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#include "polynomial.h"
#include "field_rationals.h"
#include "printer.h"
#include "log.h"
#include <sstream>
#include <iostream>
static int rIndex(int i, int j, int N, bool withMasses)
{
if(j<i){i^=j;j^=i;i^=j;}
int r=withMasses*N;
for(int I=0;I<N;I++)
for(int J=I+1;J<N;J++)
{
if((I==i)&&(J==j))return r;
r++;
}
assert(0);
}
static int sIndex(int i, int j, int N, bool withMasses)
{
return rIndex(i,j,N,withMasses)+N*(N-1)/2;
}
static Polynomial S(PolynomialRing const &r, int N, bool withMasses, int i, int j, bool withSVariables)
{
Polynomial ret(r);
int n=r.getNumberOfVariables();
if(withSVariables)
{
ret+=Term(r.getField().zHomomorphism(1),Monomial(r,IntegerVector::standardVector(n,sIndex(i,j,N,withMasses))));
}
else
{
ret+=Term(r.getField().zHomomorphism(-1),Monomial(r,IntegerVector(n)));
ret+=Term(r.getField().zHomomorphism(1),Monomial(r,-3*IntegerVector::standardVector(n,rIndex(i,j,N,withMasses))));
}
return ret;
}
static Polynomial rPolynomial(PolynomialRing const &r, int N, bool withMasses, int i, int j, int exponent=2)
{
if(i==j)return Polynomial(r);
return Term(r.getField().zHomomorphism(1),Monomial(r,exponent*IntegerVector::standardVector(r.getNumberOfVariables(),rIndex(i,j,N,withMasses))));
}
static vector<string> variableNames(int N, bool withMasses, bool withSVariables)
{
vector<string> ret;
if(withMasses)
{
for(int i=0;i<N;i++)
{
stringstream s;
s<<"m"<<i+1;
ret.push_back(s.str());
}
}
for(int i=0;i<N;i++)
for(int j=i+1;j<N;j++)
{
stringstream s;
s<<"r"<<i+1<<j+1;
ret.push_back(s.str());
}
if(withSVariables)
{
for(int i=0;i<N;i++)
for(int j=i+1;j<N;j++)
{
stringstream s;
s<<"S"<<i+1<<j+1;
ret.push_back(s.str());
}
}
return ret;
}
Polynomial AlbouyChencinerEquation(PolynomialRing const &r, int N, bool withMasses, int i, int j, bool symmetric, bool withSVariables, bool saturate)
{
int n=r.getNumberOfVariables();
Polynomial ret(r);
for(int k=0;k<N;k++)
{
Term massTerm=Term(r.getField().zHomomorphism(1),Monomial(r,withMasses*IntegerVector::standardVector(n,k)));
if(i!=k)
ret+=massTerm*
(
S(r,N,withMasses,i,k,withSVariables)*(
rPolynomial(r,N,withMasses,j,k)
-rPolynomial(r,N,withMasses,i,k)
-rPolynomial(r,N,withMasses,i,j)
)
);
if(symmetric)
if(j!=k)
ret+=massTerm*
(
S(r,N,withMasses,j,k,withSVariables)*(
rPolynomial(r,N,withMasses,i,k)
-rPolynomial(r,N,withMasses,j,k)
-rPolynomial(r,N,withMasses,i,j)
)
);
}
if(saturate)ret.saturate();
return ret;
}
PolynomialSet AlbouyChencinerEquations(int N, bool withMasses, bool symmetric, bool withSVariables, bool saturate)
{
PolynomialRing r(Q,variableNames(N,withMasses,withSVariables));
PolynomialSet ret(r);
for(int i=0;i<N;i++)
{
if(!symmetric)
for(int j=0;j<i;j++)
ret.push_back(AlbouyChencinerEquation(r,N,withMasses,i,j,symmetric,withSVariables,saturate));
for(int j=i+1;j<N;j++)
ret.push_back(AlbouyChencinerEquation(r,N,withMasses,i,j,symmetric,withSVariables,saturate));
}
return ret;
}
PolynomialSet DziobekEquations(PolynomialRing const &r, int N, bool withMasses, bool withSVariables, bool saturate)
{
PolynomialSet ret(r);
list<int> a;
for(int i=4;i<N;i++)
a.push_back(0);
a.push_back(1);
a.push_back(1);
a.push_back(1);
a.push_back(1);
do
{
list<int>::const_iterator i=a.begin();
int I=0;
while((*i)==0){i++;I++;}
int first=I;
do{i++;I++;}while((*i)==0);
int second=I;
do{i++;I++;}while((*i)==0);
int third=I;
do{i++;I++;}while((*i)==0);
int fourth=I;
// cerr<<first<<second<<third<<fourth;
Polynomial f1=S(r,N,withMasses,first,second,withSVariables)*S(r,N,withMasses,third,fourth,withSVariables)-S(r,N,withMasses,first,third,withSVariables)*S(r,N,withMasses,second,fourth,withSVariables);
if(saturate)f1.saturate();
Polynomial f2=S(r,N,withMasses,first,third,withSVariables)*S(r,N,withMasses,second,fourth,withSVariables)-S(r,N,withMasses,first,fourth,withSVariables)*S(r,N,withMasses,second,third,withSVariables);
if(saturate)f2.saturate();
Polynomial f3=S(r,N,withMasses,first,second,withSVariables)*S(r,N,withMasses,third,fourth,withSVariables)-S(r,N,withMasses,first,fourth,withSVariables)*S(r,N,withMasses,second,third,withSVariables);
if(saturate)f3.saturate();
ret.push_back(f1);
ret.push_back(f2);
ret.push_back(f3);
}
while(next_permutation(a.begin(),a.end()));
return ret;
}
static Polynomial mlookup(PolynomialRing const &r, int N, bool withMasses,int i,int j)
{
if(i==j)return r.zero();
if(i==0 || j==0)return r.one();
return Polynomial(Term(r.getField().zHomomorphism(1),Monomial(r,2*IntegerVector::standardVector(r.getNumberOfVariables(),rIndex(i-1,j-1,N,withMasses)))));
}
PolynomialSet nbodyDeterminants(PolynomialRing const &r, int N, bool withMasses, int determinantSize)
{
vector<int> l;
for(int i=0;i<N+1-determinantSize;i++)
l.push_back(1);
for(int i=0;i<determinantSize-1;i++)
l.push_back(0);
PolynomialSet ret(r);
if(determinantSize==N+2)return ret;
do
{
vector<int> indexList;
indexList.push_back(0);
for(int i=0;i<l.size();i++)if(l[i]==0)indexList.push_back(i+1);
log1
{
for(int A=0;A<determinantSize;A++)
{
for(int B=0;B<determinantSize;B++)
AsciiPrinter(Stderr)<<mlookup(r,N,withMasses,indexList[A],indexList[B])<<";";
cerr<<endl;
}
}
vector<int> perm;
for(int i=0;i<indexList.size();i++)
perm.push_back(i);
Polynomial p(r);
do
{
Polynomial prod=r.one();
for(int j=0;j<perm.size();j++)
{
prod*=mlookup(r,N,withMasses,indexList[j],indexList[perm[j]]);
}
int s=1;
for(int x=0;x<perm.size();x++)
for(int y=0;y<x;y++)
if(perm[y]>perm[x])s*=-1;
if(s==1)
p+=prod;
else
p-=prod;
}
while(next_permutation(perm.begin(),perm.end()));
ret.push_back(p);
}
while(prev_permutation(l.begin(),l.end()));
return ret;
}
Polynomial massEquation(PolynomialRing const &r, int N, bool withMasses, bool saturate)
{
Polynomial ret(r);
for(int i=0;i<N;i++)
for(int j=0;j<i;j++)
{
Polynomial mm=r.one();
if(withMasses)mm=Polynomial(Term(r.getField().zHomomorphism(1),Monomial(r,IntegerVector::standardVector(r.getNumberOfVariables(),i)+IntegerVector::standardVector(r.getNumberOfVariables(),j))));
ret+=(rPolynomial(r,N,withMasses,i,j,2)-rPolynomial(r,N,withMasses,i,j,-1))*mm;
}
if(saturate)ret.saturate();
return ret;
}
Polynomial SEquation(PolynomialRing const &r, int N, bool withMasses, int i, int j, bool withSVariables, bool saturate=true)
{
Polynomial ret(r);
int n=r.getNumberOfVariables();
ret-=Term(r.getField().zHomomorphism(1),Monomial(r,IntegerVector::standardVector(n,sIndex(i,j,N,withMasses))));
ret+=Term(r.getField().zHomomorphism(-1),Monomial(r,IntegerVector(n)));
ret+=Term(r.getField().zHomomorphism(1),Monomial(r,-3*IntegerVector::standardVector(n,rIndex(i,j,N,withMasses))));
if(saturate)ret.saturate();
return ret;
}
PolynomialSet SEquations(PolynomialRing const &r, int N, bool withMasses, bool saturate)
{
PolynomialSet ret(r);
for(int i=0;i<N;i++)
for(int j=0;j<i;j++)
{
ret.push_back(SEquation(r,N,withMasses,i,j,true,saturate));
}
return ret;
}
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