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CGAL 6.0 - Number Types
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Classes | |
| struct | 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. | |
| 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. | |
| 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. | |
| 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. | |
| OutputIterator CGAL::compute_roots_of_2 | ( | const RT & | a, |
| const RT & | b, | ||
| const RT & | c, | ||
| OutputIterator | oit | ||
| ) |
#include <CGAL/Root_of_traits.h>
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.
OutputIterator is required to accept Root_of_traits<RT>::Root_of_2.
Multiplicities are not reported.
RT is an IntegralDomainWithoutDivision. RootOf_2 CGAL::Root_of_traits<RT> CGAL::make_root_of_2() CGAL::make_sqrt() CGAL::Sqrt_extension<NT,ROOT> | Root_of_traits< RT >::Root_of_2 CGAL::make_root_of_2 | ( | const RT & | a, |
| const RT & | b, | ||
| const RT & | c, | ||
| bool | s | ||
| ) |
#include <CGAL/Root_of_traits.h>
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.
RT is an IntegralDomainWithoutDivision. RootOf_2 CGAL::Root_of_traits<RT> CGAL::make_sqrt() CGAL::compute_roots_of_2() CGAL::Sqrt_extension<NT,ROOT> | Root_of_traits< RT >::Root_of_2 CGAL::make_root_of_2 | ( | RT | alpha, |
| RT | beta, | ||
| RT | gamma | ||
| ) |
#include <CGAL/Root_of_traits.h>
The function make_root_of_2() constructs an algebraic number of degree 2 over a ring number type.
Constructs the number \( \alpha+ \beta\sqrt{\gamma}\).
RT is an IntegralDomainWithoutDivision. RootOf_2 CGAL::Root_of_traits<RT> CGAL::make_sqrt() CGAL::compute_roots_of_2() CGAL::Sqrt_extension<NT,ROOT> | Root_of_traits< RT >::Root_of_2 CGAL::make_sqrt | ( | const RT & | x | ) |
#include <CGAL/Root_of_traits.h>
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 \( 2\).
RT is a RealEmbeddable IntegralDomain. RootOf_2 CGAL::make_root_of_2() CGAL::Root_of_traits<RT>