IsCommutativeRing( R )
IsCommutativeRing
returns true
if the ring R is commutative and
false
otherwise.
A ring R is called commutative if for all elements r and s of R we have r s = s r.
gap> IsCommutativeRing( Integers ); true
IsCommutativeRing
first tests whether the flag R.isCommutativeRing
is bound. If the flag is bound, it returns this value. Otherwise it
calls R.operations.IsCommutativeRing( R )
, remembers the returned
value in R.isCommutativeRing
, and returns it.
The default function called this way is RingOps.IsCommutativeRing
,
which tests whether all the generators commute if the component
R.generators
is bound, and tests whether all elements commute
otherwise, unless R is infinite. This function is seldom overlaid,
because most rings already have the flag bound.
GAP 3.4.4