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general improvements typos/layout/consistency 

use 'fo' as creation variable
This commit is contained in:
Michael Hemmer 2008-09-18 11:45:29 +00:00
parent 5a0a179939
commit 09efa13296
45 changed files with 111 additions and 100 deletions
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2
Polynomial/doc_tex/Polynomial_ref/Exponent_vector.tex
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@ -39,7 +39,7 @@ to the last/outermost variable of a multivariate polynomial.
\ccc{LessThanComparable}\\
\ccCreation
\ccCreationVariable{ev}
\ccCreationVariable{fo}
%\ccc{DefaultConstructible}\\
\ccConstructor{Exponent_vector();}

2
Polynomial/doc_tex/Polynomial_ref/Polynomial.tex
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@ -85,7 +85,7 @@ the zero polynomial is represented by a single zero coefficient.
\ccCreation
\ccCreationVariable{poly}
\ccCreationVariable{fo}
\ccConstructor{Polynomial ();}
{Introduces an variable initialized with 0.}
\ccGlue

8
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d.tex
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@ -152,11 +152,11 @@ is not a model of \ccc{UniqueFactorizationDomain}, this is of type \ccc{CGAL::Nu
%pseudo division
\ccNestedType{Pseudo_division }
{ A model of \ccc{PolynomialTraits_d::Pseudo_division}.}\ccGlue
{ A model of \ccc{PolynomialTraits_d::PseudoDivision}.}\ccGlue
\ccNestedType{Pseudo_division_remainder}
{ A model of \ccc{PolynomialTraits_d::Pseudo_division_remainder}.}\ccGlue
{ A model of \ccc{PolynomialTraits_d::PseudoDivisionRemainder}.}\ccGlue
\ccNestedType{Pseudo_division_quotient }
{ A model of \ccc{PolynomialTraits_d::Pseudo_division_quotient}.}
{ A model of \ccc{PolynomialTraits_d::PseudoDivisionQuotient}.}
%utcf
@ -167,7 +167,7 @@ is not a model of \ccc{UniqueFactorizationDomain}, this is of type \ccc{CGAL::Nu
{ A model of \ccc{PolynomialTraits_d::IntegralDivisionUpToConstantFactor}.}
\ccGlue
\ccNestedType{Content_up_to_constant_factor}
{ A model of \ccc{PolynomialTraits_d::ContentUpToConstantFactor}.}
{ A model of \ccc{PolynomialTraits_d::UnivariateContentUpToConstantFactor}.}
\ccGlue
\ccNestedType{Square_free_factorize_up_to_constant_factor}
{ A model of \ccc{PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor}.}

9
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Canonicalize.tex
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@ -3,8 +3,8 @@
\ccDefinition
This \ccc{AdaptableUnaryFunction} computes a unique representative from the set:
$\{ q | \lambda * q = p with \lambda \in R \}$, where $p$ is the given polynomial and
$R$ the base of the polynomial ring.
$\{ q | \lambda * q = p\ for\ some\ \lambda \in R \}$,
where $p$ is the given polynomial and $R$ the base of the polynomial ring.
In particular, the computed polynomial has the same zero set as the given one.
In case \ccc{PolynomialTraits::Innermost_coefficient_type} is a model of \ccc{Field},
@ -30,8 +30,9 @@ For all other cases the notion of uniqueness is up to the concrete model.
\ccOperations
\ccCreationVariable{canonicalize}
\ccMethod{result_type operator()(first_argument_type f);}{}
\ccCreationVariable{fo}
\ccMethod{result_type operator()(first_argument_type p);}{
Returns the cononical representative of $p$.}

4
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Compare.tex
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@ -15,7 +15,7 @@ This functor is well defined if \ccc{PolynomialTraits_d::Innermost_coefficient_t
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{compare}
\ccCreationVariable{fo}
\ccTypedef{typedef CGAL::Comparison_result result_type;}{}
\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type;}{}
@ -24,7 +24,7 @@ This functor is well defined if \ccc{PolynomialTraits_d::Innermost_coefficient_t
\ccOperations
\ccCreationVariable{compare}
\ccCreationVariable{fo}
\ccMethod{result_type operator()(first_argument_type f,
second_argument_type g);}
{Compare two polynomials.}

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_ConstructPolynomial.tex
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@ -13,7 +13,7 @@ to construct objects of type \ccc{PolynomialTraits_d::Polynomial_d}.
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxx}{xxxxxxxxxxx}{}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}
\ccCreationVariable{construct_polynomial}
\ccCreationVariable{fo}
\ccOperations
\ccMethod{result_type operator()();}
{Construct the zero polynomial.}

4
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Degree.tex
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@ -11,7 +11,7 @@ $p$ is not zero.\\
For instance the total degree of $p = x_0^2x_1^3+x_1^4$ with respect to $x_1$ is $4$.
The degree of the zero polynomial is set to $0$. From the mathematical point of view this should
be $-inf$, but this would imply an inconvenient return type.
be $-infinity$, but this would imply an inconvenient return type.
@ -23,7 +23,7 @@ be $-inf$, but this would imply an inconvenient return type.
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{degree}
\ccCreationVariable{fo}
\ccTypedef{typedef int result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_DegreeVector.tex
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@ -14,7 +14,7 @@ the innermost leading coefficient of a
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{degree_vector}
\ccCreationVariable{fo}
\ccTypedef{typedef Exponent_vector result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}

4
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Differentiate.tex
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@ -10,7 +10,7 @@ This \ccc{AdaptableUnaryFunction} computes the derivative of a
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{differentiate}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}
\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}
@ -29,5 +29,5 @@ This \ccc{AdaptableUnaryFunction} computes the derivative of a
\ccSeeAlso
\ccRefIdfierPage{Polynomial_d}\\
\ccRefIdfierPage{PolynomialTraits_d}
\ccRefIdfierPage{PolynomialTraits_d}\\
\end{ccRefConcept}

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Evaluate.tex
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@ -10,7 +10,7 @@ This \ccc{AdaptableBinaryFunction} evaluates
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{evaluate}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Coefficient_type result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Coefficient_type second_argument_type;}{}

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_EvaluateHomogeneous.tex
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@ -13,7 +13,7 @@ $p(u,v) = u^3 + uv^2$ and evaluated as such.
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{evaluate_homogeneous}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Coefficient_type result_type;}{}
\ccOperations

4
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_GcdUpToConstantFactor.tex
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@ -14,7 +14,7 @@ domain one can consider its quotient field $Q(R)$ for which $gcd$s of
polynomials exist.
This functor computes $gcd\_utcf(f,g) = D * gcd(f,g)$,
for some $D \in R$ such that $gcd\_utcf(f,g) \in R[x_0,\dots,x_{d-1}]$.\\
for some $D \in R$ such that $gcd\_utcf(f,g) \in R[x_0,\dots,x_{d-1}]$.
Hence, $gcd\_utcf(f,g)$ may not be a divisor of $f$ and $g$ in $R[x_0,\dots,x_{d-1}]$.
\ccRefines
@ -25,7 +25,7 @@ Hence, $gcd\_utcf(f,g)$ may not be a divisor of $f$ and $g$ in $R[x_0,\dots,x_{d
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{gcd_utcf}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d second_argument_type;}{}

8
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_GetCoefficient.tex
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@ -15,18 +15,18 @@ This \ccc{AdaptableBinaryFunction} provides access to coefficients of a
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type ;}{}
\ccTypedef{typedef int second_argument_type;}{}
\ccCreationVariable{get_coefficient}
\ccCreationVariable{fo}
\ccOperations
\ccMethod{result_type operator()( first_argument_type p,
second_argument_type e);}{
Returns coefficient of $x_{d-1}^e$ by value,
where $x_{d-1}$ is the outermost variable.}
For given polynomial $p$ this operator returns the coefficient
of $x_{d-1}^e$ by value, where $x_{d-1}$ is the outermost variable.}
\ccMethod{result_type operator()( first_argument_type p,
second_argument_type e,
int i);}{
Returns coefficient of $x_{i}^e$ by value.
For given polynomial $p$ this operator returns coefficient of $x_{i}^e$ by value.
}
%\ccHasModels

5
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_GetInnermostCoefficient.tex
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@ -18,12 +18,13 @@ the (multivariate) monomial specified by the given \ccc{Exponent_vector}.
\ccGlue
\ccTypedef{typedef Exponent_vector second_argument_type;}{}
\ccCreationVariable{get_innermost_coefficient}
\ccCreationVariable{fo}
\ccOperations
\ccMethod{result_type operator()( first_argument_type p,
second_argument_type v);}{
Returns the innermost coefficient of the monomial defined by the given \ccc{Exponent_vector} $v$. }
For given polynomial $p$ this operator returns the innermost coefficient of the
monomial corresponding to the given \ccc{Exponent_vector} $v$. }
%\ccHasModels

4
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_InnermostLeadingCoefficient.tex
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@ -3,13 +3,13 @@
\ccDefinition
This \ccc{AdaptableUnaryFunction} computes the innermost leading coefficient
of a \ccc{PolynomialTraits_d::Polynomial_d}. The innermost leading coefficient is recursively defined as the innermost leading coefficient of the leading coefficient of $p$. In case $p$ is univariate it coincides with the leading coefficient.
of a \ccc{PolynomialTraits_d::Polynomial_d} $p$. The innermost leading coefficient is recursively defined as the innermost leading coefficient of the leading coefficient of $p$. In case $p$ is univariate it coincides with the leading coefficient.
\ccRefines
\ccc{AdaptableUnaryFunction}
\ccTypes
\ccCreationVariable{innermost_leading_coefficient}
\ccCreationVariable{fo}
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccTypedef{typedef PolynomialTraits_d::Innermost_coefficient_type result_type;}{}
\ccGlue

4
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_IntegralDivisionUpToConstantFactor.tex
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@ -18,7 +18,7 @@ field of the base ring $R$, \ccc{PolynomialTraits_d::Innermost_coefficient_type}
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{integral_division_utcf}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d second_argument_type;}{}
@ -27,7 +27,7 @@ field of the base ring $R$, \ccc{PolynomialTraits_d::Innermost_coefficient_type}
\ccMethod{result_type operator()(first_argument_type f,
second_argument_type g);}
{return a denominator-free, constant multiple of $f/g$}
{Returns a denominator-free, constant multiple of $f/g$.}

5
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Invert.tex
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@ -18,7 +18,7 @@ order of the coefficients with respect to the specified variable.
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{invert}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}
@ -36,5 +36,6 @@ order of the coefficients with respect to the specified variable.
\ccSeeAlso
\ccRefIdfierPage{Polynomial_d}\\
\ccRefIdfierPage{PolynomialTraits_d}
\ccRefIdfierPage{PolynomialTraits_d}\\
\end{ccRefConcept}

4
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_IsZeroAt.tex
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@ -11,7 +11,7 @@ which is represented as an iterator range.
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{is_zero_at}
\ccCreationVariable{fo}
\ccTypedef{typedef bool result_type;}{}\ccGlue
\ccOperations
@ -22,7 +22,7 @@ result_type operator()(PolynomialTraits_d::Polynomial_d p,
InputIterator end );}{
Computes whether $p$ is zero at the Cartesian point given by the iterator range,
where $begin$ is referring to the innermost variable.
\ccPrecond (end-begin == \ccc{PolynomialTraits_d::d})
\ccPrecond{(end-begin == \ccc{PolynomialTraits_d::d})}
}
%\ccHasModels

7
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_IsZeroAtHomogeneous.tex
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@ -15,19 +15,20 @@ polynomial $p(x_0,x_1,w) = x_0^2x_1^3+x_1^4w^1$.
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{is_zero_at_homogeneous}
\ccCreationVariable{fo}
\ccTypedef{typedef bool result_type;}{}\ccGlue
\ccOperations
\ccMethod{
template <class InputIterator>
\ccMethod{result_type operator()(PolynomialTraits_d::Polynomial_d p,
result_type operator()(PolynomialTraits_d::Polynomial_d p,
InputIterator begin,
InputIterator end );}{
Computes whether $p$ is zero at the homogeneous point given by the iterator range,
where $begin$ is referring to the innermost variable.
\ccPrecond{\ccc{std::iterator_traits< InputIterator >::value_type} is
\ccc{PolynomialTraits_d::Innermost_coefficient_type}.}
\ccPrecond
\ccPrecond{(end-begin == \ccc{PolynomialTraits_d::d}+1)}
}
%\ccHasModels

4
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_LeadingCoefficient.tex
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@ -6,11 +6,11 @@ This \ccc{AdaptableBinaryFunction} computes the leading coefficient
of a \ccc{PolynomialTraits_d::Polynomial_d}.
\ccRefines
\ccc{AdaptableBinaryFunction}
\ccc{AdaptableUnaryFunction}
\ccTypes
\ccCreationVariable{leading_coefficient}
\ccCreationVariable{fo}
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccTypedef{typedef PolynomialTraits_d::Coefficient_type result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}\ccGlue

9
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_MakeSquareFree.tex
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@ -13,19 +13,19 @@ Given this decomposition, the square free part is defined as the product $g_1 \
which is computed by this functor.
\ccRefines
\ccc{AdaptableBinaryFunction}
\ccc{AdaptableUnaryFunction}
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{make_square_free}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}
\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}
\ccOperations
\ccMethod{result_type operator()(argument_type p);}
{ return the square-free part of $p$.}
{ Returns the square-free part of $p$.}
%\ccHasModels
@ -34,5 +34,6 @@ which is computed by this functor.
\ccRefIdfierPage{Polynomial_d}\\
\ccRefIdfierPage{PolynomialTraits_d}\\
\ccRefIdfierPage{PolynomialTraits_d::Canonicalize}
\ccRefIdfierPage{PolynomialTraits_d::Canonicalize}\\
\end{ccRefConcept}

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Move.tex
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@ -17,7 +17,7 @@ This function may be used to make a certain variable the outer most variable.
\ccOperations
\ccCreationVariable{move}
\ccCreationVariable{fo}
\ccMethod{result_type operator()(PolynomialTraits_d::Polynomial_d,
int i, int j);}{
This function moves the variable at position $i$ to its new position $j$ and returns

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_MultivariateContent.tex
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@ -14,7 +14,7 @@ This functor is well defined if \ccc{PolynomialTraits_d::Innermost_coefficient_t
\ccTypes
\ccCreationVariable{multivariate_content}
\ccCreationVariable{fo}
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx}{xxx}{}
\ccTypedef{typedef PolynomialTraits_d::Innermost_coefficient_type result_type;}{}
\ccGlue

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Negate.tex
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@ -15,7 +15,7 @@ of all odd coefficients with respect to the specified variable.
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{negate}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PseudoDivision.tex
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@ -5,7 +5,7 @@
This \ccc{AdaptableFunctor} computes the so called {\em pseudo division}
of to polynomials $f$ and $g$.
Given $f$ and $g \not 0$ this functor computes quotient $q$ and
Given $f$ and $g \neq 0$ this functor computes quotient $q$ and
remainder $r$ such that $D \cdot f = g \cdot q + r$ and $degree(r) < degree(g)$,
where $ D = leading\_coefficient(g)^{max(0, degree(f)-degree(g)+1)}$

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PseudoDivisionQuotient.tex
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@ -5,7 +5,7 @@
This \ccc{AdaptableBinaryFunction} computes the quotient of the so
called {\em pseudo division} of to polynomials $f$ and $g$.
Given $f$ and $g \not 0$ on can compute quotient $q$ and remainder $r$
Given $f$ and $g \neq 0$ on can compute quotient $q$ and remainder $r$
such that $D \cdot f = g \cdot q + r$ and $degree(r) < degree(g)$,
where $ D = leading\_coefficient(g)^{max(0, degree(f)-degree(g)+1)}$

4
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_PseudoDivisionRemainder.tex
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@ -1,11 +1,11 @@
\begin{ccRefConcept}{PolynomialTraits_d::PseudoDivisionRemainder}
\ccDefinition
This \ccc{AdaptableBinaryFunction} computes the remainder of the so called
{\em pseudo division} of to polynomials $f$ and $g$.
Given $f$ and $g \not 0$ one can compute quotient $q$ and remainder $r$
Given $f$ and $g \neq 0$ one can compute quotient $q$ and remainder $r$
such that $D \cdot f = g \cdot q + r$ and $degree(r) < degree(g)$,
where $ D = leading\_coefficient(g)^{max(0, degree(f)-degree(g)+1)}$

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Resultant.tex
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@ -29,7 +29,7 @@ For more information we refer to, e.g., \cite{gg-mca-99}.
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{resultant}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Coefficient_type result_type;}{}
\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type;}{}

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Scale.tex
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@ -13,7 +13,7 @@ the polynomial is considered as a univariate polynomial in one specific variable
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{scale}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type;}{}
\ccGlue

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_ScaleHomogeneous.tex
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@ -16,7 +16,7 @@ Note that $a$ and $b$ are of type \ccc{PolynomialTraits_d::Coefficient_type}.
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{scale_homogeneous}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}
\ccOperations

18
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Shift.tex
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@ -1,27 +1,29 @@
\begin{ccRefConcept}{PolynomialTraits_d::Shift}
\ccDefinition
This \ccc{AdaptableFunctor} multiplies a \ccc{PolynomialTraits_d::Polynomial_d} by
the given power of the specified variable.
This \ccc{AdaptableBinaryFunction} multiplies a \ccc{PolynomialTraits_d::Polynomial_d}
by the given power of the specified variable.
This functor is provided for efficiency reasons, since multiplication by some variable
will in general correspond to a shift of coefficients in the internal representation.
\ccRefines
\ccc{AdaptableFunctor}
\ccc{AdaptableBinaryFunction}
\ccTypes
\ccCreationVariable{shift}
\ccCreationVariable{fo}
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type;}{}
\ccTypedef{typedef int second_argument_type;}{}
\ccOperations
\ccMethod{result_type operator()(PolynomialTraits_d::Polynomial_d p,
int e);}
\ccMethod{result_type operator()(first_argument_type p,
second_argument_type e);}
{ return $p * x_{d-1}^e$
\ccPrecond $0 \leq e$ }
\ccMethod{result_type operator()(PolynomialTraits_d::Polynomial_d p,
int e,
\ccMethod{result_type operator()(first_argument_type p,
second_argument_type e,
int i);}
{ Same as first operator but for variable $x_i$.
\ccPrecond $0 \leq e$

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SignAt.tex
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@ -14,7 +14,7 @@ This functor is well defined if \ccc{PolynomialTraits_d::Innermost_coefficient_t
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{sign_at}
\ccCreationVariable{fo}
\ccTypedef{typedef CGAL::Sign result_type;}{}\ccGlue
\ccOperations

7
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SignAtHomogeneous.tex
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@ -18,12 +18,13 @@ This functor is well defined if \ccc{PolynomialTraits_d::Innermost_coefficient_t
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{sign_at_homogeneous}
\ccCreationVariable{fo}
\ccTypedef{typedef CGAL::Sign result_type;}{}\ccGlue
\ccOperations
template <class InputIterator>
\ccMethod{result_type operator()(PolynomialTraits_d::Polynomial_d p,
\ccMethod{
template <class InputIterator>
result_type operator()(PolynomialTraits_d::Polynomial_d p,
InputIterator begin,
InputIterator end );}{
Returns the sign of $p$ at the given homogeneous point, where $begin$ is

5
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SquareFreeFactorize.tex
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@ -25,7 +25,7 @@ DefaultConstructible\\
\ccOperations
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{sqff}
\ccCreationVariable{fo}
\ccMethod{template<class OutputIterator>
OutputIterator operator()(PolynomialTraits_d::Polynomial_d p,
@ -38,8 +38,7 @@ OutputIterator operator()(PolynomialTraits_d::Polynomial_d p,
\ccMethod{template<class OutputIterator>
OutputIterator operator()(PolynomialTraits_d::Polynomial_d p,
OutputIterator it,
PolynomialTraits_d::Innermost_coefficient_type& a);}
OutputIterator it);}
{ As the first operator, just not computing the factor $a$. }
%\ccHasModels

5
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SquareFreeFactorizeUpToConstantFactor.tex
View File

@ -29,12 +29,11 @@ DefaultConstructible\\
\ccOperations
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{sqff_utcf}
\ccCreationVariable{fo}
\ccMethod{template<class OutputIterator>
OutputIterator operator()(PolynomialTraits_d::Polynomial_d p,
OutputIterator it,
PolynomialTraits_d::Innermost_coefficient_type& a);}
OutputIterator it);}
{ computes square-free factorization of $p$.\\
The \ccc{OutputIterator} must allow the value type
\ccc{std::pair<PolynomialTraits_d::Polynomial_d,int>}.

1
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Sturm_habicht_sequence.tex
View File

@ -13,6 +13,7 @@ The result is written in an output range,
starting with the $0$th Sturm-Habicht polynomial (which is equal to
the discriminant of $f$ up to a multiple of the leading coefficient)
\ccCreationVariable{fo}
\ccOperations
\ccMethod{template<typename OutputIterator>
OutputIterator operator()(Polynomial_d f,

1
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Sturm_habicht_sequence_with_cofactors.tex
View File

@ -6,6 +6,7 @@ Computes the Sturm-Habicht sequence of a polynomials $f$ of type
Additionally, it computes two ranges of cofactors, {\tt co\_f} and {\tt co\_fx}
with the property that {\tt stha[i] == co\_f[i] f + co\_fx[i] f'}.
\ccCreationVariable{fo}
\ccOperations
\ccMethod{template< typename OutputIterator1,
typename OutputIterator2,

21
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Substitute.tex
View File

@ -5,31 +5,34 @@ This \ccc{Functor} substitutes all variables of a given multivariate
\ccc{PolynomialTraits_d::Polynomial_d} by the values given in the
iterator range, where begin refers the the value for the innermost variable.
Note that the \ccc{result_type} is the coercion type of the value type of the
given iterator range and \ccc{PolynomialTraits_d::Innermost_coefficient_type}.
In particular \ccc{std::iterator_traits<Input_iterator>::value_type} must be at least
\ccc{ExplicitInteroperable} with \ccc{PolynomialTraits_d::Innermost_coefficient_type}.
\ccRefines
Assignable\\
CopyConstructible\\
DefaultConstructible\\
% \ccTypes
\ccTypes
Note that the \ccc{result_type} is the coercion type of the value type of the
given iterator range and \ccc{PolynomialTraits_d::Innermost_coefficient_type}.
In particular \ccc{std::iterator_traits<Input_iterator>::value_type} must be at least
\ccc{ExplicitInteroperable} with \ccc{PolynomialTraits_d::Innermost_coefficient_type}.
Hence, it can not be provided as a public type in advance.
% no public types
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{substitute}
\ccCreationVariable{fo}
\ccOperations
\ccMethod{
template<class Input_iterator>
result_type operator()(PolynomialTraits_d::Polynomial_d p,
result_type operator()(PolynomialTraits_d::Polynomial_d p,
Input_iterator begin, Input_iterator end);}{
Substitutes each variable of $p$ by the values given in the iterator range,
where begin refers to the innermost variable $x_0$.
\ccPrecond The length of the iterator range is \ccc{PolynomialTraits_d::d}.}
\ccPrecond{(end-begin == \ccc{PolynomialTraits_d::d})}
}
%\ccHasModels

18
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_SubstituteHomogeneous.tex
View File

@ -10,22 +10,22 @@ Hence the iterator range is required to be of length \ccc{PolynomialTraits_d::d+
For instance the polynomial $p(x_0,x_1) = x_0^2x_1^3+x_1^4$ is interpreted as the homogeneous
polynomial $p(x_0,x_1,w) = x_0^2x_1^3+x_1^4w^1$.
Note that the \ccc{result_type} is the coercion type of the value type of the
given iterator range and \ccc{PolynomialTraits_d::Innermost_coefficient_type}.
In particular \ccc{std::iterator_traits<Input_iterator>::value_type} must be at least
\ccc{ExplicitInteroperable} with \ccc{PolynomialTraits_d::Innermost_coefficient_type}.
\ccRefines
Assignable\\
CopyConstructible\\
DefaultConstructible\\
% \ccTypes
\ccTypes
Note that the \ccc{result_type} is the coercion type of the value type of the
given iterator range and \ccc{PolynomialTraits_d::Innermost_coefficient_type}.
In particular \ccc{std::iterator_traits<Input_iterator>::value_type} must be at least
\ccc{ExplicitInteroperable} with \ccc{PolynomialTraits_d::Innermost_coefficient_type}.
Hence, it can not be provided as a public type in advance.
% no public types
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{substitute_homogeneous}
\ccCreationVariable{fo}
\ccOperations
\ccMethod{
@ -36,8 +36,8 @@ Substitute each variable of $p$ by the values given in the iterator range, where
$p$ is interpreted as a homogeneous polynomial in all variables.
The begin iterator refers to the innermost variable $x_0$.
The homogeneous degree is considered as equal to the total degree of $p$.
\ccPrecond The length of the iterator range is \ccc{PolynomialTraits_d::d+1}.}
\ccPrecond{(end-begin == \ccc{PolynomialTraits_d::d})+1}
}
%\ccHasModels

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Swap.tex
View File

@ -15,7 +15,7 @@ This \ccc{AdaptableFunctor} swaps two variables of a multivariate polynomial.
\ccOperations
\ccCreationVariable{swap}
\ccCreationVariable{fo}
\ccMethod{result_type operator()(PolynomialTraits_d::Polynomial_d,
int i, int j);}
{ return polynomial with interchanged variables $x_i$,$x_j$.

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_TotalDegree.tex
View File

@ -28,7 +28,7 @@ be $-inf$, but this would imply an inconvenient return type.
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}
\ccOperations
\ccCreationVariable{total_degree}
\ccCreationVariable{fo}
\ccMethod{result_type operator()(argument_type p);}
{Computes the total degree of $p$.}

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_Translate.tex
View File

@ -13,7 +13,7 @@ the polynomial is considered as a univariate polynomial in one specific variable
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{translate}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}
\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type;}{}

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_TranslateHomogeneous.tex
View File

@ -16,7 +16,7 @@ Note that $a$ and $b$ are of type \ccc{PolynomialTraits_d::Coefficient_type}.
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccCreationVariable{translate_homogeneous}
\ccCreationVariable{fo}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}\ccGlue
\ccOperations

2
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_UnivariateContent.tex
View File

@ -16,7 +16,7 @@ a \ccc{Field} or a \ccc{UniqueFactorizationDomain}.
\ccTypes
\ccCreationVariable{univariate_content}
\ccCreationVariable{fo}
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccTypedef{typedef PolynomialTraits_d::Coefficient_type result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}\ccGlue

8
Polynomial/doc_tex/Polynomial_ref/PolynomialTraits_d_UnivariateContentUpToConstantFactor.tex
View File

@ -2,7 +2,7 @@
\ccDefinition
This \ccc{AdaptableBinaryFunction} computes the content of a
This \ccc{AdaptableUnaryFunction} computes the content of a
\ccc{PolynomialTraits_d::Polynomial_d}
with respect to the univariate (recursive) view on the
polynomial {\em up to a constant factor (utcf)}, that is,
@ -15,14 +15,14 @@ However, a concept \ccc{PolynomialTraits_d::MultivariateContentUpToConstantFacto
does not exist since the result is trivial.
\ccRefines
\ccc{AdaptableBinaryFunction}
\ccc{AdaptableUnaryFunction}
\ccCreationVariable{fo}
\ccTypes
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
\ccTypedef{typedef PolynomialTraits_d::Coefficient_type result_type;}{}\ccGlue
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type;}{}\ccGlue
\ccTypedef{typedef int second_argument_type;}{}
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}
\ccOperations
\ccMethod{result_type operator()(first_argument_type p);}