r = s
r < s
The equality operator =
evaluates to true
if the two ring elements
r and s are equal, and to false
otherwise. The inequality operator
<
evaluates to true
if the two ring elements r and s are not
equal, and to false
otherwise. Note that any two ring elements can be
compared, even if they do not lie in compatible rings. In this case they
can, of course, never be equal. For each type of rings the equality of
those ring elements is given in the respective chapter.
Ring elements can also be compared with objects of other types. Of course they are never equal.
r < s
r <= s
r s
r = s
The operators <
, <=
, , and
=
evaluate to true
if the ring
element r is less than, less than or equal to, greater than, or greater
than or equal to the ring element s, and to false
otherwise. For
each type of rings the definition of the ordering of those ring elements
is given in the respective chapter. The ordering of ring elements is as
follows. Rationals are smallest, next are cyclotomics, followed by
finite ring elements.
Ring elements can also be compared with objects of other types. They are smaller than everything else.
GAP 3.4.4