mirror of https://github.com/CGAL/cgal
57 lines
1.6 KiB
C++
57 lines
1.6 KiB
C++
/// \addtogroup PkgAlgebraicFoundations Algebraic Foundations
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/// @{
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/// \addtogroup PkgAlgebraicFoundationsConcepts Concepts
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/// @{
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///
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/// This `AdaptableUnaryFunction` computes the unit part of a given ring
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/// element.
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/// The mathematical definition of unit part is as follows: Two ring elements \f$a\f$
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/// and \f$b\f$ are said to be associate if there exists an invertible ring element
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/// (i.e. a unit) \f$u\f$ such that \f$a = ub\f$. This defines an equivalence relation.
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/// We can distinguish exactly one element of every equivalence class as being
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/// unit normal. Then each element of a ring possesses a factorization into a unit
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/// (called its unit part) and a unit-normal ring element
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/// (called its unit normal associate).
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/// For the integers, the non-negative numbers are by convention unit normal,
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/// hence the unit-part of a non-zero integer is its sign. For a `Field`, every
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/// non-zero element is a unit and is its own unit part, its unit normal
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/// associate being one. The unit part of zero is, by convention, one.
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/// \refines ::AdaptableUnaryFunction
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/// \sa `AlgebraicStructureTraits`
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class AlgebraicStructureTraits::UnitPart {
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public:
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/// \name Types
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/// @{
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/*!
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Is `AlgebraicStructureTraits::Type`.
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*/
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typedef Hidden_type result_type;
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/// @}
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/// \name Types
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/// @{
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/*!
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Is `AlgebraicStructureTraits::Type`.
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*/
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typedef Hidden_type argument_type;
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/// @}
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/// \name Operations
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/// @{
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/*!
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returns the unit part of \f$x\f$.
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*/
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result_type operator()(argument_type x);
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/// @}
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}; /* concept AlgebraicStructureTraits::UnitPart */
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/// @}
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/// @}
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