mirror of https://github.com/CGAL/cgal
move note outside the brief
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\ingroup PkgPolynomialConcepts
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\ingroup PkgPolynomialConcepts
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\cgalConcept
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\cgalConcept
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<B>Note:</B> This functor is optional!
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Computes the polynomial subresultant of two polynomials \f$ p\f$ and \f$ q\f$ of
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Computes the polynomial subresultant of two polynomials \f$ p\f$ and \f$ q\f$ of
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type `PolynomialTraits_d::Polynomial_d` with respect to outermost variable.
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type `PolynomialTraits_d::Polynomial_d` with respect to outermost variable.
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Let
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Let
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@ -23,6 +21,8 @@ The result is written in an output range, starting with the \f$ 0\f$-th subresul
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\f$ \mathrm{Sres}_0(p,q)\f$
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\f$ \mathrm{Sres}_0(p,q)\f$
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(aka as the resultant of \f$ p\f$ and \f$ q\f$).
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(aka as the resultant of \f$ p\f$ and \f$ q\f$).
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\note This functor is optional.
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `CopyConstructible`
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\cgalRefines `CopyConstructible`
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\cgalRefines `DefaultConstructible`
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\cgalRefines `DefaultConstructible`
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\ingroup PkgPolynomialConcepts
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\ingroup PkgPolynomialConcepts
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\cgalConcept
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\cgalConcept
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<B>Note:</B> This functor is optional!
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Computes the polynomial subresultant of two polynomials \f$ p\f$ and \f$ q\f$ of degree
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Computes the polynomial subresultant of two polynomials \f$ p\f$ and \f$ q\f$ of degree
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\f$ n\f$ and \f$ m\f$, respectively,
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\f$ n\f$ and \f$ m\f$, respectively,
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as defined in the documentation of `PolynomialTraits_d::PolynomialSubresultants`.
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as defined in the documentation of `PolynomialTraits_d::PolynomialSubresultants`.
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@ -16,6 +14,8 @@ the <I>cofactors</I> of \f$ \mathrm{Sres}_i(p,q)\f$.
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The result is written in three output ranges, each of length \f$ \min\{n,m\}+1\f$,
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The result is written in three output ranges, each of length \f$ \min\{n,m\}+1\f$,
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starting with the \f$ 0\f$-th subresultant and the corresponding cofactors.
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starting with the \f$ 0\f$-th subresultant and the corresponding cofactors.
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\note This functor is optional.
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `CopyConstructible`
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\cgalRefines `CopyConstructible`
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\cgalRefines `DefaultConstructible`
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\cgalRefines `DefaultConstructible`
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\ingroup PkgPolynomialConcepts
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\ingroup PkgPolynomialConcepts
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\cgalConcept
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\cgalConcept
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<B>Note:</B> This functor is optional!
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Computes the principal leading coefficients of the Sturm-Habicht sequence
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Computes the principal leading coefficients of the Sturm-Habicht sequence
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of a polynomials \f$ f\f$ of type `PolynomialTraits_d::Polynomial_d`
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of a polynomials \f$ f\f$ of type `PolynomialTraits_d::Polynomial_d`
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with respect a certain variable \f$ x_i\f$.
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with respect a certain variable \f$ x_i\f$.
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on the resulting sequence to count the number of distinct real roots of
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on the resulting sequence to count the number of distinct real roots of
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the polynomial \f$ f\f$.
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the polynomial \f$ f\f$.
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\note This functor is optional.
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `CopyConstructible`
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\cgalRefines `CopyConstructible`
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\cgalRefines `DefaultConstructible`
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\cgalRefines `DefaultConstructible`
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\ingroup PkgPolynomialConcepts
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\ingroup PkgPolynomialConcepts
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\cgalConcept
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\cgalConcept
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<B>Note:</B> This functor is optional!
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Computes the principal subresultant of two polynomials \f$ p\f$ and \f$ q\f$ of
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Computes the principal subresultant of two polynomials \f$ p\f$ and \f$ q\f$ of
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type `PolynomialTraits_d::Coefficient_type`
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type `PolynomialTraits_d::Coefficient_type`
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with respect to the outermost variable.
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with respect to the outermost variable.
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@ -19,6 +17,8 @@ principal subresultant \f$ \mathrm{sres}_0(p,q)\f$
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,aka as the resultant of \f$ p\f$ and \f$ q\f$.
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,aka as the resultant of \f$ p\f$ and \f$ q\f$.
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(Note that \f$ \mathrm{sres}_0(p,q)=\mathrm{Sres}_0(p,q)\f$ by definition)
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(Note that \f$ \mathrm{sres}_0(p,q)=\mathrm{Sres}_0(p,q)\f$ by definition)
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\note This functor is optional.
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `CopyConstructible`
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\cgalRefines `CopyConstructible`
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\cgalRefines `DefaultConstructible`
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\cgalRefines `DefaultConstructible`
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\ingroup PkgPolynomialConcepts
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\ingroup PkgPolynomialConcepts
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\cgalConcept
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\cgalConcept
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<B>Note:</B> This functor is optional!
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Computes the Sturm-Habicht sequence
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Computes the Sturm-Habicht sequence
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(aka the signed subresultant sequence)
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(aka the signed subresultant sequence)
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of a polynomial \f$ f\f$ of type
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of a polynomial \f$ f\f$ of type
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starting with the \f$ 0\f$-th Sturm-Habicht polynomial (which is equal to
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starting with the \f$ 0\f$-th Sturm-Habicht polynomial (which is equal to
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the discriminant of \f$ f\f$ up to a multiple of the leading coefficient).
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the discriminant of \f$ f\f$ up to a multiple of the leading coefficient).
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\note This functor is optional.
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `CopyConstructible`
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\cgalRefines `CopyConstructible`
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\cgalRefines `DefaultConstructible`
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\cgalRefines `DefaultConstructible`
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\ingroup PkgPolynomialConcepts
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\ingroup PkgPolynomialConcepts
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\cgalConcept
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\cgalConcept
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<B>Note:</B> This functor is optional!
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Computes the Sturm-Habicht polynomials of a polynomial \f$ f\f$ of degree \f$ n\f$,
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Computes the Sturm-Habicht polynomials of a polynomial \f$ f\f$ of degree \f$ n\f$,
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as defined in the documentation of `PolynomialTraits_d::SturmHabichtSequence`.
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as defined in the documentation of `PolynomialTraits_d::SturmHabichtSequence`.
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Moreover, for \f$ \mathrm{Stha}_i(f)\f$, polynomials \f$ u_i\f$ and \f$ v_i\f$
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Moreover, for \f$ \mathrm{Stha}_i(f)\f$, polynomials \f$ u_i\f$ and \f$ v_i\f$
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starting with the \f$ 0\f$-th Sturm-Habicht polynomial \f$ \mathrm{Stha_0(f)}\f$
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starting with the \f$ 0\f$-th Sturm-Habicht polynomial \f$ \mathrm{Stha_0(f)}\f$
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and the corresponding cofactors.
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and the corresponding cofactors.
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\note This functor is optional.
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `AdaptableBinaryFunction`
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\cgalRefines `CopyConstructible`
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\cgalRefines `CopyConstructible`
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\cgalRefines `DefaultConstructible`
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\cgalRefines `DefaultConstructible`
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