5.13 IsAssociated

IsAssociated( r, s )
IsAssociated( R, r, s )

In the first form IsAssociated returns true if the two ring elements r and s are associated in their default ring (see DefaultRing) and false otherwise. In the second form IsAssociated returns true if the two ring elements r and s are associated in the ring R and false otherwise.

Two elements r and s of a ring R are called associates if there is a unit u of R such that r u = s.

    gap> IsAssociated( Integers, 2, 3 );
    false
    gap> IsAssociated( Integers, 17, -17 );
    true 

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

The default function called this way is RingOps.IsAssociated, which tries to compute the quotient of r and s and returns true if the quotient exists and is a unit. Special categories of rings overlay this default function with more efficient functions.

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