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Data Structures | Macros | Functions
bigintmat.h File Reference
#include "coeffs/coeffs.h"

Go to the source code of this file.

Data Structures

class  bigintmat
 Matrices of numbers. More...
 

Macros

#define BIMATELEM(M, I, J)   (M)[(I-1)*(M).cols()+J-1]
 

Functions

bool operator== (const bigintmat &lhr, const bigintmat &rhr)
 
bool operator!= (const bigintmat &lhr, const bigintmat &rhr)
 
bigintmatbimAdd (bigintmat *a, bigintmat *b)
 Matrix-Add/-Sub/-Mult so oder mit operator+/-/* ? @Note: NULL as a result means an error (non-compatible matrices?) More...
 
bigintmatbimAdd (bigintmat *a, long b)
 
bigintmatbimSub (bigintmat *a, bigintmat *b)
 
bigintmatbimSub (bigintmat *a, long b)
 
bigintmatbimMult (bigintmat *a, bigintmat *b)
 
bigintmatbimMult (bigintmat *a, long b)
 
bigintmatbimMult (bigintmat *a, number b, const coeffs cf)
 
bigintmatbimCopy (const bigintmat *b)
 same as copy constructor - apart from it being able to accept NULL as input More...
 
intvecbim2iv (bigintmat *b)
 
bigintmativ2bim (intvec *b, const coeffs C)
 
bigintmatbimChangeCoeff (bigintmat *a, coeffs cnew)
 Liefert Kopier von Matrix a zurück, mit coeffs cnew statt den ursprünglichen. More...
 
void bimMult (bigintmat *a, bigintmat *b, bigintmat *c)
 Multipliziert Matrix a und b und speichert Ergebnis in c. More...
 
number solveAx (bigintmat *A, bigintmat *b, bigintmat *x)
 solve Ax=b*d. x needs to be pre-allocated to the same number of columns as b. the minimal denominator d is returned. Currently available for Z, Q and Z/nZ (and possibly for all fields: d=1 there) Beware that the internal functions can find the kernel as well - but the interface is lacking. More...
 
int kernbase (bigintmat *a, bigintmat *c, number p, coeffs q)
 a basis for the nullspace of a mod p: only used internally in Round2. Don't use it. More...
 
bool nCoeffs_are_equal (coeffs r, coeffs s)
 
void diagonalForm (bigintmat *a, bigintmat **b, bigintmat **c)
 

Macro Definition Documentation

◆ BIMATELEM

#define BIMATELEM (   M,
  I,
 
)    (M)[(I-1)*(M).cols()+J-1]

Definition at line 133 of file bigintmat.h.

Function Documentation

◆ bim2iv()

intvec * bim2iv ( bigintmat b)

Definition at line 341 of file bigintmat.cc.

342{
343 intvec * iv = new intvec(b->rows(), b->cols(), 0);
344 for (int i=0; i<(b->rows())*(b->cols()); i++)
345 (*iv)[i] = n_Int((*b)[i], b->basecoeffs()); // Geht das so?
346 return iv;
347}
int i
Definition: cfEzgcd.cc:132
CanonicalForm b
Definition: cfModGcd.cc:4103
Definition: intvec.h:23
static FORCE_INLINE long n_Int(number &n, const coeffs r)
conversion of n to an int; 0 if not possible in Z/pZ: the representing int lying in (-p/2 ....
Definition: coeffs.h:544

◆ bimAdd() [1/2]

bigintmat * bimAdd ( bigintmat a,
bigintmat b 
)

Matrix-Add/-Sub/-Mult so oder mit operator+/-/* ? @Note: NULL as a result means an error (non-compatible matrices?)

Definition at line 182 of file bigintmat.cc.

183{
184 if (a->cols() != b->cols()) return NULL;
185 if (a->rows() != b->rows()) return NULL;
186 if (a->basecoeffs() != b->basecoeffs()) { return NULL; }
187
188 const coeffs basecoeffs = a->basecoeffs();
189
190 int i;
191
192 bigintmat * bim = new bigintmat(a->rows(), a->cols(), basecoeffs);
193
194 for (i=a->rows()*a->cols()-1;i>=0; i--)
195 bim->rawset(i, n_Add((*a)[i], (*b)[i], basecoeffs), basecoeffs);
196
197 return bim;
198}
Matrices of numbers.
Definition: bigintmat.h:51
int cols() const
Definition: bigintmat.h:144
int rows() const
Definition: bigintmat.h:145
void rawset(int i, number n, const coeffs C=NULL)
replace an entry with the given number n (only delete old). NOTE: starts at [0]. Should be named set_...
Definition: bigintmat.h:196
coeffs basecoeffs() const
Definition: bigintmat.h:146
static FORCE_INLINE number n_Add(number a, number b, const coeffs r)
return the sum of 'a' and 'b', i.e., a+b
Definition: coeffs.h:647
The main handler for Singular numbers which are suitable for Singular polynomials.
#define NULL
Definition: omList.c:12

◆ bimAdd() [2/2]

bigintmat * bimAdd ( bigintmat a,
long  b 
)

Definition at line 199 of file bigintmat.cc.

200{
201
202 const int mn = si_min(a->rows(),a->cols());
203
204 const coeffs basecoeffs = a->basecoeffs();
205 number bb=n_Init(b,basecoeffs);
206
207 int i;
208
209 bigintmat * bim = new bigintmat(a->rows(),a->cols() , basecoeffs);
210
211 for (i=1; i<=mn; i++)
212 BIMATELEM(*bim,i,i)=n_Add(BIMATELEM(*a,i,i), bb, basecoeffs);
213
214 n_Delete(&bb,basecoeffs);
215 return bim;
216}
static int si_min(const int a, const int b)
Definition: auxiliary.h:125
#define BIMATELEM(M, I, J)
Definition: bigintmat.h:133
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:452
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
Definition: coeffs.h:535

◆ bimChangeCoeff()

bigintmat * bimChangeCoeff ( bigintmat a,
coeffs  cnew 
)

Liefert Kopier von Matrix a zurück, mit coeffs cnew statt den ursprünglichen.

Definition at line 1804 of file bigintmat.cc.

1805{
1806 coeffs cold = a->basecoeffs();
1807 bigintmat *b = new bigintmat(a->rows(), a->cols(), cnew);
1808 // Erzeugt Karte von alten coeffs nach neuen
1809 nMapFunc f = n_SetMap(cold, cnew);
1810 number t1;
1811 number t2;
1812 // apply map to all entries.
1813 for (int i=1; i<=a->rows(); i++)
1814 {
1815 for (int j=1; j<=a->cols(); j++)
1816 {
1817 t1 = a->get(i, j);
1818 t2 = f(t1, cold, cnew);
1819 b->set(i, j, t2);
1820 n_Delete(&t1, cold);
1821 n_Delete(&t2, cnew);
1822 }
1823 }
1824 return b;
1825}
FILE * f
Definition: checklibs.c:9
number get(int i, int j) const
get a copy of an entry. NOTE: starts at [1,1]
Definition: bigintmat.cc:119
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
Definition: coeffs.h:697
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:73
int j
Definition: facHensel.cc:110

◆ bimCopy()

bigintmat * bimCopy ( const bigintmat b)

same as copy constructor - apart from it being able to accept NULL as input

Definition at line 405 of file bigintmat.cc.

406{
407 if (b == NULL)
408 return NULL;
409
410 return new bigintmat(b);
411}

◆ bimMult() [1/4]

bigintmat * bimMult ( bigintmat a,
bigintmat b 
)

Definition at line 255 of file bigintmat.cc.

256{
257 const int ca = a->cols();
258 const int cb = b->cols();
259
260 const int ra = a->rows();
261 const int rb = b->rows();
262
263 if (ca != rb)
264 {
265#ifndef SING_NDEBUG
266 Werror("wrong bigintmat sizes at multiplication a * b: acols: %d != brows: %d\n", ca, rb);
267#endif
268 return NULL;
269 }
270
271 assume (ca == rb);
272
273 if (a->basecoeffs() != b->basecoeffs()) { return NULL; }
274
275 const coeffs basecoeffs = a->basecoeffs();
276
277 int i, j, k;
278
279 number sum;
280
281 bigintmat * bim = new bigintmat(ra, cb, basecoeffs);
282
283 for (i=1; i<=ra; i++)
284 for (j=1; j<=cb; j++)
285 {
286 sum = n_Init(0, basecoeffs);
287
288 for (k=1; k<=ca; k++)
289 {
290 number prod = n_Mult( BIMATELEM(*a, i, k), BIMATELEM(*b, k, j), basecoeffs);
291
292 n_InpAdd(sum, prod, basecoeffs);
293
294 n_Delete(&prod, basecoeffs);
295 }
296 bim->rawset(i, j, sum, basecoeffs);
297 }
298 return bim;
299}
int k
Definition: cfEzgcd.cc:99
static FORCE_INLINE number n_Mult(number a, number b, const coeffs r)
return the product of 'a' and 'b', i.e., a*b
Definition: coeffs.h:633
static FORCE_INLINE void n_InpAdd(number &a, number b, const coeffs r)
addition of 'a' and 'b'; replacement of 'a' by the sum a+b
Definition: coeffs.h:643
fq_nmod_poly_t prod
Definition: facHensel.cc:100
#define assume(x)
Definition: mod2.h:389
void Werror(const char *fmt,...)
Definition: reporter.cc:189

◆ bimMult() [2/4]

void bimMult ( bigintmat a,
bigintmat b,
bigintmat c 
)

Multipliziert Matrix a und b und speichert Ergebnis in c.

Definition at line 1932 of file bigintmat.cc.

1933{
1934 if (!nCoeffs_are_equal(a->basecoeffs(), b->basecoeffs()))
1935 {
1936 WerrorS("Error in bimMult. Coeffs do not agree!");
1937 return;
1938 }
1939 if ((a->rows() != c->rows()) || (b->cols() != c->cols()) || (a->cols() != b->rows()))
1940 {
1941 WerrorS("Error in bimMult. Dimensions do not agree!");
1942 return;
1943 }
1944 bigintmat *tmp = bimMult(a, b);
1945 c->copy(tmp);
1946
1947 delete tmp;
1948}
bool nCoeffs_are_equal(coeffs r, coeffs s)
Definition: bigintmat.cc:2645
bigintmat * bimMult(bigintmat *a, bigintmat *b)
Definition: bigintmat.cc:255
bool copy(bigintmat *b)
Kopiert Einträge von b auf Bigintmat.
Definition: bigintmat.cc:1259
void WerrorS(const char *s)
Definition: feFopen.cc:24

◆ bimMult() [3/4]

bigintmat * bimMult ( bigintmat a,
long  b 
)

Definition at line 301 of file bigintmat.cc.

302{
303
304 const int mn = a->rows()*a->cols();
305
306 const coeffs basecoeffs = a->basecoeffs();
307 number bb=n_Init(b,basecoeffs);
308
309 int i;
310
311 bigintmat * bim = new bigintmat(a->rows(),a->cols() , basecoeffs);
312
313 for (i=0; i<mn; i++)
314 bim->rawset(i, n_Mult((*a)[i], bb, basecoeffs), basecoeffs);
315
316 n_Delete(&bb,basecoeffs);
317 return bim;
318}

◆ bimMult() [4/4]

bigintmat * bimMult ( bigintmat a,
number  b,
const coeffs  cf 
)

Definition at line 320 of file bigintmat.cc.

321{
322 if (cf!=a->basecoeffs()) return NULL;
323
324 const int mn = a->rows()*a->cols();
325
326 const coeffs basecoeffs = a->basecoeffs();
327
328 int i;
329
330 bigintmat * bim = new bigintmat(a->rows(),a->cols() , basecoeffs);
331
332 for (i=0; i<mn; i++)
333 bim->rawset(i, n_Mult((*a)[i], b, basecoeffs), basecoeffs);
334
335 return bim;
336}
CanonicalForm cf
Definition: cfModGcd.cc:4083

◆ bimSub() [1/2]

bigintmat * bimSub ( bigintmat a,
bigintmat b 
)

Definition at line 218 of file bigintmat.cc.

219{
220 if (a->cols() != b->cols()) return NULL;
221 if (a->rows() != b->rows()) return NULL;
222 if (a->basecoeffs() != b->basecoeffs()) { return NULL; }
223
224 const coeffs basecoeffs = a->basecoeffs();
225
226 int i;
227
228 bigintmat * bim = new bigintmat(a->rows(), a->cols(), basecoeffs);
229
230 for (i=a->rows()*a->cols()-1;i>=0; i--)
231 bim->rawset(i, n_Sub((*a)[i], (*b)[i], basecoeffs), basecoeffs);
232
233 return bim;
234}
static FORCE_INLINE number n_Sub(number a, number b, const coeffs r)
return the difference of 'a' and 'b', i.e., a-b
Definition: coeffs.h:652

◆ bimSub() [2/2]

bigintmat * bimSub ( bigintmat a,
long  b 
)

Definition at line 236 of file bigintmat.cc.

237{
238 const int mn = si_min(a->rows(),a->cols());
239
240 const coeffs basecoeffs = a->basecoeffs();
241 number bb=n_Init(b,basecoeffs);
242
243 int i;
244
245 bigintmat * bim = new bigintmat(a->rows(),a->cols() , basecoeffs);
246
247 for (i=1; i<=mn; i++)
248 BIMATELEM(*bim,i,i)=n_Sub(BIMATELEM(*a,i,i), bb, basecoeffs);
249
250 n_Delete(&bb,basecoeffs);
251 return bim;
252}

◆ diagonalForm()

void diagonalForm ( bigintmat a,
bigintmat **  b,
bigintmat **  c 
)

Definition at line 2475 of file bigintmat.cc.

2476{
2477 bigintmat * t, *s, *a=A;
2478 coeffs R = a->basecoeffs();
2479 if (T)
2480 {
2481 *T = new bigintmat(a->cols(), a->cols(), R),
2482 (*T)->one();
2483 t = new bigintmat(*T);
2484 }
2485 else
2486 {
2487 t = *T;
2488 }
2489
2490 if (S)
2491 {
2492 *S = new bigintmat(a->rows(), a->rows(), R);
2493 (*S)->one();
2494 s = new bigintmat(*S);
2495 }
2496 else
2497 {
2498 s = *S;
2499 }
2500
2501 int flip=0;
2502 do
2503 {
2504 bigintmat * x, *X;
2505 if (flip)
2506 {
2507 x = s;
2508 X = *S;
2509 }
2510 else
2511 {
2512 x = t;
2513 X = *T;
2514 }
2515
2516 if (x)
2517 {
2518 x->one();
2519 bigintmat * r = new bigintmat(a->rows()+a->cols(), a->cols(), R);
2520 bigintmat * rw = new bigintmat(1, a->cols(), R);
2521 for(int i=0; i<a->cols(); i++)
2522 {
2523 x->getrow(i+1, rw);
2524 r->setrow(i+1, rw);
2525 }
2526 for (int i=0; i<a->rows(); i++)
2527 {
2528 a->getrow(i+1, rw);
2529 r->setrow(i+a->cols()+1, rw);
2530 }
2531 r->hnf();
2532 for(int i=0; i<a->cols(); i++)
2533 {
2534 r->getrow(i+1, rw);
2535 x->setrow(i+1, rw);
2536 }
2537 for(int i=0; i<a->rows(); i++)
2538 {
2539 r->getrow(i+a->cols()+1, rw);
2540 a->setrow(i+1, rw);
2541 }
2542 delete rw;
2543 delete r;
2544
2545#if 0
2546 Print("X: %ld\n", X);
2547 X->Print();
2548 Print("\nx: %ld\n", x);
2549 x->Print();
2550#endif
2551 bimMult(X, x, X);
2552#if 0
2553 Print("\n2:X: %ld %ld %ld\n", X, *S, *T);
2554 X->Print();
2555 Print("\n2:x: %ld\n", x);
2556 x->Print();
2557 PrintLn();
2558#endif
2559 }
2560 else
2561 {
2562 a->hnf();
2563 }
2564
2565 int diag = 1;
2566 for(int i=a->rows(); diag && i>0; i--)
2567 {
2568 for(int j=a->cols(); j>0; j--)
2569 {
2570 if ((a->rows()-i)!=(a->cols()-j) && !n_IsZero(a->view(i, j), R))
2571 {
2572 diag = 0;
2573 break;
2574 }
2575 }
2576 }
2577#if 0
2578 PrintS("Diag ? %d\n", diag);
2579 a->Print();
2580 PrintLn();
2581#endif
2582 if (diag) break;
2583
2584 a = a->transpose(); // leaks - I need to write inpTranspose
2585 flip = 1-flip;
2586 } while (1);
2587 if (flip)
2588 a = a->transpose();
2589
2590 if (S) *S = (*S)->transpose();
2591 if (s) delete s;
2592 if (t) delete t;
2593 A->copy(a);
2594}
Variable x
Definition: cfModGcd.cc:4082
void Print()
IO: simply prints the matrix to the current output (screen?)
Definition: bigintmat.cc:443
void hnf()
transforms INPLACE to HNF
Definition: bigintmat.cc:1660
bigintmat * transpose()
Definition: bigintmat.cc:37
void setrow(int i, bigintmat *m)
Setzt i-te Zeile gleich übergebenem Vektor (Matrix) m.
Definition: bigintmat.cc:860
number view(int i, int j) const
view an entry an entry. NOTE: starts at [1,1]
Definition: bigintmat.cc:127
void one()
Macht Matrix (Falls quadratisch) zu Einheitsmatrix.
Definition: bigintmat.cc:1325
void getrow(int i, bigintmat *a)
Schreibt i-te Zeile in Vektor (Matrix) a.
Definition: bigintmat.cc:791
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition: coeffs.h:461
#define Print
Definition: emacs.cc:80
const CanonicalForm int s
Definition: facAbsFact.cc:51
std::pair< ideal, ring > flip(const ideal I, const ring r, const gfan::ZVector interiorPoint, const gfan::ZVector facetNormal, const gfan::ZVector adjustedInteriorPoint, const gfan::ZVector adjustedFacetNormal)
Definition: flip.cc:17
STATIC_VAR jList * T
Definition: janet.cc:30
void PrintS(const char *s)
Definition: reporter.cc:284
void PrintLn()
Definition: reporter.cc:310
#define R
Definition: sirandom.c:27
#define A
Definition: sirandom.c:24

◆ iv2bim()

bigintmat * iv2bim ( intvec b,
const coeffs  C 
)

Definition at line 349 of file bigintmat.cc.

350{
351 const int l = (b->rows())*(b->cols());
352 bigintmat * bim = new bigintmat(b->rows(), b->cols(), C);
353
354 for (int i=0; i < l; i++)
355 bim->rawset(i, n_Init((*b)[i], C), C);
356
357 return bim;
358}
int l
Definition: cfEzgcd.cc:100

◆ kernbase()

int kernbase ( bigintmat a,
bigintmat c,
number  p,
coeffs  q 
)

a basis for the nullspace of a mod p: only used internally in Round2. Don't use it.

Definition at line 2600 of file bigintmat.cc.

2601{
2602#if 0
2603 PrintS("Kernel of ");
2604 a->Print();
2605 PrintS(" modulo ");
2606 n_Print(p, q);
2607 PrintLn();
2608#endif
2609
2610 coeffs coe = numbercoeffs(p, q);
2611 bigintmat *m = bimChangeCoeff(a, coe), *U, *V;
2612 diagonalForm(m, &U, &V);
2613#if 0
2614 PrintS("\ndiag form: ");
2615 m->Print();
2616 PrintS("\nU:\n");
2617 U->Print();
2618 PrintS("\nV:\n");
2619 V->Print();
2620 PrintLn();
2621#endif
2622
2623 int rg = 0;
2624#undef MIN
2625#define MIN(a,b) (a < b ? a : b)
2626 for(rg=0; rg<MIN(m->rows(), m->cols()) && !n_IsZero(m->view(m->rows()-rg,m->cols()-rg), coe); rg++);
2627
2628 bigintmat * k = new bigintmat(m->cols(), m->rows(), coe);
2629 for(int i=0; i<rg; i++)
2630 {
2631 number A = n_Ann(m->view(m->rows()-i, m->cols()-i), coe);
2632 k->set(m->cols()-i, i+1, A);
2633 n_Delete(&A, coe);
2634 }
2635 for(int i=rg; i<m->cols(); i++)
2636 {
2637 k->set(m->cols()-i, i+1-rg, n_Init(1, coe));
2638 }
2639 bimMult(V, k, k);
2640 c->copy(bimChangeCoeff(k, q));
2641 return c->cols();
2642}
bigintmat * bimChangeCoeff(bigintmat *a, coeffs cnew)
Liefert Kopier von Matrix a zurück, mit coeffs cnew statt den ursprünglichen.
Definition: bigintmat.cc:1804
#define MIN(a, b)
void diagonalForm(bigintmat *A, bigintmat **S, bigintmat **T)
Definition: bigintmat.cc:2475
static coeffs numbercoeffs(number n, coeffs c)
create Z/nA of type n_Zn
Definition: bigintmat.cc:21
int m
Definition: cfEzgcd.cc:128
int p
Definition: cfModGcd.cc:4078
static FORCE_INLINE number n_Ann(number a, const coeffs r)
if r is a ring with zero divisors, return an annihilator!=0 of b otherwise return NULL
Definition: coeffs.h:676
void n_Print(number &a, const coeffs r)
print a number (BEWARE of string buffers!) mostly for debugging
Definition: numbers.cc:667

◆ nCoeffs_are_equal()

bool nCoeffs_are_equal ( coeffs  r,
coeffs  s 
)

Definition at line 2645 of file bigintmat.cc.

2646{
2647 if ((r == NULL) || (s == NULL))
2648 return false;
2649 if (r == s)
2650 return true;
2651 if ((getCoeffType(r)==n_Z) && (getCoeffType(s)==n_Z))
2652 return true;
2653 if ((getCoeffType(r)==n_Zp) && (getCoeffType(s)==n_Zp))
2654 {
2655 if (r->ch == s->ch)
2656 return true;
2657 else
2658 return false;
2659 }
2660 // n_Zn stimmt wahrscheinlich noch nicht
2661 if ((getCoeffType(r)==n_Zn) && (getCoeffType(s)==n_Zn))
2662 {
2663 if (r->ch == s->ch)
2664 return true;
2665 else
2666 return false;
2667 }
2668 if ((getCoeffType(r)==n_Q) && (getCoeffType(s)==n_Q))
2669 return true;
2670 // FALL n_Zn FEHLT NOCH!
2671 //if ((getCoeffType(r)==n_Zn) && (getCoeffType(s)==n_Zn))
2672 return false;
2673}
@ n_Q
rational (GMP) numbers
Definition: coeffs.h:30
@ n_Zn
only used if HAVE_RINGS is defined
Definition: coeffs.h:44
@ n_Zp
\F{p < 2^31}
Definition: coeffs.h:29
@ n_Z
only used if HAVE_RINGS is defined
Definition: coeffs.h:43
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:422

◆ operator!=()

bool operator!= ( const bigintmat lhr,
const bigintmat rhr 
)

Definition at line 176 of file bigintmat.cc.

177{
178 return !(lhr==rhr);
179}

◆ operator==()

bool operator== ( const bigintmat lhr,
const bigintmat rhr 
)

Definition at line 159 of file bigintmat.cc.

160{
161 if (&lhr == &rhr) { return true; }
162 if (lhr.cols() != rhr.cols()) { return false; }
163 if (lhr.rows() != rhr.rows()) { return false; }
164 if (lhr.basecoeffs() != rhr.basecoeffs()) { return false; }
165
166 const int l = (lhr.rows())*(lhr.cols());
167
168 for (int i=0; i < l; i++)
169 {
170 if (!n_Equal(lhr[i], rhr[i], lhr.basecoeffs())) { return false; }
171 }
172
173 return true;
174}
static FORCE_INLINE BOOLEAN n_Equal(number a, number b, const coeffs r)
TRUE iff 'a' and 'b' represent the same number; they may have different representations.
Definition: coeffs.h:457

◆ solveAx()

number solveAx ( bigintmat A,
bigintmat b,
bigintmat x 
)

solve Ax=b*d. x needs to be pre-allocated to the same number of columns as b. the minimal denominator d is returned. Currently available for Z, Q and Z/nZ (and possibly for all fields: d=1 there) Beware that the internal functions can find the kernel as well - but the interface is lacking.

Definition at line 2430 of file bigintmat.cc.

2431{
2432#if 0
2433 PrintS("Solve Ax=b for A=\n");
2434 A->Print();
2435 PrintS("\nb = \n");
2436 b->Print();
2437 PrintS("\nx = \n");
2438 x->Print();
2439 PrintLn();
2440#endif
2441
2442 coeffs R = A->basecoeffs();
2443 assume (R == b->basecoeffs());
2444 assume (R == x->basecoeffs());
2445 assume ((x->cols() == b->cols()) && (x->rows() == A->cols()) && (A->rows() == b->rows()));
2446
2447 switch (getCoeffType(R))
2448 {
2449 #ifdef HAVE_RINGS
2450 case n_Z:
2451 return solveAx_dixon(A, b, x, NULL);
2452 case n_Zn:
2453 case n_Znm:
2454 case n_Z2m:
2455 return solveAx_howell(A, b, x, NULL);
2456 #endif
2457 case n_Zp:
2458 case n_Q:
2459 case n_GF:
2460 case n_algExt:
2461 case n_transExt:
2462 WarnS("have field, should use Gauss or better");
2463 break;
2464 default:
2465 if (R->cfXExtGcd && R->cfAnn)
2466 { //assume it's Euclidean
2467 return solveAx_howell(A, b, x, NULL);
2468 }
2469 WerrorS("have no solve algorithm");
2470 break;
2471 }
2472 return NULL;
2473}
static number solveAx_dixon(bigintmat *A, bigintmat *B, bigintmat *x, bigintmat *kern)
Definition: bigintmat.cc:2108
static number solveAx_howell(bigintmat *A, bigintmat *b, bigintmat *x, bigintmat *kern)
Definition: bigintmat.cc:2298
@ n_GF
\GF{p^n < 2^16}
Definition: coeffs.h:32
@ n_Znm
only used if HAVE_RINGS is defined
Definition: coeffs.h:45
@ n_algExt
used for all algebraic extensions, i.e., the top-most extension in an extension tower is algebraic
Definition: coeffs.h:35
@ n_Z2m
only used if HAVE_RINGS is defined
Definition: coeffs.h:46
@ n_transExt
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
Definition: coeffs.h:38
#define WarnS
Definition: emacs.cc:78