My Project
Loading...
Searching...
No Matches
Macros | Functions
bigintmat.cc File Reference
#include "misc/auxiliary.h"
#include "coeffs/bigintmat.h"
#include "misc/intvec.h"
#include "coeffs/rmodulon.h"
#include <cmath>

Go to the source code of this file.

Macros

#define swap(_i, _j)
 
#define MIN(a, b)   (a < b ? a : b)
 

Functions

static coeffs numbercoeffs (number n, coeffs c)
 create Z/nA of type n_Zn More...
 
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)
 
intvecbim2iv (bigintmat *b)
 
bigintmativ2bim (intvec *b, const coeffs C)
 
bigintmatbimCopy (const bigintmat *b)
 same as copy constructor - apart from it being able to accept NULL as input More...
 
static int intArrSum (int *a, int length)
 
static int findLongest (int *a, int length)
 
static int getShorter (int *a, int l, int j, int cols, int rows)
 
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...
 
static void reduce_mod_howell (bigintmat *A, bigintmat *b, bigintmat *eps, bigintmat *x)
 
static bigintmatprependIdentity (bigintmat *A)
 
static number bimFarey (bigintmat *A, number N, bigintmat *L)
 
static number solveAx_dixon (bigintmat *A, bigintmat *B, bigintmat *x, bigintmat *kern)
 
static number solveAx_howell (bigintmat *A, bigintmat *b, bigintmat *x, bigintmat *kern)
 
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...
 
void diagonalForm (bigintmat *A, bigintmat **S, bigintmat **T)
 
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)
 

Macro Definition Documentation

◆ MIN

#define MIN (   a,
  b 
)    (a < b ? a : b)

◆ swap

#define swap (   _i,
  _j 
)
Value:
int __i = (_i), __j=(_j); \
number c = v[__i]; \
v[__i] = v[__j]; \
v[__j] = c \
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39

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}

◆ bimFarey()

static number bimFarey ( bigintmat A,
number  N,
bigintmat L 
)
static

Definition at line 2048 of file bigintmat.cc.

2049{
2050 coeffs Z = A->basecoeffs(),
2051 Q = nInitChar(n_Q, 0);
2052 number den = n_Init(1, Z);
2053 nMapFunc f = n_SetMap(Q, Z);
2054
2055 for(int i=1; i<= A->rows(); i++)
2056 {
2057 for(int j=1; j<= A->cols(); j++)
2058 {
2059 number ad = n_Mult(den, A->view(i, j), Z);
2060 number re = n_IntMod(ad, N, Z);
2061 n_Delete(&ad, Z);
2062 number q = n_Farey(re, N, Z);
2063 n_Delete(&re, Z);
2064 if (!q)
2065 {
2066 n_Delete(&ad, Z);
2067 n_Delete(&den, Z);
2068 return NULL;
2069 }
2070
2071 number d = n_GetDenom(q, Q),
2072 n = n_GetNumerator(q, Q);
2073
2074 n_Delete(&q, Q);
2075 n_Delete(&ad, Z);
2076 number dz = f(d, Q, Z),
2077 nz = f(n, Q, Z);
2078 n_Delete(&d, Q);
2079 n_Delete(&n, Q);
2080
2081 if (!n_IsOne(dz, Z))
2082 {
2083 L->skalmult(dz, Z);
2084 n_InpMult(den, dz, Z);
2085#if 0
2086 PrintS("den increasing to ");
2087 n_Print(den, Z);
2088 PrintLn();
2089#endif
2090 }
2091 n_Delete(&dz, Z);
2092 L->rawset(i, j, nz);
2093 }
2094 }
2095
2096 nKillChar(Q);
2097 PrintS("bimFarey worked\n");
2098#if 0
2099 L->Print();
2100 PrintS("\n * 1/");
2101 n_Print(den, Z);
2102 PrintLn();
2103#endif
2104 return den;
2105}
CanonicalForm den(const CanonicalForm &f)
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:56
void Print()
IO: simply prints the matrix to the current output (screen?)
Definition: bigintmat.cc:443
bool skalmult(number b, coeffs c)
Multipliziert zur Matrix den Skalar b hinzu.
Definition: bigintmat.cc:938
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 number n_GetDenom(number &n, const coeffs r)
return the denominator of n (if elements of r are by nature not fractional, result is 1)
Definition: coeffs.h:600
@ n_Q
rational (GMP) numbers
Definition: coeffs.h:30
void n_Print(number &a, const coeffs r)
print a number (BEWARE of string buffers!) mostly for debugging
Definition: numbers.cc:667
static FORCE_INLINE number n_Farey(number a, number b, const coeffs r)
Definition: coeffs.h:764
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
Definition: numbers.cc:413
static FORCE_INLINE number n_IntMod(number a, number b, const coeffs r)
for r a field, return n_Init(0,r) always: n_Div(a,b,r)*b+n_IntMod(a,b,r)==a n_IntMod(a,...
Definition: coeffs.h:625
static FORCE_INLINE void n_InpMult(number &a, number b, const coeffs r)
multiplication of 'a' and 'b'; replacement of 'a' by the product a*b
Definition: coeffs.h:638
static FORCE_INLINE number n_GetNumerator(number &n, const coeffs r)
return the numerator of n (if elements of r are by nature not fractional, result is n)
Definition: coeffs.h:605
void nKillChar(coeffs r)
undo all initialisations
Definition: numbers.cc:568
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
Definition: coeffs.h:465
void PrintS(const char *s)
Definition: reporter.cc:284
void PrintLn()
Definition: reporter.cc:310
#define A
Definition: sirandom.c:24
#define Q
Definition: sirandom.c:26

◆ 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 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 **  S,
bigintmat **  T 
)

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 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
#define R
Definition: sirandom.c:27

◆ findLongest()

static int findLongest ( int *  a,
int  length 
)
static

Definition at line 537 of file bigintmat.cc.

538{
539 int l = 0;
540 int index;
541 for (int i=0; i<length; i++)
542 {
543 if (a[i] > l)
544 {
545 l = a[i];
546 index = i;
547 }
548 }
549 return index;
550}
int l
Definition: cfEzgcd.cc:100
static BOOLEAN length(leftv result, leftv arg)
Definition: interval.cc:257
static int index(p_Length length, p_Ord ord)
Definition: p_Procs_Impl.h:592

◆ getShorter()

static int getShorter ( int *  a,
int  l,
int  j,
int  cols,
int  rows 
)
static

Definition at line 552 of file bigintmat.cc.

553{
554 int sndlong = 0;
555 int min;
556 for (int i=0; i<rows; i++)
557 {
558 int index = cols*i+j;
559 if ((a[index] > sndlong) && (a[index] < l))
560 {
561 min = floor(log10((double)cols))+floor(log10((double)rows))+5;
562 if ((a[index] < min) && (min < l))
563 sndlong = min;
564 else
565 sndlong = a[index];
566 }
567 }
568 if (sndlong == 0)
569 {
570 min = floor(log10((double)cols))+floor(log10((double)rows))+5;
571 if (min < l)
572 sndlong = min;
573 else
574 sndlong = 1;
575 }
576 return sndlong;
577}
static int min(int a, int b)
Definition: fast_mult.cc:268
const signed long floor(const ampf< Precision > &x)
Definition: amp.h:773
const ampf< Precision > log10(const ampf< Precision > &x)
Definition: amp.h:1022

◆ intArrSum()

static int intArrSum ( int *  a,
int  length 
)
static

Definition at line 529 of file bigintmat.cc.

530{
531 int sum = 0;
532 for (int i=0; i<length; i++)
533 sum += a[i];
534 return sum;
535}

◆ 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}

◆ 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

◆ 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_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

◆ numbercoeffs()

static coeffs numbercoeffs ( number  n,
coeffs  c 
)
static

create Z/nA of type n_Zn

Definition at line 21 of file bigintmat.cc.

22{
23 mpz_t p;
24 number2mpz(n, c, p);
25 ZnmInfo *pp = new ZnmInfo;
26 pp->base = p;
27 pp->exp = 1;
28 coeffs nc = nInitChar(n_Zn, (void*)pp);
29 mpz_clear(p);
30 delete pp;
31 return nc;
32}
CanonicalForm FACTORY_PUBLIC pp(const CanonicalForm &)
CanonicalForm pp ( const CanonicalForm & f )
Definition: cf_gcd.cc:676
static FORCE_INLINE void number2mpz(number n, coeffs c, mpz_t m)
Definition: coeffs.h:984

◆ 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

◆ prependIdentity()

static bigintmat * prependIdentity ( bigintmat A)
static

Definition at line 2036 of file bigintmat.cc.

2037{
2038 coeffs R = A->basecoeffs();
2039 bigintmat *m = new bigintmat(A->rows()+A->cols(), A->cols(), R);
2040 m->copySubmatInto(A, 1, 1, A->rows(), A->cols(), A->cols()+1, 1);
2041 number one = n_Init(1, R);
2042 for(int i=1; i<= A->cols(); i++)
2043 m->set(i,i,one);
2044 n_Delete(&one, R);
2045 return m;
2046}

◆ reduce_mod_howell()

static void reduce_mod_howell ( bigintmat A,
bigintmat b,
bigintmat eps,
bigintmat x 
)
static

Definition at line 1950 of file bigintmat.cc.

1951{
1952 //write b = Ax + eps where eps is "small" in the sense of bounded by the
1953 //pivot entries in H. H does not need to be Howell (or HNF) but need
1954 //to be triagonal in the same direction.
1955 //b can have multiple columns.
1956#if 0
1957 PrintS("reduce_mod_howell: A:\n");
1958 A->Print();
1959 PrintS("\nb:\n");
1960 b->Print();
1961#endif
1962
1963 coeffs R = A->basecoeffs();
1964 assume(x->basecoeffs() == R);
1965 assume(b->basecoeffs() == R);
1966 assume(eps->basecoeffs() == R);
1967 if (!A->cols())
1968 {
1969 x->zero();
1970 eps->copy(b);
1971
1972#if 0
1973 PrintS("\nx:\n");
1974 x->Print();
1975 PrintS("\neps:\n");
1976 eps->Print();
1977 PrintS("\n****************************************\n");
1978#endif
1979 return;
1980 }
1981
1982 bigintmat * B = new bigintmat(b->rows(), 1, R);
1983 for(int i=1; i<= b->cols(); i++)
1984 {
1985 int A_col = A->cols();
1986 b->getcol(i, B);
1987 for(int j = B->rows(); j>0; j--)
1988 {
1989 number Ai = A->view(A->rows() - B->rows() + j, A_col);
1990 if (n_IsZero(Ai, R) &&
1991 n_IsZero(B->view(j, 1), R))
1992 {
1993 continue; //all is fine: 0*x = 0
1994 }
1995 else if (n_IsZero(B->view(j, 1), R))
1996 {
1997 x->rawset(x->rows() - B->rows() + j, i, n_Init(0, R));
1998 A_col--;
1999 }
2000 else if (n_IsZero(Ai, R))
2001 {
2002 A_col--;
2003 }
2004 else
2005 {
2006 // "solve" ax=b, possibly enlarging d
2007 number Bj = B->view(j, 1);
2008 number q = n_Div(Bj, Ai, R);
2009 x->rawset(x->rows() - B->rows() + j, i, q);
2010 for(int k=j; k>B->rows() - A->rows(); k--)
2011 {
2012 //B[k] = B[k] - x[k]A[k][j]
2013 number s = n_Mult(q, A->view(A->rows() - B->rows() + k, A_col), R);
2014 B->rawset(k, 1, n_Sub(B->view(k, 1), s, R));
2015 n_Delete(&s, R);
2016 }
2017 A_col--;
2018 }
2019 if (!A_col)
2020 {
2021 break;
2022 }
2023 }
2024 eps->setcol(i, B);
2025 }
2026 delete B;
2027#if 0
2028 PrintS("\nx:\n");
2029 x->Print();
2030 PrintS("\neps:\n");
2031 eps->Print();
2032 PrintS("\n****************************************\n");
2033#endif
2034}
void setcol(int j, bigintmat *m)
Setzt j-te Spalte gleich übergebenem Vektor (Matrix) m.
Definition: bigintmat.cc:826
static FORCE_INLINE number n_Div(number a, number b, const coeffs r)
return the quotient of 'a' and 'b', i.e., a/b; raises an error if 'b' is not invertible in r exceptio...
Definition: coeffs.h:612
b *CanonicalForm B
Definition: facBivar.cc:52

◆ 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

◆ solveAx_dixon()

static number solveAx_dixon ( bigintmat A,
bigintmat B,
bigintmat x,
bigintmat kern 
)
static

Definition at line 2108 of file bigintmat.cc.

2108 {
2109 coeffs R = A->basecoeffs();
2110
2111 assume(getCoeffType(R) == n_Z);
2112
2113 number p = n_Init(536870909, R); // PreviousPrime(2^29); not clever
2114 coeffs Rp = numbercoeffs(p, R); // R/pR
2115 bigintmat *Ap = bimChangeCoeff(A, Rp),
2116 *m = prependIdentity(Ap),
2117 *Tp, *Hp;
2118 delete Ap;
2119
2120 m->howell();
2121 Hp = new bigintmat(A->rows(), A->cols(), Rp);
2122 Hp->copySubmatInto(m, A->cols()+1, 1, A->rows(), A->cols(), 1, 1);
2123 Tp = new bigintmat(A->cols(), A->cols(), Rp);
2124 Tp->copySubmatInto(m, 1, 1, A->cols(), A->cols(), 1, 1);
2125
2126 int i, j;
2127
2128 for(i=1; i<= A->cols(); i++)
2129 {
2130 for(j=m->rows(); j>A->cols(); j--)
2131 {
2132 if (!n_IsZero(m->view(j, i), Rp)) break;
2133 }
2134 if (j>A->cols()) break;
2135 }
2136// Print("Found nullity (kern dim) of %d\n", i-1);
2137 bigintmat * kp = new bigintmat(A->cols(), i-1, Rp);
2138 kp->copySubmatInto(Tp, 1, 1, A->cols(), i-1, 1, 1);
2139 kp->howell();
2140
2141 delete m;
2142
2143 //Hp is the mod-p howell form
2144 //Tp the transformation, mod p
2145 //kp a basis for the kernel, in howell form, mod p
2146
2147 bigintmat * eps_p = new bigintmat(B->rows(), B->cols(), Rp),
2148 * x_p = new bigintmat(A->cols(), B->cols(), Rp),
2149 * fps_p = new bigintmat(kp->cols(), B->cols(), Rp);
2150
2151 //initial solution
2152
2153 number zero = n_Init(0, R);
2154 x->skalmult(zero, R);
2155 n_Delete(&zero, R);
2156
2157 bigintmat * b = new bigintmat(B);
2158 number pp = n_Init(1, R);
2159 i = 1;
2160 do
2161 {
2162 bigintmat * b_p = bimChangeCoeff(b, Rp), * s;
2163 bigintmat * t1, *t2;
2164 reduce_mod_howell(Hp, b_p, eps_p, x_p);
2165 delete b_p;
2166 if (!eps_p->isZero())
2167 {
2168 PrintS("no solution, since no modular solution\n");
2169
2170 delete eps_p;
2171 delete x_p;
2172 delete Hp;
2173 delete kp;
2174 delete Tp;
2175 delete b;
2176 n_Delete(&pp, R);
2177 n_Delete(&p, R);
2178 nKillChar(Rp);
2179
2180 return NULL;
2181 }
2182 t1 = bimMult(Tp, x_p);
2183 delete x_p;
2184 x_p = t1;
2185 reduce_mod_howell(kp, x_p, x_p, fps_p); //we're not all interested in fps_p
2186 s = bimChangeCoeff(x_p, R);
2187 t1 = bimMult(A, s);
2188 t2 = bimSub(b, t1);
2189 t2->skaldiv(p);
2190 delete b;
2191 delete t1;
2192 b = t2;
2193 s->skalmult(pp, R);
2194 t1 = bimAdd(x, s);
2195 delete s;
2196 x->swapMatrix(t1);
2197 delete t1;
2198
2199 if(kern && i==1)
2200 {
2201 bigintmat * ker = bimChangeCoeff(kp, R);
2202 t1 = bimMult(A, ker);
2203 t1->skaldiv(p);
2204 t1->skalmult(n_Init(-1, R), R);
2205 b->appendCol(t1);
2206 delete t1;
2207 x->appendCol(ker);
2208 delete ker;
2209 x_p->extendCols(kp->cols());
2210 eps_p->extendCols(kp->cols());
2211 fps_p->extendCols(kp->cols());
2212 }
2213
2214 n_InpMult(pp, p, R);
2215
2216 if (b->isZero())
2217 {
2218 //exact solution found, stop
2219 delete eps_p;
2220 delete fps_p;
2221 delete x_p;
2222 delete Hp;
2223 delete kp;
2224 delete Tp;
2225 delete b;
2226 n_Delete(&pp, R);
2227 n_Delete(&p, R);
2228 nKillChar(Rp);
2229
2230 return n_Init(1, R);
2231 }
2232 else
2233 {
2234 bigintmat *y = new bigintmat(x->rows(), x->cols(), R);
2235 number d = bimFarey(x, pp, y);
2236 if (d)
2237 {
2238 bigintmat *c = bimMult(A, y);
2239 bigintmat *bd = new bigintmat(B);
2240 bd->skalmult(d, R);
2241 if (kern)
2242 {
2243 bd->extendCols(kp->cols());
2244 }
2245 if (*c == *bd)
2246 {
2247 x->swapMatrix(y);
2248 delete y;
2249 delete c;
2250 if (kern)
2251 {
2252 y = new bigintmat(x->rows(), B->cols(), R);
2253 c = new bigintmat(x->rows(), kp->cols(), R);
2254 x->splitcol(y, c);
2255 x->swapMatrix(y);
2256 delete y;
2257 kern->swapMatrix(c);
2258 delete c;
2259 }
2260
2261 delete bd;
2262
2263 delete eps_p;
2264 delete fps_p;
2265 delete x_p;
2266 delete Hp;
2267 delete kp;
2268 delete Tp;
2269 delete b;
2270 n_Delete(&pp, R);
2271 n_Delete(&p, R);
2272 nKillChar(Rp);
2273
2274 return d;
2275 }
2276 delete c;
2277 delete bd;
2278 n_Delete(&d, R);
2279 }
2280 delete y;
2281 }
2282 i++;
2283 } while (1);
2284 delete eps_p;
2285 delete fps_p;
2286 delete x_p;
2287 delete Hp;
2288 delete kp;
2289 delete Tp;
2290 n_Delete(&pp, R);
2291 n_Delete(&p, R);
2292 nKillChar(Rp);
2293 return NULL;
2294}
static void reduce_mod_howell(bigintmat *A, bigintmat *b, bigintmat *eps, bigintmat *x)
Definition: bigintmat.cc:1950
static bigintmat * prependIdentity(bigintmat *A)
Definition: bigintmat.cc:2036
bigintmat * bimSub(bigintmat *a, bigintmat *b)
Definition: bigintmat.cc:218
static number bimFarey(bigintmat *A, number N, bigintmat *L)
Definition: bigintmat.cc:2048
bigintmat * bimAdd(bigintmat *a, bigintmat *b)
Matrix-Add/-Sub/-Mult so oder mit operator+/-/* ? @Note: NULL as a result means an error (non-compati...
Definition: bigintmat.cc:182
CF_NO_INLINE bool isZero() const
void swapMatrix(bigintmat *a)
Definition: bigintmat.cc:1566
int isZero()
Definition: bigintmat.cc:1363
void extendCols(int i)
append i zero-columns to the matrix
Definition: bigintmat.cc:1076
void skaldiv(number b)
Macht Ganzzahldivision aller Matrixeinträge mit b.
Definition: bigintmat.cc:1861
void copySubmatInto(bigintmat *, int sr, int sc, int nr, int nc, int tr, int tc)
copy the submatrix of b, staring at (a,b) having n rows, m cols into the given matrix at pos....
Definition: bigintmat.cc:1287
void howell()
dito, but Howell form (only different for zero-divsors)
Definition: bigintmat.cc:1585
const CanonicalForm int const CFList const Variable & y
Definition: facAbsFact.cc:53

◆ solveAx_howell()

static number solveAx_howell ( bigintmat A,
bigintmat b,
bigintmat x,
bigintmat kern 
)
static

Definition at line 2298 of file bigintmat.cc.

2299{
2300 // try to solve Ax=b, more precisely, find
2301 // number d
2302 // bigintmat x
2303 // sth. Ax=db
2304 // where d is small-ish (divides the determinant of A if this makes sense)
2305 // return 0 if there is no solution.
2306 //
2307 // if kern is non-NULL, return a basis for the kernel
2308
2309 //Algo: we do row-howell (triangular matrix). The idea is
2310 // Ax = b <=> AT T^-1x = b
2311 // y := T^-1 x, solve AT y = b
2312 // and return Ty.
2313 //Howell does not compute the trafo, hence we need to cheat:
2314 //B := (I_n | A^t)^t, then the top part of the Howell form of
2315 //B will give a useful trafo
2316 //Then we can find x by back-substitution and lcm/gcd to find the denominator
2317 //The defining property of Howell makes this work.
2318
2319 coeffs R = A->basecoeffs();
2321 m->howell(); // since m contains the identity, we'll have A->cols()
2322 // many cols.
2323 number den = n_Init(1, R);
2324
2325 bigintmat * B = new bigintmat(A->rows(), 1, R);
2326 for(int i=1; i<= b->cols(); i++)
2327 {
2328 int A_col = A->cols();
2329 b->getcol(i, B);
2330 B->skalmult(den, R);
2331 for(int j = B->rows(); j>0; j--)
2332 {
2333 number Ai = m->view(m->rows()-B->rows() + j, A_col);
2334 if (n_IsZero(Ai, R) &&
2335 n_IsZero(B->view(j, 1), R))
2336 {
2337 continue; //all is fine: 0*x = 0
2338 }
2339 else if (n_IsZero(B->view(j, 1), R))
2340 {
2341 x->rawset(x->rows() - B->rows() + j, i, n_Init(0, R));
2342 A_col--;
2343 }
2344 else if (n_IsZero(Ai, R))
2345 {
2346 delete m;
2347 delete B;
2348 n_Delete(&den, R);
2349 return 0;
2350 }
2351 else
2352 {
2353 // solve ax=db, possibly enlarging d
2354 // so x = db/a
2355 number Bj = B->view(j, 1);
2356 number g = n_Gcd(Bj, Ai, R);
2357 number xi;
2358 if (n_Equal(Ai, g, R))
2359 { //good: den stable!
2360 xi = n_Div(Bj, Ai, R);
2361 }
2362 else
2363 { //den <- den * (a/g), so old sol. needs to be adjusted
2364 number inc_d = n_Div(Ai, g, R);
2365 n_InpMult(den, inc_d, R);
2366 x->skalmult(inc_d, R);
2367 B->skalmult(inc_d, R);
2368 xi = n_Div(Bj, g, R);
2369 n_Delete(&inc_d, R);
2370 } //now for the back-substitution:
2371 x->rawset(x->rows() - B->rows() + j, i, xi);
2372 for(int k=j; k>0; k--)
2373 {
2374 //B[k] = B[k] - x[k]A[k][j]
2375 number s = n_Mult(xi, m->view(m->rows()-B->rows() + k, A_col), R);
2376 B->rawset(k, 1, n_Sub(B->view(k, 1), s, R));
2377 n_Delete(&s, R);
2378 }
2379 n_Delete(&g, R);
2380 A_col--;
2381 }
2382 if (!A_col)
2383 {
2384 if (B->isZero()) break;
2385 else
2386 {
2387 delete m;
2388 delete B;
2389 n_Delete(&den, R);
2390 return 0;
2391 }
2392 }
2393 }
2394 }
2395 delete B;
2396 bigintmat *T = new bigintmat(A->cols(), A->cols(), R);
2397 T->copySubmatInto(m, 1, 1, A->cols(), A->cols(), 1, 1);
2398 if (kern)
2399 {
2400 int i, j;
2401 for(i=1; i<= A->cols(); i++)
2402 {
2403 for(j=m->rows(); j>A->cols(); j--)
2404 {
2405 if (!n_IsZero(m->view(j, i), R)) break;
2406 }
2407 if (j>A->cols()) break;
2408 }
2409 Print("Found nullity (kern dim) of %d\n", i-1);
2410 bigintmat * ker = new bigintmat(A->rows(), i-1, R);
2411 ker->copySubmatInto(T, 1, 1, A->rows(), i-1, 1, 1);
2412 kern->swapMatrix(ker);
2413 delete ker;
2414 }
2415 delete m;
2416 bigintmat * y = bimMult(T, x);
2417 x->swapMatrix(y);
2418 delete y;
2419 x->simplifyContentDen(&den);
2420#if 0
2421 PrintS("sol = 1/");
2422 n_Print(den, R);
2423 PrintS(" *\n");
2424 x->Print();
2425 PrintLn();
2426#endif
2427 return den;
2428}
g
Definition: cfModGcd.cc:4090
static FORCE_INLINE number n_Gcd(number a, number b, const coeffs r)
in Z: return the gcd of 'a' and 'b' in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ,...
Definition: coeffs.h:661