CGAL 5.1.3  Algebraic Foundations

AdaptableBinaryFunction
providing the gcd.
The greatest common divisor ( \( gcd\)) of ring elements \( x\) and \( y\) is the unique ring element \( d\) (up to a unit) with the property that any common divisor of \( x\) and \( y\) also divides \( d\). (In other words: \( d\) is the greatest lower bound of \( x\) and \( y\) in the partial order of divisibility.) We demand the \( gcd\) to be unitnormal (i.e. have unit part 1).
\( gcd(0,0)\) is defined as \( 0\), since \( 0\) is the greatest element with respect to the partial order of divisibility. This is because an element \( a \in R\) is said to divide \( b \in R\), iff \( \exists r \in R\) such that \( a \cdot r = b\). Thus, \( 0\) is divided by every element of the Ring, in particular by itself.
AlgebraicStructureTraits
Types  
typedef unspecified_type  result_type 
Is AlgebraicStructureTraits::Type .  
typedef unspecified_type  first_argument 
Is AlgebraicStructureTraits::Type .  
typedef unspecified_type  second_argument 
Is AlgebraicStructureTraits::Type .  
Operations  
result_type  operator() (first_argument_type x, second_argument_type y) 
returns \( gcd(x,y)\).  
template<class NT1 , class NT2 >  
result_type  operator() (NT1 x, NT2 y) 
This operator is defined if NT1 and NT2 are ExplicitInteroperable with coercion type AlgebraicStructureTraits::Type .  