mirror of https://github.com/CGAL/cgal
805 lines
29 KiB
TeX
805 lines
29 KiB
TeX
|
|
|
|
% GetCoefficient
|
|
% GetInnermostCoefficient
|
|
% ConstructCoefficientConstIteratorRange
|
|
% ConstructInnermostCoefficientConstIteratorRange
|
|
|
|
% Permute
|
|
\begin{ccRefFunction}{permute}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Permute}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d, class InputIterator >
|
|
Polynomial_traits_d<Polynomial_d>::Permute::result_type
|
|
permute(const Polynomial_d& p, InputIterator begin, InputIterator end );
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Permute}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Permute}\\
|
|
\end{ccRefFunction}
|
|
|
|
% Swap
|
|
\begin{ccRefFunction}{swap}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Swap}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Swap::result_type
|
|
swap(const Polynomial_d& p, int i, int j);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Swap}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Swap}\\
|
|
\end{ccRefFunction}
|
|
|
|
% Move
|
|
\begin{ccRefFunction}{move}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Move}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Move::result_type
|
|
move(const Polynomial_d& p, int i, int j);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Move}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Move}\\
|
|
\end{ccRefFunction}
|
|
|
|
% Degree
|
|
\begin{ccRefFunction}{degree}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Degree}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Degree::result_type
|
|
degree(const Polynomial_d& p,
|
|
int i,
|
|
index = Polynomial_traits_d<Polynomial_d>::d-1);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Degree}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Degree}\\
|
|
\end{ccRefFunction}
|
|
|
|
% TotalDegree
|
|
\begin{ccRefFunction}{total_degree}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::TotalDegree}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Total_degree::result_type
|
|
total_degree(const Polynomial_d& p);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Total_degree}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::TotalDegree}\\
|
|
\end{ccRefFunction}
|
|
|
|
% DegreeVector
|
|
\begin{ccRefFunction}{degree_vector}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::DegreeVector}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Degree_vector::result_type
|
|
degree_vector(const Polynomial_d& p);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::DegreeVector}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Degree_vector}\\
|
|
\end{ccRefFunction}
|
|
|
|
% LeadingCoefficient
|
|
\begin{ccRefFunction}{leading_coefficient}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::LeadingCoefficient}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Leading_coefficient::result_type
|
|
leading_coefficient(const Polynomial_d& p);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Leading_coefficient}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::LeadingCoefficient}\\
|
|
\end{ccRefFunction}
|
|
|
|
% InnermostLeadingCoefficient
|
|
\begin{ccRefFunction}{innermost_leading_coefficient}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept
|
|
\ccc{PolynomialTraits_d::InnermostLeadingCoefficient}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Innermost_leading_coefficient::result_type
|
|
innermost_leading_coefficient(const Polynomial_d& p);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::InnermostLeadingCoefficient}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::InnermostLeadingCoefficient}\\
|
|
\end{ccRefFunction}
|
|
|
|
% Canonicalize
|
|
\begin{ccRefFunction}{canonicalize}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Canonicalize}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Canonicalize::result_type
|
|
canonicalize(const Polynomial_d& p);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Canonicalize}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Canonicalize}\\
|
|
\end{ccRefFunction}
|
|
|
|
% Differentiate
|
|
\begin{ccRefFunction}{differentiate}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Differentiate}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Differentiate::result_type
|
|
differentiate(const Polynomial_d& p,
|
|
index = Polynomial_traits_d<Polynomial_d>::d-1 );
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Differentiate}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Differentiate}\\
|
|
\end{ccRefFunction}
|
|
|
|
% Evaluate
|
|
\begin{ccRefFunction}{evaluate}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Evaluate}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Evaluate::result_type
|
|
evaluate(const Polynomial_d& p,
|
|
Polynomial_traits_d<Polynomial_d>::Coefficient_type x);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Evaluate}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Evaluate}\\
|
|
\end{ccRefFunction}
|
|
% EvaluateHomogeneous
|
|
\begin{ccRefFunction}{evaluate_homogeneous}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::EvaluateHomogeneous}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Evaluate_homogeneous::result_type
|
|
evaluate_homogeneous(
|
|
const Polynomial_d& p,
|
|
Polynomial_traits_d<Polynomial_d>::Coefficient_type u,
|
|
Polynomial_traits_d<Polynomial_d>::Coefficient_type v);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Evaluate_homogeneous}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::EvaluateHomogeneous}\\
|
|
\end{ccRefFunction}
|
|
|
|
% Substitute
|
|
\begin{ccRefFunction}{substitute}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Substitute}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template < class Polynomial_d, class InputIterator >
|
|
CGAL::Coercion_traits<
|
|
Polynomial_traits_d<Polynomial_d>::Innermost_coefficient,
|
|
std::iterator_traits<Input_iterator>::value_type
|
|
>::Type
|
|
substitute(
|
|
const Polynomial_d& p, InputIterator begin, InputIterator end);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Substitute}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Substitute}\\
|
|
\end{ccRefFunction}
|
|
% IsZeroAt
|
|
\begin{ccRefFunction}{is_zero_at}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::IsZeroAt}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template < class Polynomial_d, class InputIterator >
|
|
Polynomial_traits_d<Polynomial_d>::Is_zero_at::result_type
|
|
is_zero_at(
|
|
const Polynomial_d& p, InputIterator begin, InputIterator end);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Is_zero_at}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::IsZeroAt}\\
|
|
\end{ccRefFunction}
|
|
% SignAt
|
|
\begin{ccRefFunction}{sign_at}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::SignAt}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template < class Polynomial_d, class InputIterator >
|
|
Polynomial_traits_d<Polynomial_d>::Sign_at::result_type
|
|
sign_at(
|
|
const Polynomial_d& p, InputIterator begin, InputIterator end);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Sign_at}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::SignAt}\\
|
|
\end{ccRefFunction}
|
|
|
|
|
|
% SubstituteHomogeneous
|
|
\begin{ccRefFunction}{substitute_homogeneous}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::SubstituteHomogeneous}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template < class Polynomial_d, class InputIterator >
|
|
CGAL::Coercion_traits<
|
|
Polynomial_traits_d<Polynomial_d>::Innermost_coefficient,
|
|
std::iterator_traits<Input_iterator>::value_type
|
|
>::Type
|
|
substitute_homogeneous(
|
|
const Polynomial_d& p, InputIterator begin, InputIterator end);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Substitute_homogeneous}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::SubstituteHomogeneous}\\
|
|
\end{ccRefFunction}
|
|
% IsZeroAtHomogeneous
|
|
\begin{ccRefFunction}{is_zero_at_homogeneous}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::IsZeroAtHomogeneous}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template < class Polynomial_d, class InputIterator >
|
|
Polynomial_traits_d<Polynomial_d>::Is_zero_at_homogeneous::result_type
|
|
is_zero_at_homogeneous(
|
|
const Polynomial_d& p, InputIterator begin, InputIterator end);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Is_zero_at_homogeneous}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::IsZeroAtHomogeneous}\\
|
|
\end{ccRefFunction}
|
|
% SignAtHomogeneous
|
|
\begin{ccRefFunction}{sign_at_homogeneous}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::SignAtHomogeneous}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template < class Polynomial_d, class InputIterator >
|
|
Polynomial_traits_d<Polynomial_d>::Sign_at_homogeneous::result_type
|
|
sign_at_homogeneous(
|
|
const Polynomial_d& p, InputIterator begin, InputIterator end);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Sign_at_homogeneous}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::SignAtHomogeneous}\\
|
|
\end{ccRefFunction}
|
|
|
|
% Compare
|
|
\begin{ccRefFunction}{compare}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Compare}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Compare::result_type
|
|
compare(const Polynomial_d& p, const Polynomial_d& q);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Compare}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Compare}\\
|
|
\end{ccRefFunction}
|
|
|
|
% UnivariateContent
|
|
\begin{ccRefFunction}{univariate_content}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::UnivariateContent}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Univariate_content::result_type
|
|
univariate_content(const Polynomial_d& p);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::UnivariateContent}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Univariate_Content}\\
|
|
\end{ccRefFunction}
|
|
|
|
% MultivariateContent
|
|
\begin{ccRefFunction}{multivariate_content}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::MultivariateContent}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Multivariate_content::result_type
|
|
multivariate_content(const Polynomial_d& p);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Multivariate_content}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::MultivariateContent}\\
|
|
\end{ccRefFunction}
|
|
|
|
% SquareFreeFactorize
|
|
\begin{ccRefFunction}{square_free_factorize}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::SquareFreeFactorize}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d, class OutputIterator >
|
|
OutputIterator
|
|
square_free_factorize(
|
|
const Polynomial_d& p,
|
|
OutputIterator it,
|
|
Polynomial_traits_d<Polynomial>::Innermost_coefficient& a);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Square_free_factorize}.
|
|
}
|
|
\ccFunction{
|
|
template <class Polynomial_d, class OutputIterator >
|
|
OutputIterator
|
|
square_free_factorize(const Polynomial_d& p, OutputIterator it);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Square_free_factorize}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::SquareFreeFactorize}\\
|
|
\end{ccRefFunction}
|
|
% MakeSquareFree
|
|
\begin{ccRefFunction}{make_square_free}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::MakeSquareFree}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Make_square_free::result_type
|
|
make_square_free(const Polynomial_d& p);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Make_square_free}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::MakeSquareFree}\\
|
|
\end{ccRefFunction}
|
|
|
|
% PseudoDivision
|
|
\begin{ccRefFunction}{pseudo_division}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::PseudoDivision}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
void
|
|
pseudo_division(
|
|
const Polynomial_d& f, const Polynomial_d& g,
|
|
Polynomial_d& q, Polynomial_d& r, Polynomial_traits_d<Polynomial_d>::Coefficient_type& D );
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Pseudo_division}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::PseudoDivision}\\
|
|
\end{ccRefFunction}
|
|
|
|
% PseudoDivisionQuotient
|
|
\begin{ccRefFunction}{pseudo_division_quotient}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::PseudoDivisionQuotient}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Pseudo_division_quotient::result_type
|
|
pseudo_division_quotient(const Polynomial_d& p, const Polynomial_d& q);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Pseudo_division_quotient}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::PseudoDivisionQuotient}\\
|
|
\end{ccRefFunction}
|
|
|
|
% PseudoDivisionRemainder
|
|
\begin{ccRefFunction}{pseudo_division_remainder}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::PseudoDivisionRemainder}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Pseudo_division_remainder::result_type
|
|
pseudo_division_remainder(const Polynomial_d& p, const Polynomial_d& q);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Pseudo_division_remainder}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::PseudoDivisionRemainder}\\
|
|
\end{ccRefFunction}
|
|
|
|
% GcdUpToConstantFactor
|
|
\begin{ccRefFunction}{gcd_up_to_constant_factor}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::GcdUpToConstantFactor}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Gcd_up_to_constant_factor::result_type
|
|
gcd_up_to_constant_factor(const Polynomial_d& p, const Polynomial_d& q);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Gcd_up_to_constant_factor}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::GcdUpToConstantFactor}\\
|
|
\end{ccRefFunction}
|
|
|
|
% IntegralDivisionUpToConstantFactor
|
|
\begin{ccRefFunction}{integral_division_up_to_constant_factor}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::IntegralDivisionUpToConstantFactor}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Integral_division_up_to_constant_factor::result_type
|
|
integral_division_up_to_constant_factor(const Polynomial_d& p, const Polynomial_d& q);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Integral_division_up_to_constant_factor}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::IntegralDivisionUpToConstantFactor}\\
|
|
\end{ccRefFunction}
|
|
% UnivariateContentUpToConstantFactor
|
|
\begin{ccRefFunction}{univariate_content_up_to_constant_factor}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::UnivariateContentUpToConstantFactor}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Univariate_content_up_to_constant_factor::result_type
|
|
univariate_content_up_to_constant_factor(const Polynomial_d& p);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Univariate_content_up_to_constant_factor}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::UnivariateContentUpToConstantFactor}\\
|
|
\end{ccRefFunction}
|
|
|
|
% SquareFreeFactorizeUpToConstantFactorUpToConstantFactor
|
|
\begin{ccRefFunction}{square_free_factorize_up_to_constant_factor}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d, class OutputIterator >
|
|
OutputIterator
|
|
square_free_factorize_up_to_constant_factor(const Polynomial_d& p, OutputIterator it);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Square_free_factorize_up_to_constant_factor}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor}\\
|
|
\end{ccRefFunction}
|
|
|
|
% Shift
|
|
\begin{ccRefFunction}{shift}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Shift}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Shift::result_type
|
|
shift(const Polynomial_d& p, int i, int index = Polynomial_traits_d<Polynomial_d>::d-1);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Shift}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Shift}\\
|
|
\end{ccRefFunction}
|
|
% Negate
|
|
\begin{ccRefFunction}{negate}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Negate}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Negate::result_type
|
|
negate(const Polynomial_d& p, int index = Polynomial_traits_d<Polynomial_d>::d-1);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Negate}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Negate}\\
|
|
\end{ccRefFunction}
|
|
% Invert
|
|
\begin{ccRefFunction}{invert}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Invert}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Invert::result_type
|
|
invert(const Polynomial_d& p, int index = Polynomial_traits_d<Polynomial_d>::d-1);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Invert}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Invert}\\
|
|
\end{ccRefFunction}
|
|
% Translate
|
|
\begin{ccRefFunction}{translate}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Translate}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Translate::result_type
|
|
translate(
|
|
const Polynomial_d& p,
|
|
const Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& a,
|
|
int index = Polynomial_traits_d<Polynomial_d>::d-1);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Translate}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Translate}\\
|
|
\end{ccRefFunction}
|
|
% TranslateHomogeneous
|
|
\begin{ccRefFunction}{translate_homogeneous}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::TranslateHomogeneous}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Translate_homogeneous::result_type
|
|
translate_homogeneous(
|
|
const Polynomial_d& p,
|
|
const Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& u,
|
|
const Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& v,
|
|
int index = Polynomial_traits_d<Polynomial_d>::d-1);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Translate_homogeneous}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::TranslateHomogeneous}\\
|
|
\end{ccRefFunction}
|
|
|
|
% Scale
|
|
\begin{ccRefFunction}{scale}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Scale}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Scale::result_type
|
|
scale(
|
|
const Polynomial_d& p,
|
|
const Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& a,
|
|
int index = Polynomial_traits_d<Polynomial_d>::d-1);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Scale}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Scale}\\
|
|
\end{ccRefFunction}
|
|
% ScaleHomogeneous
|
|
\begin{ccRefFunction}{scale_homogeneous}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::ScaleHomogeneous}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Scale_homogeneous::result_type
|
|
scale_homogeneous(
|
|
const Polynomial_d& p,
|
|
const Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& u,
|
|
const Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type& v,
|
|
int index = Polynomial_traits_d<Polynomial_d>::d-1);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Scale_homogeneous}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::ScaleHomogeneous}\\
|
|
\end{ccRefFunction}
|
|
% Resultant
|
|
|
|
|
|
|
|
% Compare
|
|
\begin{ccRefFunction}{resultant}
|
|
\ccDefinition
|
|
For a given \ccc{Polynomial_d} the function \ccRefName\ adapts the
|
|
according functor in \ccc{Polynomial_traits_d<Polynomial_d>}. \\ \\
|
|
For more details see the concept \ccc{PolynomialTraits_d::Resultant}. \\ \\
|
|
\ccInclude{CGAL/polynomial_utils.h}
|
|
\ccFunction{
|
|
template <class Polynomial_d>
|
|
Polynomial_traits_d<Polynomial_d>::Resultant::result_type
|
|
resultant(const Polynomial_d& p, const Polynomial_d& q);
|
|
}{
|
|
Adapts \ccc{Polynomial_traits_d<Polynomial_d>::Resultant}.
|
|
}
|
|
\ccSeeAlso
|
|
\ccRefConceptPage{Polynomial_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d}\\
|
|
\ccRefConceptPage{PolynomialTraits_d::Resultant}\\
|
|
\end{ccRefFunction}
|