5.12 Units

Units( R )

Units returns the group of units of the ring R. This may either be returned as a list or as a group described by a group record (see Groups).

An element r is called a unit of a ring R, if r has an inverse in R. It is easy to see that the set of units forms a multiplicative group.

    gap> Units( Integers );
    [ -1, 1 ] 

Units first tests whether the component R.units is bound. If the component is bound, it returns this value. Otherwise it calls R.operations.Units( R ), remembers the returned value in R.units, and returns it.

The default function called this way is RingOps.Units, which runs over all elements of R and tests for each whether it is a unit, provided that R is finite. Special categories of rings overlay this default function with more efficient functions.

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