CGAL 4.7 - Algebraic Foundations: Field Concept Reference

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CGAL 4.7 - Algebraic Foundations

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Field Concept Reference
Concepts

## Definition

A model of `Field` is an `IntegralDomain` in which every non-zero element has a multiplicative inverse. Thus, one can divide by any non-zero element. Hence division is defined for any divisor != 0. For a Field, we require this division operation to be available through operators / and /=.

Moreover, `CGAL::Algebraic_structure_traits< Field >` is a model of `AlgebraicStructureTraits` providing:

- `CGAL::Algebraic_structure_traits< Field >::Algebraic_category` derived from `CGAL::Field_tag`
- `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Inverse` which is a model of `AlgebraicStructureTraits_::Inverse`

Refines:
  `IntegralDomain`

See Also
  `IntegralDomainWithoutDivision`
  `IntegralDomain`
  `UniqueFactorizationDomain`
  `EuclideanRing`
  `Field`
  `FieldWithSqrt`
  `FieldWithKthRoot`
  `FieldWithRootOf`
  `AlgebraicStructureTraits`

## Operations

Field | operator/ (const Field &a, const Field &b)
Field | operator/= (const Field &b)