Mapping Distribute, losing constant factor

*To*: mathgroup at smc.vnet.net*Subject*: [mg124542] Mapping Distribute, losing constant factor*From*: Stefan Salanski <wutchamacallit27 at gmail.com>*Date*: Tue, 24 Jan 2012 05:05:41 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hello all, I ran across this interesting problem in some quick calculations i was doing with matrix generators. the following matrix was the result of a generator function i defined, but the error persists if i just copy this in by itself: a = {{1+1/2 E^-\[Theta] (-1+E^\[Theta])^2,1/2 E^-\[Theta] (-1+E^\ [Theta]) (1+E^\[Theta]),0,0},{1/2 E^-\[Theta] (-1+E^\[Theta]) (1+E^\ [Theta]),1+1/2 E^-\[Theta] (-1+E^\[Theta])^2,0,0},{0,0,1,0},{0,0,0,1}} My goal being to simplify this and obtain the sinh and cosh function representations, i found that using Expand followed by ExpToTrig works perfectly: In[13]:= ExpToTrig[Expand[a]] Out[13]= {{Cosh[\[Theta]], Sinh[\[Theta]], 0, 0}, {Sinh[\[Theta]], Cosh[\[Theta]], 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}} However, my first attempt at simplifying involved using Distribute (which was my first guess for getting it into a nice form). And it was using distribute that i noticed the constant factor 1/2 in each matrix element was dropped. Distribute[a] didnt change anything, so I mapped it over a as follows: In[17]:= Map[Distribute, a, 2] Out[17]= {{2 + E^-\[Theta] (-1 + E^\[Theta])^2, -E^-\[Theta] + E^\ [Theta], 0, 0}, {-E^-\[Theta] + E^\[Theta], 2 + E^-\[Theta] (-1 + E^\ [Theta])^2, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}} The factors of 1/2 in the non-trivial matrix elements seem to have disappeared. Though testing it on individual elements works fine (though doesn't seem to have done a whole lot of distributing, maybe because the Head is Plus, and not Times or something else) In[22]:= Distribute[a[[1, 1]]] Out[22]= 1 + 1/2 E^-\[Theta] (-1 + E^\[Theta])^2 So my question is whether this disappearance of the 1/2 factor is a bug, or due to a lack of understanding of Distribute and/or Map on my part. -Stefan Salanski University of Virginia

**Follow-Ups**:**Re: Mapping Distribute, losing constant factor***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>