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Updated doc

This commit is contained in:
Michael Kerber 2009-03-19 16:21:28 +00:00
parent b040a513e9
commit 50b5cc984f
7 changed files with 31 additions and 13 deletions
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3
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PolynomialSubresultants.tex
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@ -1,4 +1,7 @@
\begin{ccRefConcept}{PolynomialTraits_d::PolynomialSubresultants} \begin{ccRefConcept}{PolynomialTraits_d::PolynomialSubresultants}
\textbf{Note:} This functor is optional!
\ccDefinition \ccDefinition
Computes the polynomial subresultant of two polynomials $p$ and $q$ of Computes the polynomial subresultant of two polynomials $p$ and $q$ of

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Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PolynomialSubresultantsWithCofactors.tex
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@ -1,4 +1,7 @@
\begin{ccRefConcept}{PolynomialTraits_d::PolynomialSubresultantsWithCofactors} \begin{ccRefConcept}{PolynomialTraits_d::PolynomialSubresultantsWithCofactors}
\textbf{Note:} This functor is optional!
\ccDefinition \ccDefinition
Computes the polynomial subresultant of two polynomials $p$ and $q$ of degree 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 A default implementation for the case that
\ccc{Polynomial_traits_d::Coefficient_type} \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}. is provided by the function \ccc{CGAL::polynomial_subresultants_with_cofactors}.
\ccCreationVariable{fo} \ccCreationVariable{fo}

5
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PrincipalSturmHabichtSequence.tex
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@ -1,4 +1,7 @@
\begin{ccRefConcept}{PolynomialTraits_d::PrincipalSturmHabichtSequence} \begin{ccRefConcept}{PolynomialTraits_d::PrincipalSturmHabichtSequence}
\textbf{Note:} This functor is optional!
\ccDefinition \ccDefinition
Computes the principal leading coefficients of the Sturm-Habicht sequence Computes the principal leading coefficients of the Sturm-Habicht sequence
@ -17,7 +20,7 @@ the polynomial~$f$.
A default implementation for the case that A default implementation for the case that
\ccc{Polynomial_traits_d::Coefficient_type} \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}. is provided by the function \ccc{CGAL::principal_sturm_habicht_sequence}.
\ccOperations \ccOperations

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Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PrincipalSubresultants.tex
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@ -1,4 +1,7 @@
\begin{ccRefConcept}{PolynomialTraits_d::PrincipalSubresultants} \begin{ccRefConcept}{PolynomialTraits_d::PrincipalSubresultants}
\textbf{Note:} This functor is optional!
\ccDefinition \ccDefinition
Computes the principal subresultant of two polynomials $p$ and $q$ of 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 A default implementation for the case that
\ccc{Polynomial_traits_d::Coefficient_type} \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}. is provided by the function \ccc{CGAL::principal_subresultants}.
\ccOperations \ccOperations

5
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SturmHabichtSequence.tex
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@ -1,4 +1,7 @@
\begin{ccRefConcept}{PolynomialTraits_d::SturmHabichtSequence} \begin{ccRefConcept}{PolynomialTraits_d::SturmHabichtSequence}
\textbf{Note:} This functor is optional!
\ccDefinition \ccDefinition
Computes the Sturm-Habicht sequence 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 A default implementation for the case that
\ccc{Polynomial_traits_d::Coefficient_type} \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}. is provided by the function \ccc{CGAL::sturm_habicht_sequence}.
\ccCreationVariable{fo} \ccCreationVariable{fo}

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Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SturmHabichtSequenceWithCofactors.tex
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@ -1,4 +1,7 @@
\begin{ccRefConcept}{PolynomialTraits_d::SturmHabichtSequenceWithCofactors} \begin{ccRefConcept}{PolynomialTraits_d::SturmHabichtSequenceWithCofactors}
\textbf{Note:} This functor is optional!
\ccDefinition \ccDefinition
Computes the Sturm-Habicht polynomials of a polynomial $f$ of degree $n$, 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 A default implementation for the case that
\ccc{Polynomial_traits_d::Coefficient_type} \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}. is provided by the function \ccc{CGAL::sturm_habicht_sequence_with_cofactors}.
Computes the Sturm-Habicht sequence of a polynomials $f$ of type Computes the Sturm-Habicht sequence of a polynomials $f$ of type

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Polynomial/doc_tex/Polynomial_ref/polynomial_utils.tex
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@ -811,15 +811,15 @@ Computes the polynomial subresultants
of two polynomials, defined as in the concept of two polynomials, defined as in the concept
\ccc{Polynomial_traits_d::PolynomialSubresultants}, \ccc{Polynomial_traits_d::PolynomialSubresultants},
if \ccc{PolynomialTraits_d::Coefficient_type} 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 The computation method depends on the algebraic category of
\ccc{PolynomialTraits_d::Coefficient_type}. \ccc{PolynomialTraits_d::Coefficient_type}.
if it models \ccc{CGAL::Integral_division}, if it models \ccc{CGAL::IntegralDomain},
the subresultants are computed the subresultants are computed
by a pseudo-division approach~\cite{ducos-optimizations}. by a pseudo-division approach~\cite{ducos-optimizations}.
If they only model a 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 are computed by evaluating the determinants directly, avoiding divisions
completely~\cite{kerber-division}. completely~\cite{kerber-division}.
@ -846,7 +846,7 @@ Computes the polynomial subresultants
of two polynomials and their cofactors, defined as in the concept of two polynomials and their cofactors, defined as in the concept
\ccc{Polynomial_traits_d::PolynomialSubresultantsWithCofactors}, \ccc{Polynomial_traits_d::PolynomialSubresultantsWithCofactors},
if \ccc{PolynomialTraits_d::Coefficient_type} 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 \ccOperations
\ccFunction{template<typename Polynomial_traits_d, \ccFunction{template<typename Polynomial_traits_d,
@ -879,7 +879,7 @@ Computes the principal subresultants
of two polynomials, defined as in the concept of two polynomials, defined as in the concept
\ccc{Polynomial_traits_d::PrincipalSubresultants}, \ccc{Polynomial_traits_d::PrincipalSubresultants},
if \ccc{PolynomialTraits_d::Coefficient_type} 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}.
\ccOperations \ccOperations
\ccFunction{template<typename Polynomial_traits_d,typename OutputIterator> \ccFunction{template<typename Polynomial_traits_d,typename OutputIterator>
@ -904,7 +904,7 @@ Computes the Sturm-Habicht-polynomials
of a polynomial, defined as in the concept of a polynomial, defined as in the concept
\ccc{Polynomial_traits_d::SturmHabichtSequence}, \ccc{Polynomial_traits_d::SturmHabichtSequence},
if \ccc{PolynomialTraits_d::Coefficient_type} 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}, The computation works simply by calling \ccc{CGAL::polynomial_subresultants},
and adjusting the signs. and adjusting the signs.
@ -931,7 +931,7 @@ Computes the Sturm-Habicht-sequence of a polynomial
and its cofactors, defined as in the concept and its cofactors, defined as in the concept
\ccc{Polynomial_traits_d::SturmHabichtSequenceWithCofactors}, \ccc{Polynomial_traits_d::SturmHabichtSequenceWithCofactors},
if \ccc{PolynomialTraits_d::Coefficient_type} 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 \ccOperations
\ccFunction{template<typename Polynomial_traits_d, \ccFunction{template<typename Polynomial_traits_d,
@ -964,7 +964,7 @@ Computes the principal Sturm-Habicht coefficients
of a polynomial, defined as in the concept of a polynomial, defined as in the concept
\ccc{Polynomial_traits_d::PrincipalSturmHabichtSequence}, \ccc{Polynomial_traits_d::PrincipalSturmHabichtSequence},
if \ccc{PolynomialTraits_d::Coefficient_type} 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}.
\ccOperations \ccOperations
\ccFunction{ template <typename Polynomial_traits_d,typename OutputIterator> inline \ccFunction{ template <typename Polynomial_traits_d,typename OutputIterator> inline