Re: problem with Collect[] for long polynomial
- To: mathgroup at smc.vnet.net
- Subject: [mg37295] Re: problem with Collect[] for long polynomial
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Tue, 22 Oct 2002 04:47:19 -0400 (EDT)
- References: <ap07gi$c52$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Troy,
The reason for your difficulty shows up in the following:
eqn = 2 +5x+ (x - 1)^2 == 3 +7x+ (x - 1)^3;
Collect[eqn, x]
2 + (-1 + x)^2 + 5*x == 3 + (-1 + x)^3 + 7*x
(Collect[#1, x] & ) /@ eqn
3 + 3*x + x^2 == 2 + 10*x - 3*x^2 + x^3
You need to map the use of Collect onto the sides of the equation.
--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565
"Troy Goodson" <Troy.D.Goodson at jpl.nasa.gov> wrote in message
news:ap07gi$c52$1 at smc.vnet.net...
> 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.
>