | prune (a); |
---|
147 | if (!b1) Off(SW_USE_QGCD); |
---|
148 | if ( rField_is_Zp_a(r)) p_Norm(res,r); // leading coef. 1 |
---|
149 | } |
---|
150 | else |
---|
151 | { |
---|
152 | convSingTrP(f,r); |
---|
153 | convSingTrP(g,r); |
---|
154 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
155 | res= convFactoryPSingTrP( gcd( F, G ),r ); |
---|
156 | } |
---|
157 | } |
---|
158 | else if (r->cf->convSingNFactoryN==ndConvSingNFactoryN) |
---|
159 | WerrorS( feNotImplemented ); |
---|
160 | else |
---|
161 | { // handle user type coeffs: |
---|
162 | setCharacteristic( rInternalChar(r) ); |
---|
163 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g, r ) ); |
---|
164 | res=convFactoryPSingP( gcd( F, G ) , r); |
---|
165 | } |
---|
166 | Off(SW_RATIONAL); |
---|
167 | return res; |
---|
168 | } |
---|
169 | |
---|
170 | poly singclap_gcd_and_divide ( poly& f, poly& g, const ring r) |
---|
171 | { |
---|
172 | poly res=NULL; |
---|
173 | |
---|
174 | if (g == NULL) |
---|
175 | { |
---|
176 | res= f; |
---|
177 | f=p_One (r); |
---|
178 | return res; |
---|
179 | } |
---|
180 | if (f==NULL) |
---|
181 | { |
---|
182 | res= g; |
---|
183 | g=p_One (r); |
---|
184 | return res; |
---|
185 | } |
---|
186 | if (pNext(g)==NULL) |
---|
187 | { |
---|
188 | poly G=p_GcdMon(g,f,r); |
---|
189 | if (!n_IsOne(pGetCoeff(G),r->cf) |
---|
190 | || (!p_IsConstant(G,r))) |
---|
191 | { |
---|
192 | f=p_Div_mm(f,G,r); |
---|
193 | g=p_Div_mm(g,G,r); |
---|
194 | } |
---|
195 | return G; |
---|
196 | } |
---|
197 | else if (pNext(f)==NULL) |
---|
198 | { |
---|
199 | poly G=p_GcdMon(f,g,r); |
---|
200 | if (!n_IsOne(pGetCoeff(G),r->cf) |
---|
201 | || (!p_IsConstant(G,r))) |
---|
202 | { |
---|
203 | f=p_Div_mm(f,G,r); |
---|
204 | g=p_Div_mm(g,G,r); |
---|
205 | } |
---|
206 | return G; |
---|
207 | } |
---|
208 | |
---|
209 | Off(SW_RATIONAL); |
---|
210 | CanonicalForm F,G,GCD; |
---|
211 | if (rField_is_Q(r) || (rField_is_Zp(r)) |
---|
212 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
213 | { |
---|
214 | bool b1=isOn(SW_USE_EZGCD_P); |
---|
215 | setCharacteristic( rInternalChar(r) ); |
---|
216 | F=convSingPFactoryP( f,r ); |
---|
217 | G=convSingPFactoryP( g,r ); |
---|
218 | GCD=gcd(F,G); |
---|
219 | if (!GCD.isOne()) |
---|
220 | { |
---|
221 | p_Delete(&f,r); |
---|
222 | p_Delete(&g,r); |
---|
223 | if (getCharacteristic() == 0) |
---|
224 | On (SW_RATIONAL); |
---|
225 | F /= GCD; |
---|
226 | G /= GCD; |
---|
227 | if (getCharacteristic() == 0) |
---|
228 | { |
---|
229 | CanonicalForm denF= bCommonDen (F); |
---|
230 | CanonicalForm denG= bCommonDen (G); |
---|
231 | G *= denG; |
---|
232 | F *= denF; |
---|
233 | Off (SW_RATIONAL); |
---|
234 | CanonicalForm gcddenFdenG= gcd (denG, denF); |
---|
235 | denG /= gcddenFdenG; |
---|
236 | denF /= gcddenFdenG; |
---|
237 | On (SW_RATIONAL); |
---|
238 | G *= denF; |
---|
239 | F *= denG; |
---|
240 | } |
---|
241 | f=convFactoryPSingP( F, r); |
---|
242 | g=convFactoryPSingP( G, r); |
---|
243 | } |
---|
244 | res=convFactoryPSingP( GCD , r); |
---|
245 | if (!b1) Off (SW_USE_EZGCD_P); |
---|
246 | } |
---|
247 | // and over Q(a) / Fp(a) |
---|
248 | else if ( r->cf->extRing ) |
---|
249 | { |
---|
250 | if ( rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
251 | else setCharacteristic( rInternalChar(r) ); |
---|
252 | if (r->cf->extRing->qideal!=NULL) |
---|
253 | { |
---|
254 | bool b1=isOn(SW_USE_QGCD); |
---|
255 | if ( rField_is_Q_a(r) ) On(SW_USE_QGCD); |
---|
256 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
257 | r->cf->extRing); |
---|
258 | Variable a=rootOf(mipo); |
---|
259 | F=( convSingAPFactoryAP( f,a,r ) ); |
---|
260 | G=( convSingAPFactoryAP( g,a,r ) ); |
---|
261 | GCD=gcd(F,G); |
---|
262 | if (!GCD.isOne()) |
---|
263 | { |
---|
264 | p_Delete(&f,r); |
---|
265 | p_Delete(&g,r); |
---|
266 | if (getCharacteristic() == 0) |
---|
267 | On (SW_RATIONAL); |
---|
268 | F /= GCD; |
---|
269 | G /= GCD; |
---|
270 | if (getCharacteristic() == 0) |
---|
271 | { |
---|
272 | CanonicalForm denF= bCommonDen (F); |
---|
273 | CanonicalForm denG= bCommonDen (G); |
---|
274 | G *= denG; |
---|
275 | F *= denF; |
---|
276 | Off (SW_RATIONAL); |
---|
277 | CanonicalForm gcddenFdenG= gcd (denG, denF); |
---|
278 | denG /= gcddenFdenG; |
---|
279 | denF /= gcddenFdenG; |
---|
280 | On (SW_RATIONAL); |
---|
281 | G *= denF; |
---|
282 | F *= denG; |
---|
283 | } |
---|
284 | f= convFactoryAPSingAP( F,r ); |
---|
285 | g= convFactoryAPSingAP( G,r ); |
---|
286 | } |
---|
287 | res= convFactoryAPSingAP( GCD,r ); |
---|
288 | prune (a); |
---|
289 | if (!b1) Off(SW_USE_QGCD); |
---|
290 | } |
---|
291 | else |
---|
292 | { |
---|
293 | F=( convSingTrPFactoryP( f,r ) ); |
---|
294 | G=( convSingTrPFactoryP( g,r ) ); |
---|
295 | GCD=gcd(F,G); |
---|
296 | if (!GCD.isOne()) |
---|
297 | { |
---|
298 | p_Delete(&f,r); |
---|
299 | p_Delete(&g,r); |
---|
300 | if (getCharacteristic() == 0) |
---|
301 | On (SW_RATIONAL); |
---|
302 | F /= GCD; |
---|
303 | G /= GCD; |
---|
304 | if (getCharacteristic() == 0) |
---|
305 | { |
---|
306 | CanonicalForm denF= bCommonDen (F); |
---|
307 | CanonicalForm denG= bCommonDen (G); |
---|
308 | G *= denG; |
---|
309 | F *= denF; |
---|
310 | Off (SW_RATIONAL); |
---|
311 | CanonicalForm gcddenFdenG= gcd (denG, denF); |
---|
312 | denG /= gcddenFdenG; |
---|
313 | denF /= gcddenFdenG; |
---|
314 | On (SW_RATIONAL); |
---|
315 | G *= denF; |
---|
316 | F *= denG; |
---|
317 | } |
---|
318 | f= convFactoryPSingTrP( F,r ); |
---|
319 | g= convFactoryPSingTrP( G,r ); |
---|
320 | } |
---|
321 | res= convFactoryPSingTrP( GCD,r ); |
---|
322 | } |
---|
323 | } |
---|
324 | else |
---|
325 | WerrorS( feNotImplemented ); |
---|
326 | Off(SW_RATIONAL); |
---|
327 | return res; |
---|
328 | } |
---|
329 | |
---|
330 | /*2 find the maximal exponent of var(i) in poly p*/ |
---|
331 | int pGetExp_Var(poly p, int i, const ring r) |
---|
332 | { |
---|
333 | int m=0; |
---|
334 | int mm; |
---|
335 | while (p!=NULL) |
---|
336 | { |
---|
337 | mm=p_GetExp(p,i,r); |
---|
338 | if (mm>m) m=mm; |
---|
339 | pIter(p); |
---|
340 | } |
---|
341 | return m; |
---|
342 | } |
---|
343 | |
---|
344 | // destroys f,g,x |
---|
345 | poly singclap_resultant ( poly f, poly g , poly x, const ring r) |
---|
346 | { |
---|
347 | poly res=NULL; |
---|
348 | int i=p_IsPurePower(x, r); |
---|
349 | if (i==0) |
---|
350 | { |
---|
351 | WerrorS("3rd argument must be a ring variable"); |
---|
352 | goto resultant_returns_res; |
---|
353 | } |
---|
354 | if ((f==NULL) || (g==NULL)) |
---|
355 | goto resultant_returns_res; |
---|
356 | // for now there is only the possibility to handle polynomials over |
---|
357 | // Q and Fp ... |
---|
358 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
359 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
360 | { |
---|
361 | Variable X(i); |
---|
362 | setCharacteristic( rInternalChar(r) ); |
---|
363 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
---|
364 | res=convFactoryPSingP( resultant( F, G, X),r ); |
---|
365 | Off(SW_RATIONAL); |
---|
366 | goto resultant_returns_res; |
---|
367 | } |
---|
368 | // and over Q(a) / Fp(a) |
---|
369 | else if (r->cf->extRing!=NULL) |
---|
370 | { |
---|
371 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
372 | else setCharacteristic( rInternalChar(r) ); |
---|
373 | Variable X(i+rPar(r)); |
---|
374 | if (r->cf->extRing->qideal!=NULL) |
---|
375 | { |
---|
376 | //Variable X(i); |
---|
377 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
378 | r->cf->extRing); |
---|
379 | Variable a=rootOf(mipo); |
---|
380 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
381 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
382 | res= convFactoryAPSingAP( resultant( F, G, X ),r ); |
---|
383 | prune (a); |
---|
384 | } |
---|
385 | else |
---|
386 | { |
---|
387 | //Variable X(i+rPar(currRing)); |
---|
388 | number nf,ng; |
---|
389 | p_Cleardenom_n(f,r,nf);p_Cleardenom_n(g,r,ng); |
---|
390 | int ef,eg; |
---|
391 | ef=pGetExp_Var(f,i,r); |
---|
392 | eg=pGetExp_Var(g,i,r); |
---|
393 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
394 | res= convFactoryPSingTrP( resultant( F, G, X ),r ); |
---|
395 | if ((nf!=NULL)&&(!n_IsOne(nf,r->cf))) |
---|
396 | { |
---|
397 | number n=n_Invers(nf,r->cf); |
---|
398 | while(eg>0) |
---|
399 | { |
---|
400 | res=__p_Mult_nn(res,n,r); |
---|
401 | eg--; |
---|
402 | } |
---|
403 | n_Delete(&n,r->cf); |
---|
404 | } |
---|
405 | n_Delete(&nf,r->cf); |
---|
406 | if ((ng!=NULL)&&(!n_IsOne(ng,r->cf))) |
---|
407 | { |
---|
408 | number n=n_Invers(ng,r->cf); |
---|
409 | while(ef>0) |
---|
410 | { |
---|
411 | res=__p_Mult_nn(res,n,r); |
---|
412 | ef--; |
---|
413 | } |
---|
414 | n_Delete(&n,r->cf); |
---|
415 | } |
---|
416 | n_Delete(&ng,r->cf); |
---|
417 | } |
---|
418 | Off(SW_RATIONAL); |
---|
419 | goto resultant_returns_res; |
---|
420 | } |
---|
421 | else |
---|
422 | WerrorS( feNotImplemented ); |
---|
423 | resultant_returns_res: |
---|
424 | p_Delete(&f,r); |
---|
425 | p_Delete(&g,r); |
---|
426 | p_Delete(&x,r); |
---|
427 | return res; |
---|
428 | } |
---|
429 | //poly singclap_resultant ( poly f, poly g , poly x) |
---|
430 | //{ |
---|
431 | // int i=pVar(x); |
---|
432 | // if (i==0) |
---|
433 | // { |
---|
434 | // WerrorS("ringvar expected"); |
---|
435 | // return NULL; |
---|
436 | // } |
---|
437 | // ideal I=idInit(1,1); |
---|
438 | // |
---|
439 | // // get the coeffs von f wrt. x: |
---|
440 | // I->m[0]=pCopy(f); |
---|
441 | // matrix ffi=mpCoeffs(I,i); |
---|
442 | // ffi->rank=1; |
---|
443 | // ffi->ncols=ffi->nrows; |
---|
444 | // ffi->nrows=1; |
---|
445 | // ideal fi=(ideal)ffi; |
---|
446 | // |
---|
447 | // // get the coeffs von g wrt. x: |
---|
448 | // I->m[0]=pCopy(g); |
---|
449 | // matrix ggi=mpCoeffs(I,i); |
---|
450 | // ggi->rank=1; |
---|
451 | // ggi->ncols=ggi->nrows; |
---|
452 | // ggi->nrows=1; |
---|
453 | // ideal gi=(ideal)ggi; |
---|
454 | // |
---|
455 | // // contruct the matrix: |
---|
456 | // int fn=IDELEMS(fi); //= deg(f,x)+1 |
---|
457 | // int gn=IDELEMS(gi); //= deg(g,x)+1 |
---|
458 | // matrix m=mpNew(fn+gn-2,fn+gn-2); |
---|
459 | // if(m==NULL) |
---|
460 | // { |
---|
461 | // return NULL; |
---|
462 | // } |
---|
463 | // |
---|
464 | // // enter the coeffs into m: |
---|
465 | // int j; |
---|
466 | // for(i=0;i<gn-1;i++) |
---|
467 | // { |
---|
468 | // for(j=0;j<fn;j++) |
---|
469 | // { |
---|
470 | // MATELEM(m,i+1,fn-j+i)=pCopy(fi->m[j]); |
---|
471 | // } |
---|
472 | // } |
---|
473 | // for(i=0;i<fn-1;i++) |
---|
474 | // { |
---|
475 | // for(j=0;j<gn;j++) |
---|
476 | // { |
---|
477 | // MATELEM(m,gn+i,gn-j+i)=pCopy(gi->m[j]); |
---|
478 | // } |
---|
479 | // } |
---|
480 | // |
---|
481 | // poly r=mpDet(m); |
---|
482 | // |
---|
483 | // idDelete(&fi); |
---|
484 | // idDelete(&gi); |
---|
485 | // idDelete((ideal *)&m); |
---|
486 | // return r; |
---|
487 | //} |
---|
488 | |
---|
489 | BOOLEAN singclap_extgcd ( poly f, poly g, poly &res, poly &pa, poly &pb , const ring r) |
---|
490 | { |
---|
491 | // for now there is only the possibility to handle univariate |
---|
492 | // polynomials over |
---|
493 | // Q and Fp ... |
---|
494 | res=NULL;pa=NULL;pb=NULL; |
---|
495 | On(SW_SYMMETRIC_FF); |
---|
496 | if ( rField_is_Q(r) || rField_is_Zp(r) |
---|
497 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
498 | { |
---|
499 | setCharacteristic( rInternalChar(r) ); |
---|
500 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r) ); |
---|
501 | CanonicalForm FpG=F+G; |
---|
502 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
---|
503 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
---|
504 | { |
---|
505 | Off(SW_RATIONAL); |
---|
506 | WerrorS("not univariate"); |
---|
507 | return TRUE; |
---|
508 | } |
---|
509 | CanonicalForm Fa,Gb; |
---|
510 | On(SW_RATIONAL); |
---|
511 | res=convFactoryPSingP( extgcd( F, G, Fa, Gb ),r ); |
---|
512 | pa=convFactoryPSingP(Fa,r); |
---|
513 | pb=convFactoryPSingP(Gb,r); |
---|
514 | Off(SW_RATIONAL); |
---|
515 | } |
---|
516 | // and over Q(a) / Fp(a) |
---|
517 | else if ( r->cf->extRing!=NULL ) |
---|
518 | { |
---|
519 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
520 | else setCharacteristic( rInternalChar(r) ); |
---|
521 | CanonicalForm Fa,Gb; |
---|
522 | if (r->cf->extRing->qideal!=NULL) |
---|
523 | { |
---|
524 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
525 | r->cf->extRing); |
---|
526 | Variable a=rootOf(mipo); |
---|
527 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
528 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
529 | CanonicalForm FpG=F+G; |
---|
530 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
---|
531 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
---|
532 | { |
---|
533 | WerrorS("not univariate"); |
---|
534 | return TRUE; |
---|
535 | } |
---|
536 | res= convFactoryAPSingAP( extgcd( F, G, Fa, Gb ),r ); |
---|
537 | pa=convFactoryAPSingAP(Fa,r); |
---|
538 | pb=convFactoryAPSingAP(Gb,r); |
---|
539 | prune (a); |
---|
540 | } |
---|
541 | else |
---|
542 | { |
---|
543 | CanonicalForm F( convSingTrPFactoryP( f, r ) ), G( convSingTrPFactoryP( g, r ) ); |
---|
544 | CanonicalForm FpG=F+G; |
---|
545 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
---|
546 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
---|
547 | { |
---|
548 | Off(SW_RATIONAL); |
---|
549 | WerrorS("not univariate"); |
---|
550 | return TRUE; |
---|
551 | } |
---|
552 | res= convFactoryPSingTrP( extgcd( F, G, Fa, Gb ), r ); |
---|
553 | pa=convFactoryPSingTrP(Fa, r); |
---|
554 | pb=convFactoryPSingTrP(Gb, r); |
---|
555 | } |
---|
556 | Off(SW_RATIONAL); |
---|
557 | } |
---|
558 | else |
---|
559 | { |
---|
560 | WerrorS( feNotImplemented ); |
---|
561 | return TRUE; |
---|
562 | } |
---|
563 | #ifndef SING_NDEBUG |
---|
564 | // checking the result of extgcd: |
---|
565 | poly dummy; |
---|
566 | dummy=p_Sub(p_Add_q(pp_Mult_qq(f,pa,r),pp_Mult_qq(g,pb,r),r),p_Copy(res,r),r); |
---|
567 | if (dummy!=NULL) |
---|
568 | { |
---|
569 | PrintS("extgcd( ");p_Write(f,r);p_Write0(g,r);PrintS(" )\n"); |
---|
570 | PrintS("extgcd( ");p_Write(f,r);p_Write0(g,r);PrintS(" )\n"); |
---|
571 | p_Delete(&dummy,r); |
---|
572 | } |
---|
573 | #endif |
---|
574 | return FALSE; |
---|
575 | } |
---|
576 | |
---|
577 | poly singclap_pmult ( poly f, poly g, const ring r ) |
---|
578 | { |
---|
579 | poly res=NULL; |
---|
580 | On(SW_RATIONAL); |
---|
581 | if (rField_is_Zp(r) || rField_is_Q(r) || rField_is_Z(r) |
---|
582 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
583 | { |
---|
584 | if (rField_is_Z(r)) Off(SW_RATIONAL); |
---|
585 | setCharacteristic( rInternalChar(r) ); |
---|
586 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
---|
587 | res = convFactoryPSingP( F * G,r ); |
---|
588 | } |
---|
589 | else if (r->cf->extRing!=NULL) |
---|
590 | { |
---|
591 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
592 | else setCharacteristic( rInternalChar(r) ); |
---|
593 | if (r->cf->extRing->qideal!=NULL) |
---|
594 | { |
---|
595 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
596 | r->cf->extRing); |
---|
597 | Variable a=rootOf(mipo); |
---|
598 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
599 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
600 | res= convFactoryAPSingAP( F * G, r ); |
---|
601 | prune (a); |
---|
602 | } |
---|
603 | else |
---|
604 | { |
---|
605 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
606 | res= convFactoryPSingTrP( F * G,r ); |
---|
607 | } |
---|
608 | } |
---|
609 | #if 0 // not yet working |
---|
610 | else if (rField_is_GF()) |
---|
611 | { |
---|
612 | //Print("GF(%d^%d)\n",nfCharP,nfMinPoly[0]); |
---|
613 | setCharacteristic( nfCharP,nfMinPoly[0], currRing->parameter[0][0] ); |
---|
614 | CanonicalForm F( convSingGFFactoryGF( f ) ), G( convSingGFFactoryGF( g ) ); |
---|
615 | res = convFactoryGFSingGF( F * G ); |
---|
616 | } |
---|
617 | #endif |
---|
618 | else |
---|
619 | WerrorS( feNotImplemented ); |
---|
620 | Off(SW_RATIONAL); |
---|
621 | return res; |
---|
622 | } |
---|
623 | |
---|
624 | poly singclap_pdivide ( poly f, poly g, const ring r ) |
---|
625 | { |
---|
626 | poly res=NULL; |
---|
627 | |
---|
628 | #ifdef HAVE_FLINT |
---|
629 | #if __FLINT_RELEASE >= 20503 |
---|
630 | /* |
---|
631 | If the division is not exact, control will pass to factory where the |
---|
632 | polynomials can be divided using the ordering that factory chooses. |
---|
633 | */ |
---|
634 | if (rField_is_Zp(r)) |
---|
635 | { |
---|
636 | nmod_mpoly_ctx_t ctx; |
---|
637 | if (!convSingRFlintR(ctx,r)) |
---|
638 | { |
---|
639 | res = Flint_Divide_MP(f,0,g,0,ctx,r); |
---|
640 | if (res != NULL) |
---|
641 | return res; |
---|
642 | } |
---|
643 | } |
---|
644 | else |
---|
645 | if (rField_is_Q(r)) |
---|
646 | { |
---|
647 | fmpq_mpoly_ctx_t ctx; |
---|
648 | if (!convSingRFlintR(ctx,r)) |
---|
649 | { |
---|
650 | res = Flint_Divide_MP(f,0,g,0,ctx,r); |
---|
651 | if (res != NULL) |
---|
652 | return res; |
---|
653 | } |
---|
654 | } |
---|
655 | #endif |
---|
656 | #endif |
---|
657 | |
---|
658 | On(SW_RATIONAL); |
---|
659 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
660 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
661 | { |
---|
662 | setCharacteristic( rInternalChar(r) ); |
---|
663 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
---|
664 | res = convFactoryPSingP( F / G,r ); |
---|
665 | } |
---|
666 | // div is not implemented for ZZ coeffs in factory |
---|
667 | else if (r->cf->extRing!=NULL) |
---|
668 | { |
---|
669 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
670 | else setCharacteristic( rInternalChar(r) ); |
---|
671 | if (r->cf->extRing->qideal!=NULL) |
---|
672 | { |
---|
673 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
674 | r->cf->extRing); |
---|
675 | Variable a=rootOf(mipo); |
---|
676 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
677 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
678 | res= convFactoryAPSingAP( F / G, r ); |
---|
679 | prune (a); |
---|
680 | } |
---|
681 | else |
---|
682 | { |
---|
683 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
684 | res= convFactoryPSingTrP( F / G,r ); |
---|
685 | } |
---|
686 | } |
---|
687 | #if 0 // not yet working |
---|
688 | else if (rField_is_GF()) |
---|
689 | { |
---|
690 | //Print("GF(%d^%d)\n",nfCharP,nfMinPoly[0]); |
---|
691 | setCharacteristic( nfCharP,nfMinPoly[0], currRing->parameter[0][0] ); |
---|
692 | CanonicalForm F( convSingGFFactoryGF( f ) ), G( convSingGFFactoryGF( g ) ); |
---|
693 | res = convFactoryGFSingGF( F / G ); |
---|
694 | } |
---|
695 | #endif |
---|
696 | else |
---|
697 | WerrorS( feNotImplemented ); |
---|
698 | Off(SW_RATIONAL); |
---|
699 | return res; |
---|
700 | } |
---|
701 | |
---|
702 | poly singclap_pmod ( poly f, poly g, const ring r ) |
---|
703 | { |
---|
704 | poly res=NULL; |
---|
705 | On(SW_RATIONAL); |
---|
706 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
707 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
708 | { |
---|
709 | setCharacteristic( rInternalChar(r) ); |
---|
710 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
---|
711 | CanonicalForm Q,R; |
---|
712 | divrem(F,G,Q,R); |
---|
713 | res = convFactoryPSingP(R,r); |
---|
714 | //res = convFactoryPSingP( F-(F/G)*G,r ); |
---|
715 | } |
---|
716 | // mod is not implemented for ZZ coeffs in factory |
---|
717 | else if (r->cf->extRing!=NULL) |
---|
718 | { |
---|
719 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
720 | else setCharacteristic( rInternalChar(r) ); |
---|
721 | if (r->cf->extRing->qideal!=NULL) |
---|
722 | { |
---|
723 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
724 | r->cf->extRing); |
---|
725 | Variable a=rootOf(mipo); |
---|
726 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
727 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
728 | CanonicalForm Q,R; |
---|
729 | divrem(F,G,Q,R); |
---|
730 | res = convFactoryAPSingAP(R,r); |
---|
731 | //res= convFactoryAPSingAP( F-(F/G)*G, r ); |
---|
732 | prune (a); |
---|
733 | } |
---|
734 | else |
---|
735 | { |
---|
736 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
737 | CanonicalForm Q,R; |
---|
738 | divrem(F,G,Q,R); |
---|
739 | res = convFactoryPSingTrP(R,r); |
---|
740 | //res= convFactoryPSingTrP( F-(F/G)*G,r ); |
---|
741 | } |
---|
742 | } |
---|
743 | #if 0 // not yet working |
---|
744 | else if (rField_is_GF()) |
---|
745 | { |
---|
746 | //Print("GF(%d^%d)\n",nfCharP,nfMinPoly[0]); |
---|
747 | setCharacteristic( nfCharP,nfMinPoly[0], currRing->parameter[0][0] ); |
---|
748 | CanonicalForm F( convSingGFFactoryGF( f ) ), G( convSingGFFactoryGF( g ) ); |
---|
749 | res = convFactoryGFSingGF( F / G ); |
---|
750 | } |
---|
751 | #endif |
---|
752 | else |
---|
753 | WerrorS( feNotImplemented ); |
---|
754 | Off(SW_RATIONAL); |
---|
755 | return res; |
---|
756 | } |
---|
757 | |
---|
758 | #if 0 |
---|
759 | // unused |
---|
760 | void singclap_divide_content ( poly f, const ring r ) |
---|
761 | { |
---|
762 | if ( f==NULL ) |
---|
763 | { |
---|
764 | return; |
---|
765 | } |
---|
766 | else if ( pNext( f ) == NULL ) |
---|
767 | { |
---|
768 | p_SetCoeff( f, n_Init( 1, r->cf ), r ); |
---|
769 | return; |
---|
770 | } |
---|
771 | else |
---|
772 | { |
---|
773 | if ( rField_is_Q_a(r) ) |
---|
774 | setCharacteristic( 0 ); |
---|
775 | else if ( rField_is_Zp_a(r) ) |
---|
776 | setCharacteristic( -rChar(r) ); |
---|
777 | else |
---|
778 | return; /* not implemented*/ |
---|
779 | |
---|
780 | CFList L; |
---|
781 | CanonicalForm g, h; |
---|
782 | poly p = pNext(f); |
---|
783 | |
---|
784 | // first attemp: find 2 smallest g: |
---|
785 | |
---|
786 | number g1=pGetCoeff(f); |
---|
787 | number g2=pGetCoeff(p); // p==pNext(f); |
---|
788 | pIter(p); |
---|
789 | int sz1=n_Size(g1, r->cf); |
---|
790 | int sz2=n_Size(g2, r->cf); |
---|
791 | if (sz1>sz2) |
---|
792 | { |
---|
793 | number gg=g1; |
---|
794 | g1=g2; g2=gg; |
---|
795 | int sz=sz1; |
---|
796 | sz1=sz2; sz2=sz; |
---|
797 | } |
---|
798 | while (p!=NULL) |
---|
799 | { |
---|
800 | int n_sz=n_Size(pGetCoeff(p),r->cf); |
---|
801 | if (n_sz<sz1) |
---|
802 | { |
---|
803 | sz2=sz1; |
---|
804 | g2=g1; |
---|
805 | g1=pGetCoeff(p); |
---|
806 | sz1=n_sz; |
---|
807 | if (sz1<=3) break; |
---|
808 | } |
---|
809 | else if(n_sz<sz2) |
---|
810 | { |
---|
811 | sz2=n_sz; |
---|
812 | g2=pGetCoeff(p); |
---|
813 | sz2=n_sz; |
---|
814 | } |
---|
815 | pIter(p); |
---|
816 | } |
---|
817 | g = convSingPFactoryP( NUM(((fraction)g1)), r->cf->extRing ); |
---|
818 | g = gcd( g, convSingPFactoryP( NUM(((fraction)g2)) , r->cf->extRing)); |
---|
819 | |
---|
820 | // second run: gcd's |
---|
821 | |
---|
822 | p = f; |
---|
823 | while ( (p != NULL) && (g != 1) && ( g != 0)) |
---|
824 | { |
---|
825 | h = convSingPFactoryP( NUM(((fraction)pGetCoeff(p))), r->cf->extRing ); |
---|
826 | pIter( p ); |
---|
827 | |
---|
828 | g = gcd( g, h ); |
---|
829 | |
---|
830 | L.append( h ); |
---|
831 | } |
---|
832 | if (( g == 1 ) || (g == 0)) |
---|
833 | { |
---|
834 | // pTest(f); |
---|
835 | return; |
---|
836 | } |
---|
837 | else |
---|
838 | { |
---|
839 | CFListIterator i; |
---|
840 | for ( i = L, p = f; i.hasItem(); i++, p=pNext(p) ) |
---|
841 | { |
---|
842 | fraction c=(fraction)pGetCoeff(p); |
---|
843 | p_Delete(&(NUM(c)),r->cf->extRing); // 2nd arg used to be nacRing |
---|
844 | NUM(c)=convFactoryPSingP( i.getItem() / g, r->cf->extRing ); |
---|
845 | //nTest((number)c); |
---|
846 | //#ifdef LDEBUG |
---|
847 | //number cn=(number)c; |
---|
848 | //StringSetS(""); nWrite(nt); StringAppend(" ==> "); |
---|
849 | //nWrite(cn);PrintS(StringEndS("\n")); // NOTE/TODO: use StringAppendS("\n"); omFree(s); |
---|
850 | //#endif |
---|
851 | } |
---|
852 | } |
---|
853 | // pTest(f); |
---|
854 | } |
---|
855 | } |
---|
856 | #endif |
---|
857 | |
---|
858 | BOOLEAN count_Factors(ideal I, intvec *v,int j, poly &f, poly fac, const ring r) |
---|
859 | { |
---|
860 | p_Test(f,r); |
---|
861 | p_Test(fac,r); |
---|
862 | int e=0; |
---|
863 | if (!p_IsConstant(fac,r)) |
---|
864 | { |
---|
865 | #ifdef FACTORIZE2_DEBUG |
---|
866 | printf("start count_Factors(%d), Fdeg=%d, factor deg=%d\n",j,p_Totaldegree(f,r),p_Totaldegree(fac,r)); |
---|
867 | p_wrp(fac,r);PrintLn(); |
---|
868 | #endif |
---|
869 | On(SW_RATIONAL); |
---|
870 | CanonicalForm F, FAC,Q,R; |
---|
871 | Variable a; |
---|
872 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
873 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
874 | { |
---|
875 | F=convSingPFactoryP( f,r ); |
---|
876 | FAC=convSingPFactoryP( fac,r ); |
---|
877 | } |
---|
878 | else if (r->cf->extRing!=NULL) |
---|
879 | { |
---|
880 | if (r->cf->extRing->qideal!=NULL) |
---|
881 | { |
---|
882 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
883 | r->cf->extRing); |
---|
884 | a=rootOf(mipo); |
---|
885 | F=convSingAPFactoryAP( f,a,r ); |
---|
886 | FAC=convSingAPFactoryAP( fac,a,r ); |
---|
887 | } |
---|
888 | else |
---|
889 | { |
---|
890 | F=convSingTrPFactoryP( f,r ); |
---|
891 | FAC=convSingTrPFactoryP( fac,r ); |
---|
892 | } |
---|
893 | } |
---|
894 | else |
---|
895 | WerrorS( feNotImplemented ); |
---|
896 | |
---|
897 | poly q; |
---|
898 | loop |
---|
899 | { |
---|
900 | Q=F; |
---|
901 | Q/=FAC; |
---|
902 | R=Q; |
---|
903 | R*=FAC; |
---|
904 | R-=F; |
---|
905 | if (R.isZero()) |
---|
906 | { |
---|
907 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
908 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
909 | { |
---|
910 | q = convFactoryPSingP( Q,r ); |
---|
911 | } |
---|
912 | else if (r->cf->extRing!=NULL) |
---|
913 | { |
---|
914 | if (r->cf->extRing->qideal!=NULL) |
---|
915 | { |
---|
916 | q= convFactoryAPSingAP( Q,r ); |
---|
917 | } |
---|
918 | else |
---|
919 | { |
---|
920 | q= convFactoryPSingTrP( Q,r ); |
---|
921 | } |
---|
922 | } |
---|
923 | e++; p_Delete(&f,r); f=q; q=NULL; F=Q; |
---|
924 | } |
---|
925 | else |
---|
926 | { |
---|
927 | break; |
---|
928 | } |
---|
929 | } |
---|
930 | if (r->cf->extRing!=NULL) |
---|
931 | if (r->cf->extRing->qideal!=NULL) |
---|
932 | prune (a); |
---|
933 | if (e==0) |
---|
934 | { |
---|
935 | Off(SW_RATIONAL); |
---|
936 | return FALSE; |
---|
937 | } |
---|
938 | } |
---|
939 | else e=1; |
---|
940 | I->m[j]=fac; |
---|
941 | if (v!=NULL) (*v)[j]=e; |
---|
942 | Off(SW_RATIONAL); |
---|
943 | return TRUE; |
---|
944 | } |
---|
945 | |
---|
946 | VAR int singclap_factorize_retry; |
---|
947 | |
---|
948 | ideal singclap_factorize ( poly f, intvec ** v , int with_exps, const ring r) |
---|
949 | /* destroys f, sets *v */ |
---|
950 | { |
---|
951 | p_Test(f,r); |
---|
952 | #ifdef FACTORIZE2_DEBUG |
---|
953 | printf("singclap_factorize, degree %ld\n",p_Totaldegree(f,r)); |
---|
954 | #endif |
---|
955 | // with_exps: 3,1 return only true factors, no exponents |
---|
956 | // 2 return true factors and exponents |
---|
957 | // 0 return coeff, factors and exponents |
---|
958 | BOOLEAN save_errorreported=errorreported; |
---|
959 | |
---|
960 | ideal res=NULL; |
---|
961 | |
---|
962 | // handle factorize(0) ========================================= |
---|
963 | if (f==NULL) |
---|
964 | { |
---|
965 | res=idInit(1,1); |
---|
966 | if (with_exps!=1) |
---|
967 | { |
---|
968 | (*v)=new intvec(1); |
---|
969 | (**v)[0]=1; |
---|
970 | } |
---|
971 | return res; |
---|
972 | } |
---|
973 | // handle factorize(mon) ========================================= |
---|
974 | if (pNext(f)==NULL) |
---|
975 | { |
---|
976 | int i=0; |
---|
977 | int n=0; |
---|
978 | int e; |
---|
979 | for(i=rVar(r);i>0;i--) if(p_GetExp(f,i,r)!=0) n++; |
---|
980 | if (with_exps==0) n++; // with coeff |
---|
981 | res=idInit(si_max(n,1),1); |
---|
982 | switch(with_exps) |
---|
983 | { |
---|
984 | case 0: // with coef & exp. |
---|
985 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
986 | // no break |
---|
987 | case 2: // with exp. |
---|
988 | (*v)=new intvec(si_max(1,n)); |
---|
989 | (**v)[0]=1; |
---|
990 | // no break |
---|
991 | case 1: ; |
---|
992 | #ifdef TEST |
---|
993 | default: ; |
---|
994 | #endif |
---|
995 | } |
---|
996 | if (n==0) |
---|
997 | { |
---|
998 | if (res->m[0]==NULL) res->m[0]=p_One(r); |
---|
999 | // (**v)[0]=1; is already done |
---|
1000 | } |
---|
1001 | else |
---|
1002 | { |
---|
1003 | for(i=rVar(r);i>0;i--) |
---|
1004 | { |
---|
1005 | e=p_GetExp(f,i,r); |
---|
1006 | if(e!=0) |
---|
1007 | { |
---|
1008 | n--; |
---|
1009 | poly p=p_One(r); |
---|
1010 | p_SetExp(p,i,1,r); |
---|
1011 | p_Setm(p,r); |
---|
1012 | res->m[n]=p; |
---|
1013 | if (with_exps!=1) (**v)[n]=e; |
---|
1014 | } |
---|
1015 | } |
---|
1016 | } |
---|
1017 | p_Delete(&f,r); |
---|
1018 | return res; |
---|
1019 | } |
---|
1020 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
1021 | // use factory/libfac in general ============================== |
---|
1022 | Variable dummy(-1); prune(dummy); // remove all (tmp.) extensions |
---|
1023 | Off(SW_RATIONAL); |
---|
1024 | On(SW_SYMMETRIC_FF); |
---|
1025 | CFFList L; |
---|
1026 | number N=NULL; |
---|
1027 | number NN=NULL; |
---|
1028 | number old_lead_coeff=n_Copy(pGetCoeff(f), r->cf); |
---|
1029 | |
---|
1030 | Variable a; |
---|
1031 | if (r->cf->convSingNFactoryN!=ndConvSingNFactoryN) |
---|
1032 | { |
---|
1033 | if (rField_is_Q(r) || rField_is_Q_a(r) || rField_is_Z(r)) /* Q, Q(a), Z */ |
---|
1034 | { |
---|
1035 | //if (f!=NULL) // already tested at start of routine |
---|
1036 | { |
---|
1037 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
1038 | if (with_exps==0) |
---|
1039 | N=n_Copy(n0,r->cf); |
---|
1040 | if (rField_is_Z(r)) p_Content(f, r); |
---|
1041 | else p_Cleardenom(f, r); |
---|
1042 | //after here f should not have a denominator!! and no content |
---|
1043 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
1044 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
1045 | n_Delete(&n0,r->cf); |
---|
1046 | if (with_exps==0) |
---|
1047 | { |
---|
1048 | n_Delete(&N,r->cf); |
---|
1049 | N=n_Copy(NN,r->cf); |
---|
1050 | } |
---|
1051 | } |
---|
1052 | } |
---|
1053 | else if (rField_is_Zp_a(r)) |
---|
1054 | { |
---|
1055 | //if (f!=NULL) // already tested at start of routine |
---|
1056 | if (singclap_factorize_retry==0) |
---|
1057 | { |
---|
1058 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
1059 | if (with_exps==0) |
---|
1060 | N=n_Copy(n0,r->cf); |
---|
1061 | p_Norm(f,r); |
---|
1062 | p_Cleardenom(f, r); |
---|
1063 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
1064 | n_Delete(&n0,r->cf); |
---|
1065 | if (with_exps==0) |
---|
1066 | { |
---|
1067 | n_Delete(&N,r->cf); |
---|
1068 | N=n_Copy(NN,r->cf); |
---|
1069 | } |
---|
1070 | } |
---|
1071 | } |
---|
1072 | if (rField_is_Q(r) || rField_is_Zp(r) || rField_is_Z(r) || rField_is_Zn(r)) |
---|
1073 | { |
---|
1074 | setCharacteristic( rInternalChar(r) ); |
---|
1075 | if (errorreported) goto notImpl; // char too large |
---|
1076 | CanonicalForm F( convSingPFactoryP( f,r ) ); |
---|
1077 | L = factorize( F ); |
---|
1078 | } |
---|
1079 | // and over Q(a) / Fp(a) |
---|
1080 | else if (r->cf->extRing!=NULL) |
---|
1081 | { |
---|
1082 | if (rField_is_Q_a (r)) setCharacteristic (0); |
---|
1083 | else setCharacteristic( rInternalChar(r) ); |
---|
1084 | if (errorreported) goto notImpl; // char too large |
---|
1085 | if (r->cf->extRing->qideal!=NULL) /*algebraic extension */ |
---|
1086 | { |
---|
1087 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
1088 | r->cf->extRing); |
---|
1089 | a=rootOf(mipo); |
---|
1090 | CanonicalForm F( convSingAPFactoryAP( f, a, r ) ); |
---|
1091 | L = factorize( F, a ); |
---|
1092 | prune(a); |
---|
1093 | } |
---|
1094 | else /* rational functions */ |
---|
1095 | { |
---|
1096 | CanonicalForm F( convSingTrPFactoryP( f,r ) ); |
---|
1097 | L = factorize( F ); |
---|
1098 | } |
---|
1099 | } |
---|
1100 | else |
---|
1101 | { |
---|
1102 | goto notImpl; |
---|
1103 | } |
---|
1104 | } |
---|
1105 | else |
---|
1106 | { |
---|
1107 | goto notImpl; |
---|
1108 | } |
---|
1109 | if (errorreported) |
---|
1110 | { |
---|
1111 | errorreported=FALSE; |
---|
1112 | } |
---|
1113 | { |
---|
1114 | poly ff=p_Copy(f,r); // a copy for the retry stuff |
---|
1115 | // the first factor should be a constant |
---|
1116 | if ( ! L.getFirst().factor().inCoeffDomain() ) |
---|
1117 | L.insert(CFFactor(1,1)); |
---|
1118 | // convert into ideal |
---|
1119 | int n = L.length(); |
---|
1120 | if (n==0) n=1; |
---|
1121 | CFFListIterator J=L; |
---|
1122 | int j=0; |
---|
1123 | if (with_exps!=1) |
---|
1124 | { |
---|
1125 | if ((with_exps==2)&&(n>1)) |
---|
1126 | { |
---|
1127 | n--; |
---|
1128 | J++; |
---|
1129 | } |
---|
1130 | *v = new intvec( n ); |
---|
1131 | } |
---|
1132 | res = idInit( n ,1); |
---|
1133 | for ( ; J.hasItem(); J++, j++ ) |
---|
1134 | { |
---|
1135 | if (with_exps!=1) (**v)[j] = J.getItem().exp(); |
---|
1136 | if (rField_is_Zp(r) || rField_is_Q(r)|| rField_is_Z(r) |
---|
1137 | || rField_is_Zn(r)) /* Q, Fp, Z */ |
---|
1138 | { |
---|
1139 | //count_Factors(res,*v,f, j, convFactoryPSingP( J.getItem().factor() ); |
---|
1140 | res->m[j] = convFactoryPSingP( J.getItem().factor(),r ); |
---|
1141 | } |
---|
1142 | #if 0 |
---|
1143 | else if (rField_is_GF()) |
---|
1144 | res->m[j] = convFactoryGFSingGF( J.getItem().factor() ); |
---|
1145 | #endif |
---|
1146 | else if (r->cf->extRing!=NULL) /* Q(a), Fp(a) */ |
---|
1147 | { |
---|
1148 | #ifndef SING_NDEBUG |
---|
1149 | intvec *w=NULL; |
---|
1150 | if (v!=NULL) w=*v; |
---|
1151 | #endif |
---|
1152 | if (r->cf->extRing->qideal==NULL) |
---|
1153 | { |
---|
1154 | #ifdef SING_NDEBUG |
---|
1155 | res->m[j]= convFactoryPSingTrP( J.getItem().factor(),r ); |
---|
1156 | #else |
---|
1157 | if(!count_Factors(res,w,j,ff,convFactoryPSingTrP( J.getItem().factor(),r ),r)) |
---|
1158 | { |
---|
1159 | if (w!=NULL) |
---|
1160 | (*w)[j]=1; |
---|
1161 | res->m[j]=p_One(r); |
---|
1162 | } |
---|
1163 | #endif |
---|
1164 | } |
---|
1165 | else |
---|
1166 | { |
---|
1167 | #ifdef SING_NDEBUG |
---|
1168 | res->m[j]= convFactoryAPSingAP( J.getItem().factor(),r ); |
---|
1169 | #else |
---|
1170 | if (!count_Factors(res,w,j,ff,convFactoryAPSingAP( J.getItem().factor(),r ),r)) |
---|
1171 | { |
---|
1172 | if (w!=NULL) |
---|
1173 | (*w)[j]=1; |
---|
1174 | res->m[j]=p_One(r); |
---|
1175 | } |
---|
1176 | #endif |
---|
1177 | } |
---|
1178 | } |
---|
1179 | } |
---|
1180 | if (r->cf->extRing!=NULL) |
---|
1181 | if (r->cf->extRing->qideal!=NULL) |
---|
1182 | prune (a); |
---|
1183 | #ifndef SING_NDEBUG |
---|
1184 | if ((r->cf->extRing!=NULL) && (!p_IsConstant(ff,r))) |
---|
1185 | { |
---|
1186 | singclap_factorize_retry++; |
---|
1187 | if (singclap_factorize_retry<3) |
---|
1188 | { |
---|
1189 | int jj; |
---|
1190 | #ifdef FACTORIZE2_DEBUG |
---|
1191 | printf("factorize_retry\n"); |
---|
1192 | #endif |
---|
1193 | intvec *ww=NULL; |
---|
1194 | id_Test(res,r); |
---|
1195 | ideal h=singclap_factorize ( ff, &ww , with_exps, r ); |
---|
1196 | id_Test(h,r); |
---|
1197 | int l=(*v)->length(); |
---|
1198 | (*v)->resize(l+ww->length()); |
---|
1199 | for(jj=0;jj<ww->length();jj++) |
---|
1200 | (**v)[jj+l]=(*ww)[jj]; |
---|
1201 | delete ww; |
---|
1202 | ideal hh=idInit(IDELEMS(res)+IDELEMS(h),1); |
---|
1203 | for(jj=IDELEMS(res)-1;jj>=0;jj--) |
---|
1204 | { |
---|
1205 | hh->m[jj]=res->m[jj]; |
---|
1206 | res->m[jj]=NULL; |
---|
1207 | } |
---|
1208 | for(jj=IDELEMS(h)-1;jj>=0;jj--) |
---|
1209 | { |
---|
1210 | hh->m[jj+IDELEMS(res)]=h->m[jj]; |
---|
1211 | h->m[jj]=NULL; |
---|
1212 | } |
---|
1213 | id_Delete(&res,r); |
---|
1214 | id_Delete(&h,r); |
---|
1215 | res=hh; |
---|
1216 | id_Test(res,r); |
---|
1217 | ff=NULL; |
---|
1218 | } |
---|
1219 | else |
---|
1220 | { |
---|
1221 | WarnS("problem with factorize"); |
---|
1222 | #if 0 |
---|
1223 | pWrite(ff); |
---|
1224 | idShow(res); |
---|
1225 | #endif |
---|
1226 | id_Delete(&res,r); |
---|
1227 | res=idInit(2,1); |
---|
1228 | res->m[0]=p_One(r); |
---|
1229 | res->m[1]=ff; ff=NULL; |
---|
1230 | } |
---|
1231 | } |
---|
1232 | #endif |
---|
1233 | p_Delete(&ff,r); |
---|
1234 | if (N!=NULL) |
---|
1235 | { |
---|
1236 | __p_Mult_nn(res->m[0],N,r); |
---|
1237 | n_Delete(&N,r->cf); |
---|
1238 | N=NULL; |
---|
1239 | } |
---|
1240 | // delete constants |
---|
1241 | if (res!=NULL) |
---|
1242 | { |
---|
1243 | int i=IDELEMS(res)-1; |
---|
1244 | int j=0; |
---|
1245 | for(;i>=0;i--) |
---|
1246 | { |
---|
1247 | if ((res->m[i]!=NULL) |
---|
1248 | && (pNext(res->m[i])==NULL) |
---|
1249 | && (p_IsConstant(res->m[i],r))) |
---|
1250 | { |
---|
1251 | if (with_exps!=0) |
---|
1252 | { |
---|
1253 | p_Delete(&(res->m[i]),r); |
---|
1254 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
1255 | (**v)[i]=0; |
---|
1256 | j++; |
---|
1257 | } |
---|
1258 | else if (i!=0) |
---|
1259 | { |
---|
1260 | while ((v!=NULL) && ((*v)!=NULL) && ((**v)[i]>1)) |
---|
1261 | { |
---|
1262 | res->m[0]=p_Mult_q(res->m[0],p_Copy(res->m[i],r),r); |
---|
1263 | (**v)[i]--; |
---|
1264 | } |
---|
1265 | res->m[0]=p_Mult_q(res->m[0],res->m[i],r); |
---|
1266 | res->m[i]=NULL; |
---|
1267 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
1268 | (**v)[i]=1; |
---|
1269 | j++; |
---|
1270 | } |
---|
1271 | } |
---|
1272 | } |
---|
1273 | if (j>0) |
---|
1274 | { |
---|
1275 | idSkipZeroes(res); |
---|
1276 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
1277 | { |
---|
1278 | intvec *w=*v; |
---|
1279 | int len=IDELEMS(res); |
---|
1280 | *v = new intvec( len ); |
---|
1281 | for (i=0,j=0;i<si_min(w->length(),len);i++) |
---|
1282 | { |
---|
1283 | if((*w)[i]!=0) |
---|
1284 | { |
---|
1285 | (**v)[j]=(*w)[i]; j++; |
---|
1286 | } |
---|
1287 | } |
---|
1288 | delete w; |
---|
1289 | } |
---|
1290 | } |
---|
1291 | if (res->m[0]==NULL) |
---|
1292 | { |
---|
1293 | res->m[0]=p_One(r); |
---|
1294 | } |
---|
1295 | } |
---|
1296 | } |
---|
1297 | if (rField_is_Q_a(r) && (r->cf->extRing->qideal!=NULL)) |
---|
1298 | { |
---|
1299 | int i=IDELEMS(res)-1; |
---|
1300 | int stop=1; |
---|
1301 | if (with_exps!=0) stop=0; |
---|
1302 | for(;i>=stop;i--) |
---|
1303 | { |
---|
1304 | p_Norm(res->m[i],r); |
---|
1305 | } |
---|
1306 | if (with_exps==0) p_SetCoeff(res->m[0],old_lead_coeff,r); |
---|
1307 | else n_Delete(&old_lead_coeff,r->cf); |
---|
1308 | } |
---|
1309 | else |
---|
1310 | n_Delete(&old_lead_coeff,r->cf); |
---|
1311 | errorreported=save_errorreported; |
---|
1312 | notImpl: |
---|
1313 | prune(a); |
---|
1314 | if (res==NULL) |
---|
1315 | { |
---|
1316 | WerrorS( feNotImplemented ); |
---|
1317 | if ((v!=NULL) && ((*v)!=NULL) &&(with_exps==2)) |
---|
1318 | { |
---|
1319 | *v = new intvec( 1 ); |
---|
1320 | (*v)[0]=1; |
---|
1321 | } |
---|
1322 | res=idInit(2,1); |
---|
1323 | res->m[0]=p_One(r); |
---|
1324 | res->m[1]=f; |
---|
1325 | } |
---|
1326 | else p_Delete(&f,r); |
---|
1327 | if (NN!=NULL) |
---|
1328 | { |
---|
1329 | n_Delete(&NN,r->cf); |
---|
1330 | } |
---|
1331 | if (N!=NULL) |
---|
1332 | { |
---|
1333 | n_Delete(&N,r->cf); |
---|
1334 | } |
---|
1335 | return res; |
---|
1336 | } |
---|
1337 | |
---|
1338 | ideal singclap_sqrfree ( poly f, intvec ** v , int with_exps, const ring r) |
---|
1339 | { |
---|
1340 | p_Test(f,r); |
---|
1341 | #ifdef FACTORIZE2_DEBUG |
---|
1342 | printf("singclap_sqrfree, degree %d\n",pTotaldegree(f)); |
---|
1343 | #endif |
---|
1344 | // with_exps: 3,1 return only true factors, no exponents |
---|
1345 | // 2 return true factors and exponents |
---|
1346 | // 0 return coeff, factors and exponents |
---|
1347 | BOOLEAN save_errorreported=errorreported; |
---|
1348 | |
---|
1349 | ideal res=NULL; |
---|
1350 | |
---|
1351 | // handle factorize(0) ========================================= |
---|
1352 | if (f==NULL) |
---|
1353 | { |
---|
1354 | res=idInit(1,1); |
---|
1355 | if (with_exps!=1 && with_exps!=3) |
---|
1356 | { |
---|
1357 | (*v)=new intvec(1); |
---|
1358 | (**v)[0]=1; |
---|
1359 | } |
---|
1360 | return res; |
---|
1361 | } |
---|
1362 | // handle factorize(mon) ========================================= |
---|
1363 | if (pNext(f)==NULL) |
---|
1364 | { |
---|
1365 | int i=0; |
---|
1366 | int n=0; |
---|
1367 | int e; |
---|
1368 | for(i=rVar(r);i>0;i--) if(p_GetExp(f,i,r)!=0) n++; |
---|
1369 | if (with_exps==0 || with_exps==3) n++; // with coeff |
---|
1370 | res=idInit(si_max(n,1),1); |
---|
1371 | if(with_exps!=1) |
---|
1372 | { |
---|
1373 | (*v)=new intvec(si_max(1,n)); |
---|
1374 | (**v)[0]=1; |
---|
1375 | } |
---|
1376 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
1377 | if (n==0) |
---|
1378 | { |
---|
1379 | res->m[0]=p_One(r); |
---|
1380 | // (**v)[0]=1; is already done |
---|
1381 | } |
---|
1382 | else |
---|
1383 | { |
---|
1384 | for(i=rVar(r);i>0;i--) |
---|
1385 | { |
---|
1386 | e=p_GetExp(f,i,r); |
---|
1387 | if(e!=0) |
---|
1388 | { |
---|
1389 | n--; |
---|
1390 | poly p=p_One(r); |
---|
1391 | p_SetExp(p,i,1,r); |
---|
1392 | p_Setm(p,r); |
---|
1393 | res->m[n]=p; |
---|
1394 | if (with_exps!=1) (**v)[n]=e; |
---|
1395 | } |
---|
1396 | } |
---|
1397 | } |
---|
1398 | p_Delete(&f,r); |
---|
1399 | return res; |
---|
1400 | } |
---|
1401 | //PrintS("S:");pWrite(f);PrintLn(); |
---|
1402 | // use factory/libfac in general ============================== |
---|
1403 | Off(SW_RATIONAL); |
---|
1404 | On(SW_SYMMETRIC_FF); |
---|
1405 | CFFList L; |
---|
1406 | number N=NULL; |
---|
1407 | number NN=NULL; |
---|
1408 | number old_lead_coeff=n_Copy(pGetCoeff(f), r->cf); |
---|
1409 | Variable a; |
---|
1410 | |
---|
1411 | if (!rField_is_Zp(r) && !rField_is_Zp_a(r)) /* Q, Q(a) */ |
---|
1412 | { |
---|
1413 | //if (f!=NULL) // already tested at start of routine |
---|
1414 | number n0=n_Copy(old_lead_coeff,r->cf); |
---|
1415 | if (with_exps==0 || with_exps==3) |
---|
1416 | N=n_Copy(n0,r->cf); |
---|
1417 | p_Cleardenom(f, r); |
---|
1418 | //after here f should not have a denominator!! |
---|
1419 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
1420 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
1421 | n_Delete(&n0,r->cf); |
---|
1422 | if (with_exps==0 || with_exps==3) |
---|
1423 | { |
---|
1424 | n_Delete(&N,r->cf); |
---|
1425 | N=n_Copy(NN,r->cf); |
---|
1426 | } |
---|
1427 | } |
---|
1428 | else if (rField_is_Zp_a(r)) |
---|
1429 | { |
---|
1430 | //if (f!=NULL) // already tested at start of routine |
---|
1431 | if (singclap_factorize_retry==0) |
---|
1432 | { |
---|
1433 | number n0=n_Copy(old_lead_coeff,r->cf); |
---|
1434 | if (with_exps==0 || with_exps==3) |
---|
1435 | N=n_Copy(n0,r->cf); |
---|
1436 | p_Norm(f,r); |
---|
1437 | p_Cleardenom(f, r); |
---|
1438 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
1439 | n_Delete(&n0,r->cf); |
---|
1440 | if (with_exps==0 || with_exps==3) |
---|
1441 | { |
---|
1442 | n_Delete(&N,r->cf); |
---|
1443 | N=n_Copy(NN,r->cf); |
---|
1444 | } |
---|
1445 | } |
---|
1446 | } |
---|
1447 | if (rField_is_Q(r) || rField_is_Zp(r) |
---|
1448 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
1449 | { |
---|
1450 | setCharacteristic( rInternalChar(r) ); |
---|
1451 | CanonicalForm F( convSingPFactoryP( f,r ) ); |
---|
1452 | L = sqrFree( F ); |
---|
1453 | } |
---|
1454 | else if (r->cf->extRing!=NULL) |
---|
1455 | { |
---|
1456 | if (rField_is_Q_a (r)) setCharacteristic (0); |
---|
1457 | else setCharacteristic( rInternalChar(r) ); |
---|
1458 | if (r->cf->extRing->qideal!=NULL) |
---|
1459 | { |
---|
1460 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
1461 | r->cf->extRing); |
---|
1462 | a=rootOf(mipo); |
---|
1463 | CanonicalForm F( convSingAPFactoryAP( f, a, r ) ); |
---|
1464 | L= sqrFree (F); |
---|
1465 | } |
---|
1466 | else |
---|
1467 | { |
---|
1468 | CanonicalForm F( convSingTrPFactoryP( f,r ) ); |
---|
1469 | L = sqrFree( F ); |
---|
1470 | } |
---|
1471 | } |
---|
1472 | #if 0 |
---|
1473 | else if (rField_is_GF()) |
---|
1474 | { |
---|
1475 | int c=rInternalChar(r); |
---|
1476 | setCharacteristic( c, primepower(c) ); |
---|
1477 | CanonicalForm F( convSingGFFactoryGF( f ) ); |
---|
1478 | if (F.isUnivariate()) |
---|
1479 | { |
---|
1480 | L = factorize( F ); |
---|
1481 | } |
---|
1482 | else |
---|
1483 | { |
---|
1484 | goto notImpl; |
---|
1485 | } |
---|
1486 | } |
---|
1487 | #endif |
---|
1488 | else |
---|
1489 | { |
---|
1490 | goto notImpl; |
---|
1491 | } |
---|
1492 | { |
---|
1493 | // convert into ideal |
---|
1494 | int n = L.length(); |
---|
1495 | if (n==0) n=1; |
---|
1496 | CFFListIterator J=L; |
---|
1497 | int j=0; |
---|
1498 | if (with_exps!=1) |
---|
1499 | { |
---|
1500 | if ((with_exps==2)&&(n>1)) |
---|
1501 | { |
---|
1502 | n--; |
---|
1503 | J++; |
---|
1504 | } |
---|
1505 | *v = new intvec( n ); |
---|
1506 | } |
---|
1507 | else if (L.getFirst().factor().inCoeffDomain() && with_exps!=3) |
---|
1508 | { |
---|
1509 | n--; |
---|
1510 | J++; |
---|
1511 | } |
---|
1512 | res = idInit( n ,1); |
---|
1513 | for ( ; J.hasItem(); J++, j++ ) |
---|
1514 | { |
---|
1515 | if (with_exps!=1 && with_exps!=3) (**v)[j] = J.getItem().exp(); |
---|
1516 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
1517 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
1518 | res->m[j] = convFactoryPSingP( J.getItem().factor(),r ); |
---|
1519 | else if (r->cf->extRing!=NULL) /* Q(a), Fp(a) */ |
---|
1520 | { |
---|
1521 | if (r->cf->extRing->qideal==NULL) |
---|
1522 | res->m[j]=convFactoryPSingTrP( J.getItem().factor(),r ); |
---|
1523 | else |
---|
1524 | res->m[j]=convFactoryAPSingAP( J.getItem().factor(),r ); |
---|
1525 | } |
---|
1526 | } |
---|
1527 | if (res->m[0]==NULL) |
---|
1528 | { |
---|
1529 | res->m[0]=p_One(r); |
---|
1530 | } |
---|
1531 | if (N!=NULL) |
---|
1532 | { |
---|
1533 | __p_Mult_nn(res->m[0],N,r); |
---|
1534 | n_Delete(&N,r->cf); |
---|
1535 | N=NULL; |
---|
1536 | } |
---|
1537 | } |
---|
1538 | if (r->cf->extRing!=NULL) |
---|
1539 | if (r->cf->extRing->qideal!=NULL) |
---|
1540 | prune (a); |
---|
1541 | if (rField_is_Q_a(r) && (r->cf->extRing->qideal!=NULL)) |
---|
1542 | { |
---|
1543 | int i=IDELEMS(res)-1; |
---|
1544 | int stop=1; |
---|
1545 | if (with_exps!=0 || with_exps==3) stop=0; |
---|
1546 | for(;i>=stop;i--) |
---|
1547 | { |
---|
1548 | p_Norm(res->m[i],r); |
---|
1549 | } |
---|
1550 | if (with_exps==0 || with_exps==3) p_SetCoeff(res->m[0],old_lead_coeff,r); |
---|
1551 | else n_Delete(&old_lead_coeff,r->cf); |
---|
1552 | } |
---|
1553 | else |
---|
1554 | n_Delete(&old_lead_coeff,r->cf); |
---|
1555 | p_Delete(&f,r); |
---|
1556 | errorreported=save_errorreported; |
---|
1557 | notImpl: |
---|
1558 | if (res==NULL) |
---|
1559 | WerrorS( feNotImplemented ); |
---|
1560 | if (NN!=NULL) |
---|
1561 | { |
---|
1562 | n_Delete(&NN,r->cf); |
---|
1563 | } |
---|
1564 | if (N!=NULL) |
---|
1565 | { |
---|
1566 | n_Delete(&N,r->cf); |
---|
1567 | } |
---|
1568 | return res; |
---|
1569 | } |
---|
1570 | |
---|
1571 | matrix singclap_irrCharSeries ( ideal I, const ring r) |
---|
1572 | { |
---|
1573 | if (idIs0(I)) return mpNew(1,1); |
---|
1574 | |
---|
1575 | // for now there is only the possibility to handle polynomials over |
---|
1576 | // Q and Fp ... |
---|
1577 | matrix res=NULL; |
---|
1578 | int i; |
---|
1579 | Off(SW_RATIONAL); |
---|
1580 | On(SW_SYMMETRIC_FF); |
---|
1581 | CFList L; |
---|
1582 | ListCFList LL; |
---|
1583 | if (rField_is_Q(r) || rField_is_Zp(r) |
---|
1584 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
1585 | { |
---|
1586 | setCharacteristic( rInternalChar(r) ); |
---|
1587 | for(i=0;i<IDELEMS(I);i++) |
---|
1588 | { |
---|
1589 | poly p=I->m[i]; |
---|
1590 | if (p!=NULL) |
---|
1591 | { |
---|
1592 | p=p_Copy(p,r); |
---|
1593 | p_Cleardenom(p, r); |
---|
1594 | L.append(convSingPFactoryP(p,r)); |
---|
1595 | p_Delete(&p,r); |
---|
1596 | } |
---|
1597 | } |
---|
1598 | } |
---|
1599 | // and over Q(a) / Fp(a) |
---|
1600 | else if (nCoeff_is_transExt (r->cf)) |
---|
1601 | { |
---|
1602 | setCharacteristic( rInternalChar(r) ); |
---|
1603 | for(i=0;i<IDELEMS(I);i++) |
---|
1604 | { |
---|
1605 | poly p=I->m[i]; |
---|
1606 | if (p!=NULL) |
---|
1607 | { |
---|
1608 | p=p_Copy(p,r); |
---|
1609 | p_Cleardenom(p, r); |
---|
1610 | L.append(convSingTrPFactoryP(p,r)); |
---|
1611 | p_Delete(&p,r); |
---|
1612 | } |
---|
1613 | } |
---|
1614 | } |
---|
1615 | else |
---|
1616 | { |
---|
1617 | WerrorS( feNotImplemented ); |
---|
1618 | return res; |
---|
1619 | } |
---|
1620 | |
---|
1621 | // a very bad work-around --- FIX IT in libfac |
---|
1622 | // should be fixed as of 2001/6/27 |
---|
1623 | int tries=0; |
---|
1624 | int m,n; |
---|
1625 | ListIterator<CFList> LLi; |
---|
1626 | loop |
---|
1627 | { |
---|
1628 | LL=irrCharSeries(L); |
---|
1629 | m= LL.length(); // Anzahl Zeilen |
---|
1630 | n=0; |
---|
1631 | for ( LLi = LL; LLi.hasItem(); LLi++ ) |
---|
1632 | { |
---|
1633 | n = si_max(LLi.getItem().length(),n); |
---|
1634 | } |
---|
1635 | if ((m!=0) && (n!=0)) break; |
---|
1636 | tries++; |
---|
1637 | if (tries>=5) break; |
---|
1638 | } |
---|
1639 | if ((m==0) || (n==0)) |
---|
1640 | { |
---|
1641 | Warn("char_series returns %d x %d matrix from %d input polys (%d)", |
---|
1642 | m,n,IDELEMS(I)+1,LL.length()); |
---|
1643 | iiWriteMatrix((matrix)I,"I",2,r,0); |
---|
1644 | m=si_max(m,1); |
---|
1645 | n=si_max(n,1); |
---|
1646 | } |
---|
1647 | res=mpNew(m,n); |
---|
1648 | CFListIterator Li; |
---|
1649 | for ( m=1, LLi = LL; LLi.hasItem(); LLi++, m++ ) |
---|
1650 | { |
---|
1651 | for (n=1, Li = LLi.getItem(); Li.hasItem(); Li++, n++) |
---|
1652 | { |
---|
1653 | if (rField_is_Q(r) || rField_is_Zp(r) |
---|
1654 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
1655 | MATELEM(res,m,n)=convFactoryPSingP(Li.getItem(),r); |
---|
1656 | else |
---|
1657 | MATELEM(res,m,n)=convFactoryPSingTrP(Li.getItem(),r); |
---|
1658 | } |
---|
1659 | } |
---|
1660 | Off(SW_RATIONAL); |
---|
1661 | return res; |
---|
1662 | } |
---|
1663 | |
---|
1664 | char* singclap_neworder ( ideal I, const ring r) |
---|
1665 | { |
---|
1666 | int i; |
---|
1667 | Off(SW_RATIONAL); |
---|
1668 | On(SW_SYMMETRIC_FF); |
---|
1669 | CFList L; |
---|
1670 | if (rField_is_Q(r) || rField_is_Zp(r) |
---|
1671 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
1672 | { |
---|
1673 | setCharacteristic( rInternalChar(r) ); |
---|
1674 | for(i=0;i<IDELEMS(I);i++) |
---|
1675 | { |
---|
1676 | poly p=I->m[i]; |
---|
1677 | if (p!=NULL) |
---|
1678 | { |
---|
1679 | p=p_Copy(p,r); |
---|
1680 | p_Cleardenom(p, r); |
---|
1681 | L.append(convSingPFactoryP(p,r)); |
---|
1682 | } |
---|
1683 | } |
---|
1684 | } |
---|
1685 | // and over Q(a) / Fp(a) |
---|
1686 | else if (nCoeff_is_transExt (r->cf)) |
---|
1687 | { |
---|
1688 | setCharacteristic( rInternalChar(r) ); |
---|
1689 | for(i=0;i<IDELEMS(I);i++) |
---|
1690 | { |
---|
1691 | poly p=I->m[i]; |
---|
1692 | if (p!=NULL) |
---|
1693 | { |
---|
1694 | p=p_Copy(p,r); |
---|
1695 | p_Cleardenom(p, r); |
---|
1696 | L.append(convSingTrPFactoryP(p,r)); |
---|
1697 | } |
---|
1698 | } |
---|
1699 | } |
---|
1700 | else |
---|
1701 | { |
---|
1702 | WerrorS( feNotImplemented ); |
---|
1703 | return NULL; |
---|
1704 | } |
---|
1705 | |
---|
1706 | List<int> IL=neworderint(L); |
---|
1707 | ListIterator<int> Li; |
---|
1708 | StringSetS(""); |
---|
1709 | Li = IL; |
---|
1710 | int offs=rPar(r); |
---|
1711 | int* mark=(int*)omAlloc0((rVar(r)+offs)*sizeof(int)); |
---|
1712 | int cnt=rVar(r)+offs; |
---|
1713 | loop |
---|
1714 | { |
---|
1715 | if(! Li.hasItem()) break; |
---|
1716 | BOOLEAN done=TRUE; |
---|
1717 | i=Li.getItem()-1; |
---|
1718 | mark[i]=1; |
---|
1719 | if (i<offs) |
---|
1720 | { |
---|
1721 | done=FALSE; |
---|
1722 | //StringAppendS(r->parameter[i]); |
---|
1723 | } |
---|
1724 | else |
---|
1725 | { |
---|
1726 | StringAppendS(r->names[i-offs]); |
---|
1727 | } |
---|
1728 | Li++; |
---|
1729 | cnt--; |
---|
1730 | if(cnt==0) break; |
---|
1731 | if (done) StringAppendS(","); |
---|
1732 | } |
---|
1733 | for(i=0;i<rVar(r)+offs;i++) |
---|
1734 | { |
---|
1735 | BOOLEAN done=TRUE; |
---|
1736 | if(mark[i]==0) |
---|
1737 | { |
---|
1738 | if (i<offs) |
---|
1739 | { |
---|
1740 | done=FALSE; |
---|
1741 | //StringAppendS(r->parameter[i]); |
---|
1742 | } |
---|
1743 | else |
---|
1744 | { |
---|
1745 | StringAppendS(r->names[i-offs]); |
---|
1746 | } |
---|
1747 | cnt--; |
---|
1748 | if(cnt==0) break; |
---|
1749 | if (done) StringAppendS(","); |
---|
1750 | } |
---|
1751 | } |
---|
1752 | char * s=StringEndS(); |
---|
1753 | if (s[strlen(s)-1]==',') s[strlen(s)-1]='\0'; |
---|
1754 | return s; |
---|
1755 | } |
---|
1756 | |
---|
1757 | poly singclap_det( const matrix m, const ring s ) |
---|
1758 | { |
---|
1759 | int r=m->rows(); |
---|
1760 | if (r!=m->cols()) |
---|
1761 | { |
---|
1762 | Werror("det of %d x %d matrix",r,m->cols()); |
---|
1763 | return NULL; |
---|
1764 | } |
---|
1765 | poly res=NULL; |
---|
1766 | CFMatrix M(r,r); |
---|
1767 | int i,j; |
---|
1768 | for(i=r;i>0;i--) |
---|
1769 | { |
---|
1770 | for(j=r;j>0;j--) |
---|
1771 | { |
---|
1772 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s); |
---|
1773 | } |
---|
1774 | } |
---|
1775 | res= convFactoryPSingP( determinant(M,r),s ) ; |
---|
1776 | Off(SW_RATIONAL); |
---|
1777 | return res; |
---|
1778 | } |
---|
1779 | |
---|
1780 | int singclap_det_i( intvec * m, const ring /*r*/) |
---|
1781 | { |
---|
1782 | // assume( r == currRing ); // Anything else is not guaranted to work! |
---|
1783 | |
---|
1784 | setCharacteristic( 0 ); // ? |
---|
1785 | CFMatrix M(m->rows(),m->cols()); |
---|
1786 | int i,j; |
---|
1787 | for(i=m->rows();i>0;i--) |
---|
1788 | { |
---|
1789 | for(j=m->cols();j>0;j--) |
---|
1790 | { |
---|
1791 | M(i,j)=IMATELEM(*m,i,j); |
---|
1792 | } |
---|
1793 | } |
---|
1794 | int res= convFactoryISingI( determinant(M,m->rows()) ) ; |
---|
1795 | return res; |
---|
1796 | } |
---|
1797 | |
---|
1798 | number singclap_det_bi( bigintmat * m, const coeffs cf) |
---|
1799 | { |
---|
1800 | assume(m->basecoeffs()==cf); |
---|
1801 | CFMatrix M(m->rows(),m->cols()); |
---|
1802 | int i,j; |
---|
1803 | BOOLEAN setchar=TRUE; |
---|
1804 | for(i=m->rows();i>0;i--) |
---|
1805 | { |
---|
1806 | for(j=m->cols();j>0;j--) |
---|
1807 | { |
---|
1808 | M(i,j)=n_convSingNFactoryN(BIMATELEM(*m,i,j),setchar,cf); |
---|
1809 | setchar=FALSE; |
---|
1810 | } |
---|
1811 | } |
---|
1812 | number res=n_convFactoryNSingN( determinant(M,m->rows()),cf ) ; |
---|
1813 | return res; |
---|
1814 | } |
---|
1815 | |
---|
1816 | #if defined(HAVE_NTL) || defined(AHVE_FLINT) |
---|
1817 | matrix singntl_HNF(matrix m, const ring s ) |
---|
1818 | { |
---|
1819 | int r=m->rows(); |
---|
1820 | if (r!=m->cols()) |
---|
1821 | { |
---|
1822 | Werror("HNF of %d x %d matrix",r,m->cols()); |
---|
1823 | return NULL; |
---|
1824 | } |
---|
1825 | |
---|
1826 | matrix res=mpNew(r,r); |
---|
1827 | |
---|
1828 | if (rField_is_Q(s)) |
---|
1829 | { |
---|
1830 | |
---|
1831 | CFMatrix M(r,r); |
---|
1832 | int i,j; |
---|
1833 | for(i=r;i>0;i--) |
---|
1834 | { |
---|
1835 | for(j=r;j>0;j--) |
---|
1836 | { |
---|
1837 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s ); |
---|
1838 | } |
---|
1839 | } |
---|
1840 | CFMatrix *MM=cf_HNF(M); |
---|
1841 | for(i=r;i>0;i--) |
---|
1842 | { |
---|
1843 | for(j=r;j>0;j--) |
---|
1844 | { |
---|
1845 | MATELEM(res,i,j)=convFactoryPSingP((*MM)(i,j),s); |
---|
1846 | } |
---|
1847 | } |
---|
1848 | delete MM; |
---|
1849 | } |
---|
1850 | return res; |
---|
1851 | } |
---|
1852 | |
---|
1853 | intvec* singntl_HNF(intvec* m) |
---|
1854 | { |
---|
1855 | int r=m->rows(); |
---|
1856 | if (r!=m->cols()) |
---|
1857 | { |
---|
1858 | Werror("HNF of %d x %d matrix",r,m->cols()); |
---|
1859 | return NULL; |
---|
1860 | } |
---|
1861 | setCharacteristic( 0 ); |
---|
1862 | CFMatrix M(r,r); |
---|
1863 | int i,j; |
---|
1864 | for(i=r;i>0;i--) |
---|
1865 | { |
---|
1866 | for(j=r;j>0;j--) |
---|
1867 | { |
---|
1868 | M(i,j)=IMATELEM(*m,i,j); |
---|
1869 | } |
---|
1870 | } |
---|
1871 | CFMatrix *MM=cf_HNF(M); |
---|
1872 | intvec *mm=ivCopy(m); |
---|
1873 | for(i=r;i>0;i--) |
---|
1874 | { |
---|
1875 | for(j=r;j>0;j--) |
---|
1876 | { |
---|
1877 | IMATELEM(*mm,i,j)=convFactoryISingI((*MM)(i,j)); |
---|
1878 | } |
---|
1879 | } |
---|
1880 | delete MM; |
---|
1881 | return mm; |
---|
1882 | } |
---|
1883 | |
---|
1884 | bigintmat* singntl_HNF(bigintmat* b) |
---|
1885 | { |
---|
1886 | int r=b->rows(); |
---|
1887 | if (r!=b->cols()) |
---|
1888 | { |
---|
1889 | Werror("HNF of %d x %d matrix",r,b->cols()); |
---|
1890 | return NULL; |
---|
1891 | } |
---|
1892 | setCharacteristic( 0 ); |
---|
1893 | CFMatrix M(r,r); |
---|
1894 | int i,j; |
---|
1895 | for(i=r;i>0;i--) |
---|
1896 | { |
---|
1897 | for(j=r;j>0;j--) |
---|
1898 | { |
---|
1899 | M(i,j)=n_convSingNFactoryN(BIMATELEM(*b,i,j),FALSE,b->basecoeffs()); |
---|
1900 | } |
---|
1901 | } |
---|
1902 | CFMatrix *MM=cf_HNF(M); |
---|
1903 | bigintmat *mm=bimCopy(b); |
---|
1904 | for(i=r;i>0;i--) |
---|
1905 | { |
---|
1906 | for(j=r;j>0;j--) |
---|
1907 | { |
---|
1908 | BIMATELEM(*mm,i,j)=n_convFactoryNSingN((*MM)(i,j),b->basecoeffs()); |
---|
1909 | } |
---|
1910 | } |
---|
1911 | delete MM; |
---|
1912 | return mm; |
---|
1913 | } |
---|
1914 | |
---|
1915 | matrix singntl_LLL(matrix m, const ring s ) |
---|
1916 | { |
---|
1917 | int r=m->rows(); |
---|
1918 | int c=m->cols(); |
---|
1919 | matrix res=mpNew(r,c); |
---|
1920 | if (rField_is_Q(s)) |
---|
1921 | { |
---|
1922 | CFMatrix M(r,c); |
---|
1923 | int i,j; |
---|
1924 | for(i=r;i>0;i--) |
---|
1925 | { |
---|
1926 | for(j=c;j>0;j--) |
---|
1927 | { |
---|
1928 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s); |
---|
1929 | } |
---|
1930 | } |
---|
1931 | CFMatrix *MM=cf_LLL(M); |
---|
1932 | for(i=r;i>0;i--) |
---|
1933 | { |
---|
1934 | for(j=c;j>0;j--) |
---|
1935 | { |
---|
1936 | MATELEM(res,i,j)=convFactoryPSingP((*MM)(i,j),s); |
---|
1937 | } |
---|
1938 | } |
---|
1939 | delete MM; |
---|
1940 | } |
---|
1941 | return res; |
---|
1942 | } |
---|
1943 | |
---|
1944 | intvec* singntl_LLL(intvec* m) |
---|
1945 | { |
---|
1946 | int r=m->rows(); |
---|
1947 | int c=m->cols(); |
---|
1948 | setCharacteristic( 0 ); |
---|
1949 | CFMatrix M(r,c); |
---|
1950 | int i,j; |
---|
1951 | for(i=r;i>0;i--) |
---|
1952 | { |
---|
1953 | for(j=c;j>0;j--) |
---|
1954 | { |
---|
1955 | M(i,j)=IMATELEM(*m,i,j); |
---|
1956 | } |
---|
1957 | } |
---|
1958 | CFMatrix *MM=cf_LLL(M); |
---|
1959 | intvec *mm=ivCopy(m); |
---|
1960 | for(i=r;i>0;i--) |
---|
1961 | { |
---|
1962 | for(j=c;j>0;j--) |
---|
1963 | { |
---|
1964 | IMATELEM(*mm,i,j)=convFactoryISingI((*MM)(i,j)); |
---|
1965 | } |
---|
1966 | } |
---|
1967 | delete MM; |
---|
1968 | return mm; |
---|
1969 | } |
---|
1970 | #else |
---|
1971 | matrix singntl_HNF(matrix m, const ring s ) |
---|
1972 | { |
---|
1973 | WerrorS("NTL/FLINT missing"); |
---|
1974 | return NULL; |
---|
1975 | } |
---|
1976 | |
---|
1977 | intvec* singntl_HNF(intvec* m) |
---|
1978 | { |
---|
1979 | WerrorS("NTL/FLINT missing"); |
---|
1980 | return NULL; |
---|
1981 | } |
---|
1982 | |
---|
1983 | matrix singntl_LLL(matrix m, const ring s ) |
---|
1984 | { |
---|
1985 | WerrorS("NTL/FLINT missing"); |
---|
1986 | return NULL; |
---|
1987 | } |
---|
1988 | |
---|
1989 | intvec* singntl_LLL(intvec* m) |
---|
1990 | { |
---|
1991 | WerrorS("NTL/FLINT missing"); |
---|
1992 | return NULL; |
---|
1993 | } |
---|
1994 | #endif |
---|
1995 | |
---|
1996 | #ifdef HAVE_NTL |
---|
1997 | matrix singntl_rref(matrix m, const ring R) |
---|
1998 | { |
---|
1999 | int r=m->rows(); |
---|
2000 | int c=m->cols(); |
---|
2001 | int i,j; |
---|
2002 | matrix M=mpNew(r,c); |
---|
2003 | if (rField_is_Zp(R)) |
---|
2004 | { |
---|
2005 | zz_p::init(rChar(R)); |
---|
2006 | mat_zz_p *NTLM=new mat_zz_p; |
---|
2007 | NTLM->SetDims(r,c); |
---|
2008 | for(i=r;i>0;i--) |
---|
2009 | { |
---|
2010 | for(j=c;j>0;j--) |
---|
2011 | { |
---|
2012 | poly h=MATELEM(m,i,j); |
---|
2013 | if (h!=NULL) |
---|
2014 | { |
---|
2015 | if (p_Totaldegree(h,R)==0) |
---|
2016 | { |
---|
2017 | (*NTLM)(i,j)=(long)p_GetCoeff(h,R); |
---|
2018 | } |
---|
2019 | else |
---|
2020 | { |
---|
2021 | WerrorS("smatrix for rref is not constant"); |
---|
2022 | return M; |
---|
2023 | } |
---|
2024 | } |
---|
2025 | } |
---|
2026 | } |
---|
2027 | gauss(*NTLM); |
---|
2028 | for(i=r;i>0;i--) |
---|
2029 | { |
---|
2030 | for(j=c;j>0;j--) |
---|
2031 | { |
---|
2032 | number n=n_Init(rep((*NTLM)(i,j)),R->cf); |
---|
2033 | if(!n_IsZero(n,R->cf)) |
---|
2034 | { |
---|
2035 | poly p=p_NSet(n,R); |
---|
2036 | MATELEM(M,i,j)=p; |
---|
2037 | } |
---|
2038 | } |
---|
2039 | } |
---|
2040 | delete NTLM; |
---|
2041 | } |
---|
2042 | else |
---|
2043 | { |
---|
2044 | WerrorS("not implemented for these coefficients"); |
---|
2045 | } |
---|
2046 | return M; |
---|
2047 | } |
---|
2048 | #endif |
---|
2049 | |
---|
2050 | #ifdef HAVE_NTL |
---|
2051 | ideal singntl_rref(ideal m, const ring R) /*assume smatrix m*/ |
---|
2052 | { |
---|
2053 | int r=m->rank; |
---|
2054 | int c=m->ncols; |
---|
2055 | int i,j; |
---|
2056 | ideal M=idInit(c,r); |
---|
2057 | if (rField_is_Zp(R)) |
---|
2058 | { |
---|
2059 | zz_p::init(rChar(R)); |
---|
2060 | mat_zz_p *NTLM=new mat_zz_p; |
---|
2061 | NTLM->SetDims(r,c); |
---|
2062 | for(j=c-1;j>=0;j--) |
---|
2063 | { |
---|
2064 | poly h=m->m[j]; |
---|
2065 | while(h!=NULL) |
---|
2066 | { |
---|
2067 | i=p_GetComp(h,R); |
---|
2068 | if (p_Totaldegree(h,R)==0) |
---|
2069 | (*NTLM)(i,j+1)=(long)p_GetCoeff(h,R); |
---|
2070 | else |
---|
2071 | { |
---|
2072 | WerrorS("smatrix for rref is not constant"); |
---|
2073 | return M; |
---|
2074 | } |
---|
2075 | pIter(h); |
---|
2076 | } |
---|
2077 | } |
---|
2078 | gauss(*NTLM); |
---|
2079 | for(i=r;i>0;i--) |
---|
2080 | { |
---|
2081 | for(j=c;j>0;j--) |
---|
2082 | { |
---|
2083 | number n=n_Init(rep((*NTLM)(i,j)),R->cf); |
---|
2084 | if(!n_IsZero(n,R->cf)) |
---|
2085 | { |
---|
2086 | poly p=p_NSet(n,R); |
---|
2087 | p_SetComp(p,i,R); |
---|
2088 | M->m[j-1]=p_Add_q(M->m[j-1],p,R); |
---|
2089 | } |
---|
2090 | } |
---|
2091 | } |
---|
2092 | delete NTLM; |
---|
2093 | } |
---|
2094 | else |
---|
2095 | { |
---|
2096 | WerrorS("not implemented for these coefficients"); |
---|
2097 | } |
---|
2098 | return M; |
---|
2099 | } |
---|
2100 | #endif |
---|
2101 | |
---|
2102 | #if defined(HAVE_NTL) || defined(HAVE_FLINT) |
---|
2103 | ideal singclap_absFactorize ( poly f, ideal & mipos, intvec ** exps, int & numFactors, const ring r) |
---|
2104 | { |
---|
2105 | p_Test(f, r); |
---|
2106 | |
---|
2107 | ideal res=NULL; |
---|
2108 | |
---|
2109 | int offs = rPar(r); |
---|
2110 | if (f==NULL) |
---|
2111 | { |
---|
2112 | res= idInit (1, 1); |
---|
2113 | mipos= idInit (1, 1); |
---|
2114 | mipos->m[0]= convFactoryPSingTrP (Variable (offs), r); //overkill |
---|
2115 | (*exps)=new intvec (1); |
---|
2116 | (**exps)[0]= 1; |
---|
2117 | numFactors= 0; |
---|
2118 | return res; |
---|
2119 | } |
---|
2120 | CanonicalForm F( convSingTrPFactoryP( f, r) ); |
---|
2121 | |
---|
2122 | bool isRat= isOn (SW_RATIONAL); |
---|
2123 | if (!isRat) |
---|
2124 | On (SW_RATIONAL); |
---|
2125 | |
---|
2126 | CFAFList absFactors= absFactorize (F); |
---|
2127 | |
---|
2128 | int n= absFactors.length(); |
---|
2129 | *exps=new intvec (n); |
---|
2130 | |
---|
2131 | res= idInit (n, 1); |
---|
2132 | |
---|
2133 | mipos= idInit (n, 1); |
---|
2134 | |
---|
2135 | Variable x= Variable (offs); |
---|
2136 | Variable alpha; |
---|
2137 | int i= 0; |
---|
2138 | numFactors= 0; |
---|
2139 | int count; |
---|
2140 | CFAFListIterator iter= absFactors; |
---|
2141 | CanonicalForm lead= iter.getItem().factor(); |
---|
2142 | if (iter.getItem().factor().inCoeffDomain()) |
---|
2143 | { |
---|
2144 | i++; |
---|
2145 | iter++; |
---|
2146 | } |
---|
2147 | for (; iter.hasItem(); iter++, i++) |
---|
2148 | { |
---|
2149 | (**exps)[i]= iter.getItem().exp(); |
---|
2150 | alpha= iter.getItem().minpoly().mvar(); |
---|
2151 | if (iter.getItem().minpoly().isOne()) |
---|
2152 | lead /= power (bCommonDen (iter.getItem().factor()), iter.getItem().exp()); |
---|
2153 | else |
---|
2154 | lead /= power (power (bCommonDen (iter.getItem().factor()), degree (iter.getItem().minpoly())), iter.getItem().exp()); |
---|
2155 | res->m[i]= convFactoryPSingTrP (replacevar (iter.getItem().factor()*bCommonDen (iter.getItem().factor()), alpha, x), r); |
---|
2156 | if (iter.getItem().minpoly().isOne()) |
---|
2157 | { |
---|
2158 | count= iter.getItem().exp(); |
---|
2159 | mipos->m[i]= convFactoryPSingTrP (x,r); |
---|
2160 | } |
---|
2161 | else |
---|
2162 | { |
---|
2163 | count= iter.getItem().exp()*degree (iter.getItem().minpoly()); |
---|
2164 | mipos->m[i]= convFactoryPSingTrP (replacevar (iter.getItem().minpoly(), alpha, x), r); |
---|
2165 | } |
---|
2166 | if (!iter.getItem().minpoly().isOne()) |
---|
2167 | prune (alpha); |
---|
2168 | numFactors += count; |
---|
2169 | } |
---|
2170 | if (!isRat) |
---|
2171 | Off (SW_RATIONAL); |
---|
2172 | |
---|
2173 | (**exps)[0]= 1; |
---|
2174 | res->m[0]= convFactoryPSingTrP (lead, r); |
---|
2175 | mipos->m[0]= convFactoryPSingTrP (x, r); |
---|
2176 | return res; |
---|
2177 | } |
---|
2178 | |
---|
2179 | #else |
---|
2180 | ideal singclap_absFactorize ( poly f, ideal & mipos, intvec ** exps, int & numFactors, const ring r) |
---|
2181 | { |
---|
2182 | WerrorS("NTL/FLINT missing: absFactorize"); |
---|
2183 | return NULL; |
---|
2184 | } |
---|
2185 | |
---|
2186 | #endif /* HAVE_NTL */ |
---|
2187 | |
---|
2188 | int * Zp_roots(poly p, const ring r) |
---|
2189 | { |
---|
2190 | CanonicalForm pp=convSingPFactoryP(p,r); |
---|
2191 | return Zp_roots(pp); |
---|
2192 | } |
---|