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replace is well defined by a simple (less confusing) "is defined"

This commit is contained in:
Michael Hemmer 2011-10-25 15:05:55 +00:00
parent 5f4f11e2df
commit 59d256f06d
28 changed files with 32 additions and 27 deletions
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2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/AlgebraicStructureTraits_Div.tex
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@ -27,7 +27,7 @@ with remainder.
second_argument_type y);}{}
\ccMethod{template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);}
{This operator is well defined if \ccc{NT1} and \ccc{NT2} are \ccc{ExplicitInteroperable}
{This operator is defined if \ccc{NT1} and \ccc{NT2} are \ccc{ExplicitInteroperable}
with coercion type \ccc{AlgebraicStructureTraits::Type}. }
%\ccHasModels

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/AlgebraicStructureTraits_DivMod.tex
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@ -106,7 +106,7 @@ The following table illustrates the behavior for integers:
\ccMethod{template <class NT1, class NT2> result_type
operator()(NT1 x, NT2 y, third_argument_type q, fourth_argument_type r);}
{This operator is well defined if \ccc{NT1} and \ccc{NT2} are \ccc{ExplicitInteroperable}
{This operator is defined if \ccc{NT1} and \ccc{NT2} are \ccc{ExplicitInteroperable}
with coercion type \ccc{AlgebraicStructureTraits::Type}. }
%\ccHasModels

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/AlgebraicStructureTraits_Gcd.tex
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@ -37,7 +37,7 @@ Thus, $0$ is divided by every element of the Ring, in particular by itself.
{ returns $gcd(x,y)$. }
\ccMethod{template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);}
{This operator is well defined if \ccc{NT1} and \ccc{NT2} are \ccc{ExplicitInteroperable}
{This operator is defined if \ccc{NT1} and \ccc{NT2} are \ccc{ExplicitInteroperable}
with coercion type \ccc{AlgebraicStructureTraits::Type}. }
%\ccHasModels

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/AlgebraicStructureTraits_IntegralDivision.tex
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@ -34,7 +34,7 @@ $z$ is uniquely defined if it exists.
\ccMethod{template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);}
{This operator is well defined if \ccc{NT1} and \ccc{NT2} are \ccc{ExplicitInteroperable}
{This operator is defined if \ccc{NT1} and \ccc{NT2} are \ccc{ExplicitInteroperable}
with coercion type \ccc{AlgebraicStructureTraits::Type}. }
%\ccHasModels

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/AlgebraicStructureTraits_Mod.tex
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@ -26,7 +26,7 @@
second_argument_type y);}{}
\ccMethod{template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);}
{This operator is well defined if \ccc{NT1} and \ccc{NT2} are \ccc{ExplicitInteroperable}
{This operator is defined if \ccc{NT1} and \ccc{NT2} are \ccc{ExplicitInteroperable}
with coercion type \ccc{AlgebraicStructureTraits::Type}. }
%\ccHasModels

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/RealEmbeddableTraits_Compare.tex
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@ -27,7 +27,7 @@
\ccMethod{template <class NT1, class NT2>
result_type operator()(NT1 x, NT2 y);}{
This operator is well defined if \ccc{NT1} and \ccc{NT2} are
This operator is defined if \ccc{NT1} and \ccc{NT2} are
\ccc{ExplicitInteroperable} with coercion type
\ccc{RealEmbeddableTraits::Type}. }

3
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/RealEmbeddableTraits_ToDouble.tex
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@ -4,6 +4,9 @@
\ccc{AdaptableUnaryFunction} computes a double approximation of a real
embeddable number.
Remark: In order to control the quality of approximation one has to resort
to methods that are specific to NT. There are no general guarantees whatsoever.
\ccRefines

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/abs.tex
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@ -4,7 +4,7 @@
The template function \ccRefName\ returns the absolute value of a number.
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{RealEmbeddable} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/compare.tex
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@ -8,7 +8,7 @@ the second, i.e. it returns \ccc{CGAL::LARGER} if $x$ is larger then $y$.
In case the argument types \ccc{NT1} and \ccc{NT2} differ,
\ccRefName\ is performed with the semantic of the type determined via
\ccc{Coercion_traits}.
The function is guaranteed to be well defined in case this type
The function is defined if this type
is a model of the \ccc{RealEmbeddable} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/div.tex
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@ -11,7 +11,7 @@ Thus, the \ccc{result_type} is well defined if \ccc{NT1} and \ccc{NT2}
are a model of \ccc{ExplicitInteroperable}. \\
The actual \ccRefName\ is performed with the semantic of that type.
The function is guaranteed to be well defined in case \ccc{result_type}
The function is defined if \ccc{result_type}
is a model of the \ccc{EuclideanRing} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/div_mod.tex
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@ -11,7 +11,7 @@ Thus, the \ccc{result_type} is well defined if \ccc{NT1} and \ccc{NT2}
are a model of \ccc{ExplicitInteroperable}. \\
The actual \ccRefName\ is performed with the semantic of that type.
The function is guaranteed to be well defined in case \ccc{result_type}
The function is defined if \ccc{result_type}
is a model of the \ccc{EuclideanRing} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/gcd.tex
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@ -10,7 +10,7 @@ Thus, the \ccc{result_type} is well defined if \ccc{NT1} and \ccc{NT2}
are a model of \ccc{ExplicitInteroperable}. \\
The actual \ccRefName\ is performed with the semantic of that type.
The function is guaranteed to be well defined in case \ccc{result_type}
The function is defined if \ccc{result_type}
is a model of the \ccc{UniqueFactorizationDomain} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/integral_division.tex
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@ -14,7 +14,7 @@ Thus, the \ccc{result_type} is well defined if \ccc{NT1} and \ccc{NT2}
are a model of \ccc{ExplicitInteroperable}. \\
The actual \ccRefName\ is performed with the semantic of that type.
The function is guaranteed to be well defined in case \ccc{result_type}
The function is defined if \ccc{result_type}
is a model of the \ccc{IntegralDomain} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/inverse.tex
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@ -4,7 +4,7 @@
The function \ccRefName\ returns the inverse element with respect to multiplication.
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{Field} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/is_negative.tex
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@ -3,7 +3,7 @@
\ccDefinition
The template function \ccRefName\ determines if a value is negative or not.
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{RealEmbeddable} concept.

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/is_one.tex
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@ -3,7 +3,7 @@
\ccDefinition
The function \ccRefName\ determines if a value is equal to 1 or not.\\
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{IntegralDomainWithoutDivision} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/is_positive.tex
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@ -3,7 +3,7 @@
\ccDefinition
The template function \ccRefName\ determines if a value is positive or not.
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{RealEmbeddable} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/is_zero.tex
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@ -3,7 +3,7 @@
\ccDefinition
The function \ccRefName\ determines if a value is equal to 0 or not.\\
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{RealEmbeddable} or of
the \ccc{IntegralDomainWithoutDivision} concept.

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/kth_root.tex
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@ -4,7 +4,7 @@
The function \ccRefName\ returns the k-th root of a value.
The function is guaranteed to be well defined in case the second argument type
The function is defined if the second argument type
is a model of the \ccc{FieldWithKthRoot} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/mod.tex
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@ -10,7 +10,7 @@ Thus, the \ccc{result_type} is well defined if \ccc{NT1} and \ccc{NT2}
are a model of \ccc{ExplicitInteroperable}. \\
The actual \ccRefName\ is performed with the semantic of that type.
The function is guaranteed to be well defined in case \ccc{result_type}
The function is defined if \ccc{result_type}
is a model of the \ccc{EuclideanRing} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/root_of.tex
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@ -5,7 +5,7 @@
The function \ccRefName\ computes a real root of a square-free univariate
polynomial.
The function is guaranteed to be well defined in case the value type, \ccc{NT},
The function is defined if the value type, \ccc{NT},
of the iterator range is a model of the \ccc{FieldWithRootOf} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/sign.tex
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@ -4,7 +4,7 @@
The template function \ccRefName\ returns the sign of a number.
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{RealEmbeddable} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/simplify.tex
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@ -4,7 +4,7 @@
The function \ccRefName\ may simplify a given object.
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{IntegralDomainWithoutDivision} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/sqrt.tex
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@ -4,7 +4,7 @@
The function \ccRefName\ returns the square root of a value.
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{FieldWithSqrt} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/square.tex
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@ -3,7 +3,7 @@
\ccDefinition
The function \ccRefName\ returns the square of a number.\\
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{IntegralDomainWithoutDivision} concept.
\ccInclude{CGAL/number_utils.h}

4
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/to_double.tex
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@ -3,9 +3,11 @@
\ccDefinition
The template function \ccRefName\ returns an double approximation of a number.
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{RealEmbeddable} concept.
Remark: In order to control the quality of approximation one has to resort to methods that are specific to NT. There are no general guarantees whatsoever.
\ccInclude{CGAL/number_utils.h}
\ccFunction{template <class NT> double to_double(const NT& x);}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/to_interval.tex
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@ -5,7 +5,7 @@
The template function \ccRefName\ computes for a given real embeddable
number $x$ a double interval containing $x$.
This interval is represented by a \ccc{std::pair<double,double>}.
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{RealEmbeddable} concept.
\ccInclude{CGAL/number_utils.h}

2
Algebraic_foundations/doc_tex/Algebraic_foundations_ref/unit_part.tex
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@ -5,7 +5,7 @@
The function \ccRefName\ computes the unit part of a given ring
element.
The function is guaranteed to be well defined in case the argument type
The function is defined if the argument type
is a model of the \ccc{IntegralDomainWithoutDivision} concept.
\ccInclude{CGAL/number_utils.h}