Polynomial Polynomial::embeddedInto(PolynomialRing const &r2, list<int> const *chosenVariables)const
{
Polynomial q(r2);
if(chosenVariables)
{
assert(chosenVariables->size()==r2.getNumberOfVariables());
}
for(TermMap::const_iterator i=terms.begin();i!=terms.end();i++)
{
IntegerVector v=i->first.exponent;
if(chosenVariables)
v=v.subvector(*chosenVariables);
else
v.resize(r2.getNumberOfVariables());
FieldElement e=i->second;
q+=Term(e,Monomial(r2,v));
}
if(isMarked())
{
IntegerVector m=marked.m.exponent;
//AsciiPrinter(Stderr)<<*this<<"\n";
if(chosenVariables)
m=m.subvector(*chosenVariables);
else
m.resize(r2.getNumberOfVariables());
q.mark(Monomial(r2,m));
}
// q.marked.m.exponent.resize(r2.getNumberOfVariables());
return q;
}
void Polynomial::saturate(int variableNum)//does not compute sugar
{
if(!terms.empty())
{
IntegerVector smallest=terms.begin()->first.exponent;
for(TermMap::iterator i=terms.begin();i!=terms.end();i++)
smallest=min(smallest,i->first.exponent);
if(variableNum!=-1)
{
for(int j=0;j<smallest.size();j++)if(j!=variableNum)smallest[j]=0;
}
Polynomial p(theRing);
for(TermMap::iterator i=terms.begin();i!=terms.end();i++)
p.terms.insert(p.terms.end(),TermMap::value_type(Monomial(theRing,i->first.exponent-smallest),i->second));
terms=p.terms;
if(isMarked())
{
marked.m.exponent-=smallest;
}
}
}
Polynomial Polynomial::homogenization(PolynomialRing const &newRing, IntegerVector const *w)const //does not compute sugar
{
int degree;
Polynomial ret(newRing);
if(w)
degree=this->degree(*w);
else
degree=totalDegree();
IntegerVector m;
for(TermMap::const_iterator i=terms.begin();i!=terms.end();i++)
{
IntegerVector v=i->first.exponent;
int d;
if(w)
d=dot(v,*w);
else
d=v.sum();
IntegerVector a(v.size());
a.grow(a.size()+1);
v.grow(v.size()+1);
a[a.size()-1]=degree-d;
v+=a;
ret+=Term(i->second,Monomial(newRing,v));
if(isMarked())if(marked.m.exponent==i->first.exponent)m=v;
}
if(isMarked())
{
IntegerVector v=m;
if(m.size()==newRing.getNumberOfVariables())
{
ret.mark(Monomial(newRing,v));
}
// assert(m.size()==newRing.getNumberOfVariables());
// ret.mark(Monomial(newRing,m));
}
return ret;
}
void Polynomial::operator*=(const Monomial &m)
{
sugar+=m.exponent.sum();
Polynomial p(theRing);
for(TermMap::iterator i=terms.begin();i!=terms.end();i++)
{
FieldElement prod=i->second;
p.terms.insert(p.terms.end(),TermMap::value_type(Monomial(theRing,i->first.exponent+m.exponent),prod));
}
terms=p.terms;
}
void Polynomial::madd(const Term &m, const Polynomial &p)
{
if(p.terms.empty())return; //added May 7 2005
int sugar2=p.getSugar()+m.m.exponent.sum();
if(sugar2>sugar)sugar=sugar2;
TermMap::iterator i=terms.lower_bound(Monomial(theRing,p.terms.begin()->first.exponent+m.m.exponent));
for(TermMap::const_iterator j=p.terms.begin();j!=p.terms.end();j++)
{
while(i!=terms.end() && TermMapCompare()(i->first,Monomial(theRing,j->first.exponent+m.m.exponent)))i++;
if(i==terms.end())
{
terms.insert(i,TermMap::value_type(Monomial(theRing,j->first.exponent+m.m.exponent),j->second*m.c));
}
else
{
if(!TermMapCompare()(Monomial(theRing,j->first.exponent+m.m.exponent),i->first))
{ // they must be equal
FieldElement c=i->second+j->second*m.c;
if(c.isZero())
{
TermMap::iterator oldI=i;
i++;
terms.erase(oldI);
}
else
{
i->second=c;
}
}
else
{
terms.insert(i,TermMap::value_type(Monomial(theRing,j->first.exponent+m.m.exponent),j->second*m.c));
}
}
}
}
void Polynomial::changeNumberOfVariables(int n)
{
PolynomialRing newRing=theRing;//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111111111111!!!!!!
Polynomial q(newRing);
for(TermMap::iterator i=terms.begin();i!=terms.end();i++)
{
IntegerVector v=i->first.exponent;
v.resize(n);
FieldElement e=i->second;
q+=Term(e,Monomial(theRing,v));
}
if(isMarked())marked.m.exponent.resize(n);
terms=q.terms;
}
Monomial Monomial::operator * (const Monomial& p) const {
Monomial ans = Monomial();
for (auto it = _multipliers.cbegin(); it != _multipliers.cend(); ++it) {
ans._multipliers.insert(*it);
}
for (auto it = p._multipliers.cbegin(); it != p._multipliers.cend(); ++it) {
if (!ans._multipliers.insert(*it).second) {
ans._multipliers.at(it->first) += it->second;
}
if (ans._multipliers.at(it->first) == 0) {
ans._multipliers.erase(it->first);
}
}
return ans;
}
Polynomial Polynomial::derivative()const
{
Polynomial ret(theRing);
for(TermMap::const_iterator i=terms.begin();i!=terms.end();i++)
{
IntegerVector v=i->first.exponent;
assert(v.size()==1);
if(v[0]!=0)
{
v[0]--;
ret+=Term(i->second*theRing.getField().zHomomorphism(v[0]+1),Monomial(theRing,v));
}
}
return ret;
}
Polynomial Polynomial::deHomogenizationInSameRing()const
{
Polynomial ret(getRing());
int n=getRing().getNumberOfVariables();
assert(n>0);
for(TermMap::const_iterator i=terms.begin();i!=terms.end();i++)
{
IntegerVector v=i->first.exponent;
v[n-1]=0;
FieldElement e=i->second;
ret+=Term(e,Monomial(theRing,v));
}
if(isMarked())
{
ret.marked.m.exponent=marked.m.exponent.subvector(0,n-1);
ret.isMarkedBool=true;
}
return ret;
}
void Polynomial::operator*=(const Term &t)
{
sugar+=t.m.exponent.sum();
// faster multiplication
Polynomial p(theRing);
for(TermMap::iterator i=terms.begin();i!=terms.end();i++)
{
FieldElement prod=i->second;
prod*=t.c;
p.terms.insert(p.terms.end(),TermMap::value_type(Monomial(theRing,i->first.exponent+t.m.exponent),prod));
}
terms=p.terms;
// slow multiplication
/* Polynomial p;
for(TermMap::iterator i=terms.begin();i!=terms.end();i++)
{
Term T(i->second,i->first);
T*=t;
p+=T;
}
terms=p.terms;
*/
}
Polynomial::Polynomial(const LinearCombination& linearCombination)
: monomials_(), constant_(linearCombination.constant_) {
for (const LinearTerm& linearTerm : linearCombination.linearTerms_) {
monomials_.push_back(Monomial(linearTerm));
}
}
Monomial pow(const Variable& x, int degree) {
return Monomial(x, degree);
}
Monomial operator * (const Monomial& p, const Variable& x) {
return Monomial(x) * p;
}
Monomial operator * (const Variable& x, const Variable& y) {
return Monomial(x) * Monomial(y);
}
