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bigintmat.h
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1 /****************************************
2 * Computer Algebra System SINGULAR *
3 ****************************************/
4 /*
5 * ABSTRACT: class bigintmat: matrices of number
6 *
7 * Matrices are stored as 1-dim c-arrays but interpreted 2-dim as matrices.
8 * Both modes of addressing are supported, note however, that the 1-dim
9 * adressing starts at 0, the 2-dim at 1.
10 *
11 * Matrices are meant to represent column modules, thus the default
12 * operations are always by column.
13 *
14 * While basic operations are supported over any ring (coeff), some more
15 * advanced ones require more special rings: eg. echelon forms, solving
16 * of linear equations is only effective over principal ideal or even
17 * Euclidean rings.
18 *
19 * Be careful with the get/set/view/rawset functions to understand which
20 * arguments are copied/ deleted or only assigned.
21 */
22 
23 #ifndef BIGINTMAT_H
24 #define BIGINTMAT_H
25 
26 #include "coeffs/coeffs.h"
27 
28 /**
29  * @class bigintmat bigintmat.h <coeffs/bigintmat.h>
30  *
31  * Matrices of numbers
32  *
33  * Matrices are stored as 1-dim c-arrays but interpreted 2-dim as matrices.
34  * Both modes of addressing are supported, note however, that the 1-dim
35  * adressing starts at 0, the 2-dim at 1.
36  *
37  * Matrices are meant to represent column modules, thus the default
38  * operations are always by column.
39  *
40  * While basic operations are supported over any ring (coeff), some more
41  * advanced ones require more special rings: eg. echelon forms, solving
42  * of linear equations is only effective over principal ideal or even
43  * Euclidean rings.
44  *
45  * Be careful with the get/set/view/rawset functions to understand which
46  * arguments are copied/ deleted or only assigned.
47  *
48  * @Note: no reference counting here!
49  */
50 class bigintmat
51 {
52  private:
54  number *v;
55  int row;
56  int col;
57  public:
58 
59  bigintmat(): m_coeffs(NULL), v(NULL), row(1), col(0){}
60 
61  bigintmat * transpose();
62 
63  /// transpose in place
64  void inpTranspose();
65 
66 
67  /// constructor: the r times c zero-matrix. Beware that the creation
68  /// of a large zero matrix is expensive in terms of time and memory.
69  bigintmat(int r, int c, const coeffs n): m_coeffs(n), v(NULL), row(r), col(c)
70  {
71  assume (rows() >= 0);
72  assume (cols() >= 0);
73 
74  const int l = r*c;
75 
76  if (l>0) /*(r>0) && (c>0) */
77  {
78  v = (number *)omAlloc(sizeof(number)*l);
79 
80  assume (basecoeffs() != NULL);
81  for (int i = l - 1; i>=0; i--)
82  {
83  v[i] = n_Init(0, basecoeffs());
84  }
85  }
86  }
87 
88  /// copy constructor
90  {
91  const int l = row*col;
92 
93  if (l > 0)
94  {
95  assume (rows() > 0);
96  assume (cols() > 0);
97 
98  assume (m->v != NULL);
99 
100  v = (number *)omAlloc(sizeof(number)*row*col);
101 
102  assume (basecoeffs() != NULL);
103 
104  for (int i = l-1; i>=0; i--)
105  {
106  v[i] = n_Copy((*m)[i], basecoeffs());
107  }
108  }
109  }
110  /// dubious: 1-dim access to 2-dim array. Entries are read row by row.
111  inline number& operator[](int i)
112  {
113 #ifndef SING_NDEBUG
114  if((i<0)||(i>=row*col))
115  {
116  Werror("wrong bigintmat index:%d\n",i);
117  }
118  assume ( !((i<0)||(i>=row*col)) );
119 #endif
120  return v[i]; // Hier sollte imho kein nlCopy rein...
121  }
122  inline const number& operator[](int i) const
123  {
124 #ifndef SING_NDEBUG
125  if((i<0)||(i>=row*col))
126  {
127  Werror("wrong bigintmat index:%d\n",i);
128  }
129  assume ( !((i<0)||(i>=row*col)) );
130 #endif
131  return v[i];
132  }
133 #define BIMATELEM(M,I,J) (M)[(I-1)*(M).cols()+J-1]
134 
135  /// UEberladener *=-Operator (fuer int und bigint)
136  /// Frage hier: *= verwenden oder lieber = und * einzeln?
137  /// problem: what about non-commuting rings. Is this from left or right?
138  void operator*=(int intop);
139 
140  /// inplace version of skalar mult. CHANGES input.
141  void inpMult(number bintop, const coeffs C = NULL);
142 
143  inline int length() { return col*row; }
144  inline int cols() const { return col; }
145  inline int rows() const { return row; }
146  inline coeffs basecoeffs() const { return m_coeffs; }
147 
148  /// canonical destructor.
150  {
151  if (v!=NULL)
152  {
153  for (int i=row*col-1;i>=0; i--) { n_Delete(&(v[i]), basecoeffs()); }
154  omFreeSize((ADDRESS)v, sizeof(number)*row*col);
155  v=NULL;
156  }
157  }
158 
159  /// helper function to map from 2-dim coordinates, starting by 1 to
160  /// 1-dim coordinate, starting by 0
161  int index(int r, int c) const
162  {
163  assume (rows() >= 0 && cols() >= 0);
164 
165  assume (r > 0 && c > 0);
166  assume (r <= rows() && c <= cols());
167 
168  const int index = ((r-1)*cols() + (c-1));
169 
170  assume (index >= 0 && index < rows() * cols());
171  return index;
172  }
173 
174  /// get a copy of an entry. NOTE: starts at [1,1]
175  number get(int i, int j) const;
176  /// view an entry an entry. NOTE: starts at [1,1]
177  //do NOT delete.
178  number view(int i, int j) const;
179 
180  /// get a copy of an entry. NOTE: starts at [0]
181  number get(int i) const;
182  /// view an entry. NOTE: starts at [0]
183  number view(int i) const;
184 
185  /// replace an entry with a copy (delete old + copy new!).
186  /// NOTE: starts at [1,1]
187  void set(int i, int j, number n, const coeffs C = NULL);
188 
189  /// replace an entry with a copy (delete old + copy new!).
190  /// NOTE: starts at [0]
191  void set(int i, number n, const coeffs C = NULL);
192 
193 
194  /// replace an entry with the given number n (only delete old).
195  /// NOTE: starts at [0]. Should be named set_transfer
196  inline void rawset(int i, number n, const coeffs C = NULL)
197  {
198  assume (C == NULL || C == basecoeffs());
199  assume (i >= 0);
200  const int l = rows() * cols();
201  assume (i<l);
202 
203  if (i < l)
204  {
205  n_Delete(&(v[i]), basecoeffs()); v[i] = n;
206  }
207 #ifndef SING_NDEBUG
208  else
209  {
210  Werror("wrong bigintmat index:%d\n",i);
211  }
212 #endif
213  }
214 
215  /// as above, but the 2-dim version
216  inline void rawset(int i, int j, number n, const coeffs C = NULL)
217  {
218  rawset( index(i,j), n, C);
219  }
220 
221  ///IO: String returns a singular string containing the matrix, needs
222  /// freeing afterwards
223  char * String();
224  ///IO: writes the matrix into the current internal string buffer which
225  /// must be started/ allocated before (e.g. @ref StringSetS)
226  void Write();
227  ///IO: simply prints the matrix to the current output (screen?)
228  void Print();
229 
230  /**
231  * Returns a string as it would have been printed in the interpreter.
232  * Used e.g. in print functions of various blackbox types.
233  */
234  char * StringAsPrinted();
235  void pprint(int maxwid);
236  int compare(const bigintmat* op) const;
237  int * getwid(int maxwid);
238 
239 
240  // Funktionen von Kira, Jan, Marco
241  // !WICHTIG: Überall, wo eine number übergeben wird, und damit gearbeitet wird, die coeffs mitübergeben und erst
242  // überprüfen, ob diese mit basecoeffs übereinstimmen. Falls nein: Breche ab!
243 
244  /// swap columns i and j
245  void swap(int i, int j);
246 
247  /// swap rows i and j
248  void swaprow(int i, int j);
249 
250  ///find index of 1st non-zero entry in row i
251  int findnonzero(int i);
252 
253  ///find index of 1st non-zero entry in column j
254  int findcolnonzero(int j);
255 
256  ///copies the j-th column into the matrix a - which needs to be pre-allocated with the correct size.
257  void getcol(int j, bigintmat *a);
258 
259  ///copies the no-columns staring by j (so j...j+no-1) into the pre-allocated a
260  void getColRange(int j, int no, bigintmat *a);
261 
262  void getrow(int i, bigintmat *a); ///< Schreibt i-te Zeile in Vektor (Matrix) a
263  void setcol(int j, bigintmat *m); ///< Setzt j-te Spalte gleich übergebenem Vektor (Matrix) m
264  void setrow(int i, bigintmat *m); ///< Setzt i-te Zeile gleich übergebenem Vektor (Matrix) m
265 
266  ///horizontally join the matrices, m <- m|a
267  void appendCol (bigintmat *a);
268 
269  ///append i zero-columns to the matrix
270  void extendCols (int i);
271 
272  bool add(bigintmat *b); ///< Addiert zur Matrix die Matrix b dazu. Return false => an error occurred
273  bool sub(bigintmat *b); ///< Subtrahiert ...
274  bool skalmult(number b, coeffs c); ///< Multipliziert zur Matrix den Skalar b hinzu
275  bool addcol(int i, int j, number a, coeffs c); ///< addiert a-faches der j-ten Spalte zur i-ten dazu
276  bool addrow(int i, int j, number a, coeffs c); ///< ... Zeile ...
277  void colskalmult(int i, number a, coeffs c); ///< Multipliziert zur i-ten Spalte den Skalar a hinzu
278  void rowskalmult(int i, number a, coeffs c); ///< ... Zeile ...
279  void coltransform(int i, int j, number a, number b, number c, number d); ///< transforms cols (i,j) using the 2x2 matrix ((a,b)(c,d)) (hopefully)
280  void concatrow(bigintmat *a, bigintmat *b); ///< Fügt zwei Matrixen untereinander/nebeneinander in gegebene Matrix ein, bzw spaltet gegebenen Matrix auf
281  void concatcol(bigintmat *a, bigintmat *b);
282  void splitrow(bigintmat *a, bigintmat *b); ///< Speichert in Matrix a den oberen, in b den unteren Teil der Matrix, vorausgesetzt die Dimensionen stimmen überein
283  void splitcol(bigintmat *a, bigintmat *b); ///< ... linken ... rechten ...
284  void splitcol(bigintmat *a, int i); ///< Speichert die ersten i Spalten als Teilmatrix in a
285  void splitrow(bigintmat *a, int i); ///< ... Zeilen ...
286  bool copy(bigintmat *b); ///< Kopiert Einträge von b auf Bigintmat
287  void copySubmatInto(bigintmat *, int sr, int sc, int nr, int nc, int tr, int tc);
288  void one(); ///< Macht Matrix (Falls quadratisch) zu Einheitsmatrix
289  int isOne(); ///< is matrix is identity
290  void zero(); ///< Setzt alle Einträge auf 0
291  int isZero();
292  int colIsZero(int i);
293  bigintmat *elim(int i, int j); ///< Liefert Streichungsmatrix (i-te Zeile und j-te Spalte gestrichen) zurück
294  number pseudoinv(bigintmat *a); ///< Speichert in Matrix a die Pseudoinverse, liefert den Nenner zurück
295  number trace(); ///< the trace ....
296  number det(); ///< det (via LaPlace in general, hnf for euc. rings)
297  number hnfdet(); ///< det via HNF
298  /// Primzahlen als long long int, müssen noch in number umgewandelt werden?
299  void hnf(); ///< transforms INPLACE to HNF
300  void howell(); ///<dito, but Howell form (only different for zero-divsors)
301  void swapMatrix(bigintmat * a);
302  #ifdef HAVE_RINGS
303  bigintmat * modhnf(number p, coeffs c); ///< computes HNF(this | p*I)
304  #endif
305  bigintmat * modgauss(number p, coeffs c);
306  void skaldiv(number b); ///< Macht Ganzzahldivision aller Matrixeinträge mit b
307  void colskaldiv(int j, number b); ///< Macht Ganzzahldivision aller j-ten Spalteneinträge mit b
308  void mod(number p); ///< Reduziert komplette Matrix modulo p
309  bigintmat* inpmod(number p, coeffs c); ///< Liefert Kopie der Matrix zurück, allerdings im Ring Z modulo p
310  number content(); ///<the content, the gcd of all entries. Only makes sense for Euclidean rings (or possibly constructive PIR)
311  void simplifyContentDen(number *den); ///< ensures that Gcd(den, content)=1
312  ///< enden hier wieder
313 };
314 
315 bool operator==(const bigintmat & lhr, const bigintmat & rhr);
316 bool operator!=(const bigintmat & lhr, const bigintmat & rhr);
317 
318 /// Matrix-Add/-Sub/-Mult so oder mit operator+/-/* ?
319 /// @Note: NULL as a result means an error (non-compatible matrices?)
321 bigintmat * bimAdd(bigintmat * a, int b);
323 bigintmat * bimSub(bigintmat * a, int b);
325 bigintmat * bimMult(bigintmat * a, int b);
326 bigintmat * bimMult(bigintmat * a, number b, const coeffs cf);
327 
328 ///same as copy constructor - apart from it being able to accept NULL as input
329 bigintmat * bimCopy(const bigintmat * b);
330 
331 class intvec;
332 intvec * bim2iv(bigintmat * b);
333 bigintmat * iv2bim(intvec * b, const coeffs C);
334 
335 // Wieder von Kira, Jan, Marco
336 bigintmat * bimChangeCoeff(bigintmat *a, coeffs cnew); ///< Liefert Kopier von Matrix a zurück, mit coeffs cnew statt den ursprünglichen
337 void bimMult(bigintmat *a, bigintmat *b, bigintmat *c); ///< Multipliziert Matrix a und b und speichert Ergebnis in c
338 
339 ///solve Ax=b*d. x needs to be pre-allocated to the same number of columns as b.
340 /// the minimal denominator d is returned. Currently available for Z, Q and Z/nZ (and possibly for all fields: d=1 there)
341 ///Beware that the internal functions can find the kernel as well - but the interface is lacking.
342 number solveAx(bigintmat *A, bigintmat *b, bigintmat *x); // solves Ax=b*d for a minimal denominator d. if x needs to have as many cols as b
343 
344 ///a basis for the nullspace of a mod p: only used internally in Round2.
345 /// Don't use it.
346 int kernbase (bigintmat *a, bigintmat *c, number p, coeffs q);
348 // enden wieder
349 void diagonalForm(bigintmat *a, bigintmat **b, bigintmat **c);
350 
351 #endif /* #ifndef BIGINTMAT_H */
void * ADDRESS
Definition: auxiliary.h:135
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: bigintmat.cc:2601
bigintmat * bimSub(bigintmat *a, bigintmat *b)
Definition: bigintmat.cc:218
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...
Definition: bigintmat.cc:2431
void diagonalForm(bigintmat *a, bigintmat **b, bigintmat **c)
Definition: bigintmat.cc:2476
bool nCoeffs_are_equal(coeffs r, coeffs s)
Definition: bigintmat.cc:2646
bigintmat * bimChangeCoeff(bigintmat *a, coeffs cnew)
Liefert Kopier von Matrix a zurück, mit coeffs cnew statt den ursprünglichen.
Definition: bigintmat.cc:1805
bigintmat * bimMult(bigintmat *a, bigintmat *b)
Definition: bigintmat.cc:255
bigintmat * iv2bim(intvec *b, const coeffs C)
Definition: bigintmat.cc:349
bigintmat * bimCopy(const bigintmat *b)
same as copy constructor - apart from it being able to accept NULL as input
Definition: bigintmat.cc:405
bool operator!=(const bigintmat &lhr, const bigintmat &rhr)
Definition: bigintmat.cc:176
intvec * bim2iv(bigintmat *b)
Definition: bigintmat.cc:341
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
bool operator==(const bigintmat &lhr, const bigintmat &rhr)
Definition: bigintmat.cc:159
CanonicalForm den(const CanonicalForm &f)
int l
Definition: cfEzgcd.cc:93
int m
Definition: cfEzgcd.cc:121
int i
Definition: cfEzgcd.cc:125
Variable x
Definition: cfModGcd.cc:4023
int p
Definition: cfModGcd.cc:4019
CanonicalForm cf
Definition: cfModGcd.cc:4024
CanonicalForm b
Definition: cfModGcd.cc:4044
Matrices of numbers.
Definition: bigintmat.h:51
void Print()
IO: simply prints the matrix to the current output (screen?)
Definition: bigintmat.cc:443
~bigintmat()
canonical destructor.
Definition: bigintmat.h:149
void colskaldiv(int j, number b)
Macht Ganzzahldivision aller j-ten Spalteneinträge mit b.
Definition: bigintmat.cc:1877
const number & operator[](int i) const
Definition: bigintmat.h:122
int length()
Definition: bigintmat.h:143
number det()
det (via LaPlace in general, hnf for euc. rings)
Definition: bigintmat.cc:1513
bigintmat * modgauss(number p, coeffs c)
void splitrow(bigintmat *a, bigintmat *b)
Speichert in Matrix a den oberen, in b den unteren Teil der Matrix, vorausgesetzt die Dimensionen sti...
Definition: bigintmat.cc:1128
coeffs m_coeffs
Definition: bigintmat.h:53
int isOne()
is matrix is identity
Definition: bigintmat.cc:1301
void zero()
Setzt alle Einträge auf 0.
Definition: bigintmat.cc:1351
void appendCol(bigintmat *a)
horizontally join the matrices, m <- m|a
Definition: bigintmat.cc:1084
number trace()
the trace ....
Definition: bigintmat.cc:1499
bool addrow(int i, int j, number a, coeffs c)
... Zeile ...
Definition: bigintmat.cc:984
void swap(int i, int j)
swap columns i and j
Definition: bigintmat.cc:686
void coltransform(int i, int j, number a, number b, number c, number d)
transforms cols (i,j) using the 2x2 matrix ((a,b)(c,d)) (hopefully)
Definition: bigintmat.cc:1890
bool addcol(int i, int j, number a, coeffs c)
addiert a-faches der j-ten Spalte zur i-ten dazu
Definition: bigintmat.cc:960
number * v
Definition: bigintmat.h:54
void hnf()
transforms INPLACE to HNF
Definition: bigintmat.cc:1661
char * StringAsPrinted()
Returns a string as it would have been printed in the interpreter.
Definition: bigintmat.cc:451
void swapMatrix(bigintmat *a)
Definition: bigintmat.cc:1567
int cols() const
Definition: bigintmat.h:144
int isZero()
Definition: bigintmat.cc:1364
number hnfdet()
det via HNF Primzahlen als long long int, müssen noch in number umgewandelt werden?
Definition: bigintmat.cc:1546
int findnonzero(int i)
find index of 1st non-zero entry in row i
Definition: bigintmat.cc:724
bigintmat * modhnf(number p, coeffs c)
computes HNF(this | p*I)
Definition: bigintmat.cc:1833
void setcol(int j, bigintmat *m)
Setzt j-te Spalte gleich übergebenem Vektor (Matrix) m.
Definition: bigintmat.cc:827
bool add(bigintmat *b)
Addiert zur Matrix die Matrix b dazu. Return false => an error occurred.
Definition: bigintmat.cc:895
number & operator[](int i)
dubious: 1-dim access to 2-dim array. Entries are read row by row.
Definition: bigintmat.h:111
int * getwid(int maxwid)
Definition: bigintmat.cc:580
void inpMult(number bintop, const coeffs C=NULL)
inplace version of skalar mult. CHANGES input.
Definition: bigintmat.cc:145
bigintmat * transpose()
Definition: bigintmat.cc:37
void setrow(int i, bigintmat *m)
Setzt i-te Zeile gleich übergebenem Vektor (Matrix) m.
Definition: bigintmat.cc:861
void Write()
IO: writes the matrix into the current internal string buffer which must be started/ allocated before...
Definition: bigintmat.cc:413
void rowskalmult(int i, number a, coeffs c)
... Zeile ...
Definition: bigintmat.cc:1024
bool skalmult(number b, coeffs c)
Multipliziert zur Matrix den Skalar b hinzu.
Definition: bigintmat.cc:939
void simplifyContentDen(number *den)
ensures that Gcd(den, content)=1 enden hier wieder
Definition: bigintmat.cc:2689
void extendCols(int i)
append i zero-columns to the matrix
Definition: bigintmat.cc:1077
void splitcol(bigintmat *a, bigintmat *b)
... linken ... rechten ...
Definition: bigintmat.cc:1170
number content()
the content, the gcd of all entries. Only makes sense for Euclidean rings (or possibly constructive P...
Definition: bigintmat.cc:2676
void skaldiv(number b)
Macht Ganzzahldivision aller Matrixeinträge mit b.
Definition: bigintmat.cc:1862
void colskalmult(int i, number a, coeffs c)
Multipliziert zur i-ten Spalte den Skalar a hinzu.
Definition: bigintmat.cc:1008
int colIsZero(int i)
Definition: bigintmat.cc:1578
bool copy(bigintmat *b)
Kopiert Einträge von b auf Bigintmat.
Definition: bigintmat.cc:1260
int index(int r, int c) const
helper function to map from 2-dim coordinates, starting by 1 to 1-dim coordinate, starting by 0
Definition: bigintmat.h:161
void getcol(int j, bigintmat *a)
copies the j-th column into the matrix a - which needs to be pre-allocated with the correct size.
Definition: bigintmat.cc:748
number pseudoinv(bigintmat *a)
Speichert in Matrix a die Pseudoinverse, liefert den Nenner zurück.
Definition: bigintmat.cc:1416
int col
Definition: bigintmat.h:56
bigintmat(const bigintmat *m)
copy constructor
Definition: bigintmat.h:89
int rows() const
Definition: bigintmat.h:145
number get(int i, int j) const
get a copy of an entry. NOTE: starts at [1,1]
Definition: bigintmat.cc:119
bigintmat * inpmod(number p, coeffs c)
Liefert Kopie der Matrix zurück, allerdings im Ring Z modulo p.
void pprint(int maxwid)
Definition: bigintmat.cc:611
void getColRange(int j, int no, bigintmat *a)
copies the no-columns staring by j (so j...j+no-1) into the pre-allocated a
Definition: bigintmat.cc:779
void rawset(int i, int j, number n, const coeffs C=NULL)
as above, but the 2-dim version
Definition: bigintmat.h:216
void concatcol(bigintmat *a, bigintmat *b)
Definition: bigintmat.cc:1099
int findcolnonzero(int j)
find index of 1st non-zero entry in column j
Definition: bigintmat.cc:736
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:1288
number view(int i, int j) const
view an entry an entry. NOTE: starts at [1,1]
Definition: bigintmat.cc:127
void inpTranspose()
transpose in place
Definition: bigintmat.cc:50
void one()
Macht Matrix (Falls quadratisch) zu Einheitsmatrix.
Definition: bigintmat.cc:1326
void howell()
dito, but Howell form (only different for zero-divsors)
Definition: bigintmat.cc:1586
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
bigintmat(int r, int c, const coeffs n)
constructor: the r times c zero-matrix. Beware that the creation of a large zero matrix is expensive ...
Definition: bigintmat.h:69
void operator*=(int intop)
UEberladener *=-Operator (fuer int und bigint) Frage hier: *= verwenden oder lieber = und * einzeln?...
Definition: bigintmat.cc:136
coeffs basecoeffs() const
Definition: bigintmat.h:146
void getrow(int i, bigintmat *a)
Schreibt i-te Zeile in Vektor (Matrix) a.
Definition: bigintmat.cc:792
void concatrow(bigintmat *a, bigintmat *b)
Fügt zwei Matrixen untereinander/nebeneinander in gegebene Matrix ein, bzw spaltet gegebenen Matrix a...
Definition: bigintmat.cc:1040
bigintmat()
Definition: bigintmat.h:59
void set(int i, int j, number n, const coeffs C=NULL)
replace an entry with a copy (delete old + copy new!). NOTE: starts at [1,1]
Definition: bigintmat.cc:95
bigintmat * elim(int i, int j)
Liefert Streichungsmatrix (i-te Zeile und j-te Spalte gestrichen) zurück.
Definition: bigintmat.cc:1382
int compare(const bigintmat *op) const
Definition: bigintmat.cc:362
bool sub(bigintmat *b)
Subtrahiert ...
Definition: bigintmat.cc:917
int row
Definition: bigintmat.h:55
char * String()
IO: String returns a singular string containing the matrix, needs freeing afterwards.
Definition: bigintmat.cc:436
void swaprow(int i, int j)
swap rows i and j
Definition: bigintmat.cc:705
void mod(number p)
Reduziert komplette Matrix modulo p.
Definition: bigintmat.cc:1917
Definition: intvec.h:23
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
Definition: coeffs.h:451
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:455
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:538
const CanonicalForm int s
Definition: facAbsFact.cc:55
int j
Definition: facHensel.cc:105
#define assume(x)
Definition: mod2.h:390
The main handler for Singular numbers which are suitable for Singular polynomials.
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omAlloc(size)
Definition: omAllocDecl.h:210
#define NULL
Definition: omList.c:12
void Werror(const char *fmt,...)
Definition: reporter.cc:189
#define A
Definition: sirandom.c:24