Path: utzoo!utgpu!utstat!jarvis.csri.toronto.edu!mailrus!cornell!calvin!johns
From: johns@calvin.EE.CORNELL.EDU (John Sahr)
Newsgroups: comp.lang.c
Subject: Re: Addition of pointers
Summary: pointers an "affine space"
Keywords: Pointer addition
Message-ID: <1065@calvin.EE.CORNELL.EDU>
Date: 13 May 89 16:45:59 GMT
References: <2299@mit-caf.MIT.EDU> <542@lakart.UUCP>
Reply-To: johns@calvin.ee.cornell.edu.UUCP (John Sahr)
Organization: Cornell Space Plasma Physics Group
Lines: 37

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@calvin.ee.cornell.edu; UUCP: {rochester,cmcl2}!cornell!calvin!johns