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#include "determinantpoly.h"
#include <iostream>
#include "printer.h"
#include "buchberger.h"
#include "wallideal.h"
#include "termorder.h"
#include "tropical2.h"
#include "tropicaldeterminant.h"
#include "log.h"
using namespace std;
static list<int> interval(int n, bool sqrt)
{
list<int> ret;
for(int i=0;((sqrt)?i*i:i)<n;i++)ret.push_back(i);
return ret;
}
class PolyMatrix
{
public:
class PolyMatrixEntry
{
public:
bool isZero;
Polynomial p;
int maxDegree,mminDegree;
vector<Polynomial> forms;
PolyMatrixEntry(Polynomial const &p_, IntegerVector const &w):
p(p_),
isZero(p_.isZero())
{
if(p.isZero())
{
maxDegree=td_minusInfinity;
mminDegree=td_minusInfinity;
return;
}
maxDegree=p_.degree(w);
mminDegree=p_.degree(-w);
// debug<<maxDegree<<minDegree<<"\n";
for(int i=0;i<=maxDegree+mminDegree;i++)forms.push_back(Polynomial(p.getRing()));
for(TermMap::const_iterator i=p.terms.begin();i!=p.terms.end();i++)
{
forms[dot(i->first.exponent,w)+mminDegree]+=Term(i->second,i->first);
}
}
};
list<int>::iterator indexOfSparsestRow(list<int> &rows, list<int> const &columns, int &chosenRowIteratorIndex)
{
list<int>::iterator ret=rows.end();
int bestNumberOfZeros=-1;
int I=0;
for(list<int>::iterator i=rows.begin();i!=rows.end();i++,I++)
{
int numberOfZeros=0;
for(list<int>::const_iterator j=columns.begin();j!=columns.end();j++)numberOfZeros+=data[*i][*j].isZero;
if(numberOfZeros>bestNumberOfZeros)
{
bestNumberOfZeros=numberOfZeros;
ret=i;
chosenRowIteratorIndex=I;
}
}
// cerr<<":"<<bestNumberOfZeros<<endl;
return ret;
}
vector<vector<PolyMatrixEntry> > data;
PolynomialRing theRing;
//constructor for Jacobi matrix
PolyMatrix(PolynomialSet const &generators, IntegerVector const &w, bool takeDerivatives, int numberOfDVariables=-1):
theRing(generators.getRing())
{
if(takeDerivatives)
{
int n=generators.size();
if(numberOfDVariables==-1)numberOfDVariables=n;
PolynomialSet::const_iterator I=generators.begin();
for(int i=0;i<n;i++)
{
vector<PolyMatrixEntry> row;
for(int j=0;j<numberOfDVariables;j++)
row.push_back(PolyMatrixEntry(I->derivative(j),w));
data.push_back(row);
I++;
}
}
else
{
int n=generators.size();
for(int i=0;i<n;i++)if(i*i>=n){n=i;break;}assert(n*n==generators.size());
PolynomialSet::const_iterator I=generators.begin();
for(int i=0;i<n;i++)
{
vector<PolyMatrixEntry> row;
for(int j=0;j<n;j++)
{
row.push_back(PolyMatrixEntry(*I,w));
I++;
}
data.push_back(row);
}
}
}
void print()
{
int n=data.size();
for(int i=0;i<n;i++)
{
for(int j=0;j<data[i].size();j++)
{
debug<<data[i][j].p<<",";
}
debug<<"\n";
}
}
void p(list<int> l)
{
cerr<<"{";
for(list<int>::const_iterator i=l.begin();i!=l.end();i++)
cerr<<*i<<",";
cerr<<"}\n";
}
IntegerMatrix subTropicalMatrix(bool max, list<int> const &rows, list<int> const &columns)
{
IntegerMatrix ret(rows.size(),columns.size());
list<int>::const_iterator I=rows.begin();
for(int i=0;i<ret.getHeight();i++,I++)
{
list<int>::const_iterator J=columns.begin();
for(int j=0;j<ret.getWidth();j++,J++)
ret[i][j]=(max)?data[*I][*J].maxDegree:data[*I][*J].mminDegree;
}
return ret;
}
Polynomial determinantForm(list<int> rows, list<int> columns, int degree, int level)
{
Polynomial ret(theRing);
IntegerMatrix matMax=subTropicalMatrix(true,rows,columns);
IntegerMatrix matMMin=subTropicalMatrix(false,rows,columns);
/* if(level==0)
{
debug<<matMax.getRows();
debug<<matMMin.getRows();
int maxDet=tropicalDeterminant(matMax);
int mminDet=tropicalDeterminant(matMMin);
debug<<"Max:"<<maxDet<<" Min:"<<-mminDet<<"\n";
}
*/
// debug<<matMax.getRows();
// debug<<matMMin.getRows();
int maxDet=tropicalDeterminant(matMax);
int mminDet=tropicalDeterminant(matMMin);
// assert(degree==0);
// maxDet=0;//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// mminDet=0;//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// debug<<maxDet<<" "<<mminDet<<"\n";
if(degree>maxDet)return Polynomial(theRing);
if(-degree>mminDet)return Polynomial(theRing);
if(rows.size()==1)
{
if(data[rows.front()][columns.front()].isZero)return Polynomial(theRing);
// cerr<<degree<<data[rows.front()][columns.front()].mminDegree<<endl;
return data[rows.front()][columns.front()].forms[degree+data[rows.front()][columns.front()].mminDegree];
}
int chosenRowIteratorIndex=0;
list<int>::iterator chosenRowIterator=indexOfSparsestRow(rows, columns, chosenRowIteratorIndex);//rows.begin();
int chosenrow=*chosenRowIterator;
{
list<int>::iterator temp=chosenRowIterator;temp++;
rows.erase(chosenRowIterator);
//no need to update rows afterwards since it is stored on the stack
}
/* if(level==0)cerr<<"-"<<chosenrow<<endl;
if(level==1)cerr<<"++"<<chosenrow<<endl;
if(level==2)cerr<<"***"<<chosenrow<<endl;
if(level==3)cerr<<"%%%%%%%%"<<chosenrow<<endl;
*/ int sign=1;
sign*=(1-2*(chosenRowIteratorIndex&1));
for(list<int>::iterator i=columns.begin();i!=columns.end();i++)
{
int chosencol=*i;
if(!data[chosenrow][chosencol].isZero)
{
list<int>::iterator temp=i;temp++;
columns.erase(i);
i=temp;
// int D=degree+1;
// if(data[chosenrow][chosencol].forms.size()<D)D=data[chosenrow][chosencol].forms.size();
// for(int k=0;k<D;k++)
for(int k=0;k<=data[chosenrow][chosencol].maxDegree+data[chosenrow][chosencol].mminDegree;k++)
{
//cerr<<chosenrow<<chosencol<<endl;
//cerr<<degree<<-k<<data[chosenrow][chosencol].mminDegree<<endl;
assert(k<data[chosenrow][chosencol].forms.size());
if(!data[chosenrow][chosencol].forms[k].isZero())
ret+=data[chosenrow][chosencol].forms[k]*determinantForm(rows,columns,degree-k+data[chosenrow][chosencol].mminDegree,level+1)*theRing.getField().zHomomorphism(sign);
}
columns.insert(i,chosencol);
i--;
}
sign*=-1;
}
rows.push_front(chosenrow);
return ret;
}
Polynomial initialFormOfDeterminant(bool onlyComputeInitial=true)
{
list<int> rows=interval(data.size(),0);
list<int> columns=interval(data.size(),0);
IntegerMatrix matMax=subTropicalMatrix(true,rows,columns);
IntegerMatrix matMMin=subTropicalMatrix(false,rows,columns);
int maxDet=tropicalDeterminant(matMax);
int mminDet=tropicalDeterminant(matMMin);
cerr<<"Max"<<maxDet<<"Min"<<-mminDet<<endl;
Polynomial ret(theRing);
for(int d=maxDet;d>=-mminDet;d--)
{
log1 debug<<"Computing degree "<<d<<"\n";
ret+=determinantForm(rows,columns,d,0);
if(onlyComputeInitial&&!ret.isZero())break;
}
return ret;
}
Polynomial determinant()
{
return initialFormOfDeterminant(false);
}
};
Polynomial initialFormOfDeterminant(PolynomialSet const &g, IntegerVector const &w, bool takeDerivatives)
{
PolyMatrix m(g,w,takeDerivatives);
return m.initialFormOfDeterminant();
}
list<int> toIndexed(list<int> const &l)
{
list<int> ret;
int a=0;
for(list<int>::const_iterator i=l.begin();i!=l.end();i++,a++)if(*i)ret.push_back(a);
return ret;
}
PolynomialSet jacobiMinors(PolynomialSet const &g, int codim)
{
IntegerVector w(g.getRing().getNumberOfVariables());
PolyMatrix m(g,w,true,w.size());
//log1 m.print();
PolynomialSet ret(g.getRing());
if(codim<=g.size())if(codim<=w.size())
{
list<int> rows;
for(int i=0;i<g.size()-codim;i++)rows.push_back(0);
for(int i=0;i<codim;i++)rows.push_back(1);
do
{
list<int> cols;
for(int i=0;i<w.size()-codim;i++)cols.push_back(0);
for(int i=0;i<codim;i++)cols.push_back(1);
do
{
// cerr<<rows.size()<<cols.size()<<endl;
ret.push_back(m.determinantForm(toIndexed(rows),toIndexed(cols),0,0));
}
while(next_permutation(cols.begin(),cols.end()));
}
while(next_permutation(rows.begin(),rows.end()));
}
return ret;
}
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