
Section 3.4 Definition of computer arithmetic by semimorphisms 75
S.SincefS,
+
,
g is a screen ringoid, there exists only one such element x De.
Therefore, D .e, o/ is the only element in CS that satisfies (D5).
(b), (c) and (d) are simple consequences of Theorem 3.5.
The operations defined in M
n
S and CS by Theorems 3.9 and 3.10 are quite different
from those defined in the same sets by the traditional definition of arithmetic in these
subsets in Theorems 2.6 and 2.7.
Theorems 3.9 and 3.10 already specify the definition of the arithmetic by semimor-
phisms for several of the sets displayed under D in Figure 3.2. As an example, let
R denote the linearly ...