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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.
AdaptableUnaryFunction
| AlgebraicStructureTraits::UnitPart::result_type | |
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Is AlgebraicStructureTraits::Type.
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| AlgebraicStructureTraits::UnitPart::argument_type | |
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Is AlgebraicStructureTraits::Type.
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| result_type | unit_part ( argument_type x ) | returns the unit part of x. |