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Re: About binary relations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104110] Re: About binary relations
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 19 Oct 2009 07:14:01 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <hb9jol$fl$1@smc.vnet.net> <hbc7uk$cib$1@smc.vnet.net> <200910180922.FAA16982@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

Except for some build-in domains, there is of course no direct way that 
Mathematica can define an infinite set. But you could do it indirectly 
as in the following. (Your "definitions" of the relations R1 and R2 make 
utterly no sense whatsoever, since they are defined in terms of pairs 
{r,s}, yet the defining relations use variously variables x, y, xP, yP, 
tP, z, and zP.)

   R1[r_,s_]:= s + Log[2,r] == (* ??? *)

I cannot finish the definition of R1, since I don't understand your 
example. If you meant that P is yet another relation -- which you failed 
to define -- then presumably something like yP stands for the set of all 
x related to y by P; if so then your definition still does not make 
sense, since the left hand side of the equality is a single number 
whereas the right-hand side is a set of numbers.

Perhaps if you described correctly and clearly what you were after, we 
could help.

olfa wrote:
> 
> ... what I'm looking for is relational
> computation capabilities, like for exemple for these two relations:
> R1 = {(r, s)| y + log2(x) == yP + log2(xP) && x*t == xP*tP &&  z ==
> zP}
> R2={(r, s)| y==yP &&  floor(log2(x) )==  floor(log2(xP))&& x*t+z ==
> xP*tP+zP}
> 
> and I want to compute R1 o R2, R1 U R2,etc.

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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