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#include "dimension.h"
#include "buchberger.h"
#include "log.h"
#include "printer.h"
const int bitsPerWord=64;
typedef int64 ExponentType;
ExponentType allOnes(int n)
{
if(n<64)return (((int64) 1)<<n)-1;
return -1;
}
int sum(ExponentType v)
{
int64 t0=v;
int64 t1=(t0&0x5555555555555555)+((t0>>1)&0x5555555555555555);
int64 t2=(t1&0x3333333333333333)+((t1>>2)&0x3333333333333333);
int64 t3=(t2&0x0f0f0f0f0f0f0f0f)+((t2>>4)&0x0f0f0f0f0f0f0f0f);
int64 t4=(t3&0x00ff00ff00ff00ff)+((t3>>8)&0x00ff00ff00ff00ff);
int64 t5=(t4&0x0000ffff0000ffff)+((t4>>16)&0x0000ffff0000ffff);
int64 t6=(t5&0x00000000ffffffff)+((t5>>32)&0x00000000ffffffff);
return t6;
}
static void rek64(ExponentType &ones, ExponentType &zeros, int nOnes, int nZeros, vector<ExponentType> vectors, int &best, int n)
{
if(nOnes>best)best=nOnes;
if(n-nZeros<best)return;
if(nOnes+nZeros==n)return;
#if 1
int index=0;
for(int i=0;i<n;i++,index++)
// if((!ones[i])&&(!zeros[i]))break;
if((!((((int64)1)<<i)&ones))&&(!((((int64)1)<<i)&zeros)))break;
#else
int index=nOnes+nZeros;
#endif
assert(index<n);
ones|=((int64)1)<<index;
bool good=true;
for(vector<ExponentType>::const_iterator i=vectors.begin();i!=vectors.end();i++)
if(((*i)&~ones)==0)
{
good=false;
break;
}
if(good)
{
rek64(ones,zeros,nOnes+1,nZeros,vectors,best,n);
}
ones-=((int64)1)<<index;
vector<ExponentType> vectorsSubset;
vectorsSubset.reserve(vectors.size());
for(vector<ExponentType>::const_iterator i=vectors.begin();i!=vectors.end();i++)
{
// if((*i)[index]==0)vectorsSubset.push_back(*i);
if(((*i)&(((int64)1)<<index))==0)vectorsSubset.push_back(*i);
}
zeros|=((int64)1)<<index;
rek64(ones,zeros,nOnes,nZeros+1,vectorsSubset,best,n);
zeros-=((int64)1)<<index;
}
/*
* monomialGenerators should have zero-one exponent vectors with at most 64 variables in the ring.
*/
int krullDimensionOfMonomialIdeal64(PolynomialSet const &monomialGenerators)
{
int n=monomialGenerators.getRing().getNumberOfVariables();
assert(n<=64);
vector<ExponentType> generators;
for(PolynomialSet::const_iterator i=monomialGenerators.begin();i!=monomialGenerators.end();i++)
{
ExponentType v=0;
for(int j=0;j<n;j++)v=2*v+i->getMarked().m.exponent[j];
generators.push_back(v);
}
int best=0;
ExponentType zeros=0;
ExponentType ones=0;
ExponentType possiblyOne=0;
for(vector<ExponentType>::const_iterator i=generators.begin();i!=generators.end();i++)possiblyOne=possiblyOne|*i;
ones=allOnes(n)-possiblyOne;
rek64(ones,zeros,sum(ones),sum(zeros),generators,best,n);
return best;
}
PolynomialSet radicalOfMonomialIdeal(PolynomialSet const &monomialGenerators)
{
PolynomialRing theRing=monomialGenerators.getRing();
PolynomialSet temp=monomialGenerators;
temp.markAndScale(LexicographicTermOrder()); //just to make sure that some term is marked
PolynomialSet ret(theRing);
for(PolynomialSet::const_iterator i=temp.begin();i!=temp.end();i++)
{
IntegerVector e=i->getMarked().m.exponent;
e=e.supportVector();
ret.push_back(Polynomial(Term(i->getMarked().c,Monomial(theRing,e))));
}
return ret;
}
static bool increase(IntegerVector &v, int &numberOfOnes)
{
int i=0;
while(i<v.size() && v[i]==1)
{
v[i]=0;
numberOfOnes--;
i++;
}
if(i==v.size())return false;
v[i]=1;
numberOfOnes++;
return true;
}
static int rekCallls;
static void rek(IntegerVector &ones, IntegerVector &zeros, int nOnes, int nZeros, IntegerVectorList const &vectors, int &best)
{
rekCallls++;
if(nOnes>best)best=nOnes;
if(ones.size()-nZeros<best)return;
if(nOnes+nZeros==ones.size())return;
log3
{
fprintf(Stderr,"Ones:\n");
AsciiPrinter(Stderr).printVector(ones);
fprintf(Stderr,"Zeros:\n");
AsciiPrinter(Stderr).printVector(zeros);
AsciiPrinter(Stderr).printVectorList(vectors);
}
int index=0;
for(int i=0;i<ones.size();i++,index++)
if((!ones[i])&&(!zeros[i]))break;
assert(index<ones.size());
ones[index]=1;
bool good=true;
for(IntegerVectorList::const_iterator i=vectors.begin();i!=vectors.end();i++)
if(i->divides(ones))
{
good=false;
break;
}
if(good)
{
rek(ones,zeros,nOnes+1,nZeros,vectors,best);
}
ones[index]=0;
IntegerVectorList vectorsSubset;
for(IntegerVectorList::const_iterator i=vectors.begin();i!=vectors.end();i++)
{
if((*i)[index]==0)vectorsSubset.push_back(*i);
}
if(0) // It is not clear that this is an improvement, even with an better implementation
{
IntegerVector newOnes(ones.size());
IntegerVector possiblyOne(ones.size());
for(IntegerVectorList::const_iterator i=vectors.begin();i!=vectors.end();i++)possiblyOne=max(possiblyOne,*i);
if((IntegerVector::allOnes(ones.size())-possiblyOne-ones-zeros).max()>0)
{
/* debug<<vectorsSubset;
debug<<"ones now\n"<<ones<<"\n";
debug<<"zeros now\n"<<zeros<<"\n";
debug<<"FORCED ONES:"<<IntegerVector::allOnes(ones.size())-possiblyOne<<"\n";
*/ newOnes=max(IntegerVector::allOnes(ones.size())-possiblyOne-ones-zeros,IntegerVector(ones.size()));
// debug<<"NEW ONES:"<<newOnes<<"\n";
}
nOnes+=newOnes.sum();
ones+=newOnes;
zeros[index]=1;
rek(ones,zeros,nOnes,nZeros+1,vectorsSubset,best);
ones-=newOnes;
nOnes-=newOnes.sum();
zeros[index]=0;
}
else
{
zeros[index]=1;
rek(ones,zeros,nOnes,nZeros+1,vectorsSubset,best);
zeros[index]=0;
}
}
int krullDimensionOfMonomialIdeal(PolynomialSet const &monomialGenerators)
{
// debug<<"Taking radical\n";
PolynomialSet temp=radicalOfMonomialIdeal(monomialGenerators);
// debug<<"Minimizing\n";
minimize(&temp);
// debug<<"Done\n";
if(monomialGenerators.getRing().getNumberOfVariables()<=64)return krullDimensionOfMonomialIdeal64(temp);
IntegerVectorList vectors;
for(PolynomialSet::const_iterator i=temp.begin();i!=temp.end();i++)
vectors.push_back(i->getMarked().m.exponent);
int best=0;
int n=monomialGenerators.getRing().getNumberOfVariables();
IntegerVector zeros(n);
IntegerVector ones(n);
//Preprocessing step. This can be improved.
IntegerVector possiblyOne(n);
for(IntegerVectorList::const_iterator i=vectors.begin();i!=vectors.end();i++)possiblyOne=max(possiblyOne,*i);
ones=IntegerVector::allOnes(n)-possiblyOne;
rek(ones,zeros,ones.sum(),zeros.sum(),vectors,best);
//debug<<"REKCALLS"<<rekCallls<<"\n";
return best;
}
int krullDimension(PolynomialSet const &groebnerBasis)
{
return krullDimensionOfMonomialIdeal(groebnerBasis.markedTermIdeal());
}
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