mirror of https://github.com/CGAL/cgal
66 lines
2.1 KiB
TeX
66 lines
2.1 KiB
TeX
\begin{ccRefConcept}{RealEmbeddable}
|
|
|
|
\ccDefinition
|
|
|
|
A model of this concepts represents numbers that embeddable onto the real
|
|
axis. The type obeys the algebraic structure and compares two values according
|
|
to the total order of the real numbers.
|
|
|
|
|
|
Remark:\\
|
|
If a number type is a model of both IntegralDomainWithoutDiv and
|
|
RealComparable, the number an object of that type represents for the
|
|
algebraic operations must be the same real number it represents for
|
|
comparison. It follows that the ring represented by such a number type
|
|
is a subring of the real numbers and hence has characteristic zero
|
|
( see http://mathworld.wolfram.com/CharacteristicField.html ).
|
|
|
|
|
|
\ignore{
|
|
In addition to the comparison operators, the template class
|
|
NiX::NT_traits<NT> provides three adaptable functors for number types
|
|
NT that are a model of RealComparable.
|
|
|
|
* NiX::NT_traits::Abs ()(x) is an AdaptableUnaryFunction that accepts
|
|
a number x and computes its absolute value.
|
|
|
|
* NiX::NT_traits::Sign ()(x) is an AdaptableUnaryFunction that accepts
|
|
a number x and computes its three-valued sign.
|
|
|
|
* NiX::NT_traits::Compare ()(x,y) is an AdaptableBinaryFunction that
|
|
accepts two numbers x and y and computes a three-valued comparison result.
|
|
|
|
* NiX::NT_traits::To_double ()(x) is an AdaptableUnaryFunction that
|
|
accepts a number x and computes a double approximation of x.
|
|
|
|
* NiX::NT_traits::To_Interval ()(x) is an AdaptableUnaryFunction that
|
|
accepts a number x and computes a double Interval approximation of x. It
|
|
is guaranteed that x is contained in the interval.
|
|
}
|
|
|
|
\ccRefines
|
|
\ccc{LessThanComparable}
|
|
|
|
\ccOperations
|
|
\ccFunction{bool operator< (const RealEmbeddable &a,
|
|
const RealEmbeddable &b);}{}
|
|
\ccGlue
|
|
\ccFunction{bool operator<=(const RealEmbeddable &a,
|
|
const RealEmbeddable &b);}{}
|
|
\ccGlue
|
|
\ccFunction{bool operator> (const RealEmbeddable &a,
|
|
const RealEmbeddable &b);}{}
|
|
\ccGlue
|
|
\ccFunction{bool operator>=(const RealEmbeddable &a,
|
|
const RealEmbeddable &b);}{}
|
|
\ccGlue
|
|
|
|
|
|
|
|
\ccSeeAlso
|
|
|
|
\ccRefIdfierPage{RealEmbeddableTraits}\\
|
|
|
|
\ccHasModels
|
|
|
|
\end{ccRefConcept} |