mirror of https://github.com/CGAL/cgal
fixed doxygen issue
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@ -4,17 +4,20 @@ namespace CGAL {
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/*!
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\ingroup PkgAlgebraicKerneldModels
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This class gathers necessary tools for solving and handling bivariate
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polynomial systems of general degree \f$ d\f$.
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This class is based on an algorithm computing a
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geometric-topological analysis of a single curve \cgalCite{ekw-fast-07} and of a
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pair of curves \cgalCite{ek-exact-08}.
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geometric-topological analysis of a single curve \cite ekw-fast-07 and of a
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pair of curves \cite ek-exact-08.
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The main idea behind both analyses is to compute the critical
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x-coordinates of curves and curve pairs by projection (resultants), and compute
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additional information about the critical fibers using subresultants
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and Sturm-Habicht sequences \cgalCite{grlr-sturm-habicht-98}.
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and Sturm-Habicht sequences \cite grlr-sturm-habicht-98.
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With that information, the fiber at
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critical x-coordinates is computed by a variant of the Bitstream
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Descartes method.
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See also \cgalCite{kerber-phd-09} for a comprehensive description of
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See also \cite kerber-phd-09 for a comprehensive description of
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these techniques.
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A point \f$ p\f$ of type `Algebraic_real_2` is represented
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@ -59,22 +62,22 @@ public:
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/// \name Types
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/// @{
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/*!
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/*!
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Same type as the template argument `Coeff`.
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*/
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typedef unspecified_type Coefficient;
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/*!
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/*!
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A model of `AlgebraicKernel_d_2::Polynomial_2`
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*/
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typedef unspecified_type Polynomial_2;
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/*!
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/*!
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A model of `AlgebraicKernel_d_2::AlgebraicReal_2`
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*/
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typedef unspecified_type Algebraic_real_2;
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/*!
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/*!
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The choice of `Coeff` also determines the provided bound, type.
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In case of `Coeff` is
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- `Gmpz` or `Gmpq` this is `Gmpq`
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@ -86,7 +89,7 @@ In case of `Coeff` is
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*/
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typedef unspecified_type Bound;
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/*!
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/*!
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The multiplicity type is `int`.
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*/
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typedef unspecified_type Multiplicity_type;
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