Here is the list of all concepts and classes of this package. Classes are inside the namespace CGAL. Concepts are in the global namespace.

[detail level 12]

▼NCGAL
CExponent_vector	For a given (multivariate) monomial the vector of its exponents is called the exponent vector
CPolynomial	An instance of the data type `Polynomial` represents a polynomial $p = a_0 + a_1x + ...a_ix^i$ from the ring $\mathrm{Coeff}[x]$
CPolynomial_traits_d	A model of concept `PolynomialTraits_d`
CPolynomial_type_generator	This class template provides a convenient way to obtain the type representing a multivariate polynomial with `d` variables, where `T` is the innermost coefficient type
CPolynomial_d	A model of `Polynomial_d` is representing a multivariate polynomial in $d \geq 1$ variables over some basic ring $R$ . This type is denoted as the innermost coefficient. A model of `Polynomial_d` must be accompanied by a traits class `CGAL::Polynomial_traits_d<Polynomial_d>`, which is a model of `PolynomialTraits_d`. Please have a look at the concept `PolynomialTraits_d`, since nearly all functionality related to polynomials is provided by the traits
▼CPolynomialTraits_d	A model of `PolynomialTraits_d` is associated with a type `Polynomial_d`. The type `Polynomial_d` represents a multivariate polynomial. The number of variables is denoted as the dimension $d$ of the polynomial, it is arbitrary but fixed for a certain model of this concept. Note that univariate polynomials are not excluded by this concept. In this case $d$ is just set to one
CCanonicalize	For a given polynomial $p$ this `AdaptableUnaryFunction` computes the unique representative of the set ${\cal P} := \{ q\ \|\ \lambda * q = p\ for\ some\ \lambda \in R \},$ where $R$ is the base of the polynomial ring
CCompare	This `AdaptableBinaryFunction` compares two polynomials, with respect to the lexicographic order with preference to the outermost variable
CConstructCoefficientConstIteratorRange	This `AdaptableUnaryFunction` returns a const iterator range over the coefficients of the given polynomial, with respect to the outermost variable, $x_{d-1}$ . The range starts with the coefficient for $x_{d-1}^0$
CConstructInnermostCoefficientConstIteratorRange	This `AdaptableUnaryFunction` returns a const iterator range over all innermost coefficients of the given polynomial
CConstructPolynomial	This `AdaptableFunctor` provides several operators to construct objects of type `PolynomialTraits_d::Polynomial_d`
CDegree	This `AdaptableUnaryFunction` computes the degree of a `PolynomialTraits_d::Polynomial_d` with respect to a certain variable
CDegreeVector	For a given `PolynomialTraits_d::Polynomial_d` $p$ this `AdaptableUnaryFunction` returns the degree vector, that is, it returns the exponent vector of the monomial of highest order in $p$ , where the monomial order is the lexicographic order giving outer variables a higher priority. In particular, this is the monomial that belongs to the innermost leading coefficient of $p$
CDifferentiate	This `AdaptableUnaryFunction` computes the derivative of a `PolynomialTraits_d::Polynomial_d` with respect to one variable
CEvaluate	This `AdaptableBinaryFunction` evaluates `PolynomialTraits_d::Polynomial_d` with respect to one variable
CEvaluateHomogeneous	This `AdaptableFunctor` provides evaluation of a `PolynomialTraits_d::Polynomial_d` interpreted as a homogeneous polynomial in one variable
CGcdUpToConstantFactor	This `AdaptableBinaryFunction` computes the $gcd$ up to a constant factor (utcf) of two polynomials of type `PolynomialTraits_d::Polynomial_d`
CGetCoefficient	This `AdaptableBinaryFunction` provides access to coefficients of a `PolynomialTraits_d::Polynomial_d`
CGetInnermostCoefficient	For the given `PolynomialTraits_d::Polynomial_d` this `AdaptableBinaryFunction` returns the coefficient of the (multivariate) monomial specified by the given `CGAL::Exponent_vector`
CInnermostLeadingCoefficient	This `AdaptableUnaryFunction` computes the innermost leading coefficient of a `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
CIntegralDivisionUpToConstantFactor	This `AdaptableBinaryFunction` computes the integral division of two polynomials of type `PolynomialTraits_d::Polynomial_d` up to a constant factor (utcf)
CInvert	This `AdaptableUnaryFunction` inverts one variable in a given `PolynomialTraits_d::Polynomial_d`, that is, for a given polynomial $p$ it computes $x^{degree(p)}p(1/x)$
CIsSquareFree	This `AdaptableUnaryFunction` computes whether the given a polynomial of type `PolynomialTraits_d::Polynomial_d` is square free
CIsZeroAt	This `AdaptableFunctor` returns whether a `PolynomialTraits_d::Polynomial_d` $p$ is zero at a given Cartesian point, which is represented as an iterator range
CIsZeroAtHomogeneous	This `AdaptableFunctor` returns whether a `PolynomialTraits_d::Polynomial_d` $p$ is zero at a given homogeneous point, which is given by an iterator range
CLeadingCoefficient	This `AdaptableUnaryFunction` computes the leading coefficient of a `PolynomialTraits_d::Polynomial_d`
CMakeSquareFree	This `AdaptableUnaryFunction` computes the square-free part of a polynomial of type `PolynomialTraits_d::Polynomial_d` up to a constant factor
CMonomialRepresentation	This `Functor` outputs the monomial representation of the given polynomial, that is, it writes all non zero terms of the polynomial as `std::pair<CGAL::Exponent_vector, PolynomialTraits_d::Innermost_coefficient_type>` into the given output iterator
CMove	This `AdaptableFunctor` moves a variable at position $i$ to a new position $j$ . The relative order of the other variables is preserved, that is, the variables between $x_i$ and $x_j$ (including $x_j$ ) are moved by one position while $x_i$ is moved to the former position of $x_j$
CMultivariateContent	This `AdaptableUnaryFunction` computes the content of a `PolynomialTraits_d::Polynomial_d` with respect to the symmetric view on the polynomial, that is, it computes the gcd of all innermost coefficients
CNegate	This `AdaptableUnaryFunction` computes $p(-x)$ for a given polynomial $p$
CPermute	This `AdaptableFunctor` permutes the variables of the given polynomial with respect to a permutation $\sigma$ , that is, each monomial $\prod x_i^{e_i}$ will be mapped to the monomial $\prod x_{\sigma(i)}^{e_i}$ . The permutation $\sigma$ is given by the iterator range of length `PolynomialTraits_d::d`, which is supposed to contain the second row of the permutation
CPolynomialSubresultants	Computes the polynomial subresultant of two polynomials $p$ and $q$ of type `PolynomialTraits_d::Polynomial_d` with respect to outermost variable. Let $p=\ccSum{i=0,\ldots,n}{} p_i x^i$ and $q=\ccSum{i=0,\ldots,m}{} q_i x^i$ , where $x$ is the outermost variable. The $i$ -th subresultant (with $i=0,\ldots,\min\{n,m\}$ ) is defined by
CPolynomialSubresultantsWithCofactors	Computes the polynomial subresultant of two polynomials $p$ and $q$ of degree $n$ and $m$ , respectively, as defined in the documentation of `PolynomialTraits_d::PolynomialSubresultants`. Moreover, for $\mathrm{Sres}_i(p,q)$ , polynomials $u_i$ and $v_i$ with $\deg u_i\leq m-i-1$ and $\deg v_i\leq n-i-1$ are computed such that $\mathrm{Sres}_i(p,q)=u_i p + v_i q$ . $u_i$ and $v_i$ are called the cofactors of $\mathrm{Sres}_i(p,q)$
CPrincipalSturmHabichtSequence	Computes the principal leading coefficients of the Sturm-Habicht sequence of a polynomials $f$ of type `PolynomialTraits_d::Polynomial_d` with respect a certain variable $x_i$ . This means that for the $j$ -th Sturm-Habicht polynomial, this methods returns the coefficient of $x_i^j$
CPrincipalSubresultants	Computes the principal subresultant of two polynomials $p$ and $q$ of type `PolynomialTraits_d::Coefficient_type` with respect to the outermost variable. The $i$ -th principal subresultant, $\mathrm{sres}_i(p,q)$ , is defined as the coefficient at $t^i$ of the $i$ -th polynomial subresultant $\mathrm{Sres}_i(p,q)$ . Thus, it is either the leading coefficient of $\mathrm{Sres}_i$ , or zero in the case where its degree is below $i$
CPseudoDivision	This `AdaptableFunctor` computes the pseudo division of two polynomials $f$ and $g$
CPseudoDivisionQuotient	This `AdaptableBinaryFunction` computes the quotient of the pseudo division of two polynomials $f$ and $g$
CPseudoDivisionRemainder	This `AdaptableBinaryFunction` computes the remainder of the pseudo division of two polynomials $f$ and $g$
CResultant	This `AdaptableBinaryFunction` computes the resultant of two polynomials $f$ and $g$ of type `PolynomialTraits_d::Polynomial_d` with respect to a certain variable
CScale	Given a constant $c$ this `AdaptableBinaryFunction` scales a `PolynomialTraits_d::Polynomial_d` $p$ with respect to one variable, that is, it computes $p(c\cdot x)$
CScaleHomogeneous	Given a numerator $a$ and a denominator $b$ this `AdaptableFunctor` scales a `PolynomialTraits_d::Polynomial_d` $p$ with respect to one variable, that is, it computes $b^{degree(p)}\cdot p(a/b\cdot x)$
CShift	This `AdaptableBinaryFunction` multiplies a `PolynomialTraits_d::Polynomial_d` by the given power of the specified variable
CSignAt	This `AdaptableFunctor` returns the sign of a `PolynomialTraits_d::Polynomial_d` $p$ at given Cartesian point represented as an iterator range
CSignAtHomogeneous	This `AdaptableFunctor` returns the sign of a `PolynomialTraits_d::Polynomial_d` $p$ at a given homogeneous point, which is given by an iterator range
CSquareFreeFactorize	This `Functor` computes a square-free factorization of a `PolynomialTraits_d::Polynomial_d`
CSquareFreeFactorizeUpToConstantFactor	This `AdaptableFunctor` computes a square-free factorization up to a constant factor (utcf) of a `PolynomialTraits_d::Polynomial_d`
CSturmHabichtSequence	Computes the Sturm-Habicht sequence (aka the signed subresultant sequence) of a polynomial $f$ of type `PolynomialTraits_d::Polynomial_d` with respect to a certain variable $x_i$ . The Sturm-Habicht sequence is similar to the polynomial subresultant sequence of $f$ and its derivative $f':=\frac{\partial f}{\partial x_i}$ with respect to $x_i$ . The implementation is based on the following definition:
CSturmHabichtSequenceWithCofactors	Computes the Sturm-Habicht polynomials of a polynomial $f$ of degree $n$ , as defined in the documentation of `PolynomialTraits_d::SturmHabichtSequence`. Moreover, for $\mathrm{Stha}_i(f)$ , polynomials $u_i$ and $v_i$ with $\deg u_i\leq n-i-2$ and $\deg v_i\leq n-i-1$ are computed such that $\mathrm{Sres}_i(p,q)=u_i f + v_i f'$ . $u_i$ and $v_i$ are called the cofactors of $\mathrm{Stha}_i(f)$
CSubstitute	This `Functor` substitutes all variables of a given multivariate `PolynomialTraits_d::Polynomial_d` by the values given in the iterator range, where begin refers the value for the innermost variable
CSubstituteHomogeneous	This `Functor` substitutes all variables of a given multivariate `PolynomialTraits_d::Polynomial_d` $p$ by the values given in the iterator range, where begin refers the value for the innermost variable. In contrast to `PolynomialTraits_d::Substitute` the given polynomial $p$ is interpreted as a homogeneous polynomial. Hence the iterator range is required to be of length `PolynomialTraits_d::d+1`
CSwap	This `AdaptableFunctor` swaps two variables of a multivariate polynomial
CTotalDegree	This `AdaptableUnaryFunction` computes the total degree of a `PolynomialTraits_d::Polynomial_d`
CTranslate	This `AdaptableBinaryFunction` translates a `PolynomialTraits_d::Polynomial_d` with respect to one variable, that is, for a given polynomial $p$ and constant $c$ it computes $p(x+c)$
CTranslateHomogeneous	Given numerator $a$ and denominator $b$ this `AdaptableFunctor` translates a `PolynomialTraits_d::Polynomial_d` $p$ with respect to one variable by $a/b$ , that is, it computes $b^{degree(p)}\cdot p(x+a/b)$
CUnivariateContent	This `AdaptableUnaryFunction` computes the content of a `PolynomialTraits_d::Polynomial_d` with respect to the univariate (recursive) view on the polynomial, that is, it computes the gcd of all coefficients with respect to one variable
CUnivariateContentUpToConstantFactor	This `AdaptableUnaryFunction` computes the content of a `PolynomialTraits_d::Polynomial_d` with respect to the univariate (recursive) view on the polynomial up to a constant factor (utcf), that is, it computes the $\mathrm{gcd\_utcf}$ of all coefficients with respect to one variable