CGAL 5.5.2  Algebraic Foundations

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 unitnormal ring element (called its unit normal associate).
For the integers, the nonnegative numbers are by convention unit normal, hence the unitpart of a nonzero integer is its sign. For a Field
, every nonzero 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.
AlgebraicStructureTraits
Types  
typedef unspecified_type  result_type 
Is AlgebraicStructureTraits::Type .  
typedef unspecified_type  argument_type 
Is AlgebraicStructureTraits::Type .  
Operations  
result_type  operator() (argument_type x) 
returns the unit part of \( x\).  