CGAL 5.1  Number Types

Concept to represent algebraic numbers of degree up to 2 over a RealEmbeddable
IntegralDomain
RT
.
A model of this concept is associated to this RT
via CGAL::Root_of_traits<RT>
, which provides Root_of_2
as a public type. Moreover, CGAL::Root_of_traits<RT>
provides the public type Root_of_1
, which is the quotient field of RT
. We refer to Root_of_1
as FT (for field type).
The model of RootOf_2
is a RealEmbeddable
IntegralDomain
, which is ImplicitInteroperable
with RT
, FT
. In particular, it provides the comparison operators ==, !=, <, >, <=, >=
as well as the sign
and compare
functions needed to compare elements of types RootOf_2, RT
and FT
. It also provides all arithmetic operators +,,*,/
among elements of type RootOf_2
as well as mixed forms with RT
and FT
.
However, it is important to note that arithmetic operations among elements of RootOf_2
are only allowed in the special case when they have been constructed from equations having the same discriminant, that is, if they are defined in the same algebraic extension of degree 2.
Besides construction from int, RT
and FT
the following functions provide special construction for extensions of degree 2:
ImplicitInteroperable
with RT
ImplicitInteroperable
with FT
double
(not exact)
Operations  
Same for operator  
RootOf_2 &  operator+= (const RootOf_2 &a) 
RootOf_2  operator+ (const RootOf_2 &a, const RootOf_2 &b) 
bool  operator== (const RootOf_2 &a, const RootOf_2 &b) 
bool  operator< (const RootOf_2 &a, const RootOf_2 &b) 
a
and b
are defined in the same extension.