 ## AlgebraicStructureTraits::UnitPart

### Definition

This AdaptableUnaryFunction computes the unit part of a given ring element.

The mathematical definition of unit part is as follows: Two ring elements a and b are said to be associate if there exists an invertible ring element (i.e. a unit) u such that a = ub. This defines an equivalence relation. We can distinguish exactly one element of every equivalence class as being unit normal. Then each element of a ring possesses a factorization into a unit (called its unit part) and a unit-normal ring element (called its unit normal associate).

For the integers, the non-negative numbers are by convention unit normal, hence the unit-part of a non-zero integer is its sign. For a Field, every non-zero element is a unit and is its own unit part, its unit normal associate being one. The unit part of zero is, by convention, one.

### Types

 AlgebraicStructureTraits::UnitPart::result_type Is AlgebraicStructureTraits::Type. AlgebraicStructureTraits::UnitPart::argument_type Is AlgebraicStructureTraits::Type.

### Operations

 result_type unit_part ( argument_type x ) returns the unit part of x.