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MinorInterface.cc File Reference
#include "kernel/mod2.h"
#include "kernel/linear_algebra/MinorInterface.h"
#include "kernel/linear_algebra/MinorProcessor.h"
#include "polys/simpleideals.h"
#include "coeffs/modulop.h"
#include "kernel/polys.h"
#include "kernel/structs.h"
#include "kernel/GBEngine/kstd1.h"
#include "kernel/ideals.h"

Go to the source code of this file.

Functions

bool arrayIsNumberArray (const poly *polyArray, const ideal iSB, const int length, int *intArray, poly *nfPolyArray, int &zeroCounter)
 
ideal getMinorIdeal_Int (const int *intMatrix, const int rowCount, const int columnCount, const int minorSize, const int k, const char *algorithm, const ideal i, const bool allDifferent)
 
ideal getMinorIdeal_Poly (const poly *polyMatrix, const int rowCount, const int columnCount, const int minorSize, const int k, const char *algorithm, const ideal i, const bool allDifferent)
 
ideal getMinorIdeal_toBeDone (const matrix mat, const int minorSize, const int k, const char *algorithm, const ideal i, const bool allDifferent)
 
ideal getMinorIdeal (const matrix mat, const int minorSize, const int k, const char *algorithm, const ideal iSB, const bool allDifferent)
 Returns the specified set of minors (= subdeterminantes) of the given matrix.
 
ideal getMinorIdealCache_Int (const int *intMatrix, const int rowCount, const int columnCount, const int minorSize, const int k, const ideal i, const int cacheStrategy, const int cacheN, const int cacheW, const bool allDifferent)
 
ideal getMinorIdealCache_Poly (const poly *polyMatrix, const int rowCount, const int columnCount, const int minorSize, const int k, const ideal i, const int cacheStrategy, const int cacheN, const int cacheW, const bool allDifferent)
 
ideal getMinorIdealCache_toBeDone (const matrix mat, const int minorSize, const int k, const ideal iSB, const int cacheStrategy, const int cacheN, const int cacheW, const bool allDifferent)
 
ideal getMinorIdealCache (const matrix mat, const int minorSize, const int k, const ideal iSB, const int cacheStrategy, const int cacheN, const int cacheW, const bool allDifferent)
 Returns the specified set of minors (= subdeterminantes) of the given matrix.
 
ideal getMinorIdealHeuristic (const matrix mat, const int minorSize, const int k, const ideal iSB, const bool allDifferent)
 Returns the specified set of minors (= subdeterminantes) of the given matrix.
 

Function Documentation

◆ arrayIsNumberArray()

bool arrayIsNumberArray ( const poly *  polyArray,
const ideal  iSB,
const int  length,
int intArray,
poly *  nfPolyArray,
int zeroCounter 
)

Definition at line 29 of file MinorInterface.cc.

32{
33 int n = 0; if (currRing != 0) n = currRing->N;
34 zeroCounter = 0;
35 bool result = true;
36
37 for (int i = 0; i < length; i++)
38 {
40 if (iSB != NULL)
41 {
42 poly tmp = kNF(iSB, currRing->qideal, nfPolyArray[i]);
45 }
46 if (nfPolyArray[i] == NULL)
47 {
48 intArray[i] = 0;
50 }
51 else
52 {
53 bool isConstant = true;
54 for (int j = 1; j <= n; j++)
55 if (pGetExp(nfPolyArray[i], j) > 0)
56 isConstant = false;
57 if (!isConstant) result = false;
58 else
59 {
61 if (intArray[i] == 0) zeroCounter++;
62 }
63 }
64 }
65 return result;
66}
int i
Definition cfEzgcd.cc:132
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:548
return result
int j
Definition facHensel.cc:110
static BOOLEAN length(leftv result, leftv arg)
Definition interval.cc:257
poly kNF(ideal F, ideal Q, poly p, int syzComp, int lazyReduce)
Definition kstd1.cc:3237
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition monomials.h:44
#define NULL
Definition omList.c:12
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition polys.cc:13
#define pDelete(p_ptr)
Definition polys.h:186
#define pGetExp(p, i)
Exponent.
Definition polys.h:41
#define pCopy(p)
return a copy of the poly
Definition polys.h:185

◆ getMinorIdeal()

ideal getMinorIdeal ( const matrix  m,
const int  minorSize,
const int  k,
const char algorithm,
const ideal  i,
const bool  allDifferent 
)

Returns the specified set of minors (= subdeterminantes) of the given matrix.

These minors form the set of generators of the ideal which is actually returned.
If k == 0, all non-zero minors will be computed. For k > 0, only the first k non-zero minors (to some fixed ordering among all minors) will be computed. Use k < 0 to compute the first |k| minors (including zero minors).
algorithm must be one of "Bareiss" and "Laplace".
i must be either NULL or an ideal capturing a standard basis. In the later case all minors will be reduced w.r.t. i. If allDifferent is true, each minor will be included as generator in the resulting ideal only once; otherwise as often as it occurs as minor value during the computation.

Parameters
mthe matrix from which to compute minors
minorSizethe size of the minors to be computed
kthe number of minors to be computed
algorithmthe algorithm to be used for the computation
iNULL or an ideal which encodes a standard basis
allDifferentif true each minor is considered only once
Returns
the ideal which has as generators the specified set of minors

Definition at line 238 of file MinorInterface.cc.

241{
242 /* Note that this method should be replaced by getMinorIdeal_toBeDone,
243 to enable faster computations in the case of matrices which contain
244 only numbers. But so far, this method is not yet usable as it replaces
245 the numbers by ints which may result in overflows during computations
246 of minors. */
247 int rowCount = mat->nrows;
248 int columnCount = mat->ncols;
249 poly* myPolyMatrix = (poly*)(mat->m);
251 ideal iii; /* the ideal to be filled and returned */
252
253 if ((k == 0) && (strcmp(algorithm, "Bareiss") == 0)
255 {
256 /* In this case, we call an optimized procedure, dating back to
257 Wilfried Pohl. It may be used whenever
258 - all minors are requested,
259 - requested minors need not be mutually distinct, and
260 - coefficients come from a field (i.e., the ring Z is not
261 allowed for this implementation). */
263 iSB));
264 }
265 else
266 {
267 /* copy all polynomials and reduce them w.r.t. iSB
268 (if iSB is present, i.e., not the NULL pointer) */
269
270 poly* nfPolyMatrix = (poly*)omAlloc(length*sizeof(poly));
271 if (iSB != NULL)
272 {
273 for (int i = 0; i < length; i++)
274 {
276 }
277 }
278 else
279 {
280 for (int i = 0; i < length; i++)
281 {
283 }
284 }
287
288 /* clean up */
289 for (int j = length-1; j>=0; j--) pDelete(&nfPolyMatrix[j]);
291 }
292
293 return iii;
294}
ideal getMinorIdeal_Poly(const poly *polyMatrix, const int rowCount, const int columnCount, const int minorSize, const int k, const char *algorithm, const ideal i, const bool allDifferent)
int k
Definition cfEzgcd.cc:99
ideal idMinors(matrix a, int ar, ideal R)
compute all ar-minors of the matrix a the caller of mpRecMin the elements of the result are not in R ...
Definition ideals.cc:1988
#define omAlloc(size)
#define omFree(addr)
#define rField_is_Ring(R)
Definition ring.h:490

◆ getMinorIdeal_Int()

ideal getMinorIdeal_Int ( const int intMatrix,
const int  rowCount,
const int  columnCount,
const int  minorSize,
const int  k,
const char algorithm,
const ideal  i,
const bool  allDifferent 
)

Definition at line 74 of file MinorInterface.cc.

78{
79 /* setting up a MinorProcessor for matrices with integer entries: */
82 int *myRowIndices=(int*)omAlloc(rowCount*sizeof(int));
83 for (int j = 0; j < rowCount; j++) myRowIndices[j] = j;
84 int *myColumnIndices=(int*)omAlloc(columnCount*sizeof(int));
85 for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j;
88
89 /* containers for all upcoming results: */
91 // int value = 0;
92 int collectedMinors = 0;
94
95 /* the ideal to be returned: */
96 ideal iii = idInit(1);
97
98 bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are requested,
99 omitting zero minors */
100 bool duplicatesOk = (allDifferent ? false : true);
101 int kk = ABS(k); /* absolute value of k */
102
103 /* looping over all minors: */
104 while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk)))
105 {
106 /* retrieving the next minor: */
108 poly f = NULL;
109 if (theMinor.getResult() != 0) f = pISet(theMinor.getResult());
112 }
113
114 /* before we return the result, let's omit zero generators
115 in iii which come after the computed minors */
116 ideal jjj;
117 if (collectedMinors == 0) jjj = idInit(1);
119 idDelete(&iii);
122 return jjj;
123}
static int ABS(int v)
Definition auxiliary.h:112
return false
Definition cfModGcd.cc:85
FILE * f
Definition checklibs.c:9
Class IntMinorProcessor is derived from class MinorProcessor.
void defineMatrix(const int numberOfRows, const int numberOfColumns, const int *matrix)
A method for defining a matrix with integer entries.
IntMinorValue getNextMinor(const int characteristic, const ideal &iSB, const char *algorithm)
A method for obtaining the next minor when iterating through all minors of a given size within a pre-...
Class IntMinorValue is derived from MinorValue and can be used for representing values in a cache for...
Definition Minor.h:718
void setMinorSize(const int minorSize)
Sets the size of the minor(s) of interest.
void defineSubMatrix(const int numberOfRows, const int *rowIndices, const int numberOfColumns, const int *columnIndices)
A method for defining a sub-matrix within a pre-defined matrix.
bool hasNextMinor()
A method for checking whether there is a next choice of rows and columns when iterating through all m...
#define idDelete(H)
delete an ideal
Definition ideals.h:29
BOOLEAN idInsertPolyWithTests(ideal h1, const int validEntries, const poly h2, const bool zeroOk, const bool duplicateOk)
Definition ideals.h:75
static ideal idCopyFirstK(const ideal ide, const int k)
Definition ideals.h:20
#define pISet(i)
Definition polys.h:312
int rChar(ring r)
Definition ring.cc:716
ideal idInit(int idsize, int rank)
initialise an ideal / module

◆ getMinorIdeal_Poly()

ideal getMinorIdeal_Poly ( const poly *  polyMatrix,
const int  rowCount,
const int  columnCount,
const int  minorSize,
const int  k,
const char algorithm,
const ideal  i,
const bool  allDifferent 
)

Definition at line 129 of file MinorInterface.cc.

133{
134 /* setting up a MinorProcessor for matrices with polynomial entries: */
137 int *myRowIndices=(int*)omAlloc(rowCount*sizeof(int));
138 for (int j = 0; j < rowCount; j++) myRowIndices[j] = j;
139 int *myColumnIndices=(int*)omAlloc(columnCount*sizeof(int));
140 for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j;
143
144 /* containers for all upcoming results: */
146 poly f = NULL;
147 int collectedMinors = 0;
148
149 /* the ideal to be returned: */
150 ideal iii = idInit(1);
151
152 bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are
153 requested, omitting zero minors */
154 bool duplicatesOk = (allDifferent ? false : true);
155 int kk = ABS(k); /* absolute value of k */
156#ifdef COUNT_AND_PRINT_OPERATIONS
157 printCounters ("starting", true);
158 int qqq = 0;
159#endif
160 /* looping over all minors: */
161 while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk)))
162 {
163 /* retrieving the next minor: */
165#if (defined COUNT_AND_PRINT_OPERATIONS) && (COUNT_AND_PRINT_OPERATIONS > 1)
166 qqq++;
167 Print("after %d", qqq);
168 printCounters ("-th minor", false);
169#endif
170 f = theMinor.getResult();
174 }
175#ifdef COUNT_AND_PRINT_OPERATIONS
176 printCounters ("ending", true);
177#endif
178
179 /* before we return the result, let's omit zero generators
180 in iii which come after the computed minors */
184 return(iii);
185}
void printCounters(char *prefix, bool resetToZero)
Class PolyMinorProcessor is derived from class MinorProcessor.
PolyMinorValue getNextMinor(const char *algorithm, const ideal &iSB)
A method for obtaining the next minor when iterating through all minors of a given size within a pre-...
void defineMatrix(const int numberOfRows, const int numberOfColumns, const poly *polyMatrix)
A method for defining a matrix with polynomial entries.
Class PolyMinorValue is derived from MinorValue and can be used for representing values in a cache fo...
Definition Minor.h:800
#define Print
Definition emacs.cc:80
void idKeepFirstK(ideal id, const int k)
keeps the first k (>= 1) entries of the given ideal (Note that the kept polynomials may be zero....
Definition ideals.cc:3140

◆ getMinorIdeal_toBeDone()

ideal getMinorIdeal_toBeDone ( const matrix  mat,
const int  minorSize,
const int  k,
const char algorithm,
const ideal  i,
const bool  allDifferent 
)

Definition at line 187 of file MinorInterface.cc.

190{
191 int rowCount = mat->nrows;
192 int columnCount = mat->ncols;
193 poly* myPolyMatrix = (poly*)(mat->m);
194 ideal iii; /* the ideal to be filled and returned */
195 int zz = 0;
196
197 /* divert to special implementations for pure number matrices and actual
198 polynomial matrices: */
199 int* myIntMatrix = (int*)omAlloc(rowCount * columnCount *sizeof(int));
200 poly* nfPolyMatrix = (poly*)omAlloc(rowCount * columnCount *sizeof(poly));
205 else
206 {
207 if ((k == 0) && (strcmp(algorithm, "Bareiss") == 0)
208 && (!rField_is_Z(currRing)) && (!allDifferent))
209 {
210 /* In this case, we call an optimized procedure, dating back to
211 Wilfried Pohl. It may be used whenever
212 - all minors are requested,
213 - requested minors need not be mutually distinct, and
214 - coefficients come from a field (i.e., Z is also not allowed
215 for this implementation). */
216 iii = (i == 0 ? idMinors(mat, minorSize) : idMinors(mat, minorSize, i));
217 }
218 else
219 {
222 }
223 }
224
225 /* clean up */
227 for (int j = 0; j < rowCount * columnCount; j++) pDelete(&nfPolyMatrix[j]);
229
230 return iii;
231}
ideal getMinorIdeal_Int(const int *intMatrix, const int rowCount, const int columnCount, const int minorSize, const int k, const char *algorithm, const ideal i, const bool allDifferent)
bool arrayIsNumberArray(const poly *polyArray, const ideal iSB, const int length, int *intArray, poly *nfPolyArray, int &zeroCounter)
static BOOLEAN rField_is_Z(const ring r)
Definition ring.h:514

◆ getMinorIdealCache()

ideal getMinorIdealCache ( const matrix  m,
const int  minorSize,
const int  k,
const ideal  i,
const int  cacheStrategy,
const int  cacheN,
const int  cacheW,
const bool  allDifferent 
)

Returns the specified set of minors (= subdeterminantes) of the given matrix.

These minors form the set of generators of the ideal which is actually returned.
If k == 0, all non-zero minors will be computed. For k > 0, only the first k non-zero minors (to some fixed ordering among all minors) will be computed. Use k < 0 to compute the first |k| minors (including zero minors).
The underlying algorithm is Laplace's algorithm with caching of certain subdeterminantes. The caching strategy can be set; see int MinorValue::getUtility () const in Minor.cc. cacheN is the maximum number of cached polynomials (=subdeterminantes); cacheW the maximum weight of the cache during all computations.
i must be either NULL or an ideal capturing a standard basis. In the later case all minors will be reduced w.r.t. i. If allDifferent is true, each minor will be included as generator in the resulting ideal only once; otherwise as often as it occurs as minor value during the computation.

Parameters
mthe matrix from which to compute minors
minorSizethe size of the minors to be computed
kthe number of minors to be computed
iNULL or an ideal which encodes a standard basis
cacheStrategyone of {1, .., 5}; see Minor.cc
cacheNmaximum number of cached polynomials (=subdeterminantes)
cacheWmaximum weight of the cache
allDifferentif true each minor is considered only once
Returns
the ideal which has as generators the specified set of minors

Definition at line 457 of file MinorInterface.cc.

461{
462 /* Note that this method should be replaced by getMinorIdealCache_toBeDone,
463 to enable faster computations in the case of matrices which contain
464 only numbers. But so far, this method is not yet usable as it replaces
465 the numbers by ints which may result in overflows during computations
466 of minors. */
467 int rowCount = mat->nrows;
468 int columnCount = mat->ncols;
469 poly* myPolyMatrix = (poly*)(mat->m);
471 poly* nfPolyMatrix = (poly*)omAlloc(length*sizeof(poly));
472 ideal iii; /* the ideal to be filled and returned */
473
474 /* copy all polynomials and reduce them w.r.t. iSB
475 (if iSB is present, i.e., not the NULL pointer) */
476 for (int i = 0; i < length; i++)
477 {
478 if (iSB==NULL)
480 else
481 nfPolyMatrix[i] = kNF(iSB, currRing->qideal, myPolyMatrix[i]);
482 }
483
487
488 /* clean up */
489 for (int j = 0; j < length; j++) pDelete(&nfPolyMatrix[j]);
491
492 return iii;
493}
ideal getMinorIdealCache_Poly(const poly *polyMatrix, const int rowCount, const int columnCount, const int minorSize, const int k, const ideal i, const int cacheStrategy, const int cacheN, const int cacheW, const bool allDifferent)

◆ getMinorIdealCache_Int()

ideal getMinorIdealCache_Int ( const int intMatrix,
const int  rowCount,
const int  columnCount,
const int  minorSize,
const int  k,
const ideal  i,
const int  cacheStrategy,
const int  cacheN,
const int  cacheW,
const bool  allDifferent 
)

Definition at line 302 of file MinorInterface.cc.

307{
308 /* setting up a MinorProcessor for matrices with integer entries: */
311 int *myRowIndices=(int*)omAlloc(rowCount*sizeof(int));
312 for (int j = 0; j < rowCount; j++) myRowIndices[j] = j;
313 int *myColumnIndices=(int*)omAlloc(columnCount*sizeof(int));
314 for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j;
319
320 /* containers for all upcoming results: */
322 // int value = 0;
323 int collectedMinors = 0;
325
326 /* the ideal to be returned: */
327 ideal iii = idInit(1);
328
329 bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are
330 requested, omitting zero minors */
331 bool duplicatesOk = (allDifferent ? false : true);
332 int kk = ABS(k); /* absolute value of k */
333
334 /* looping over all minors: */
335 while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk)))
336 {
337 /* retrieving the next minor: */
339 poly f = NULL;
340 if (theMinor.getResult() != 0) f = pISet(theMinor.getResult());
343 }
344
345 /* before we return the result, let's omit zero generators
346 in iii which come after the computed minors */
347 ideal jjj;
348 if (collectedMinors == 0) jjj = idInit(1);
350 idDelete(&iii);
353 return jjj;
354}
static void SetRankingStrategy(const int rankingStrategy)
A method for determining the value ranking strategy.
Definition Minor.cc:909

◆ getMinorIdealCache_Poly()

ideal getMinorIdealCache_Poly ( const poly *  polyMatrix,
const int  rowCount,
const int  columnCount,
const int  minorSize,
const int  k,
const ideal  i,
const int  cacheStrategy,
const int  cacheN,
const int  cacheW,
const bool  allDifferent 
)

Definition at line 360 of file MinorInterface.cc.

365{
366 /* setting up a MinorProcessor for matrices with polynomial entries: */
369 int *myRowIndices=(int*)omAlloc(rowCount*sizeof(int));
370 for (int j = 0; j < rowCount; j++) myRowIndices[j] = j;
371 int *myColumnIndices=(int*)omAlloc(columnCount*sizeof(int));
372 for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j;
377
378 /* containers for all upcoming results: */
380 poly f = NULL;
381 int collectedMinors = 0;
382
383 /* the ideal to be returned: */
384 ideal iii = idInit(1);
385
386 bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are
387 requested, omitting zero minors */
388 bool duplicatesOk = (allDifferent ? false : true);
389 int kk = ABS(k); /* absolute value of k */
390#ifdef COUNT_AND_PRINT_OPERATIONS
391 printCounters ("starting", true);
392 int qqq = 0;
393#endif
394 /* looping over all minors: */
395 while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk)))
396 {
397 /* retrieving the next minor: */
398 theMinor = mp.getNextMinor(cch, i);
399#if (defined COUNT_AND_PRINT_OPERATIONS) && (COUNT_AND_PRINT_OPERATIONS > 1)
400 qqq++;
401 Print("after %d", qqq);
402 printCounters ("-th minor", false);
403#endif
404 f = theMinor.getResult();
408 }
409#ifdef COUNT_AND_PRINT_OPERATIONS
410 printCounters ("ending", true);
411#endif
412
413 /* before we return the result, let's omit zero generators
414 in iii which come after the computed minors */
415 ideal jjj;
416 if (collectedMinors == 0) jjj = idInit(1);
418 idDelete(&iii);
421 return jjj;
422}

◆ getMinorIdealCache_toBeDone()

ideal getMinorIdealCache_toBeDone ( const matrix  mat,
const int  minorSize,
const int  k,
const ideal  iSB,
const int  cacheStrategy,
const int  cacheN,
const int  cacheW,
const bool  allDifferent 
)

Definition at line 424 of file MinorInterface.cc.

428{
429 int rowCount = mat->nrows;
430 int columnCount = mat->ncols;
431 poly* myPolyMatrix = (poly*)(mat->m);
432 ideal iii; /* the ideal to be filled and returned */
433 int zz = 0;
434
435 /* divert to special implementation when myPolyMatrix has only number
436 entries: */
437 int* myIntMatrix = (int*)omAlloc(rowCount * columnCount *sizeof(int));
438 poly* nfPolyMatrix = (poly*)omAlloc(rowCount * columnCount *sizeof(poly));
444 else
448
449 /* clean up */
451 for (int j = 0; j < rowCount * columnCount; j++) pDelete(&nfPolyMatrix[j]);
453
454 return iii;
455}
ideal getMinorIdealCache_Int(const int *intMatrix, const int rowCount, const int columnCount, const int minorSize, const int k, const ideal i, const int cacheStrategy, const int cacheN, const int cacheW, const bool allDifferent)

◆ getMinorIdealHeuristic()

ideal getMinorIdealHeuristic ( const matrix  m,
const int  minorSize,
const int  k,
const ideal  i,
const bool  allDifferent 
)

Returns the specified set of minors (= subdeterminantes) of the given matrix.

These minors form the set of generators of the ideal which is actually returned.
If k == 0, all non-zero minors will be computed. For k > 0, only the first k non-zero minors (to some fixed ordering among all minors) will be computed. Use k < 0 to compute the first |k| minors (including zero minors).
The algorithm is heuristically chosen among "Bareiss", "Laplace", and Laplace with caching (of subdeterminants).
i must be either NULL or an ideal capturing a standard basis. In the later case all minors will be reduced w.r.t. i. If allDifferent is true, each minor will be included as generator in the resulting ideal only once; otherwise as often as it occurs as minor value during the computation.

Parameters
mthe matrix from which to compute minors
minorSizethe size of the minors to be computed
kthe number of minors to be computed
iNULL or an ideal which encodes a standard basis
allDifferentif true each minor is considered only once
Returns
the ideal which has as generators the specified set of minors

Definition at line 495 of file MinorInterface.cc.

498{
499 int vars = currRing->N;
500
501 /* here comes the heuristic, as of 29 January 2010:
502
503 integral domain and minorSize <= 2 -> Bareiss
504 integral domain and minorSize >= 3 and vars <= 2 -> Bareiss
505 field case and minorSize >= 3 and vars = 3
506 and c in {2, 3, ..., 32749} -> Bareiss
507
508 otherwise:
509 if not all minors are requested -> Laplace, no Caching
510 otherwise:
511 minorSize >= 3 and vars <= 4 and
512 (rowCount over minorSize)*(columnCount over minorSize) >= 100
513 -> Laplace with Caching
514 minorSize >= 3 and vars >= 5 and
515 (rowCount over minorSize)*(columnCount over minorSize) >= 40
516 -> Laplace with Caching
517
518 otherwise: -> Laplace, no Caching
519 */
520
521 bool b = false; /* Bareiss */
522 bool l = false; /* Laplace without caching */
523 // bool c = false; /* Laplace with caching */
525 { /* the field case or ring Z */
526 if (minorSize <= 2) b = true;
527 else if (vars <= 2) b = true;
528 else if ((!rField_is_Ring(currRing)) && (vars == 3)
529 && (currRing->cf->ch >= 2) && (currRing->cf->ch <= NV_MAX_PRIME))
530 b = true;
531 }
532 if (!b)
533 { /* the non-Bareiss cases */
534 if (k != 0) /* this means, not all minors are requested */ l = true;
535 else
536 { /* k == 0, i.e., all minors are requested */
537 l = true;
538 }
539 }
540
541 if (b) return getMinorIdeal(mat, minorSize, k, "Bareiss", iSB,
543 else if (l) return getMinorIdeal(mat, minorSize, k, "Laplace", iSB,
545 else /* (c) */ return getMinorIdealCache(mat, minorSize, k, iSB,
546 3, 200, 100000, allDifferent);
547}
ideal getMinorIdealCache(const matrix mat, const int minorSize, const int k, const ideal iSB, const int cacheStrategy, const int cacheN, const int cacheW, const bool allDifferent)
Returns the specified set of minors (= subdeterminantes) of the given matrix.
ideal getMinorIdeal(const matrix mat, const int minorSize, const int k, const char *algorithm, const ideal iSB, const bool allDifferent)
Returns the specified set of minors (= subdeterminantes) of the given matrix.
int l
Definition cfEzgcd.cc:100
CanonicalForm b
Definition cfModGcd.cc:4111
#define NV_MAX_PRIME
Definition modulop.h:37
static BOOLEAN rField_is_Domain(const ring r)
Definition ring.h:492