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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



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