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Re: Mapping Distribute, losing constant factor
Posted:
Jan 25, 2012 7:04 AM


The reason for what you are seeing is that you are mapping Distribute no on level 2 in the expression but on level 2 and all levels below 2. If you only mapped Distribute on level 2 you would not "loose" any factors but get the effect you probably intended:
Map[Distribute, a, {2}]
{{((1/2)*(1 + E^\[Theta])^2)/E^\[Theta] + 1, (1/(E^\[Theta]*2)) + E^\[Theta]/2, 0, 0}, {(1/(E^\[Theta]*2)) + E^\[Theta]/2, ((1/2)*(1 + E^\[Theta])^2)/E^\[Theta] + 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
The reason why these factors of 1/2 seem to disappear is that distributing over level 1 elements in the expression causes terms to be added (by default Distribute distributes over Plus). As an example look at what happens to this single level 1 term:
Distribute[{1 + ((1/2)*(1 + E^\[Theta])^2)/ E^\[Theta], ((1/2)*(1 + E^\[Theta])*(1 + E^\[Theta]))/ E^\[Theta], 0, 0}]
{1 + ((1/2)*(1 + E^\[Theta])^2)/ E^\[Theta], ((1 + E^\[Theta])*(1 + E^\[Theta]))/E^\[Theta], 0, 0}
The factor 1/2 seems to have disappeared because distributing over Plus here causes the addition:
{1, ((1/2)*(1 + E^\[Theta])*(1 + E^\[Theta]))/E^\[Theta], 0, 0} + {((1/2)*(1 + E^\[Theta])^2)/ E^\[Theta], ((1/2)*(1 + E^\[Theta])*(1 + E^\[Theta]))/E^\[Theta], 0, 0}
To understand why it happens just think of what Distribute is supposed to do here or look at
Trace[Distribute[{1 + ((1/2)*(1 + E^\[Theta])^2)/E^\[Theta], ((1/2)*(1 + E^\[Theta])*(1 + E^\[Theta]))/ E^\[Theta], 0, 0}]]
Andrzej Kozlowski
On 24 Jan 2012, at 11:05, Stefan Salanski wrote:
> 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 nontrivial 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 >



