1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /* |
---|
5 | * ABSTRACT: numbers modulo n |
---|
6 | */ |
---|
7 | #include "misc/auxiliary.h" |
---|
8 | |
---|
9 | #include "misc/mylimits.h" |
---|
10 | #include "misc/prime.h" // IsPrime |
---|
11 | #include "reporter/reporter.h" |
---|
12 | |
---|
13 | #include "coeffs/si_gmp.h" |
---|
14 | #include "coeffs/coeffs.h" |
---|
15 | #include "coeffs/modulop.h" |
---|
16 | #include "coeffs/rintegers.h" |
---|
17 | #include "coeffs/numbers.h" |
---|
18 | |
---|
19 | #include "coeffs/mpr_complex.h" |
---|
20 | |
---|
21 | #include "coeffs/longrat.h" |
---|
22 | #include "coeffs/rmodulon.h" |
---|
23 | |
---|
24 | #include <string.h> |
---|
25 | |
---|
26 | #ifdef HAVE_RINGS |
---|
27 | |
---|
28 | void nrnWrite (number a, const coeffs); |
---|
29 | #ifdef LDEBUG |
---|
30 | BOOLEAN nrnDBTest (number a, const char *f, const int l, const coeffs r); |
---|
31 | #endif |
---|
32 | |
---|
33 | EXTERN_VAR omBin gmp_nrz_bin; |
---|
34 | |
---|
35 | coeffs nrnInitCfByName(char *s,n_coeffType) |
---|
36 | { |
---|
37 | const char start[]="ZZ/bigint("; |
---|
38 | const int start_len=strlen(start); |
---|
39 | if (strncmp(s,start,start_len)==0) |
---|
40 | { |
---|
41 | s+=start_len; |
---|
42 | mpz_t z; |
---|
43 | mpz_init(z); |
---|
44 | s=nEatLong(s,z); |
---|
45 | ZnmInfo info; |
---|
46 | info.base=z; |
---|
47 | info.exp= 1; |
---|
48 | while ((*s!='\0') && (*s!=')')) s++; |
---|
49 | // expect ")" or ")^exp" |
---|
50 | if (*s=='\0') { mpz_clear(z); return NULL; } |
---|
51 | if (((*s)==')') && (*(s+1)=='^')) |
---|
52 | { |
---|
53 | s=s+2; |
---|
54 | int i; |
---|
55 | s=nEati(s,&i,0); |
---|
56 | info.exp=(unsigned long)i; |
---|
57 | return nInitChar(n_Znm,(void*) &info); |
---|
58 | } |
---|
59 | else |
---|
60 | return nInitChar(n_Zn,(void*) &info); |
---|
61 | } |
---|
62 | else return NULL; |
---|
63 | } |
---|
64 | |
---|
65 | STATIC_VAR char* nrnCoeffName_buff=NULL; |
---|
66 | static char* nrnCoeffName(const coeffs r) |
---|
67 | { |
---|
68 | if(nrnCoeffName_buff!=NULL) omFree(nrnCoeffName_buff); |
---|
69 | size_t l = (size_t)mpz_sizeinbase(r->modBase, 10) + 2; |
---|
70 | char* s = (char*) omAlloc(l); |
---|
71 | l+=24; |
---|
72 | nrnCoeffName_buff=(char*)omAlloc(l); |
---|
73 | s= mpz_get_str (s, 10, r->modBase); |
---|
74 | int ll; |
---|
75 | if (nCoeff_is_Zn(r)) |
---|
76 | { |
---|
77 | if (strlen(s)<10) |
---|
78 | ll=snprintf(nrnCoeffName_buff,l,"ZZ/(%s)",s); |
---|
79 | else |
---|
80 | ll=snprintf(nrnCoeffName_buff,l,"ZZ/bigint(%s)",s); |
---|
81 | } |
---|
82 | else if (nCoeff_is_Ring_PtoM(r)) |
---|
83 | ll=snprintf(nrnCoeffName_buff,l,"ZZ/(bigint(%s)^%lu)",s,r->modExponent); |
---|
84 | assume(ll<(int)l); // otherwise nrnCoeffName_buff too small |
---|
85 | omFreeSize((ADDRESS)s, l-22); |
---|
86 | return nrnCoeffName_buff; |
---|
87 | } |
---|
88 | |
---|
89 | static BOOLEAN nrnCoeffIsEqual(const coeffs r, n_coeffType n, void * parameter) |
---|
90 | { |
---|
91 | /* test, if r is an instance of nInitCoeffs(n,parameter) */ |
---|
92 | ZnmInfo *info=(ZnmInfo*)parameter; |
---|
93 | return (n==r->type) && (r->modExponent==info->exp) |
---|
94 | && (mpz_cmp(r->modBase,info->base)==0); |
---|
95 | } |
---|
96 | |
---|
97 | static void nrnKillChar(coeffs r) |
---|
98 | { |
---|
99 | mpz_clear(r->modNumber); |
---|
100 | mpz_clear(r->modBase); |
---|
101 | omFreeBin((void *) r->modBase, gmp_nrz_bin); |
---|
102 | omFreeBin((void *) r->modNumber, gmp_nrz_bin); |
---|
103 | } |
---|
104 | |
---|
105 | static coeffs nrnQuot1(number c, const coeffs r) |
---|
106 | { |
---|
107 | coeffs rr; |
---|
108 | long ch = r->cfInt(c, r); |
---|
109 | mpz_t a,b; |
---|
110 | mpz_init_set(a, r->modNumber); |
---|
111 | mpz_init_set_ui(b, ch); |
---|
112 | mpz_t gcd; |
---|
113 | mpz_init(gcd); |
---|
114 | mpz_gcd(gcd, a,b); |
---|
115 | if(mpz_cmp_ui(gcd, 1) == 0) |
---|
116 | { |
---|
117 | WerrorS("constant in q-ideal is coprime to modulus in ground ring"); |
---|
118 | WerrorS("Unable to create qring!"); |
---|
119 | return NULL; |
---|
120 | } |
---|
121 | if(r->modExponent == 1) |
---|
122 | { |
---|
123 | ZnmInfo info; |
---|
124 | info.base = gcd; |
---|
125 | info.exp = (unsigned long) 1; |
---|
126 | rr = nInitChar(n_Zn, (void*)&info); |
---|
127 | } |
---|
128 | else |
---|
129 | { |
---|
130 | ZnmInfo info; |
---|
131 | info.base = r->modBase; |
---|
132 | int kNew = 1; |
---|
133 | mpz_t baseTokNew; |
---|
134 | mpz_init(baseTokNew); |
---|
135 | mpz_set(baseTokNew, r->modBase); |
---|
136 | while(mpz_cmp(gcd, baseTokNew) > 0) |
---|
137 | { |
---|
138 | kNew++; |
---|
139 | mpz_mul(baseTokNew, baseTokNew, r->modBase); |
---|
140 | } |
---|
141 | //printf("\nkNew = %i\n",kNew); |
---|
142 | info.exp = kNew; |
---|
143 | mpz_clear(baseTokNew); |
---|
144 | rr = nInitChar(n_Znm, (void*)&info); |
---|
145 | } |
---|
146 | mpz_clear(gcd); |
---|
147 | return(rr); |
---|
148 | } |
---|
149 | |
---|
150 | static number nrnCopy(number a, const coeffs) |
---|
151 | { |
---|
152 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
153 | mpz_init_set(erg, (mpz_ptr) a); |
---|
154 | return (number) erg; |
---|
155 | } |
---|
156 | |
---|
157 | /* |
---|
158 | * create a number from int |
---|
159 | */ |
---|
160 | static number nrnInit(long i, const coeffs r) |
---|
161 | { |
---|
162 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
163 | mpz_init_set_si(erg, i); |
---|
164 | mpz_mod(erg, erg, r->modNumber); |
---|
165 | return (number) erg; |
---|
166 | } |
---|
167 | |
---|
168 | /* |
---|
169 | * convert a number to int |
---|
170 | */ |
---|
171 | static long nrnInt(number &n, const coeffs) |
---|
172 | { |
---|
173 | return mpz_get_si((mpz_ptr) n); |
---|
174 | } |
---|
175 | |
---|
176 | #if SI_INTEGER_VARIANT==2 |
---|
177 | #define nrnDelete nrzDelete |
---|
178 | #define nrnSize nrzSize |
---|
179 | #else |
---|
180 | static void nrnDelete(number *a, const coeffs) |
---|
181 | { |
---|
182 | if (*a != NULL) |
---|
183 | { |
---|
184 | mpz_clear((mpz_ptr) *a); |
---|
185 | omFreeBin((void *) *a, gmp_nrz_bin); |
---|
186 | *a = NULL; |
---|
187 | } |
---|
188 | } |
---|
189 | static int nrnSize(number a, const coeffs) |
---|
190 | { |
---|
191 | mpz_ptr p=(mpz_ptr)a; |
---|
192 | int s=p->_mp_alloc; |
---|
193 | if (s==1) s=(mpz_cmp_ui(p,0)!=0); |
---|
194 | return s; |
---|
195 | } |
---|
196 | #endif |
---|
197 | /* |
---|
198 | * Multiply two numbers |
---|
199 | */ |
---|
200 | static number nrnMult(number a, number b, const coeffs r) |
---|
201 | { |
---|
202 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
203 | mpz_init(erg); |
---|
204 | mpz_mul(erg, (mpz_ptr)a, (mpz_ptr) b); |
---|
205 | mpz_mod(erg, erg, r->modNumber); |
---|
206 | return (number) erg; |
---|
207 | } |
---|
208 | |
---|
209 | static void nrnInpMult(number &a, number b, const coeffs r) |
---|
210 | { |
---|
211 | mpz_mul((mpz_ptr)a, (mpz_ptr)a, (mpz_ptr) b); |
---|
212 | mpz_mod((mpz_ptr)a, (mpz_ptr)a, r->modNumber); |
---|
213 | } |
---|
214 | |
---|
215 | static void nrnPower(number a, int i, number * result, const coeffs r) |
---|
216 | { |
---|
217 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
218 | mpz_init(erg); |
---|
219 | mpz_powm_ui(erg, (mpz_ptr)a, i, r->modNumber); |
---|
220 | *result = (number) erg; |
---|
221 | } |
---|
222 | |
---|
223 | static number nrnAdd(number a, number b, const coeffs r) |
---|
224 | { |
---|
225 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
226 | mpz_init(erg); |
---|
227 | mpz_add(erg, (mpz_ptr)a, (mpz_ptr) b); |
---|
228 | mpz_mod(erg, erg, r->modNumber); |
---|
229 | return (number) erg; |
---|
230 | } |
---|
231 | |
---|
232 | static void nrnInpAdd(number &a, number b, const coeffs r) |
---|
233 | { |
---|
234 | mpz_add((mpz_ptr)a, (mpz_ptr)a, (mpz_ptr) b); |
---|
235 | mpz_mod((mpz_ptr)a, (mpz_ptr)a, r->modNumber); |
---|
236 | } |
---|
237 | |
---|
238 | static number nrnSub(number a, number b, const coeffs r) |
---|
239 | { |
---|
240 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
241 | mpz_init(erg); |
---|
242 | mpz_sub(erg, (mpz_ptr)a, (mpz_ptr) b); |
---|
243 | mpz_mod(erg, erg, r->modNumber); |
---|
244 | return (number) erg; |
---|
245 | } |
---|
246 | |
---|
247 | static BOOLEAN nrnIsZero(number a, const coeffs) |
---|
248 | { |
---|
249 | return 0 == mpz_cmpabs_ui((mpz_ptr)a, 0); |
---|
250 | } |
---|
251 | |
---|
252 | static number nrnNeg(number c, const coeffs r) |
---|
253 | { |
---|
254 | if( !nrnIsZero(c, r) ) |
---|
255 | // Attention: This method operates in-place. |
---|
256 | mpz_sub((mpz_ptr)c, r->modNumber, (mpz_ptr)c); |
---|
257 | return c; |
---|
258 | } |
---|
259 | |
---|
260 | static number nrnInvers(number c, const coeffs r) |
---|
261 | { |
---|
262 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
263 | mpz_init(erg); |
---|
264 | if (nrnIsZero(c,r)) |
---|
265 | { |
---|
266 | WerrorS(nDivBy0); |
---|
267 | } |
---|
268 | else |
---|
269 | { |
---|
270 | mpz_invert(erg, (mpz_ptr)c, r->modNumber); |
---|
271 | } |
---|
272 | return (number) erg; |
---|
273 | } |
---|
274 | |
---|
275 | /* |
---|
276 | * Give the largest k, such that a = x * k, b = y * k has |
---|
277 | * a solution. |
---|
278 | * a may be NULL, b not |
---|
279 | */ |
---|
280 | static number nrnGcd(number a, number b, const coeffs r) |
---|
281 | { |
---|
282 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
283 | mpz_init_set(erg, r->modNumber); |
---|
284 | if (a != NULL) mpz_gcd(erg, erg, (mpz_ptr)a); |
---|
285 | mpz_gcd(erg, erg, (mpz_ptr)b); |
---|
286 | if(mpz_cmp(erg,r->modNumber)==0) |
---|
287 | { |
---|
288 | mpz_clear(erg); |
---|
289 | omFreeBin((ADDRESS)erg,gmp_nrz_bin); |
---|
290 | return nrnInit(0,r); |
---|
291 | } |
---|
292 | return (number)erg; |
---|
293 | } |
---|
294 | |
---|
295 | /* |
---|
296 | * Give the smallest k, such that a * x = k = b * y has a solution |
---|
297 | * TODO: lcm(gcd,gcd) better than gcd(lcm) ? |
---|
298 | */ |
---|
299 | static number nrnLcm(number a, number b, const coeffs r) |
---|
300 | { |
---|
301 | number erg = nrnGcd(NULL, a, r); |
---|
302 | number tmp = nrnGcd(NULL, b, r); |
---|
303 | mpz_lcm((mpz_ptr)erg, (mpz_ptr)erg, (mpz_ptr)tmp); |
---|
304 | nrnDelete(&tmp, r); |
---|
305 | return (number)erg; |
---|
306 | } |
---|
307 | |
---|
308 | /* Not needed any more, but may have room for improvement |
---|
309 | number nrnGcd3(number a,number b, number c,ring r) |
---|
310 | { |
---|
311 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
312 | mpz_init(erg); |
---|
313 | if (a == NULL) a = (number)r->modNumber; |
---|
314 | if (b == NULL) b = (number)r->modNumber; |
---|
315 | if (c == NULL) c = (number)r->modNumber; |
---|
316 | mpz_gcd(erg, (mpz_ptr)a, (mpz_ptr)b); |
---|
317 | mpz_gcd(erg, erg, (mpz_ptr)c); |
---|
318 | mpz_gcd(erg, erg, r->modNumber); |
---|
319 | return (number)erg; |
---|
320 | } |
---|
321 | */ |
---|
322 | |
---|
323 | /* |
---|
324 | * Give the largest k, such that a = x * k, b = y * k has |
---|
325 | * a solution and r, s, s.t. k = s*a + t*b |
---|
326 | * CF: careful: ExtGcd is wrong as implemented (or at least may not |
---|
327 | * give you what you want: |
---|
328 | * ExtGcd(5, 10 modulo 12): |
---|
329 | * the gcdext will return 5 = 1*5 + 0*10 |
---|
330 | * however, mod 12, the gcd should be 1 |
---|
331 | */ |
---|
332 | static number nrnExtGcd(number a, number b, number *s, number *t, const coeffs r) |
---|
333 | { |
---|
334 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
335 | mpz_ptr bs = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
336 | mpz_ptr bt = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
337 | mpz_init(erg); |
---|
338 | mpz_init(bs); |
---|
339 | mpz_init(bt); |
---|
340 | mpz_gcdext(erg, bs, bt, (mpz_ptr)a, (mpz_ptr)b); |
---|
341 | mpz_mod(bs, bs, r->modNumber); |
---|
342 | mpz_mod(bt, bt, r->modNumber); |
---|
343 | *s = (number)bs; |
---|
344 | *t = (number)bt; |
---|
345 | return (number)erg; |
---|
346 | } |
---|
347 | |
---|
348 | static BOOLEAN nrnIsOne(number a, const coeffs) |
---|
349 | { |
---|
350 | return 0 == mpz_cmp_si((mpz_ptr)a, 1); |
---|
351 | } |
---|
352 | |
---|
353 | static BOOLEAN nrnEqual(number a, number b, const coeffs) |
---|
354 | { |
---|
355 | return 0 == mpz_cmp((mpz_ptr)a, (mpz_ptr)b); |
---|
356 | } |
---|
357 | |
---|
358 | static number nrnGetUnit(number k, const coeffs r) |
---|
359 | { |
---|
360 | if (mpz_divisible_p(r->modNumber, (mpz_ptr)k)) return nrnInit(1,r); |
---|
361 | |
---|
362 | mpz_ptr unit = (mpz_ptr)nrnGcd(NULL, k, r); |
---|
363 | mpz_tdiv_q(unit, (mpz_ptr)k, unit); |
---|
364 | mpz_ptr gcd = (mpz_ptr)nrnGcd(NULL, (number)unit, r); |
---|
365 | if (!nrnIsOne((number)gcd,r)) |
---|
366 | { |
---|
367 | mpz_ptr ctmp; |
---|
368 | // tmp := unit^2 |
---|
369 | mpz_ptr tmp = (mpz_ptr) nrnMult((number) unit,(number) unit,r); |
---|
370 | // gcd_new := gcd(tmp, 0) |
---|
371 | mpz_ptr gcd_new = (mpz_ptr) nrnGcd(NULL, (number) tmp, r); |
---|
372 | while (!nrnEqual((number) gcd_new,(number) gcd,r)) |
---|
373 | { |
---|
374 | // gcd := gcd_new |
---|
375 | ctmp = gcd; |
---|
376 | gcd = gcd_new; |
---|
377 | gcd_new = ctmp; |
---|
378 | // tmp := tmp * unit |
---|
379 | mpz_mul(tmp, tmp, unit); |
---|
380 | mpz_mod(tmp, tmp, r->modNumber); |
---|
381 | // gcd_new := gcd(tmp, 0) |
---|
382 | mpz_gcd(gcd_new, tmp, r->modNumber); |
---|
383 | } |
---|
384 | // unit := unit + modNumber / gcd_new |
---|
385 | mpz_tdiv_q(tmp, r->modNumber, gcd_new); |
---|
386 | mpz_add(unit, unit, tmp); |
---|
387 | mpz_mod(unit, unit, r->modNumber); |
---|
388 | nrnDelete((number*) &gcd_new, r); |
---|
389 | nrnDelete((number*) &tmp, r); |
---|
390 | } |
---|
391 | nrnDelete((number*) &gcd, r); |
---|
392 | return (number)unit; |
---|
393 | } |
---|
394 | |
---|
395 | /* XExtGcd returns a unimodular matrix ((s,t)(u,v)) sth. |
---|
396 | * (a,b)^t ((st)(uv)) = (g,0)^t |
---|
397 | * Beware, the ExtGcd will not necessaairly do this. |
---|
398 | * Problem: if g = as+bt then (in Z/nZ) it follows NOT that |
---|
399 | * 1 = (a/g)s + (b/g) t |
---|
400 | * due to the zero divisors. |
---|
401 | */ |
---|
402 | |
---|
403 | //#define CF_DEB; |
---|
404 | static number nrnXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r) |
---|
405 | { |
---|
406 | number xx; |
---|
407 | #ifdef CF_DEB |
---|
408 | StringSetS("XExtGcd of "); |
---|
409 | nrnWrite(a, r); |
---|
410 | StringAppendS("\t"); |
---|
411 | nrnWrite(b, r); |
---|
412 | StringAppendS(" modulo "); |
---|
413 | nrnWrite(xx = (number)r->modNumber, r); |
---|
414 | Print("%s\n", StringEndS()); |
---|
415 | #endif |
---|
416 | |
---|
417 | mpz_ptr one = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
418 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
419 | mpz_ptr bs = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
420 | mpz_ptr bt = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
421 | mpz_ptr bu = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
422 | mpz_ptr bv = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
423 | mpz_init(erg); |
---|
424 | mpz_init(one); |
---|
425 | mpz_init_set(bs, (mpz_ptr) a); |
---|
426 | mpz_init_set(bt, (mpz_ptr) b); |
---|
427 | mpz_init(bu); |
---|
428 | mpz_init(bv); |
---|
429 | mpz_gcd(erg, bs, bt); |
---|
430 | |
---|
431 | #ifdef CF_DEB |
---|
432 | StringSetS("1st gcd:"); |
---|
433 | nrnWrite(xx= (number)erg, r); |
---|
434 | #endif |
---|
435 | |
---|
436 | mpz_gcd(erg, erg, r->modNumber); |
---|
437 | |
---|
438 | mpz_div(bs, bs, erg); |
---|
439 | mpz_div(bt, bt, erg); |
---|
440 | |
---|
441 | #ifdef CF_DEB |
---|
442 | Print("%s\n", StringEndS()); |
---|
443 | StringSetS("xgcd: "); |
---|
444 | #endif |
---|
445 | |
---|
446 | mpz_gcdext(one, bu, bv, bs, bt); |
---|
447 | number ui = nrnGetUnit(xx = (number) one, r); |
---|
448 | #ifdef CF_DEB |
---|
449 | n_Write(xx, r); |
---|
450 | StringAppendS("\t"); |
---|
451 | n_Write(ui, r); |
---|
452 | Print("%s\n", StringEndS()); |
---|
453 | #endif |
---|
454 | nrnDelete(&xx, r); |
---|
455 | if (!nrnIsOne(ui, r)) |
---|
456 | { |
---|
457 | #ifdef CF_DEB |
---|
458 | PrintS("Scaling\n"); |
---|
459 | #endif |
---|
460 | number uii = nrnInvers(ui, r); |
---|
461 | nrnDelete(&ui, r); |
---|
462 | ui = uii; |
---|
463 | mpz_ptr uu = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
464 | mpz_init_set(uu, (mpz_ptr)ui); |
---|
465 | mpz_mul(bu, bu, uu); |
---|
466 | mpz_mul(bv, bv, uu); |
---|
467 | mpz_clear(uu); |
---|
468 | omFreeBin(uu, gmp_nrz_bin); |
---|
469 | } |
---|
470 | nrnDelete(&ui, r); |
---|
471 | #ifdef CF_DEB |
---|
472 | StringSetS("xgcd"); |
---|
473 | nrnWrite(xx= (number)bs, r); |
---|
474 | StringAppendS("*"); |
---|
475 | nrnWrite(xx= (number)bu, r); |
---|
476 | StringAppendS(" + "); |
---|
477 | nrnWrite(xx= (number)bt, r); |
---|
478 | StringAppendS("*"); |
---|
479 | nrnWrite(xx= (number)bv, r); |
---|
480 | Print("%s\n", StringEndS()); |
---|
481 | #endif |
---|
482 | |
---|
483 | mpz_mod(bs, bs, r->modNumber); |
---|
484 | mpz_mod(bt, bt, r->modNumber); |
---|
485 | mpz_mod(bu, bu, r->modNumber); |
---|
486 | mpz_mod(bv, bv, r->modNumber); |
---|
487 | *s = (number)bu; |
---|
488 | *t = (number)bv; |
---|
489 | *u = (number)bt; |
---|
490 | *u = nrnNeg(*u, r); |
---|
491 | *v = (number)bs; |
---|
492 | return (number)erg; |
---|
493 | } |
---|
494 | |
---|
495 | static BOOLEAN nrnIsMOne(number a, const coeffs r) |
---|
496 | { |
---|
497 | if((r->ch==2) && (nrnIsOne(a,r))) return FALSE; |
---|
498 | mpz_t t; mpz_init_set(t, (mpz_ptr)a); |
---|
499 | mpz_add_ui(t, t, 1); |
---|
500 | bool erg = (0 == mpz_cmp(t, r->modNumber)); |
---|
501 | mpz_clear(t); |
---|
502 | return erg; |
---|
503 | } |
---|
504 | |
---|
505 | static BOOLEAN nrnGreater(number a, number b, const coeffs) |
---|
506 | { |
---|
507 | return 0 < mpz_cmp((mpz_ptr)a, (mpz_ptr)b); |
---|
508 | } |
---|
509 | |
---|
510 | static BOOLEAN nrnGreaterZero(number k, const coeffs cf) |
---|
511 | { |
---|
512 | if (cf->is_field) |
---|
513 | { |
---|
514 | if (mpz_cmp_ui(cf->modBase,2)==0) |
---|
515 | { |
---|
516 | return TRUE; |
---|
517 | } |
---|
518 | #if 0 |
---|
519 | mpz_t ch2; mpz_init_set(ch2, cf->modBase); |
---|
520 | mpz_sub_ui(ch2,ch2,1); //cf->modBase is odd |
---|
521 | mpz_divexact_ui(ch2,ch2,2); |
---|
522 | if (mpz_cmp(ch2,(mpz_ptr)k)<0) |
---|
523 | { |
---|
524 | mpz_clear(ch2); |
---|
525 | return FALSE; |
---|
526 | } |
---|
527 | mpz_clear(ch2); |
---|
528 | #endif |
---|
529 | } |
---|
530 | #if 0 |
---|
531 | else |
---|
532 | { |
---|
533 | mpz_t ch2; mpz_init_set(ch2, cf->modBase); |
---|
534 | mpz_tdiv_q_ui(ch2,ch2,2); |
---|
535 | if (mpz_cmp(ch2,(mpz_ptr)k)<0) |
---|
536 | { |
---|
537 | mpz_clear(ch2); |
---|
538 | return FALSE; |
---|
539 | } |
---|
540 | mpz_clear(ch2); |
---|
541 | } |
---|
542 | #endif |
---|
543 | return 0 < mpz_sgn1((mpz_ptr)k); |
---|
544 | } |
---|
545 | |
---|
546 | static BOOLEAN nrnIsUnit(number a, const coeffs r) |
---|
547 | { |
---|
548 | number tmp = nrnGcd(a, (number)r->modNumber, r); |
---|
549 | bool res = nrnIsOne(tmp, r); |
---|
550 | nrnDelete(&tmp, r); |
---|
551 | return res; |
---|
552 | } |
---|
553 | |
---|
554 | static number nrnAnn(number k, const coeffs r) |
---|
555 | { |
---|
556 | mpz_ptr tmp = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
557 | mpz_init(tmp); |
---|
558 | mpz_gcd(tmp, (mpz_ptr) k, r->modNumber); |
---|
559 | if (mpz_cmp_si(tmp, 1)==0) |
---|
560 | { |
---|
561 | mpz_set_ui(tmp, 0); |
---|
562 | return (number) tmp; |
---|
563 | } |
---|
564 | mpz_divexact(tmp, r->modNumber, tmp); |
---|
565 | return (number) tmp; |
---|
566 | } |
---|
567 | |
---|
568 | static BOOLEAN nrnDivBy(number a, number b, const coeffs r) |
---|
569 | { |
---|
570 | /* b divides a iff b/gcd(a, b) is a unit in the given ring: */ |
---|
571 | number n = nrnGcd(a, b, r); |
---|
572 | mpz_tdiv_q((mpz_ptr)n, (mpz_ptr)b, (mpz_ptr)n); |
---|
573 | bool result = nrnIsUnit(n, r); |
---|
574 | nrnDelete(&n, NULL); |
---|
575 | return result; |
---|
576 | } |
---|
577 | |
---|
578 | static int nrnDivComp(number a, number b, const coeffs r) |
---|
579 | { |
---|
580 | if (nrnEqual(a, b,r)) return 2; |
---|
581 | if (mpz_divisible_p((mpz_ptr) a, (mpz_ptr) b)) return -1; |
---|
582 | if (mpz_divisible_p((mpz_ptr) b, (mpz_ptr) a)) return 1; |
---|
583 | return 0; |
---|
584 | } |
---|
585 | |
---|
586 | static number nrnDiv(number a, number b, const coeffs r) |
---|
587 | { |
---|
588 | if (nrnIsZero(b,r)) |
---|
589 | { |
---|
590 | WerrorS(nDivBy0); |
---|
591 | return nrnInit(0,r); |
---|
592 | } |
---|
593 | else if (r->is_field) |
---|
594 | { |
---|
595 | number inv=nrnInvers(b,r); |
---|
596 | number erg=nrnMult(a,inv,r); |
---|
597 | nrnDelete(&inv,r); |
---|
598 | return erg; |
---|
599 | } |
---|
600 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
601 | mpz_init(erg); |
---|
602 | if (mpz_divisible_p((mpz_ptr)a, (mpz_ptr)b)) |
---|
603 | { |
---|
604 | mpz_divexact(erg, (mpz_ptr)a, (mpz_ptr)b); |
---|
605 | return (number)erg; |
---|
606 | } |
---|
607 | else |
---|
608 | { |
---|
609 | mpz_ptr gcd = (mpz_ptr)nrnGcd(a, b, r); |
---|
610 | mpz_divexact(erg, (mpz_ptr)b, gcd); |
---|
611 | if (!nrnIsUnit((number)erg, r)) |
---|
612 | { |
---|
613 | WerrorS("Division not possible, even by cancelling zero divisors."); |
---|
614 | nrnDelete((number*) &gcd, r); |
---|
615 | nrnDelete((number*) &erg, r); |
---|
616 | return (number)NULL; |
---|
617 | } |
---|
618 | // a / gcd(a,b) * [b / gcd (a,b)]^(-1) |
---|
619 | mpz_ptr tmp = (mpz_ptr)nrnInvers((number) erg,r); |
---|
620 | mpz_divexact(erg, (mpz_ptr)a, gcd); |
---|
621 | mpz_mul(erg, erg, tmp); |
---|
622 | nrnDelete((number*) &gcd, r); |
---|
623 | nrnDelete((number*) &tmp, r); |
---|
624 | mpz_mod(erg, erg, r->modNumber); |
---|
625 | return (number)erg; |
---|
626 | } |
---|
627 | } |
---|
628 | |
---|
629 | static number nrnMod(number a, number b, const coeffs r) |
---|
630 | { |
---|
631 | /* |
---|
632 | We need to return the number rr which is uniquely determined by the |
---|
633 | following two properties: |
---|
634 | (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z) |
---|
635 | (2) There exists some k in the integers Z such that a = k * b + rr. |
---|
636 | Consider g := gcd(n, |b|). Note that then |b|/g is a unit in Z/n. |
---|
637 | Now, there are three cases: |
---|
638 | (a) g = 1 |
---|
639 | Then |b| is a unit in Z/n, i.e. |b| (and also b) divides a. |
---|
640 | Thus rr = 0. |
---|
641 | (b) g <> 1 and g divides a |
---|
642 | Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0. |
---|
643 | (c) g <> 1 and g does not divide a |
---|
644 | Then denote the division with remainder of a by g as this: |
---|
645 | a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b| |
---|
646 | fulfills (1) and (2), i.e. rr := t is the correct result. Hence |
---|
647 | in this third case, rr is the remainder of division of a by g in Z. |
---|
648 | Remark: according to mpz_mod: a,b are always non-negative |
---|
649 | */ |
---|
650 | mpz_ptr g = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
651 | mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
652 | mpz_init(g); |
---|
653 | mpz_init_set_ui(rr, 0); |
---|
654 | mpz_gcd(g, (mpz_ptr)r->modNumber, (mpz_ptr)b); // g is now as above |
---|
655 | if (mpz_cmp_si(g, 1L) != 0) mpz_mod(rr, (mpz_ptr)a, g); // the case g <> 1 |
---|
656 | mpz_clear(g); |
---|
657 | omFreeBin(g, gmp_nrz_bin); |
---|
658 | return (number)rr; |
---|
659 | } |
---|
660 | |
---|
661 | /* CF: note that Z/nZ has (at least) two distinct euclidean structures |
---|
662 | * 1st phi(a) := (a mod n) which is just the structure directly |
---|
663 | * inherited from Z |
---|
664 | * 2nd phi(a) := gcd(a, n) |
---|
665 | * The 1st version is probably faster as everything just comes from Z, |
---|
666 | * but the 2nd version behaves nicely wrt. to quotient operations |
---|
667 | * and HNF and such. In agreement with nrnMod we imlement the 2nd here |
---|
668 | * |
---|
669 | * For quotrem note that if b exactly divides a, then |
---|
670 | * min(v_p(a), v_p(n)) >= min(v_p(b), v_p(n)) |
---|
671 | * so if we divide a and b by g:= gcd(a,b,n), then b becomes a |
---|
672 | * unit mod n/g. |
---|
673 | * Thus we 1st compute the remainder (similar to nrnMod) and then |
---|
674 | * the exact quotient. |
---|
675 | */ |
---|
676 | static number nrnQuotRem(number a, number b, number * rem, const coeffs r) |
---|
677 | { |
---|
678 | mpz_t g, aa, bb; |
---|
679 | mpz_ptr qq = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
680 | mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
681 | mpz_init(qq); |
---|
682 | mpz_init(rr); |
---|
683 | mpz_init(g); |
---|
684 | mpz_init_set(aa, (mpz_ptr)a); |
---|
685 | mpz_init_set(bb, (mpz_ptr)b); |
---|
686 | |
---|
687 | mpz_gcd(g, bb, r->modNumber); |
---|
688 | mpz_mod(rr, aa, g); |
---|
689 | mpz_sub(aa, aa, rr); |
---|
690 | mpz_gcd(g, aa, g); |
---|
691 | mpz_div(aa, aa, g); |
---|
692 | mpz_div(bb, bb, g); |
---|
693 | mpz_div(g, r->modNumber, g); |
---|
694 | mpz_invert(g, bb, g); |
---|
695 | mpz_mul(qq, aa, g); |
---|
696 | if (rem) |
---|
697 | *rem = (number)rr; |
---|
698 | else { |
---|
699 | mpz_clear(rr); |
---|
700 | omFreeBin(rr, gmp_nrz_bin); |
---|
701 | } |
---|
702 | mpz_clear(g); |
---|
703 | mpz_clear(aa); |
---|
704 | mpz_clear(bb); |
---|
705 | return (number) qq; |
---|
706 | } |
---|
707 | |
---|
708 | /* |
---|
709 | * Helper function for computing the module |
---|
710 | */ |
---|
711 | |
---|
712 | STATIC_VAR mpz_ptr nrnMapCoef = NULL; |
---|
713 | |
---|
714 | static number nrnMapModN(number from, const coeffs /*src*/, const coeffs dst) |
---|
715 | { |
---|
716 | return nrnMult(from, (number) nrnMapCoef, dst); |
---|
717 | } |
---|
718 | |
---|
719 | static number nrnMap2toM(number from, const coeffs /*src*/, const coeffs dst) |
---|
720 | { |
---|
721 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
722 | mpz_init(erg); |
---|
723 | mpz_mul_ui(erg, nrnMapCoef, (unsigned long)from); |
---|
724 | mpz_mod(erg, erg, dst->modNumber); |
---|
725 | return (number)erg; |
---|
726 | } |
---|
727 | |
---|
728 | static number nrnMapZp(number from, const coeffs /*src*/, const coeffs dst) |
---|
729 | { |
---|
730 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
731 | mpz_init(erg); |
---|
732 | // TODO: use npInt(...) |
---|
733 | mpz_mul_si(erg, nrnMapCoef, (unsigned long)from); |
---|
734 | mpz_mod(erg, erg, dst->modNumber); |
---|
735 | return (number)erg; |
---|
736 | } |
---|
737 | |
---|
738 | number nrnMapGMP(number from, const coeffs /*src*/, const coeffs dst) |
---|
739 | { |
---|
740 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
741 | mpz_init(erg); |
---|
742 | mpz_mod(erg, (mpz_ptr)from, dst->modNumber); |
---|
743 | return (number)erg; |
---|
744 | } |
---|
745 | |
---|
746 | static number nrnMapQ(number from, const coeffs src, const coeffs dst) |
---|
747 | { |
---|
748 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
749 | nlMPZ(erg, from, src); |
---|
750 | mpz_mod(erg, erg, dst->modNumber); |
---|
751 | return (number)erg; |
---|
752 | } |
---|
753 | |
---|
754 | #if SI_INTEGER_VARIANT==3 |
---|
755 | static number nrnMapZ(number from, const coeffs /*src*/, const coeffs dst) |
---|
756 | { |
---|
757 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
758 | if (n_Z_IS_SMALL(from)) |
---|
759 | mpz_init_set_si(erg, SR_TO_INT(from)); |
---|
760 | else |
---|
761 | mpz_init_set(erg, (mpz_ptr) from); |
---|
762 | mpz_mod(erg, erg, dst->modNumber); |
---|
763 | return (number)erg; |
---|
764 | } |
---|
765 | #elif SI_INTEGER_VARIANT==2 |
---|
766 | |
---|
767 | static number nrnMapZ(number from, const coeffs src, const coeffs dst) |
---|
768 | { |
---|
769 | if (SR_HDL(from) & SR_INT) |
---|
770 | { |
---|
771 | long f_i=SR_TO_INT(from); |
---|
772 | return nrnInit(f_i,dst); |
---|
773 | } |
---|
774 | return nrnMapGMP(from,src,dst); |
---|
775 | } |
---|
776 | #elif SI_INTEGER_VARIANT==1 |
---|
777 | static number nrnMapZ(number from, const coeffs src, const coeffs dst) |
---|
778 | { |
---|
779 | return nrnMapQ(from,src,dst); |
---|
780 | } |
---|
781 | #endif |
---|
782 | void nrnWrite (number a, const coeffs /*cf*/) |
---|
783 | { |
---|
784 | char *s,*z; |
---|
785 | if (a==NULL) |
---|
786 | { |
---|
787 | StringAppendS("o"); |
---|
788 | } |
---|
789 | else |
---|
790 | { |
---|
791 | int l=mpz_sizeinbase((mpz_ptr) a, 10) + 2; |
---|
792 | s=(char*)omAlloc(l); |
---|
793 | z=mpz_get_str(s,10,(mpz_ptr) a); |
---|
794 | StringAppendS(z); |
---|
795 | omFreeSize((ADDRESS)s,l); |
---|
796 | } |
---|
797 | } |
---|
798 | |
---|
799 | nMapFunc nrnSetMap(const coeffs src, const coeffs dst) |
---|
800 | { |
---|
801 | /* dst = nrn */ |
---|
802 | if ((src->rep==n_rep_gmp) && nCoeff_is_Z(src)) |
---|
803 | { |
---|
804 | return nrnMapZ; |
---|
805 | } |
---|
806 | if ((src->rep==n_rep_gap_gmp) /*&& nCoeff_is_Z(src)*/) |
---|
807 | { |
---|
808 | return nrnMapZ; |
---|
809 | } |
---|
810 | if (src->rep==n_rep_gap_rat) /*&& nCoeff_is_Q(src)) or Z*/ |
---|
811 | { |
---|
812 | return nrnMapQ; |
---|
813 | } |
---|
814 | // Some type of Z/n ring / field |
---|
815 | if (nCoeff_is_Zn(src) || nCoeff_is_Ring_PtoM(src) || |
---|
816 | nCoeff_is_Ring_2toM(src) || nCoeff_is_Zp(src)) |
---|
817 | { |
---|
818 | if ( (!nCoeff_is_Zp(src)) |
---|
819 | && (mpz_cmp(src->modBase, dst->modBase) == 0) |
---|
820 | && (src->modExponent == dst->modExponent)) return ndCopyMap; |
---|
821 | else |
---|
822 | { |
---|
823 | mpz_ptr nrnMapModul = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
824 | // Computing the n of Z/n |
---|
825 | if (nCoeff_is_Zp(src)) |
---|
826 | { |
---|
827 | mpz_init_set_si(nrnMapModul, src->ch); |
---|
828 | } |
---|
829 | else |
---|
830 | { |
---|
831 | mpz_init(nrnMapModul); |
---|
832 | mpz_set(nrnMapModul, src->modNumber); |
---|
833 | } |
---|
834 | // nrnMapCoef = 1 in dst if dst is a subring of src |
---|
835 | // nrnMapCoef = 0 in dst / src if src is a subring of dst |
---|
836 | if (nrnMapCoef == NULL) |
---|
837 | { |
---|
838 | nrnMapCoef = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
839 | mpz_init(nrnMapCoef); |
---|
840 | } |
---|
841 | if (mpz_divisible_p(nrnMapModul, dst->modNumber)) |
---|
842 | { |
---|
843 | mpz_set_ui(nrnMapCoef, 1); |
---|
844 | } |
---|
845 | else |
---|
846 | if (mpz_divisible_p(dst->modNumber,nrnMapModul)) |
---|
847 | { |
---|
848 | mpz_divexact(nrnMapCoef, dst->modNumber, nrnMapModul); |
---|
849 | mpz_ptr tmp = dst->modNumber; |
---|
850 | dst->modNumber = nrnMapModul; |
---|
851 | if (!nrnIsUnit((number) nrnMapCoef,dst)) |
---|
852 | { |
---|
853 | dst->modNumber = tmp; |
---|
854 | nrnDelete((number*) &nrnMapModul, dst); |
---|
855 | return NULL; |
---|
856 | } |
---|
857 | mpz_ptr inv = (mpz_ptr) nrnInvers((number) nrnMapCoef,dst); |
---|
858 | dst->modNumber = tmp; |
---|
859 | mpz_mul(nrnMapCoef, nrnMapCoef, inv); |
---|
860 | mpz_mod(nrnMapCoef, nrnMapCoef, dst->modNumber); |
---|
861 | nrnDelete((number*) &inv, dst); |
---|
862 | } |
---|
863 | else |
---|
864 | { |
---|
865 | nrnDelete((number*) &nrnMapModul, dst); |
---|
866 | return NULL; |
---|
867 | } |
---|
868 | nrnDelete((number*) &nrnMapModul, dst); |
---|
869 | if (nCoeff_is_Ring_2toM(src)) |
---|
870 | return nrnMap2toM; |
---|
871 | else if (nCoeff_is_Zp(src)) |
---|
872 | return nrnMapZp; |
---|
873 | else |
---|
874 | return nrnMapModN; |
---|
875 | } |
---|
876 | } |
---|
877 | return NULL; // default |
---|
878 | } |
---|
879 | |
---|
880 | static number nrnInitMPZ(mpz_t m, const coeffs r) |
---|
881 | { |
---|
882 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
883 | mpz_init_set(erg,m); |
---|
884 | mpz_mod(erg, erg, r->modNumber); |
---|
885 | return (number) erg; |
---|
886 | } |
---|
887 | |
---|
888 | static void nrnMPZ(mpz_t m, number &n, const coeffs) |
---|
889 | { |
---|
890 | mpz_init_set(m, (mpz_ptr)n); |
---|
891 | } |
---|
892 | |
---|
893 | /* |
---|
894 | * set the exponent (allocate and init tables) (TODO) |
---|
895 | */ |
---|
896 | |
---|
897 | static void nrnSetExp(unsigned long m, coeffs r) |
---|
898 | { |
---|
899 | /* clean up former stuff */ |
---|
900 | if (r->modNumber != NULL) mpz_clear(r->modNumber); |
---|
901 | |
---|
902 | r->modExponent= m; |
---|
903 | r->modNumber = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
904 | mpz_init_set (r->modNumber, r->modBase); |
---|
905 | mpz_pow_ui (r->modNumber, r->modNumber, m); |
---|
906 | } |
---|
907 | |
---|
908 | /* We expect this ring to be Z/n^m for some m > 0 and for some n > 2 which is not a prime. */ |
---|
909 | static void nrnInitExp(unsigned long m, coeffs r) |
---|
910 | { |
---|
911 | nrnSetExp(m, r); |
---|
912 | assume (r->modNumber != NULL); |
---|
913 | //CF: in general, the modulus is computed somewhere. I don't want to |
---|
914 | // check it's size before I construct the best ring. |
---|
915 | // if (mpz_cmp_ui(r->modNumber,2) <= 0) |
---|
916 | // WarnS("nrnInitExp failed (m in Z/m too small)"); |
---|
917 | } |
---|
918 | |
---|
919 | #ifdef LDEBUG |
---|
920 | BOOLEAN nrnDBTest (number a, const char *f, const int l, const coeffs r) |
---|
921 | { |
---|
922 | if ( (mpz_sgn1((mpz_ptr) a) < 0) || (mpz_cmp((mpz_ptr) a, r->modNumber) > 0) ) |
---|
923 | { |
---|
924 | Warn("mod-n: out of range at %s:%d\n",f,l); |
---|
925 | return FALSE; |
---|
926 | } |
---|
927 | return TRUE; |
---|
928 | } |
---|
929 | #endif |
---|
930 | |
---|
931 | /*2 |
---|
932 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
---|
933 | */ |
---|
934 | static const char * nlCPEatLongC(char *s, mpz_ptr i) |
---|
935 | { |
---|
936 | const char * start=s; |
---|
937 | if (!(*s >= '0' && *s <= '9')) |
---|
938 | { |
---|
939 | mpz_init_set_ui(i, 1); |
---|
940 | return s; |
---|
941 | } |
---|
942 | mpz_init(i); |
---|
943 | while (*s >= '0' && *s <= '9') s++; |
---|
944 | if (*s=='\0') |
---|
945 | { |
---|
946 | mpz_set_str(i,start,10); |
---|
947 | } |
---|
948 | else |
---|
949 | { |
---|
950 | char c=*s; |
---|
951 | *s='\0'; |
---|
952 | mpz_set_str(i,start,10); |
---|
953 | *s=c; |
---|
954 | } |
---|
955 | return s; |
---|
956 | } |
---|
957 | |
---|
958 | static const char * nrnRead (const char *s, number *a, const coeffs r) |
---|
959 | { |
---|
960 | mpz_ptr z = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
961 | { |
---|
962 | s = nlCPEatLongC((char *)s, z); |
---|
963 | } |
---|
964 | mpz_mod(z, z, r->modNumber); |
---|
965 | if ((*s)=='/') |
---|
966 | { |
---|
967 | mpz_ptr n = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
968 | s++; |
---|
969 | s=nlCPEatLongC((char*)s,n); |
---|
970 | if (!nrnIsOne((number)n,r)) |
---|
971 | { |
---|
972 | *a=nrnDiv((number)z,(number)n,r); |
---|
973 | mpz_clear(z); |
---|
974 | omFreeBin((void *)z, gmp_nrz_bin); |
---|
975 | mpz_clear(n); |
---|
976 | omFreeBin((void *)n, gmp_nrz_bin); |
---|
977 | } |
---|
978 | } |
---|
979 | else |
---|
980 | *a = (number) z; |
---|
981 | return s; |
---|
982 | } |
---|
983 | |
---|
984 | static number nrnConvFactoryNSingN( const CanonicalForm n, const coeffs r) |
---|
985 | { |
---|
986 | return nrnInit(n.intval(),r); |
---|
987 | } |
---|
988 | |
---|
989 | static CanonicalForm nrnConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs r ) |
---|
990 | { |
---|
991 | if (setChar) setCharacteristic( r->ch ); |
---|
992 | return CanonicalForm(nrnInt( n,r )); |
---|
993 | } |
---|
994 | |
---|
995 | /* for initializing function pointers */ |
---|
996 | BOOLEAN nrnInitChar (coeffs r, void* p) |
---|
997 | { |
---|
998 | assume( (getCoeffType(r) == n_Zn) || (getCoeffType (r) == n_Znm) ); |
---|
999 | ZnmInfo * info= (ZnmInfo *) p; |
---|
1000 | r->modBase= (mpz_ptr)nrnCopy((number)info->base, r); //this circumvents the problem |
---|
1001 | //in bigintmat.cc where we cannot create a "legal" nrn that can be freed. |
---|
1002 | //If we take a copy, we can do whatever we want. |
---|
1003 | |
---|
1004 | nrnInitExp (info->exp, r); |
---|
1005 | |
---|
1006 | /* next computation may yield wrong characteristic as r->modNumber |
---|
1007 | is a GMP number */ |
---|
1008 | r->ch = mpz_get_ui(r->modNumber); |
---|
1009 | |
---|
1010 | r->is_field=FALSE; |
---|
1011 | r->is_domain=FALSE; |
---|
1012 | r->rep=n_rep_gmp; |
---|
1013 | |
---|
1014 | r->cfInit = nrnInit; |
---|
1015 | r->cfDelete = nrnDelete; |
---|
1016 | r->cfCopy = nrnCopy; |
---|
1017 | r->cfSize = nrnSize; |
---|
1018 | r->cfInt = nrnInt; |
---|
1019 | r->cfAdd = nrnAdd; |
---|
1020 | r->cfInpAdd = nrnInpAdd; |
---|
1021 | r->cfSub = nrnSub; |
---|
1022 | r->cfMult = nrnMult; |
---|
1023 | r->cfInpMult = nrnInpMult; |
---|
1024 | r->cfDiv = nrnDiv; |
---|
1025 | r->cfAnn = nrnAnn; |
---|
1026 | r->cfIntMod = nrnMod; |
---|
1027 | r->cfExactDiv = nrnDiv; |
---|
1028 | r->cfInpNeg = nrnNeg; |
---|
1029 | r->cfInvers = nrnInvers; |
---|
1030 | r->cfDivBy = nrnDivBy; |
---|
1031 | r->cfDivComp = nrnDivComp; |
---|
1032 | r->cfGreater = nrnGreater; |
---|
1033 | r->cfEqual = nrnEqual; |
---|
1034 | r->cfIsZero = nrnIsZero; |
---|
1035 | r->cfIsOne = nrnIsOne; |
---|
1036 | r->cfIsMOne = nrnIsMOne; |
---|
1037 | r->cfGreaterZero = nrnGreaterZero; |
---|
1038 | r->cfWriteLong = nrnWrite; |
---|
1039 | r->cfRead = nrnRead; |
---|
1040 | r->cfPower = nrnPower; |
---|
1041 | r->cfSetMap = nrnSetMap; |
---|
1042 | //r->cfNormalize = ndNormalize; |
---|
1043 | r->cfLcm = nrnLcm; |
---|
1044 | r->cfGcd = nrnGcd; |
---|
1045 | r->cfIsUnit = nrnIsUnit; |
---|
1046 | r->cfGetUnit = nrnGetUnit; |
---|
1047 | r->cfExtGcd = nrnExtGcd; |
---|
1048 | r->cfXExtGcd = nrnXExtGcd; |
---|
1049 | r->cfQuotRem = nrnQuotRem; |
---|
1050 | r->cfCoeffName = nrnCoeffName; |
---|
1051 | r->nCoeffIsEqual = nrnCoeffIsEqual; |
---|
1052 | r->cfKillChar = nrnKillChar; |
---|
1053 | r->cfQuot1 = nrnQuot1; |
---|
1054 | r->cfInitMPZ = nrnInitMPZ; |
---|
1055 | r->cfMPZ = nrnMPZ; |
---|
1056 | #if SI_INTEGER_VARIANT==2 |
---|
1057 | r->cfWriteFd = nrzWriteFd; |
---|
1058 | r->cfReadFd = nrzReadFd; |
---|
1059 | #endif |
---|
1060 | |
---|
1061 | #ifdef LDEBUG |
---|
1062 | r->cfDBTest = nrnDBTest; |
---|
1063 | #endif |
---|
1064 | if ((r->modExponent==1)&&(mpz_size1(r->modBase)==1)) |
---|
1065 | { |
---|
1066 | long p=mpz_get_si(r->modBase); |
---|
1067 | if ((p<=FACTORY_MAX_PRIME)&&(p==IsPrime(p))) /*factory limit: <2^29*/ |
---|
1068 | { |
---|
1069 | r->convFactoryNSingN=nrnConvFactoryNSingN; |
---|
1070 | r->convSingNFactoryN=nrnConvSingNFactoryN; |
---|
1071 | } |
---|
1072 | } |
---|
1073 | return FALSE; |
---|
1074 | } |
---|
1075 | |
---|
1076 | #endif |
---|
1077 | /* #ifdef HAVE_RINGS */ |
---|