CGAL 4.7 - Algebraic Foundations: AlgebraicStructureTraits_ Namespace Reference

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - Algebraic Foundations

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Classes
AlgebraicStructureTraits_ Namespace Reference

## Classes

class | Div
| `AdaptableBinaryFunction` computes the integral quotient of division with remainder. More...
class | Divides
| `AdaptableBinaryFunction`, returns true if the first argument divides the second argument. More...
class | DivMod

`AdaptableFunctor` computes both integral quotient and remainder of division with remainder. The quotient \( q\) and remainder \( r\) are computed such that \( x = q*y + r\) and \( |r| < |y|\) with respect to the proper integer norm of the represented ring. For integers this norm is the absolute value. For univariate polynomials this norm is the degree. In particular, \( r\) is chosen to be \( 0\) if possible. Moreover, we require \( q\) to be minimized with respect to the proper integer norm. More...

class | Gcd
| `AdaptableBinaryFunction` providing the gcd. More...
class | IntegralDivision
| `AdaptableBinaryFunction` providing an integral division. More...
class | Inverse
| `AdaptableUnaryFunction` providing the inverse element with respect to multiplication of a `Field`. More...
class | IsOne
| `AdaptableUnaryFunction`, returns true in case the argument is the one of the ring. More...
class | IsSquare

`AdaptableBinaryFunction` that computes whether the first argument is a square. If the first argument is a square the second argument, which is taken by reference, contains the square root. Otherwise, the content of the second argument is undefined. More...

class | IsZero
| `AdaptableUnaryFunction`, returns true in case the argument is the zero element of the ring. More...
class | KthRoot
| `AdaptableBinaryFunction` providing the k-th root. More...
class | Mod
| `AdaptableBinaryFunction` computes the remainder of division with remainder. More...
class | RootOf
| `AdaptableFunctor` computes a real root of a square-free univariate polynomial. More...
class | Simplify
| This `AdaptableUnaryFunction` may simplify a given object. More...
class | Sqrt
| `AdaptableUnaryFunction` providing the square root. More...
class | Square
| `AdaptableUnaryFunction`, computing the square of the argument. More...
class | UnitPart
| This `AdaptableUnaryFunction` computes the unit part of a given ring element. More...