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. More...
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. More...
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. More...

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.

{
  int n = 0; if (currRing != 0) n = currRing->N;
  zeroCounter = 0;
  bool result = true;
 
  for (int i = 0; i < length; i++)
  {
    nfPolyArray[i] = pCopy(polyArray[i]);
    if (iSB != NULL)
    {
      poly tmp = kNF(iSB, currRing->qideal, nfPolyArray[i]);
      pDelete(&nfPolyArray[i]);
      nfPolyArray[i]=tmp;
    }
    if (nfPolyArray[i] == NULL)
    {
      intArray[i] = 0;
      zeroCounter++;
    }
    else
    {
      bool isConstant = true;
      for (int j = 1; j <= n; j++)
        if (pGetExp(nfPolyArray[i], j) > 0)
          isConstant = false;
      if (!isConstant) result = false;
      else
      {
        intArray[i] = n_Int(pGetCoeff(nfPolyArray[i]), currRing->cf);
        if (intArray[i] == 0) zeroCounter++;
      }
    }
  }
  return result;
}

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

m	the matrix from which to compute minors
minorSize	the size of the minors to be computed
k	the number of minors to be computed
algorithm	the algorithm to be used for the computation
i	NULL or an ideal which encodes a standard basis
allDifferent	if 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.

{
  /* Note that this method should be replaced by getMinorIdeal_toBeDone,
     to enable faster computations in the case of matrices which contain
     only numbers. But so far, this method is not yet usable as it replaces
     the numbers by ints which may result in overflows during computations
     of minors. */
  int rowCount = mat->nrows;
  int columnCount = mat->ncols;
  poly* myPolyMatrix = (poly*)(mat->m);
  int length = rowCount * columnCount;
  ideal iii; /* the ideal to be filled and returned */
 
  if ((k == 0) && (strcmp(algorithm, "Bareiss") == 0)
      && (!rField_is_Ring(currRing)) && (!allDifferent))
  {
    /* In this case, we call an optimized procedure, dating back to
       Wilfried Pohl. It may be used whenever
       - all minors are requested,
       - requested minors need not be mutually distinct, and
       - coefficients come from a field (i.e., the ring Z is not
         allowed for this implementation). */
    iii = (iSB == NULL ? idMinors(mat, minorSize) : idMinors(mat, minorSize,
                                                          iSB));
  }
  else
  {
  /* copy all polynomials and reduce them w.r.t. iSB
     (if iSB is present, i.e., not the NULL pointer) */
 
    poly* nfPolyMatrix = (poly*)omAlloc(length*sizeof(poly));
    if (iSB != NULL)
    {
      for (int i = 0; i < length; i++)
      {
        nfPolyMatrix[i] = kNF(iSB, currRing->qideal,myPolyMatrix[i]);
      }
    }
    else
    {
      for (int i = 0; i < length; i++)
      {
        nfPolyMatrix[i] = pCopy(myPolyMatrix[i]);
      }
    }
    iii = getMinorIdeal_Poly(nfPolyMatrix, rowCount, columnCount, minorSize,
                             k, algorithm, iSB, allDifferent);
 
    /* clean up */
    for (int j = length-1; j>=0; j--) pDelete(&nfPolyMatrix[j]);
    omFree(nfPolyMatrix);
  }
 
  return iii;
}

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.

{
  /* setting up a MinorProcessor for matrices with integer entries: */
  IntMinorProcessor mp;
  mp.defineMatrix(rowCount, columnCount, intMatrix);
  int *myRowIndices=(int*)omAlloc(rowCount*sizeof(int));
  for (int j = 0; j < rowCount; j++) myRowIndices[j] = j;
  int *myColumnIndices=(int*)omAlloc(columnCount*sizeof(int));
  for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j;
  mp.defineSubMatrix(rowCount, myRowIndices, columnCount, myColumnIndices);
  mp.setMinorSize(minorSize);
 
  /* containers for all upcoming results: */
  IntMinorValue theMinor;
  // int value = 0;
  int collectedMinors = 0;
  int characteristic = 0; if (currRing != 0) characteristic = rChar(currRing);
 
  /* the ideal to be returned: */
  ideal iii = idInit(1);
 
  bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are requested,
                                             omitting zero minors */
  bool duplicatesOk = (allDifferent ? false : true);
  int kk = ABS(k); /* absolute value of k */
 
  /* looping over all minors: */
  while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk)))
  {
    /* retrieving the next minor: */
    theMinor = mp.getNextMinor(characteristic, i, algorithm);
    poly f = NULL;
    if (theMinor.getResult() != 0) f = pISet(theMinor.getResult());
    if (idInsertPolyWithTests(iii, collectedMinors, f, zeroOk, duplicatesOk))
      collectedMinors++;
  }
 
  /* before we return the result, let's omit zero generators
     in iii which come after the computed minors */
  ideal jjj;
  if (collectedMinors == 0) jjj = idInit(1);
  else                      jjj = idCopyFirstK(iii, collectedMinors);
  idDelete(&iii);
  omFree(myColumnIndices);
  omFree(myRowIndices);
  return jjj;
}

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.

{
  /* setting up a MinorProcessor for matrices with polynomial entries: */
  PolyMinorProcessor mp;
  mp.defineMatrix(rowCount, columnCount, polyMatrix);
  int *myRowIndices=(int*)omAlloc(rowCount*sizeof(int));
  for (int j = 0; j < rowCount; j++) myRowIndices[j] = j;
  int *myColumnIndices=(int*)omAlloc(columnCount*sizeof(int));
  for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j;
  mp.defineSubMatrix(rowCount, myRowIndices, columnCount, myColumnIndices);
  mp.setMinorSize(minorSize);
 
  /* containers for all upcoming results: */
  PolyMinorValue theMinor;
  poly f = NULL;
  int collectedMinors = 0;
 
  /* the ideal to be returned: */
  ideal iii = idInit(1);
 
  bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are
                                             requested, omitting zero minors */
  bool duplicatesOk = (allDifferent ? false : true);
  int kk = ABS(k); /* absolute value of k */
#ifdef COUNT_AND_PRINT_OPERATIONS
  printCounters ("starting", true);
  int qqq = 0;
#endif
  /* looping over all minors: */
  while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk)))
  {
    /* retrieving the next minor: */
    theMinor = mp.getNextMinor(algorithm, i);
#if (defined COUNT_AND_PRINT_OPERATIONS) && (COUNT_AND_PRINT_OPERATIONS > 1)
    qqq++;
    Print("after %d", qqq);
    printCounters ("-th minor", false);
#endif
    f = theMinor.getResult();
    if (idInsertPolyWithTests(iii, collectedMinors, pCopy(f),
                              zeroOk, duplicatesOk))
      collectedMinors++;
  }
#ifdef COUNT_AND_PRINT_OPERATIONS
  printCounters ("ending", true);
#endif
 
  /* before we return the result, let's omit zero generators
     in iii which come after the computed minors */
  idKeepFirstK(iii, collectedMinors);
  omFree(myColumnIndices);
  omFree(myRowIndices);
  return(iii);
}

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.

{
  int rowCount = mat->nrows;
  int columnCount = mat->ncols;
  poly* myPolyMatrix = (poly*)(mat->m);
  ideal iii; /* the ideal to be filled and returned */
  int zz = 0;
 
  /* divert to special implementations for pure number matrices and actual
     polynomial matrices: */
  int*  myIntMatrix  = (int*)omAlloc(rowCount * columnCount *sizeof(int));
  poly* nfPolyMatrix = (poly*)omAlloc(rowCount * columnCount *sizeof(poly));
  if (arrayIsNumberArray(myPolyMatrix, i, rowCount * columnCount,
                         myIntMatrix, nfPolyMatrix, zz))
    iii = getMinorIdeal_Int(myIntMatrix, rowCount, columnCount, minorSize, k,
                            algorithm, i, allDifferent);
  else
  {
    if ((k == 0) && (strcmp(algorithm, "Bareiss") == 0)
        && (!rField_is_Z(currRing)) && (!allDifferent))
    {
      /* In this case, we call an optimized procedure, dating back to
         Wilfried Pohl. It may be used whenever
         - all minors are requested,
         - requested minors need not be mutually distinct, and
         - coefficients come from a field (i.e., Z is also not allowed
           for this implementation). */
      iii = (i == 0 ? idMinors(mat, minorSize) : idMinors(mat, minorSize, i));
    }
    else
    {
      iii = getMinorIdeal_Poly(nfPolyMatrix, rowCount, columnCount, minorSize,
                               k, algorithm, i, allDifferent);
    }
  }
 
  /* clean up */
  omFree(myIntMatrix);
  for (int j = 0; j < rowCount * columnCount; j++) pDelete(&nfPolyMatrix[j]);
  omFree(nfPolyMatrix);
 
  return iii;
}

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

m	the matrix from which to compute minors
minorSize	the size of the minors to be computed
k	the number of minors to be computed
i	NULL or an ideal which encodes a standard basis
cacheStrategy	one of {1, .., 5}; see Minor.cc
cacheN	maximum number of cached polynomials (=subdeterminantes)
cacheW	maximum weight of the cache
allDifferent	if 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.

{
  /* Note that this method should be replaced by getMinorIdealCache_toBeDone,
     to enable faster computations in the case of matrices which contain
     only numbers. But so far, this method is not yet usable as it replaces
     the numbers by ints which may result in overflows during computations
     of minors. */
  int rowCount = mat->nrows;
  int columnCount = mat->ncols;
  poly* myPolyMatrix = (poly*)(mat->m);
  int length = rowCount * columnCount;
  poly* nfPolyMatrix = (poly*)omAlloc(length*sizeof(poly));
  ideal iii; /* the ideal to be filled and returned */
 
  /* copy all polynomials and reduce them w.r.t. iSB
     (if iSB is present, i.e., not the NULL pointer) */
  for (int i = 0; i < length; i++)
  {
    if (iSB==NULL)
      nfPolyMatrix[i] = pCopy(myPolyMatrix[i]);
    else
      nfPolyMatrix[i] = kNF(iSB, currRing->qideal, myPolyMatrix[i]);
  }
 
  iii = getMinorIdealCache_Poly(nfPolyMatrix, rowCount, columnCount,
                                minorSize, k, iSB, cacheStrategy,
                                cacheN, cacheW, allDifferent);
 
  /* clean up */
  for (int j = 0; j < length; j++) pDelete(&nfPolyMatrix[j]);
  omFree(nfPolyMatrix);
 
  return iii;
}

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.

{
  /* setting up a MinorProcessor for matrices with integer entries: */
  IntMinorProcessor mp;
  mp.defineMatrix(rowCount, columnCount, intMatrix);
  int *myRowIndices=(int*)omAlloc(rowCount*sizeof(int));
  for (int j = 0; j < rowCount; j++) myRowIndices[j] = j;
  int *myColumnIndices=(int*)omAlloc(columnCount*sizeof(int));
  for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j;
  mp.defineSubMatrix(rowCount, myRowIndices, columnCount, myColumnIndices);
  mp.setMinorSize(minorSize);
  MinorValue::SetRankingStrategy(cacheStrategy);
  Cache<MinorKey, IntMinorValue> cch(cacheN, cacheW);
 
  /* containers for all upcoming results: */
  IntMinorValue theMinor;
  // int value = 0;
  int collectedMinors = 0;
  int characteristic = 0; if (currRing != 0) characteristic = rChar(currRing);
 
  /* the ideal to be returned: */
  ideal iii = idInit(1);
 
  bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are
                                             requested, omitting zero minors */
  bool duplicatesOk = (allDifferent ? false : true);
  int kk = ABS(k); /* absolute value of k */
 
  /* looping over all minors: */
  while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk)))
  {
    /* retrieving the next minor: */
    theMinor = mp.getNextMinor(cch, characteristic, i);
    poly f = NULL;
    if (theMinor.getResult() != 0) f = pISet(theMinor.getResult());
    if (idInsertPolyWithTests(iii, collectedMinors, f, zeroOk, duplicatesOk))
      collectedMinors++;
  }
 
  /* before we return the result, let's omit zero generators
     in iii which come after the computed minors */
  ideal jjj;
  if (collectedMinors == 0) jjj = idInit(1);
  else                      jjj = idCopyFirstK(iii, collectedMinors);
  idDelete(&iii);
  omFree(myColumnIndices);
  omFree(myRowIndices);
  return jjj;
}

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.

{
  /* setting up a MinorProcessor for matrices with polynomial entries: */
  PolyMinorProcessor mp;
  mp.defineMatrix(rowCount, columnCount, polyMatrix);
  int *myRowIndices=(int*)omAlloc(rowCount*sizeof(int));
  for (int j = 0; j < rowCount; j++) myRowIndices[j] = j;
  int *myColumnIndices=(int*)omAlloc(columnCount*sizeof(int));
  for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j;
  mp.defineSubMatrix(rowCount, myRowIndices, columnCount, myColumnIndices);
  mp.setMinorSize(minorSize);
  MinorValue::SetRankingStrategy(cacheStrategy);
  Cache<MinorKey, PolyMinorValue> cch(cacheN, cacheW);
 
  /* containers for all upcoming results: */
  PolyMinorValue theMinor;
  poly f = NULL;
  int collectedMinors = 0;
 
  /* the ideal to be returned: */
  ideal iii = idInit(1);
 
  bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are
                                             requested, omitting zero minors */
  bool duplicatesOk = (allDifferent ? false : true);
  int kk = ABS(k); /* absolute value of k */
#ifdef COUNT_AND_PRINT_OPERATIONS
  printCounters ("starting", true);
  int qqq = 0;
#endif
  /* looping over all minors: */
  while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk)))
  {
    /* retrieving the next minor: */
    theMinor = mp.getNextMinor(cch, i);
#if (defined COUNT_AND_PRINT_OPERATIONS) && (COUNT_AND_PRINT_OPERATIONS > 1)
    qqq++;
    Print("after %d", qqq);
    printCounters ("-th minor", false);
#endif
    f = theMinor.getResult();
    if (idInsertPolyWithTests(iii, collectedMinors, pCopy(f), zeroOk,
                              duplicatesOk))
      collectedMinors++;
  }
#ifdef COUNT_AND_PRINT_OPERATIONS
  printCounters ("ending", true);
#endif
 
  /* before we return the result, let's omit zero generators
     in iii which come after the computed minors */
  ideal jjj;
  if (collectedMinors == 0) jjj = idInit(1);
  else                      jjj = idCopyFirstK(iii, collectedMinors);
  idDelete(&iii);
  omFree(myColumnIndices);
  omFree(myRowIndices);
  return jjj;
}

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.

{
  int rowCount = mat->nrows;
  int columnCount = mat->ncols;
  poly* myPolyMatrix = (poly*)(mat->m);
  ideal iii; /* the ideal to be filled and returned */
  int zz = 0;
 
  /* divert to special implementation when myPolyMatrix has only number
     entries: */
  int*  myIntMatrix  = (int*)omAlloc(rowCount * columnCount *sizeof(int));
  poly* nfPolyMatrix = (poly*)omAlloc(rowCount * columnCount *sizeof(poly));
  if (arrayIsNumberArray(myPolyMatrix, iSB, rowCount * columnCount,
                         myIntMatrix, nfPolyMatrix, zz))
    iii = getMinorIdealCache_Int(myIntMatrix, rowCount, columnCount,
                                 minorSize, k, iSB, cacheStrategy, cacheN,
                                 cacheW, allDifferent);
  else
    iii = getMinorIdealCache_Poly(nfPolyMatrix, rowCount, columnCount,
                                  minorSize, k, iSB, cacheStrategy, cacheN,
                                  cacheW, allDifferent);
 
  /* clean up */
  omFree(myIntMatrix);
  for (int j = 0; j < rowCount * columnCount; j++) pDelete(&nfPolyMatrix[j]);
  omFree(nfPolyMatrix);
 
  return iii;
}

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

m	the matrix from which to compute minors
minorSize	the size of the minors to be computed
k	the number of minors to be computed
i	NULL or an ideal which encodes a standard basis
allDifferent	if 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.

{
  int vars = currRing->N;
 
  /* here comes the heuristic, as of 29 January 2010:
 
     integral domain and minorSize <= 2                -> Bareiss
     integral domain and minorSize >= 3 and vars <= 2  -> Bareiss
     field case and minorSize >= 3 and vars = 3
       and c in {2, 3, ..., 32749}                     -> Bareiss
 
     otherwise:
     if not all minors are requested                   -> Laplace, no Caching
     otherwise:
     minorSize >= 3 and vars <= 4 and
       (rowCount over minorSize)*(columnCount over minorSize) >= 100
                                                       -> Laplace with Caching
     minorSize >= 3 and vars >= 5 and
       (rowCount over minorSize)*(columnCount over minorSize) >= 40
                                                       -> Laplace with Caching
 
     otherwise:                                        -> Laplace, no Caching
  */
 
  bool b = false; /* Bareiss */
  bool l = false; /* Laplace without caching */
  // bool c = false; /* Laplace with caching */
  if (rField_is_Domain(currRing))
  { /* the field case or ring Z */
    if      (minorSize <= 2)                                     b = true;
    else if (vars <= 2)                                          b = true;
    else if ((!rField_is_Ring(currRing)) && (vars == 3)
             && (currRing->cf->ch >= 2) && (currRing->cf->ch <= NV_MAX_PRIME))
          b = true;
  }
  if (!b)
  { /* the non-Bareiss cases */
    if (k != 0) /* this means, not all minors are requested */   l = true;
    else
    { /* k == 0, i.e., all minors are requested */
      l = true;
    }
  }
 
  if      (b)    return getMinorIdeal(mat, minorSize, k, "Bareiss", iSB,
                                      allDifferent);
  else if (l)    return getMinorIdeal(mat, minorSize, k, "Laplace", iSB,
                                      allDifferent);
  else /* (c) */ return getMinorIdealCache(mat, minorSize, k, iSB,
                                      3, 200, 100000, allDifferent);
}