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This commit is contained in:
Andreas Fabri 2022-10-05 06:56:13 +01:00
parent a685e19ed6
commit 7afac0d118
2 changed files with 15 additions and 15 deletions
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6
Number_types/doc/Number_types/CGAL/Root_of_traits.h
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@ -6,7 +6,7 @@ namespace CGAL {
The function `compute_roots_of_2()` solves a univariate polynomial as it is defined by the The function `compute_roots_of_2()` solves a univariate polynomial as it is defined by the
coefficients given to the function. The solutions are written into the given coefficients given to the function. The solutions are written into the given
`OutputIterator`. `OutputIterator`.
Writes the real roots of the polynomial \f$ aX^2+bX+c\f$ into \f$ oit\f$ in ascending order. Writes the real roots of the polynomial \f$ aX^2+bX+c\f$ into `oit` in ascending order.
`OutputIterator` is required to accept \link Root_of_traits::Root_of_2 `Root_of_traits<RT>::Root_of_2`\endlink. `OutputIterator` is required to accept \link Root_of_traits::Root_of_2 `Root_of_traits<RT>::Root_of_2`\endlink.
@ -81,8 +81,8 @@ namespace CGAL {
/*! /*!
\ingroup nt_ralgebraic \ingroup nt_ralgebraic
The function `make_sqrt()` constructs a square root of a given value of type \f$ RT\f$. The function `make_sqrt()` constructs a square root of a given value of type `RT`.
Depending on the type \f$ RT\f$ the square root may be returned in a new type that Depending on the type `RT` the square root may be returned in a new type that
can represent algebraic extensions of degree \f$ 2\f$. can represent algebraic extensions of degree \f$ 2\f$.
\returns \f$ \sqrt{x}.\f$ \returns \f$ \sqrt{x}.\f$

24
Number_types/doc/Number_types/CGAL/Sqrt_extension.h
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@ -3,9 +3,9 @@ namespace CGAL {
/*! /*!
\ingroup nt_ralgebraic \ingroup nt_ralgebraic
An instance of this class represents an extension of the type `NT` by *one* square root of the type `ROOT`. An instance of this class represents an extension of the type `NT` by *one* square root of the type `Root`.
`NT` is required to be constructible from `ROOT`. `NT` is required to be constructible from `Root`.
`NT` is required to be an `IntegralDomainWithoutDivision`. `NT` is required to be an `IntegralDomainWithoutDivision`.
@ -23,9 +23,9 @@ The result would be in \f$ \mathbb{Z}[\sqrt{a},\sqrt{b}]\f$, which is not
representable by `Sqrt_extension<Integer,Integer>`. representable by `Sqrt_extension<Integer,Integer>`.
\attention The user is responsible to check that arithmetic operations are carried out for elements from the same extensions only. \attention The user is responsible to check that arithmetic operations are carried out for elements from the same extensions only.
This is not tested by `Sqrt_extension` for efficiency reasons. This is not tested by `Sqrt_extension` for efficiency reasons.
A violation of the precondition leads to undefined behavior. A violation of the precondition leads to undefined behavior.
Be aware that for efficiency reasons the given \f$\mathrm{root}\f$ is stored as it is given to Be aware that for efficiency reasons the given \f$\mathrm{root}\f$ is stored as it is given to
the constructor. In particular, an extension by a square root of a square is the constructor. In particular, an extension by a square root of a square is
considered as an extension. considered as an extension.
@ -104,7 +104,7 @@ In case `NT` is not `RealEmbeddable`, `DifferentExtensionComparable` as well as
\sa \cgalTagFalse \sa \cgalTagFalse
*/ */
template< typename NT, typename ROOT, template< typename NT, typename Root,
typename DifferentExtensionComparable = Tag_false, typename DifferentExtensionComparable = Tag_false,
typename FilterPredicates = Tag_false> typename FilterPredicates = Tag_false>
class Sqrt_extension { class Sqrt_extension {
@ -148,7 +148,7 @@ Sqrt_extension (int a0, int a1, int r);
/*! /*!
General constructor: `ext`\f$ = a0 + a1 \cdot sqrt(r)\f$. \pre \f$ r \neq0\f$ General constructor: `ext`\f$ = a0 + a1 \cdot sqrt(r)\f$. \pre \f$ r \neq0\f$
*/ */
Sqrt_extension (NT a0, NT a1, ROOT r); Sqrt_extension (NT a0, NT a1, Root r);
/// @} /// @}
@ -172,10 +172,10 @@ const NT & a1 () const ;
/*! /*!
Const access operator for root Const access operator for root
*/ */
const ROOT & root () const; const Root & root () const;
/*! /*!
Returns true in case root of `ext` is not zero. Returns `true` in case root of `ext` is not zero.
Note that \f$ a1 == 0 \f$ does not imply \f$ \mathrm{root} == 0\f$. Note that \f$ a1 == 0 \f$ does not imply \f$ \mathrm{root} == 0\f$.
*/ */
@ -192,7 +192,7 @@ of `ext`. see also: `AlgebraicStructureTraits::Simplify`.
void simplify (); void simplify ();
/*! /*!
returns true if `ext` represents the value zero. returns `true` if `ext` represents the value zero.
*/ */
bool is_zero () const; bool is_zero () const;
@ -326,19 +326,19 @@ In case the mode is `CGAL::IO::ASCII` the format is `EXT[a0,a1,root]`.
In case the mode is `CGAL::IO::PRETTY` the format is human readable. In case the mode is `CGAL::IO::PRETTY` the format is human readable.
\attention `operator>>` must be defined for `ROOT` and `NT`. \attention `operator>>` must be defined for `Root` and `NT`.
\relates Sqrt_extension \relates Sqrt_extension
*/ */
std::ostream& operator<<(std::ostream& os, const Sqrt_extension<NT,ROOT> &ext); std::ostream& operator<<(std::ostream& os, const Sqrt_extension<NT,Root> &ext);
/*! /*!
reads `ext` from istream `is` in format `EXT[a0,a1,root]`, the output format in mode `CGAL::IO::ASCII` reads `ext` from istream `is` in format `EXT[a0,a1,root]`, the output format in mode `CGAL::IO::ASCII`
\attention `operator<<` must be defined exist for `ROOT` and `NT`. \attention `operator<<` must be defined exist for `Root` and `NT`.
\relates Sqrt_extension \relates Sqrt_extension
*/ */
std::istream& operator>>(std::istream& is, const Sqrt_extension<NT,ROOT> &ext); std::istream& operator>>(std::istream& is, const Sqrt_extension<NT,Root> &ext);
} /* end namespace CGAL */ } /* end namespace CGAL */