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Re: problem with Collect[] for long polynomial
*To*: mathgroup at smc.vnet.net
*Subject*: [mg37315] Re: problem with Collect[] for long polynomial
*From*: Sotirios Bonanos <sbonano at mail.ariadne-t.gr>
*Date*: Wed, 23 Oct 2002 02:56:48 -0400 (EDT)
*Organization*: National Technical University of Athens, Greece
*References*: <ap07gi$c52$1@smc.vnet.net>
*Reply-to*: sbonano at mail.ariadne-t.gr
*Sender*: owner-wri-mathgroup at wolfram.com
Troy Goodson wrote:
> 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.
You have mistyped the definition of H12 - you want the last replacement
applied to H11, not H10! As written H12 is equal to H10 (the rule does not
apply).
Sorry!
S. Bonanos
http://www.inp.demokritos.gr/~sbonano/SB.html
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