From 50b5cc984fec9550e7a5231420027fc80b39395d Mon Sep 17 00:00:00 2001 From: Michael Kerber Date: Thu, 19 Mar 2009 16:21:28 +0000 Subject: [PATCH] Updated doc --- ...olynomialTraits_d_PolynomialSubresultants.tex | 3 +++ ...ts_d_PolynomialSubresultantsWithCofactors.tex | 5 ++++- ...ialTraits_d_PrincipalSturmHabichtSequence.tex | 5 ++++- ...PolynomialTraits_d_PrincipalSubresultants.tex | 5 ++++- .../PolynomialTraits_d_SturmHabichtSequence.tex | 5 ++++- ...raits_d_SturmHabichtSequenceWithCofactors.tex | 5 ++++- .../doc_tex/Polynomial_ref/polynomial_utils.tex | 16 ++++++++-------- 7 files changed, 31 insertions(+), 13 deletions(-) diff --git a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PolynomialSubresultants.tex b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PolynomialSubresultants.tex index bd5ee163f15..d64c25a67db 100644 --- a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PolynomialSubresultants.tex +++ b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PolynomialSubresultants.tex @@ -1,4 +1,7 @@ \begin{ccRefConcept}{PolynomialTraits_d::PolynomialSubresultants} + +\textbf{Note:} This functor is optional! + \ccDefinition Computes the polynomial subresultant of two polynomials $p$ and $q$ of diff --git a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PolynomialSubresultantsWithCofactors.tex b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PolynomialSubresultantsWithCofactors.tex index c67f0ef0e89..856004e3c70 100644 --- a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PolynomialSubresultantsWithCofactors.tex +++ b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PolynomialSubresultantsWithCofactors.tex @@ -1,4 +1,7 @@ \begin{ccRefConcept}{PolynomialTraits_d::PolynomialSubresultantsWithCofactors} + +\textbf{Note:} This functor is optional! + \ccDefinition Computes the polynomial subresultant of two polynomials $p$ and $q$ of degree @@ -14,7 +17,7 @@ starting with the $0$th subresultant and the corresponding cofactors. A default implementation for the case that \ccc{Polynomial_traits_d::Coefficient_type} -is a model of \ccc{CGAL::Integral_division} +is a model of \ccc{CGAL::IntegralDomain} is provided by the function \ccc{CGAL::polynomial_subresultants_with_cofactors}. \ccCreationVariable{fo} diff --git a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PrincipalSturmHabichtSequence.tex b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PrincipalSturmHabichtSequence.tex index 16c3ad15bbd..cdcce94f47a 100644 --- a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PrincipalSturmHabichtSequence.tex +++ b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PrincipalSturmHabichtSequence.tex @@ -1,4 +1,7 @@ \begin{ccRefConcept}{PolynomialTraits_d::PrincipalSturmHabichtSequence} + +\textbf{Note:} This functor is optional! + \ccDefinition Computes the principal leading coefficients of the Sturm-Habicht sequence @@ -17,7 +20,7 @@ the polynomial~$f$. A default implementation for the case that \ccc{Polynomial_traits_d::Coefficient_type} -is a model of \ccc{CGAL::Integral_domain_without_division} +is a model of \ccc{CGAL::IntegralDomainWithoutDivision} is provided by the function \ccc{CGAL::principal_sturm_habicht_sequence}. \ccOperations diff --git a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PrincipalSubresultants.tex b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PrincipalSubresultants.tex index 4f7e3cfcf64..f83c3b48728 100644 --- a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PrincipalSubresultants.tex +++ b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PrincipalSubresultants.tex @@ -1,4 +1,7 @@ \begin{ccRefConcept}{PolynomialTraits_d::PrincipalSubresultants} + +\textbf{Note:} This functor is optional! + \ccDefinition Computes the principal subresultant of two polynomials $p$ and $q$ of @@ -17,7 +20,7 @@ $\mathrm{sres}_0(p,q)$ A default implementation for the case that \ccc{Polynomial_traits_d::Coefficient_type} -is a model of \ccc{CGAL::Integral_domain_without_division} +is a model of \ccc{CGAL::IntegralDomainWithoutDivision} is provided by the function \ccc{CGAL::principal_subresultants}. \ccOperations diff --git a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SturmHabichtSequence.tex b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SturmHabichtSequence.tex index dc0ef4a9b8c..e17ae03880e 100644 --- a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SturmHabichtSequence.tex +++ b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SturmHabichtSequence.tex @@ -1,4 +1,7 @@ \begin{ccRefConcept}{PolynomialTraits_d::SturmHabichtSequence} + +\textbf{Note:} This functor is optional! + \ccDefinition Computes the Sturm-Habicht sequence @@ -26,7 +29,7 @@ the discriminant of $f$ up to a multiple of the leading coefficient) A default implementation for the case that \ccc{Polynomial_traits_d::Coefficient_type} -is a model of \ccc{CGAL::Integral_domain_without_division} +is a model of \ccc{CGAL::IntegralDomainWithoutDivision} is provided by the function \ccc{CGAL::sturm_habicht_sequence}. \ccCreationVariable{fo} diff --git a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SturmHabichtSequenceWithCofactors.tex b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SturmHabichtSequenceWithCofactors.tex index d3f1fab6cb5..f1a04de010f 100644 --- a/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SturmHabichtSequenceWithCofactors.tex +++ b/Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SturmHabichtSequenceWithCofactors.tex @@ -1,4 +1,7 @@ \begin{ccRefConcept}{PolynomialTraits_d::SturmHabichtSequenceWithCofactors} + +\textbf{Note:} This functor is optional! + \ccDefinition Computes the Sturm-Habicht polynomials of a polynomial $f$ of degree $n$, @@ -14,7 +17,7 @@ and the corresponding cofactors. A default implementation for the case that \ccc{Polynomial_traits_d::Coefficient_type} -is a model of \ccc{CGAL::Integral_division} +is a model of \ccc{CGAL::IntegralDomain} is provided by the function \ccc{CGAL::sturm_habicht_sequence_with_cofactors}. Computes the Sturm-Habicht sequence of a polynomials $f$ of type diff --git a/Polynomial/doc_tex/Polynomial_ref/polynomial_utils.tex b/Polynomial/doc_tex/Polynomial_ref/polynomial_utils.tex index 06bf4d8595e..2204e092dcf 100644 --- a/Polynomial/doc_tex/Polynomial_ref/polynomial_utils.tex +++ b/Polynomial/doc_tex/Polynomial_ref/polynomial_utils.tex @@ -811,15 +811,15 @@ Computes the polynomial subresultants of two polynomials, defined as in the concept \ccc{Polynomial_traits_d::PolynomialSubresultants}, if \ccc{PolynomialTraits_d::Coefficient_type} -is at least a model of \ccc{CGAL::Integral_domain_without_division}. +is at least a model of \ccc{CGAL::IntegralDomainWithoutDivision}. The computation method depends on the algebraic category of \ccc{PolynomialTraits_d::Coefficient_type}. -if it models \ccc{CGAL::Integral_division}, +if it models \ccc{CGAL::IntegralDomain}, the subresultants are computed by a pseudo-division approach~\cite{ducos-optimizations}. If they only model a -\ccc{CGAL::Integral_domain_without_division}, the subresultants +\ccc{CGAL::IntegralDomainWithoutDivision}, the subresultants are computed by evaluating the determinants directly, avoiding divisions completely~\cite{kerber-division}. @@ -846,7 +846,7 @@ Computes the polynomial subresultants of two polynomials and their cofactors, defined as in the concept \ccc{Polynomial_traits_d::PolynomialSubresultantsWithCofactors}, if \ccc{PolynomialTraits_d::Coefficient_type} -is at least a model of \ccc{CGAL::Integral_division}. +is at least a model of \ccc{CGAL::IntegralDomain}. \ccOperations \ccFunction{template @@ -904,7 +904,7 @@ Computes the Sturm-Habicht-polynomials of a polynomial, defined as in the concept \ccc{Polynomial_traits_d::SturmHabichtSequence}, if \ccc{PolynomialTraits_d::Coefficient_type} -is at least a model of \ccc{CGAL::Integral_domain_without_division}. +is at least a model of \ccc{CGAL::IntegralDomainWithoutDivision}. The computation works simply by calling \ccc{CGAL::polynomial_subresultants}, and adjusting the signs. @@ -931,7 +931,7 @@ Computes the Sturm-Habicht-sequence of a polynomial and its cofactors, defined as in the concept \ccc{Polynomial_traits_d::SturmHabichtSequenceWithCofactors}, if \ccc{PolynomialTraits_d::Coefficient_type} -is at least a model of \ccc{CGAL::Integral_division}. +is at least a model of \ccc{CGAL::IntegralDomain}. \ccOperations \ccFunction{template inline