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Re: prograMing: EquivalenceIndex


  • To: mathgroup@smc.vnet.net
  • Subject: [mg11215] Re: [mg11121] prograMing: EquivalenceIndex
  • From: Clemens Frey <clemens.frey@uni-bayreuth.de>
  • Date: Mon, 2 Mar 1998 23:11:06 -0500
  • Organization: University of Bayreuth, Germany
  • References: <199802240240.VAA21721@smc.vnet.net.>

Hi Xah,

some remarks on your posting about the killer version of
EquivalenceIndex
(it is running really fast), because the reflectivity-thing was a bit
confusing.

In your first article about EquivalenceIndex you  forgot to postulate
reflectivity (or "reflexivity"?) of sameTestQ, but implicitly did it by
naming "Equivalence"Index as you did...  (for non-mathematicians:
mathematical equivalence just means symmetry, transitivity and
reflectivity!).
In the end, you add this feature, and then identical elements a r e 
assumed being equal. 

But this confusion only makes a difference (I suppose) for equivalence
classes
with exactly one element (if sameTestQ satisfies symmetry and
transitivity). 
Because when there is a class containing at least two non-identical
elements, say a and b, then by symmetry:

 sameTestQ[a,b] == sameTestQ[b,a] == True
 
and by transitivity:

 ==> sameTestQ[a,a] == sameTestQ[b,b] == True.
 
kind regards
Clemens



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