Re: Peculiarities of Pi, E, etc.

*To*: mathgroup at smc.vnet.net*Subject*: [mg2188] Re: Peculiarities of Pi, E, etc.*From*: Jack Goldberg <jackgold at math.lsa.umich.edu>*Date*: Fri, 13 Oct 1995 02:24:09 -0400

Hi Group; In a lecture that I recently gave to my class in Mma I mentioned that Pi, E, EulerGamma and Catalan have heads Symbol and so Mma does not recognize them as numbers; witness NumberQ[Pi] returns False. To my suprise I noticed that Positive[Pi] returns True. This got me thinking and I tried a few experiments. Here are some of the results. D[Pi^5,Pi] returns 5 Pi^4 Integrate[E,{E,0,1}] returns 1/2 Sum[Pi, {Pi,1,3}] returns 6 This is strange indeed. It confirms a suspicion I have harbored since learning the rudiments of Mma that the treatment of these so-called "mathematical" constants (in contrast to some other kind of constants?) is inconsistent and confusing. I refrain from offering suggestions on how to do this because I'm reasonable confident that no systematic change of this sort is easy to do. Before you think I`m one of those people who pick on Mma for every little blemish, let me quickly report that Maple suffers from this same ailment! I have not tried Derive. Maybe there's more to this than meets my eye? Jack