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some more functions in polynomials and permutations

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This commit is contained in:
Jiri Pittner
2021-06-26 22:41:40 +02:00
parent 3cf56c3f36
commit 3288e51fba
5 changed files with 192 additions and 6 deletions
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66
polynomial.cc
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@@ -90,6 +90,16 @@ laerror("roots not implemented for integer polynomials");
return NRVec<typename LA_traits<int>::complextype>(1);
}
template<>
NRVec<typename LA_traits<unsigned int>::complextype> Polynomial<unsigned int>::roots() const
{
laerror("roots not implemented for integer polynomials");
return NRVec<typename LA_traits<unsigned int>::complextype>(1);
}
template <typename T>
NRVec<typename LA_traits<T>::complextype> Polynomial<T>::roots() const
{
@@ -107,7 +117,7 @@ NRVec<T> rr(degree());
int nr=0;
for(int i=0; i<degree(); ++i)
{
if(abs(r[i].imag())<thr)
if(MYABS(r[i].imag())<thr)
{
rr[nr++] = r[i].real();
}
@@ -151,7 +161,7 @@ T x=x0;
for(int i=0; i<maxit; ++i)
{
T v=value(*this,x);
if(abs(v)<thr) break;
if(MYABS(v)<thr) break;
x -= v/value(d,x);
}
@@ -185,6 +195,15 @@ laerror("SVD gcd only for floating point numbers");
return p;
}
template <>
Polynomial<unsigned int> svd_gcd(const Polynomial<unsigned int> &p, const Polynomial<unsigned int> &q, const typename LA_traits<unsigned int>::normtype thr)
{
laerror("SVD gcd only for floating point numbers");
return p;
}
template <typename T>
Polynomial<T> svd_gcd(const Polynomial<T> &p, const Polynomial<T> &q, const typename LA_traits<T>::normtype thr)
{
@@ -202,12 +221,54 @@ int d=big.degree()+small.degree()-rank;
return poly_gcd(big,small,thr,d);
}
template <typename T>
Polynomial<T> Polynomial<T>::pow(const int n) const
{
int i=n;
if(i<0) laerror("negative exponent in polynomial::pow");
if(i==0) {Polynomial<T> r(0); r[0]=(T)1; return r;}
if(i==1) return *this;
Polynomial<T>y,z;
z= *this;
while(!(i&1))
{
z = z*z;
i >>= 1;
}
y=z;
while((i >>= 1)/*!=0*/)
{
z = z*z;
if(i&1) y = y*z;
}
return y;
}
template <typename T>
Polynomial<T> Polynomial<T>::powx(const int i) const
{
if(i<0) laerror("negative exponent in polynomial::pow");
if(i==0) {Polynomial<T> r(0); r[0]= this->sum(); return r;}
if(i==1) return *this;
Polynomial<T> r(i*this->degree());
r.clear();
for(int j=0; j<=this->degree(); ++j) r[j*i] = (*this)[j];
return r;
}
template <typename T>
void Polynomial<T>::binomial(const int n)
{
resize(n,false);
for(int i=0; i<=n; ++i) (*this)[i] = (T) binom(n,i);
}
/***************************************************************************//**
* forced instantization in the corresponding object file
******************************************************************************/
template class Polynomial<int>;
template class Polynomial<unsigned int>;
template class Polynomial<double>;
template class Polynomial<std::complex<double> >;
@@ -220,6 +281,7 @@ template Polynomial<T> svd_gcd(const Polynomial<T> &p, const Polynomial<T> &q, c
INSTANTIZE(int)
INSTANTIZE(unsigned int)
INSTANTIZE(double)
INSTANTIZE(std::complex<double>)