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file obsolete due to update of according file in package Number Types

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Michael Hemmer 2007-01-29 10:07:51 +00:00
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commit 8ecd4b581f
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Algebraic_foundations/doc_tex/Algebraic_foundations_ref/Quotient.tex
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\begin{ccRefClass} {Quotient<NT>}
\label{Quotient}
%\subsection{Quotient}
\ccDefinition
An object of the class \ccStyle{Quotient<NT>} is an element of the
field of quotients of the integral domain type \ccStyle{NT}.
If \ccStyle{NT} behaves like an integer, \ccStyle{Quotient<NT>}
behaves like a rational number.
{\leda}'s class \ccStyle{rational} (see Section~\ref{leda-nt})
has been the basis for \ccStyle{Quotient<NT>}.
A \ccStyle{Quotient<NT>} \ccStyle{q} is represented as a pair of
\ccStyle{NT}s, representing numerator and denominator.
\ccc{NT} must be at least model of concept \ccc{IntegralDomainWithoutDivision}.\\
\ccc{NT} must be a model of concept \ccc{RealEmbeddable}. \\
\ccInclude{CGAL/Quotient.h}
\ccIsModel
\ccc{Field}\\
\\
\ccc{RealEmbeddable}
\ccCreation
\ccCreationVariable{q}
\ccConstructor{Quotient();}
{introduces an uninitialized variable \ccVar.}
\ccHidden \ccConstructor{Quotient(const Quotient<NT> &q);}
{copy constructor.}
\ccGlue
\ccConstructor{template <class T> Quotient<NT>(const T& t);}
{introduces the quotient \ccStyle{t/1}. NT needs to have a constructor from T.}
\ccGlue
\ccConstructor{template <class T> Quotient<NT>(const Quotient<T>& t);}
{introduces the quotient \ccStyle{NT(t.numerator())/NT(t.denominator())}.
NT needs to have a constructor from T.}
\ccGlue
\ccConstructor{Quotient(const NT& n, const NT& d)}
{introduces the quotient \ccStyle{n/d}.}
\ccOperations
%\ccSetTwoOfThreeColumns{5cm}{4cm}
%SetThreeColumns{std::ostream& }{}{\hspace*{8cm}}
There are two access functions, namely to the
numerator and the denominator of a quotient.
Note that these values are not uniquely defined.
It is guaranteed that \ccStyle{q.numerator()} and
\ccStyle{q.denominator()} return values \ccStyle{nt_num} and
\ccStyle{nt_den} such that \ccStyle{q = nt_num/nt_den}, only
if \ccStyle{q.numerator()} and \ccStyle{q.denominator()} are called
consecutively wrt \ccStyle{q}, i.e.~\ccStyle{q} is not involved in
any other operation between these calls.
\ccMethod{NT numerator() const;}
{returns a numerator of \ccStyle{q}.}
\ccGlue
\ccMethod{NT denominator() const;}
{returns a denominator of \ccStyle{q}.}
\ccHidden \ccMethod{Quotient<NT>& normalize();}
{}
The stream operations are available as well.
They assume that corresponding stream operators for type \ccc{NT} exist.
\ccFunction{std::ostream& operator<<(std::ostream& out, const Quotient<NT>& q);}
{writes \ccc{q} to ostream \ccc{out} in format ``{\tt n/d}'', where
{\tt n}$==$\ccc{q.numerator()} and {\tt d}$==$\ccc{q.denominator()}.}
\ccFunction{std::istream& operator>>(std::istream& in, Quotient<NT>& q);}
{reads \ccc{q} from istream \ccc{in}. Expected format is
``{\tt n/d}'', where {\tt n} and {\tt d} are of type \ccc{NT}.
A single {\tt n} which is not followed by a {\tt /}\ is also
accepted and interpreted as {\tt n/1}.}
The following functions are added to fulfill the \cgal\ requirements
on number types.
\ccFunction{double to_double(const Quotient<NT>& q);}
{returns some double approximation to \ccStyle{q}.}
\ccGlue
\ccFunction{bool is_valid(const Quotient<NT>& q);}
{returns true, if numerator and denominator are valid.}
\ccGlue
\ccFunction{bool is_finite(const Quotient<NT>& q);}
{returns true, if numerator and denominator are finite.}
\ccGlue
\ccFunction{Quotient<NT> sqrt(const Quotient<NT>& q);}
{returns the square root of \ccc{q}. This is supported if and only if
\ccc{NT} supports the square root as well.}
\end{ccRefClass}