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