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
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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