diff --git a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PolynomialSubresultants.h b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PolynomialSubresultants.h index 87cdc87ecc6..026c76a8848 100644 --- a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PolynomialSubresultants.h +++ b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PolynomialSubresultants.h @@ -3,8 +3,6 @@ \ingroup PkgPolynomialConcepts \cgalConcept -Note: This functor is optional! - Computes the polynomial subresultant of two polynomials \f$ p\f$ and \f$ q\f$ of type `PolynomialTraits_d::Polynomial_d` with respect to outermost variable. Let @@ -23,6 +21,8 @@ The result is written in an output range, starting with the \f$ 0\f$-th subresul \f$ \mathrm{Sres}_0(p,q)\f$ (aka as the resultant of \f$ p\f$ and \f$ q\f$). +\note This functor is optional. + \cgalRefines `AdaptableBinaryFunction` \cgalRefines `CopyConstructible` \cgalRefines `DefaultConstructible` diff --git a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PolynomialSubresultantsWithCofactors.h b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PolynomialSubresultantsWithCofactors.h index b1981463df7..56c1e14f641 100644 --- a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PolynomialSubresultantsWithCofactors.h +++ b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PolynomialSubresultantsWithCofactors.h @@ -3,8 +3,6 @@ \ingroup PkgPolynomialConcepts \cgalConcept -Note: This functor is optional! - Computes the polynomial subresultant of two polynomials \f$ p\f$ and \f$ q\f$ of degree \f$ n\f$ and \f$ m\f$, respectively, as defined in the documentation of `PolynomialTraits_d::PolynomialSubresultants`. @@ -16,6 +14,8 @@ the cofactors of \f$ \mathrm{Sres}_i(p,q)\f$. The result is written in three output ranges, each of length \f$ \min\{n,m\}+1\f$, starting with the \f$ 0\f$-th subresultant and the corresponding cofactors. +\note This functor is optional. + \cgalRefines `AdaptableBinaryFunction` \cgalRefines `CopyConstructible` \cgalRefines `DefaultConstructible` diff --git a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PrincipalSturmHabichtSequence.h b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PrincipalSturmHabichtSequence.h index bd4bd491935..376a3e279ef 100644 --- a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PrincipalSturmHabichtSequence.h +++ b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PrincipalSturmHabichtSequence.h @@ -3,8 +3,6 @@ \ingroup PkgPolynomialConcepts \cgalConcept -Note: This functor is optional! - Computes the principal leading coefficients of the Sturm-Habicht sequence of a polynomials \f$ f\f$ of type `PolynomialTraits_d::Polynomial_d` with respect a certain variable \f$ x_i\f$. @@ -19,6 +17,8 @@ In case that `PolynomialTraits_d::Coefficient_type` is `RealEmbeddable`, the fun on the resulting sequence to count the number of distinct real roots of the polynomial \f$ f\f$. +\note This functor is optional. + \cgalRefines `AdaptableBinaryFunction` \cgalRefines `CopyConstructible` \cgalRefines `DefaultConstructible` diff --git a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PrincipalSubresultants.h b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PrincipalSubresultants.h index 2cddb81e1ed..3a63bc6f76d 100644 --- a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PrincipalSubresultants.h +++ b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--PrincipalSubresultants.h @@ -3,8 +3,6 @@ \ingroup PkgPolynomialConcepts \cgalConcept -Note: This functor is optional! - Computes the principal subresultant of two polynomials \f$ p\f$ and \f$ q\f$ of type `PolynomialTraits_d::Coefficient_type` with respect to the outermost variable. @@ -19,6 +17,8 @@ principal subresultant \f$ \mathrm{sres}_0(p,q)\f$ ,aka as the resultant of \f$ p\f$ and \f$ q\f$. (Note that \f$ \mathrm{sres}_0(p,q)=\mathrm{Sres}_0(p,q)\f$ by definition) +\note This functor is optional. + \cgalRefines `AdaptableBinaryFunction` \cgalRefines `CopyConstructible` \cgalRefines `DefaultConstructible` diff --git a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--SturmHabichtSequence.h b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--SturmHabichtSequence.h index f6a4676dfc3..32478346def 100644 --- a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--SturmHabichtSequence.h +++ b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--SturmHabichtSequence.h @@ -3,8 +3,6 @@ \ingroup PkgPolynomialConcepts \cgalConcept -Note: This functor is optional! - Computes the Sturm-Habicht sequence (aka the signed subresultant sequence) of a polynomial \f$ f\f$ of type @@ -27,6 +25,8 @@ The result is written in an output range, starting with the \f$ 0\f$-th Sturm-Habicht polynomial (which is equal to the discriminant of \f$ f\f$ up to a multiple of the leading coefficient). +\note This functor is optional. + \cgalRefines `AdaptableBinaryFunction` \cgalRefines `CopyConstructible` \cgalRefines `DefaultConstructible` diff --git a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--SturmHabichtSequenceWithCofactors.h b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--SturmHabichtSequenceWithCofactors.h index e77f9b78cd2..85efdb9edf9 100644 --- a/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--SturmHabichtSequenceWithCofactors.h +++ b/Polynomial/doc/Polynomial/Concepts/PolynomialTraits_d--SturmHabichtSequenceWithCofactors.h @@ -3,8 +3,6 @@ \ingroup PkgPolynomialConcepts \cgalConcept -Note: This functor is optional! - Computes the Sturm-Habicht polynomials of a polynomial \f$ f\f$ of degree \f$ n\f$, as defined in the documentation of `PolynomialTraits_d::SturmHabichtSequence`. Moreover, for \f$ \mathrm{Stha}_i(f)\f$, polynomials \f$ u_i\f$ and \f$ v_i\f$ @@ -16,6 +14,8 @@ The result is written in three output ranges, each of length \f$ \min\{n,m\}+1\f starting with the \f$ 0\f$-th Sturm-Habicht polynomial \f$ \mathrm{Stha_0(f)}\f$ and the corresponding cofactors. +\note This functor is optional. + \cgalRefines `AdaptableBinaryFunction` \cgalRefines `CopyConstructible` \cgalRefines `DefaultConstructible`