Addition of pointers
John Sahr
johns at calvin.EE.CORNELL.EDU
Sun May 14 02:45:59 AEST 1989
This subject has gotten beaten around a bit lately, and probably doesn't
need any more beating by me. However, I was reminded about of the notion
of an "affine space" which is just like a regular vector space except that
for an affin space, there is no fixed origin.
>From V. I. Arnold, _Mathematical methods of Classical Mechanics_,
Springer-Verlag, 1978....
{begin quote, page 4}
a a+b
xx xo b xx xo
xxxxx ------> xxxxx
xxx xxx
Figure 1 Parallel Displacement
_Affine n-dimensional space A^n_ is distinguished from R^n in that
there is ``no fixed origin.'' The group R^n acts on A^n as _the group of
parallel displacements_ (figure 1):
a -> a + b, a elof A^n, b elof R^n, a + b elof A^n
[Thus the sum of two points in A^n is not defined, but their difference is
defined and is a vector in R^n.]
{end quote}
All the "b's" should be bold, and "elof" is "element of" the little "member
of" sign. "_some text_" indicates italic emphasis. R^n is R superscripted
by n.
So, this analogy puts pointers as members of a discrete one dimensional
affine space, and offsets as members of the integers ("discrete R^1").
--
John Sahr, Dept. of Electrical Eng., Cornell University, Ithaca, NY 14853
ARPA: johns at calvin.ee.cornell.edu; UUCP: {rochester,cmcl2}!cornell!calvin!johns
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