mirror of https://github.com/CGAL/cgal
120 lines
3.6 KiB
C++
120 lines
3.6 KiB
C++
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/*!
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\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
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\cgalConcept
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This is the most basic concept for algebraic structures considered within \cgal.
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A model `IntegralDomainWithoutDivision` represents an integral domain,
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i.e.\ commutative ring with 0, 1, +, * and unity free of zero divisors.
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<B>Note:</B> A model is not required to offer the always well defined integral division.
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It refines `Assignable`, `CopyConstructible`, `DefaultConstructible`
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and `FromIntConstructible`.
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It refines `EqualityComparable`, where equality is defined w.r.t.\ the ring element being represented.
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The operators unary and binary plus +, unary and binary minus -,
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multiplication * and their compound forms +=, -=, *= are required and
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implement the respective ring operations.
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Moreover, `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >` is a model of
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`AlgebraicStructureTraits` providing:
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- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Algebraic_category` \endlink derived from `CGAL::Integral_domain_without_division_tag`
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- \link AlgebraicStructureTraits::Is_zero `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Is_zero` \endlink which is a model of `AlgebraicStructureTraits_::IsZero`
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- \link AlgebraicStructureTraits::Is_one `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Is_one` \endlink which is a model of `AlgebraicStructureTraits_::IsOne`
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- \link AlgebraicStructureTraits::Square `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Square` \endlink which is a model of `AlgebraicStructureTraits_::Square`
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- \link AlgebraicStructureTraits::Simplify `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Simplify` \endlink which is a model of `AlgebraicStructureTraits_::Simplify`
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- \link AlgebraicStructureTraits::Unit_part `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Unit_part` \endlink which is a model of `AlgebraicStructureTraits_::UnitPart`
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\cgalRefines{Assignable,CopyConstructible,DefaultConstructible,EqualityComparable,FromIntConstructible}
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\sa `IntegralDomainWithoutDivision`
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\sa `IntegralDomain`
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\sa `UniqueFactorizationDomain`
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\sa `EuclideanRing`
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\sa `Field`
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\sa `FieldWithSqrt`
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\sa `FieldWithKthRoot`
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\sa `FieldWithRootOf`
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\sa `AlgebraicStructureTraits`
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*/
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class IntegralDomainWithoutDivision {
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public:
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/// \name Operations
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/// @{
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/*!
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unary plus
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*/
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IntegralDomainWithoutDivision
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operator+(const IntegralDomainWithoutDivision &a);
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/*!
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unary minus
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*/
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IntegralDomainWithoutDivision
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operator-(const IntegralDomainWithoutDivision &a);
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/*!
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*/
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IntegralDomainWithoutDivision
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operator+(const IntegralDomainWithoutDivision &a,
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const IntegralDomainWithoutDivision &b);
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/*!
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*/
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IntegralDomainWithoutDivision
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operator-(const IntegralDomainWithoutDivision &a,
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const IntegralDomainWithoutDivision &b);
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/*!
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*/
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IntegralDomainWithoutDivision
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operator*(const IntegralDomainWithoutDivision &a,
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const IntegralDomainWithoutDivision &b);
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/*!
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*/
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IntegralDomainWithoutDivision
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operator+=(const IntegralDomainWithoutDivision &b);
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/*!
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*/
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IntegralDomainWithoutDivision
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operator-=(const IntegralDomainWithoutDivision &b);
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/*!
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*/
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IntegralDomainWithoutDivision
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operator*=(const IntegralDomainWithoutDivision &b);
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/*!
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The `result_type` is convertible to `bool`.
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*/
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result_type
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operator==(const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b);
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/*!
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The `result_type` is convertible to `bool`.
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*/
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result_type
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operator!=(const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b);
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/// @}
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}; /* end IntegralDomainWithoutDivision */
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