solving vector equations in mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg34356] solving vector equations in mathematica
- From: Hal Daume III <hdaume at isi.edu>
- Date: Thu, 16 May 2002 05:08:44 -0400 (EDT)
- Organization: University of Southern California
- Sender: owner-wri-mathgroup at wolfram.com
Hi All,
I'm somewhat new to mathematica, at least in the world of vectors, and
I'm having trouble getting it to solve an equation for me.
I basically want to solve:
\sum_{i=1}^n x_i = 0
for x_k
I tried:
Solve[Sum[x[[i]],{i,1,5}] == 0, x[[2]]]
as an example, but mathematica complains:
In[118]:= Solve[Sum[w[[i]],{i=1,5}] == 0, w[[1]]]
Sum::write: Tag Set in i = 1 is Protected.
Part::partd: Part specification w[[1]] is longer than depth of object.
Part::partd: Part specification w[[1]] is longer than depth of object.
Part::partd: Part specification w[[1]] is longer than depth of object.
General::stop: Further output of Part::partd
will be suppressed during this calculation.
Out[118]= {{w[[1]] -> 0}}
I'm not exactly sure what this means.
I could write it out:
In[119]:= Solve[w1+w2+w3+w4+w5==0, w1]
Out[119]= {{w1 -> -w2 - w3 - w4 - w5}}
But this isn't very helpful in my situation (my equations are huge*), and
doesn't reflect the vector quality of the situation.
If such a thing is possible, I'd appreciate some pointers (I read the
mathematica docs on the wolfram site, but couldn't find anything talking
about this).
Thanks!
- Hal
* the equation i'm working with is something like:
sum_{C,x,y,y'} (wx . wy) (wx . wy') (|wx * wy'| (wx . wy) - |wx * wy| (wx
. wy')) / (|wx|^4 |wy|^2 |wy'|^2) == 0
where
. is dot product
* is cross product
|x| is magnitude of x
and
for vectors w=<w1,w2,...,wn>, x=<x1,x2,...,xn>,
wx = <w1*x1,w2*x2,...,wn*xn>
Thanks again.
--
Hal Daume III
"Computer science is no more about computers | hdaume at isi.edu
than astronomy is about telescopes." -Dijkstra | www.isi.edu/~hdaume