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RootOf_2

Definition

Concept to represent algebraic numbers of degree up to 2 over a RingNumberType denoted as RT.

Creation

RootOf_2 make_root_of_2 ( RT a, RT b, RT c, bool s)
Returns the smaller or larger root of the equation aX2+bX+c=0, if s is true or false, respectively.
Precondition: b2-4ac ≥ 0
RootOf_2 make_root_of_2 ( FT a, FT b, FT c, bool s)
Returns the smaller or larger root of the equation aX2+bX+c=0, if s is true or false, respectively.
Precondition: b2-4ac ≥ 0
RootOf_2 make_root_of_2 ( FT alpha, FT beta, FT gamma)
Constructs the number α+ β√γ.
Precondition: γ ≥ 0

Operations

The comparison operators ==, !=, <, >, <=, >= as well as the sign and compare functions need to be provided to compare elements of types RootOf_2, RT and FT.

In addition, the following operations must be provided:

RootOf_2 RT a + RootOf_2 r
RootOf_2 FT a + RootOf_2 r
RootOf_2 RootOf_2 r + RT a
RootOf_2 RootOf_2 r + FT a

as well as

RootOf_2 RootOf_2 r + RootOf_2 r Addition of two algebraic numbers, in the special case when they have been constructed from equations having the same discriminant.

and similarly for operators -, * and /.

RootOf_2 square ( RootOf_2 r)

RootOf_2 inverse ( RootOf_2 r)

RootOf_2 make_sqrt ( RT r)

RootOf_2 make_sqrt ( FT f)

Has Models

double (non exact)
CGAL::Root_of_2, etc

See Also

CGAL::make_root_of_2
CGAL::Root_of_2<RT>
CGAL::Root_of_traits_2<RT>
AlgebraicKernelForCircles::PolynomialForCircles_2_2
AlgebraicKernelForCircles

Next: Root_of_2<RT>
Navigation: Up   Table of Contents   Package Overview   Bibliography   Index   Title   Acknowledging CGAL
CGAL Open Source Project. Release 3.5. 1 October 2009.