mirror of https://github.com/CGAL/cgal
add forgotten refines Default/CopyConstructible
This commit is contained in:
Michael Hemmer
parent
2a57a50093
commit
00be0efc4a
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@ -70,6 +70,7 @@ the zero polynomial is represented by a single zero coefficient.
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%An empty coefficient sequence denotes an undefined value.
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\ccIsModel
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\begin{tabular}{ll}
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\ccc{Polynomial_d}\\
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\ccc{Assignable}\\
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@ -21,7 +21,9 @@ Note that the computed polynomial has the same zero set as the given one.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -10,7 +10,9 @@ This functor is well defined if \ccc{PolynomialTraits_d::Innermost_coefficient_t
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -7,7 +7,9 @@ coefficients of the given polynomial, with respect to the outermost variable, $x
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The range starts with the coefficient for $x_{d-1}^0$. \\
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -7,7 +7,9 @@ This \ccc{AdaptableUnaryFunction} returns a const iterator range over all
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innermost coefficients of the given polynomial.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -6,7 +6,9 @@ This \ccc{AdaptableFunctor} provides several operators
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to construct objects of type \ccc{PolynomialTraits_d::Polynomial_d}.
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\ccRefines
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\ccc{AdaptableFunctor}
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\ccc{AdaptableFunctor}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -17,7 +17,9 @@ be $-infinity$, but this would imply an inconvenient return type.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -10,7 +10,9 @@ variables a higher priority. In particular, this is the monomial
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that belongs to the innermost leading coefficient of $p$.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -5,7 +5,9 @@ This \ccc{AdaptableUnaryFunction} computes the derivative of a
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\ccc{PolynomialTraits_d::Polynomial_d} with respect to one variable.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -5,7 +5,9 @@ This \ccc{AdaptableBinaryFunction} evaluates
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\ccc{PolynomialTraits_d::Polynomial_d} with respect to one variable.
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -8,7 +8,9 @@ For instance the polynomial $p = 5x^2y^3 + y$ is interpreted as the homogeneous
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$p[x](u,v) = 5x^2u^3 + uv^2$ and evaluated as such.
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\ccRefines
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\ccc{AdaptableFunctor}
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\ccc{AdaptableFunctor}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -19,7 +19,9 @@ Hence, $gcd\_utcf(f,g)$ may not be a divisor of $f$ and $g$ in $R[x_0,\dots,x_{d
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -6,7 +6,9 @@ This \ccc{AdaptableBinaryFunction} provides access to coefficients of a
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\ccc{PolynomialTraits_d::Polynomial_d}.
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -7,7 +7,9 @@ For the given \ccc{PolynomialTraits_d::Polynomial_d} this
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the (multivariate) monomial specified by the given \ccc{Exponent_vector}.
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -6,7 +6,9 @@ This \ccc{AdaptableUnaryFunction} computes the innermost leading coefficient
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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.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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\ccCreationVariable{fo}
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@ -12,7 +12,9 @@ field of the base ring $R$, \ccc{PolynomialTraits_d::Innermost_coefficient_type}
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -14,7 +14,9 @@ order of the coefficients with respect to the specified variable.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -9,7 +9,9 @@ Note that this statement does cover constant factors,
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i.e., whether the multivariate content contains a square.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -6,7 +6,9 @@ This \ccc{AdaptableFunctor} returns whether a
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which is represented as an iterator range.
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\ccRefines
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\ccc{AdaptableFunctor}
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\ccc{AdaptableFunctor}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -10,7 +10,9 @@ For instance the polynomial $p(x_0,x_1) = x_0^2x_1^3+x_1^4$ is interpreted as th
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polynomial $p(x_0,x_1,w) = x_0^2x_1^3+x_1^4w^1$.
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\ccRefines
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\ccc{AdaptableFunctor}
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\ccc{AdaptableFunctor}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -6,7 +6,9 @@ This \ccc{AdaptableUnaryFunction} computes the leading coefficient
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of a \ccc{PolynomialTraits_d::Polynomial_d}.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -13,7 +13,9 @@ Given this decomposition, the square free part is defined as the product $g_1 \
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which is computed by this functor.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -11,7 +11,9 @@ This function may be used to make a certain variable the outer most variable.
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\ccRefines
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\ccc{AdaptableFunctor}
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\ccc{AdaptableFunctor}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
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@ -10,7 +10,9 @@ This functor is well defined if \ccc{PolynomialTraits_d::Innermost_coefficient_t
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\ccc{Field} or a \ccc{UniqueFactorizationDomain}.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -10,7 +10,9 @@ This functor is provided for efficiency reasons, since this operation just flips
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of all odd coefficients with respect to the specified variable.
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\ccRefines
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\ccc{AdaptableUnaryFunction}
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
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@ -17,7 +17,9 @@ In this case the iterator range should contain the sequence $[2,0,1,3]$.
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\ccRefines
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\ccc{AdaptableFunctor}
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\ccc{AdaptableFunctor}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -38,6 +38,12 @@ The result is written in an output range, starting with the $0$-th subresultant
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$\mathrm{Sres}_0(p,q)$
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(aka as the resultant of $p$ and $q$).
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\ccRefines
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccCreationVariable{fo}
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\ccOperations
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@ -15,6 +15,11 @@ the \emph{cofactors} of $\mathrm{Sres}_i(p,q)$.
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The result is written in three output ranges, each of length $\min\{n,m\}+1$,
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starting with the $0$-th subresultant and the corresponding cofactors.
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\ccRefines
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccCreationVariable{fo}
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\ccOperations
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\ccMethod{template< typename OutputIterator1,
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@ -18,6 +18,11 @@ In case that \ccc{PolynomialTraits_d::Coefficient_type} is \ccc{RealEmbeddable},
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on the resulting sequence to count the number of distinct real roots of
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the polynomial~$f$.
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\ccRefines
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccCreationVariable{fo}
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\ccOperations
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@ -18,6 +18,11 @@ principal subresultant $\mathrm{sres}_0(p,q)$
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,aka as the resultant of $p$ and $q$.
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(Note that $\mathrm{sres}_0(p,q)=\mathrm{Sres}_0(p,q)$ by definition)
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\ccRefines
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccCreationVariable{fo}
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\ccOperations
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@ -17,7 +17,9 @@ computation.
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\ccRefines
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\ccc{AdaptableFunctor}
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\ccc{AdaptableFunctor}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -12,7 +12,10 @@ where $ D = leading\_coefficient(g)^{max(0, degree(f)-degree(g)+1)}$
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This functor computes $q$.
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction} \\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccCreationVariable{fo}
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\ccTypes
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@ -12,7 +12,9 @@ where $ D = leading\_coefficient(g)^{max(0, degree(f)-degree(g)+1)}$
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This functor computes $r$.
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -66,7 +66,9 @@ More sophisticated methods may use modular arithmetic and interpolation.
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For more information we refer to, e.g., \cite{gg-mca-99}.
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
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@ -10,7 +10,9 @@ Note that this functor operates on the polynomial in the univariate view, that i
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the polynomial is considered as a univariate polynomial in one specific variable.
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -9,7 +9,9 @@ Note that this functor operates on the polynomial in the univariate view, that i
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the polynomial is considered as a univariate homogeneous polynomial in one specific variable.
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\ccRefines
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\ccc{AdaptableFunctor}
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\ccc{AdaptableFunctor}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -8,7 +8,9 @@ This functor is provided for efficiency reasons, since multiplication by some va
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will in general correspond to a shift of coefficients in the internal representation.
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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\ccCreationVariable{fo}
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@ -9,7 +9,9 @@ This functor is well defined if \ccc{PolynomialTraits_d::Innermost_coefficient_t
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\ccc{RealEmbeddable}.
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\ccRefines
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\ccc{AdaptableFunctor}
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\ccc{AdaptableFunctor}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -13,7 +13,9 @@ This functor is well defined if \ccc{PolynomialTraits_d::Innermost_coefficient_t
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\ccc{RealEmbeddable}.
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\ccRefines
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\ccc{AdaptableFunctor}
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\ccc{AdaptableFunctor}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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@ -37,6 +37,12 @@ The result is written in an output range,
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starting with the $0$-th Sturm-Habicht polynomial (which is equal to
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the discriminant of $f$ up to a multiple of the leading coefficient).
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\ccRefines
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccCreationVariable{fo}
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\ccOperations
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\ccMethod{template<typename OutputIterator>
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@ -15,6 +15,11 @@ The result is written in three output ranges, each of length $\min\{n,m\}+1$,
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starting with the $0$-th Sturm-Habicht polynomial $\mathrm{Stha_0(f)}$
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and the corresponding cofactors.
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\ccRefines
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccCreationVariable{fo}
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\ccOperations
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@ -6,7 +6,9 @@ This \ccc{AdaptableFunctor} swaps two variables of a multivariate polynomial.
|
|||
|
||||
\ccRefines
|
||||
|
||||
\ccc{AdaptableFunctor}
|
||||
\ccc{AdaptableFunctor}\\
|
||||
\ccc{CopyConstructible}\\
|
||||
\ccc{DefaultConstructible}\\
|
||||
|
||||
\ccTypes
|
||||
|
||||
|
|
|
|||
|
|
@ -18,7 +18,9 @@ be $-inf$, but this would imply an inconvenient return type.
|
|||
|
||||
|
||||
\ccRefines
|
||||
\ccc{AdaptableUnaryFunction}
|
||||
\ccc{AdaptableUnaryFunction}\\
|
||||
\ccc{CopyConstructible}\\
|
||||
\ccc{DefaultConstructible}\\
|
||||
|
||||
|
||||
\ccTypes
|
||||
|
|
|
|||
|
|
@ -9,7 +9,9 @@ Note that this functor operates on the polynomial in the univariate view, that i
|
|||
the polynomial is considered as a univariate polynomial in one specific variable.
|
||||
|
||||
\ccRefines
|
||||
\ccc{AdaptableBinaryFunction}
|
||||
\ccc{AdaptableBinaryFunction}\\
|
||||
\ccc{CopyConstructible}\\
|
||||
\ccc{DefaultConstructible}\\
|
||||
|
||||
\ccTypes
|
||||
|
||||
|
|
|
|||
|
|
@ -10,7 +10,9 @@ the polynomial is considered as a univariate homogeneous polynomial in one speci
|
|||
|
||||
|
||||
\ccRefines
|
||||
\ccc{AdaptableFunctor}
|
||||
\ccc{AdaptableFunctor}\\
|
||||
\ccc{CopyConstructible}\\
|
||||
\ccc{DefaultConstructible}\\
|
||||
|
||||
\ccTypes
|
||||
|
||||
|
|
|
|||
|
|
@ -12,7 +12,9 @@ This functor is well defined if \ccc{PolynomialTraits_d::Coefficient_type} is
|
|||
a \ccc{Field} or a \ccc{UniqueFactorizationDomain}.
|
||||
|
||||
\ccRefines
|
||||
\ccc{AdaptableUnaryFunction}
|
||||
\ccc{AdaptableUnaryFunction}\\
|
||||
\ccc{CopyConstructible}\\
|
||||
\ccc{DefaultConstructible}\\
|
||||
|
||||
\ccTypes
|
||||
|
||||
|
|
|
|||
|
|
@ -15,7 +15,9 @@ However, a concept \ccc{PolynomialTraits_d::MultivariateContentUpToConstantFacto
|
|||
does not exist since the result is trivial.
|
||||
|
||||
\ccRefines
|
||||
\ccc{AdaptableUnaryFunction}
|
||||
\ccc{AdaptableUnaryFunction}\\
|
||||
\ccc{CopyConstructible}\\
|
||||
\ccc{DefaultConstructible}\\
|
||||
\ccCreationVariable{fo}
|
||||
|
||||
\ccTypes
|
||||
|
|
|
|||
Loading…
Reference in New Issue