Classes
class	CGAL::Root_of_traits< RT >
	For a `RealEmbeddable` `IntegralDomain` `RT`, the class template `Root_of_traits<RT>` associates a type `Root_of_2`, which represents algebraic numbers of degree 2 over `RT`. More...

class	CGAL::Sqrt_extension< NT, ROOT, DifferentExtensionComparable, FilterPredicates >
	An instance of this class represents an extension of the type `NT` by one square root of the type `ROOT`. More...

Functions
template<typename RT , typename OutputIterator >
OutputIterator	CGAL::compute_roots_of_2 (const RT &a, const RT &b, const RT &c, OutputIterator oit)
	The function `compute_roots_of_2()` solves a univariate polynomial as it is defined by the coefficients given to the function. More...

template<typename RT >
Root_of_traits< RT >::Root_of_2	CGAL::make_root_of_2 (const RT &a, const RT &b, const RT &c, bool s)
	The function `make_root_of_2()` constructs an algebraic number of degree 2 over a ring number type. More...

template<typename RT >
Root_of_traits< RT >::Root_of_2	CGAL::make_root_of_2 (RT alpha, RT beta, RT gamma)
	The function `make_root_of_2()` constructs an algebraic number of degree 2 over a ring number type. More...

template<typename RT >
Root_of_traits< RT >::Root_of_2	CGAL::make_sqrt (const RT &x)
	The function `make_sqrt()` constructs a square root of a given value of type $RT$ . More...

Function Documentation

template<typename RT , typename OutputIterator >

OutputIterator CGAL::compute_roots_of_2	(	const RT &	a,
		const RT &	b,
		const RT &	c,
		OutputIterator	oit
	)

The function compute_roots_of_2() solves a univariate polynomial as it is defined by the coefficients given to the function.

The solutions are written into the given OutputIterator. Writes the real roots of the polynomial $aX^2+bX+c$ into $oit$ in ascending order.

Multiplicities are not reported.

Precondition: RT is an IntegralDomainWithoutDivision.; $a\neq0$ or $b\neq0$ .

See Also: RootOf_2; CGAL::Root_of_traits<RT>; CGAL::make_root_of_2(); CGAL::make_sqrt(); CGAL::Sqrt_extension<NT,ROOT>

#include <CGAL/Root_of_traits.h>

template<typename RT >

Root_of_traits<RT>::Root_of_2 CGAL::make_root_of_2	(	const RT &	a,
		const RT &	b,
		const RT &	c,
		bool	s
	)

The function make_root_of_2() constructs an algebraic number of degree 2 over a ring number type.

Returns the smallest real root of the polynomial $aX^2+bX+c$ if $s$ is true, and the largest root is $s$ is false.

Precondition: RT is an IntegralDomainWithoutDivision.; The polynomial has at least one real root.

See Also: RootOf_2; CGAL::Root_of_traits<RT>; CGAL::make_sqrt(); CGAL::compute_roots_of_2(); CGAL::Sqrt_extension<NT,ROOT>

#include <CGAL/Root_of_traits.h>

template<typename RT >

Root_of_traits<RT>::Root_of_2 CGAL::make_root_of_2	(	RT	alpha,
		RT	beta,
		RT	gamma
	)

The function make_root_of_2() constructs an algebraic number of degree 2 over a ring number type.

Constructs the number $\alpha+ \beta\sqrt{\gamma}$ .

See Also: RootOf_2; CGAL::Root_of_traits<RT>; CGAL::make_sqrt(); CGAL::compute_roots_of_2(); CGAL::Sqrt_extension<NT,ROOT>

#include <CGAL/Root_of_traits.h>

template<typename RT >

Root_of_traits<RT>::Root_of_2 CGAL::make_sqrt ( const RT & x)

The function make_sqrt() constructs a square root of a given value of type $RT$ .

Depending on the type $RT$ the square root may be returned in a new type that can represent algebraic extensions of degree $2$ .

#include <CGAL/Root_of_traits.h>

Classes