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Computer Arithmetic and Validity
book

Computer Arithmetic and Validity

by Ulrich Kulisch
April 2013
Intermediate to advanced content levelIntermediate to advanced
456 pages
16h 7m
English
De Gruyter
Content preview from Computer Arithmetic and Validity
54 Chapter 2 Ringoids and ve c toids
Theorem 2.7. If fR, C, g is a ringoid with the neutral elements o and e,then
fCR, C, g is also a ringoid with the neutral elements ! D .o, o/ and D .e, o/.
Moreover D .e, o/.IffR, N , C, , =g is a division ringoid, then fCR,
N , C, , =g
is also a division ringoid. If fR, C, , g is a weakly ordered ringoid, fCR, C, , g is
likewise a weakly ordered ringoid.
Proof. The properties (D1, 2, 3, 4, 7, 8) and (OD1, 2) follow directly from the defini-
tion of the operations and the corresponding properties in R. The properties (D5) and
(D9) can be shown to be valid for D .e, o/ 2 CR: (D5a) and (D5b) are easily ...
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Publisher Resources

ISBN: 9783110301731