Re: Tips for writing correct, non trivial Mathematica Libraries

*To*: mathgroup at smc.vnet.net*Subject*: [mg124453] Re: Tips for writing correct, non trivial Mathematica Libraries*From*: Nehal Patel <nehal.alum at gmail.com>*Date*: Fri, 20 Jan 2012 01:50:41 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201201191012.FAA03722@smc.vnet.net> <3609A129-8BFE-453D-B414-9C1D4366BA43@mimuw.edu.pl>

On Jan 19, 2012, at 6:39 AM, Andrzej Kozlowski wrote: > > On 19 Jan 2012, at 11:12, Bill Rowe wrote: > >>> >>> geom[list_] := Apply[Times, list]^(1/Length[list]) >> >>> So, this does a bad thing for geom[ x+ y] (returns (Sqrt[x y]) >> >> What were you expecting here? This looks correct to me > > Clearly he sees what actually is a powerful feature of Mathematica as a "bad thing". The feature is that a function whose arguments are not restricted by pattern maching can be put to a more general use. I think it's great and not "bad". If you want to restrict the function to work on lists you can do this: > Hi -- thanks for your comment. Actually I think the pattern matching is the coolest thing. my point is that when combined with how Mathematica treats + (and in general, Flat and Orderless operators) it becomes a lot harder to reason about whether a function handles all edge cases correctly. So for instance nobody would expect the geometric mean of x + y to be Sqrt[x y], it should be (x + y)^1 = x+ y Separately, GeometricMean does do something reasonable for GeometricMean[x + y] (give it a try), and I wish it were easier to see what syntax it uses.

**References**:**Re: Tips for writing correct, non trivial Mathematica Libraries***From:*Bill Rowe <readnews@sbcglobal.net>