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problem with Collect[] for long polynomial
*To*: mathgroup at smc.vnet.net
*Subject*: [mg37270] problem with Collect[] for long polynomial
*From*: Troy Goodson <Troy.D.Goodson at jpl.nasa.gov>
*Date*: Mon, 21 Oct 2002 02:29:40 -0400 (EDT)
*Organization*: JPL/Caltech
*Sender*: owner-wri-mathgroup at wolfram.com
I apologize for the length of this post, but I don't see how else to be
precise about my question.
The short story is this:
-- copy and paste the lines below into Mathematica
-- execute
-- the result is a really big expresssion, but I want the terms in this
expression
to be grouped in powers of my variable "b".
However, Collect[] doesn't appear to be working right. I call Collect[%,
b] and I think I'm getting % back. At the very least, I can clearly see
more than one term in the expression that includes b^9, for example.
I'd be very grateful if someone a little more knowledgeable than I could
execute these lines and see if they can get Collect[] to work. Of, if
this is how Collect[] is supposed to work, what command should I be
using?
Thanks,
Troy.
So, here's what I did. First, to get my equation:
denom = Sqrt[(B^2 - r^2)^2 + 4*(r^2)*(b^2)]
cnu = (2*b^2 - B^2 + r^2)/denom
snu = -2*b*Sqrt[B^2 - b^2]/denom
sif = 2*r*b/denom
cif = (r^2 - B^2)/denom
pdr = -Cos[ds]*Sin[q]*(snu*cif +
cnu*sif) - Sin[ds]*(cnu*cif - snu*sif)
HH = -(B^2 - b^2)*V^2/(r^2) + (((B*V)^2)/(
r^2) - 2*w*b*V*Cos[q]*Cos[ds] + (w*
r)^2 - (w*r*pdr)^2)*(Cos[qr])^2
Now, my equation is really HH == 0, but there's some manipulations I
want to do first. I don't know Mathematica well, so all I could see to
do was to perform operations on HH, then put the equation together.
H2 = Expand[HH]
H3 = Collect[HH, Sqrt[B^2 - b^2]]
H4 = H3*( (4 * (b*r)^2 + (B^2 - r^2)^2)^2 )
H7 = H4*(r^2)
H8 = Collect[ Cancel[H7], Sqrt[-b^2 + B^2] ]
H9 = Equal[H8, 0] /. Equal[
aa_ + Sqrt[B^2 - b^2]*bb_, 0] -> Equal[ Sqrt[B^2 - b^2]*bb, -aa]
H10 = Thread[#^2 &[H9], Equal] // ExpandAll
H11 = H10 /. Equal[ mm_ , nn_] -> Equal[ mm - nn , 0]
H12 = H10 /. Equal[ qq_ , 0] -> qq
For H3 and H8, Collect[] seems to work.
The command to get H10 I copied from a post by Andrzej Kozlowski.
H13 = Collect[H11,b]
H14 = Collect[H12,b]
but the results don't seem to be 'collected' polynomials.
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