GAP Manual: 5.14. StandardAssociate

StandardAssociate( r )
StandardAssociate( R, r )

In the first form StandardAssociate returns the standard associate of the ring element r in its default ring (see DefaultRing). In the second form StandardAssociate returns the standard associate of the ring element r in the ring R.

The standard associate of an ring element r of R is an associated element of r which is, in a ring dependent way, distinguished among the set of associates of r. For example, in the ring of integers the standard associate is the absolute value.

    gap> StandardAssociate( Integers, -17 );
    17 

StandardAssociate calls R.operations.StandardAssociate( R, r ) and returns the value.

The default function called this way is RingOps.StandardAssociate, which just signals an error, because there is no generic way even to define the standard associate. Thus special categories of rings must overlay this default function with other functions.