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RE: trouble with pattern matching & manipulating

• To: mathgroup at smc.vnet.net
• Subject: [mg37075] RE: [mg37013] trouble with pattern matching & manipulating
• From: "DrBob" <drbob at bigfoot.com>
• Date: Tue, 8 Oct 2002 07:17:37 -0400 (EDT)
• Reply-to: <drbob at bigfoot.com>
• Sender: owner-wri-mathgroup at wolfram.com

Here's a more intuitive method, perhaps:

a + b/c + d*(Sqrt[e]/c) == 0
f = %[[1, 3]]
%% /. f -> g
First@Solve[%, g]
f^2 == (g^2 /. %)

However, it occurs to me you might want a more general method to collect
a radical on one side and then square both sides.  If so, here's a
clumsy first attempt:

expr = a + b/c + d*(Sqrt[e]/c) == 0
f = First@Cases[expr, Power[a_, Rational[b_, c_]], Infinity]
power = First@Cases[f, Rational[b_, c_] -> Rational[c, b], Infinity]
coefficient = First@Cases[expr, Times[a_, f] -> a, Infinity]
Solve[expr /. coefficient f -> g, g][[1, 1]]
g^2 == (g^2 /. %)
% /. g -> coefficient f

DrBob

-----Original Message-----
From: DrBob [mailto:drbob at bigfoot.com] 
To: mathgroup at smc.vnet.net
Subject: [mg37075] RE: [mg37013] trouble with pattern matching & manipulating

Try this:

A + B/C + D*(Sqrt[E]/C) == 0
(#1 - %[[1,{1, 2}]] & ) /@ %
(C*#1 & ) /@ %
(#1^2 & ) /@ %
Simplify[%]

Also, be aware that E is the natural logarithm base, reserved for that
purpose.

DrBob

-----Original Message-----
From: Troy Goodson [mailto:Troy.D.Goodson at jpl.nasa.gov] 
To: mathgroup at smc.vnet.net
Subject: [mg37075] [mg37013] trouble with pattern matching & manipulating

I'm a newbie and, of course, the first thing I want to do is apparently 
one of the most complicated...

I have an expression that looks like this:

A + B/C + D*Sqrt[E]/C = 0

A,B,C,D, & E are all polynomials in x
I want it to look like this

(D^2)*E = (A*C + B)^2

At that point, I'll have polynomials in x on both sides.  Finally, I 
want the equation to be written out with terms grouped by powers of x, 
but I think I can do that part :)

I'll be very grateful to anyone who can give me some pointers.  Or, at 
least point me to some tutorial in the Mathematica documentation.  I've 
been looking over the documentation and I found Appendix A.5 in The 
Mathematica Book, but that doesn't help me.  I _need_ some examples. I 
did find a couple of well-written posts in this newsgroup, but not quite

close enough to what I want.

Thanks!

Troy.

=-=-=-=-=-=-=-=-=-=

FYI, here's the expression I'm working with.


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)

0 == -(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 

Although I said it's a polynomial in x, it's really a polynomial in "b" 
that I'm after.