diff --git a/Algebraic_kernel_d/doc/Algebraic_kernel_d/CGAL/Algebraic_kernel_d_2.h b/Algebraic_kernel_d/doc/Algebraic_kernel_d/CGAL/Algebraic_kernel_d_2.h index 22ad1ea49a6..7f1e7a7d00d 100644 --- a/Algebraic_kernel_d/doc/Algebraic_kernel_d/CGAL/Algebraic_kernel_d_2.h +++ b/Algebraic_kernel_d/doc/Algebraic_kernel_d/CGAL/Algebraic_kernel_d_2.h @@ -4,17 +4,20 @@ namespace CGAL { /*! \ingroup PkgAlgebraicKerneldModels +This class gathers necessary tools for solving and handling bivariate +polynomial systems of general degree \f$ d\f$. + This class is based on an algorithm computing a -geometric-topological analysis of a single curve \cgalCite{ekw-fast-07} and of a -pair of curves \cgalCite{ek-exact-08}. +geometric-topological analysis of a single curve \cite ekw-fast-07 and of a +pair of curves \cite ek-exact-08. The main idea behind both analyses is to compute the critical x-coordinates of curves and curve pairs by projection (resultants), and compute additional information about the critical fibers using subresultants -and Sturm-Habicht sequences \cgalCite{grlr-sturm-habicht-98}. +and Sturm-Habicht sequences \cite grlr-sturm-habicht-98. With that information, the fiber at critical x-coordinates is computed by a variant of the Bitstream Descartes method. -See also \cgalCite{kerber-phd-09} for a comprehensive description of +See also \cite kerber-phd-09 for a comprehensive description of these techniques. A point \f$ p\f$ of type `Algebraic_real_2` is represented @@ -59,22 +62,22 @@ public: /// \name Types /// @{ -/*! +/*! Same type as the template argument `Coeff`. */ typedef unspecified_type Coefficient; -/*! +/*! A model of `AlgebraicKernel_d_2::Polynomial_2` */ typedef unspecified_type Polynomial_2; -/*! +/*! A model of `AlgebraicKernel_d_2::AlgebraicReal_2` */ typedef unspecified_type Algebraic_real_2; -/*! +/*! The choice of `Coeff` also determines the provided bound, type. In case of `Coeff` is - `Gmpz` or `Gmpq` this is `Gmpq` @@ -86,7 +89,7 @@ In case of `Coeff` is */ typedef unspecified_type Bound; -/*! +/*! The multiplicity type is `int`. */ typedef unspecified_type Multiplicity_type;