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Re: rearranging equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22453] Re: [mg22505] rearranging equations
  • From: BobHanlon at aol.com
  • Date: Wed, 8 Mar 2000 02:21:52 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

f[x_] := 7 + 3x + 2x^2;

data = Sort[Table[{x = 10*Random[], f[x]}, {6}]];

Clear[x];

As expected, the quadratic fit to the data arrives at the quadratic 
definition used to generate the data

y == Fit[data, {1, x, x^2}, x]

y == 6.999999999999996 + 3.0000000000000133*x + 2.*x^2

Inverting the quadratic equation

(x == (x /. #)) & /@ Solve[%, x] // Simplify

{x == -0.7500000000000033 - 0.7071067811865476*
     Sqrt[-5.874999999999986 + 1.*y], 
  x == -0.7500000000000033 + 0.7071067811865476*
     Sqrt[-5.874999999999986 + 1.*y]}

Note that x is not quadratic in y. However, the quadratic terms of the series 
expansion are

Series[#[[2]], {y, 0, 2}] & /@ % // Normal

{-0.7500000000000033 - 1.713913650100259*I + 
   0.14586499149789472*I*y + 0.006207020914804047*I*y^2, 
  -0.7500000000000033 + 1.713913650100259*I - 
   0.14586499149789472*I*y - 0.006207020914804047*I*y^2}

Extracting the coefficients

CoefficientList[#, y] & /@ %

{{-0.7500000000000033 - 1.713913650100259*I, 
   0.14586499149789472*I, 0.006207020914804047*I}, 
  {-0.7500000000000033 + 1.713913650100259*I, 
   -0.14586499149789472*I, -0.006207020914804047*I}}

Bob Hanlon

In a message dated 3/4/2000 3:49:44 AM, cdeacon at .physics.mun.ca writes:

>Suppose I take some data and use Fit or Regress to obtain values for
>a,b and in the equation y=a+bx+cx^2.
>
>Is there a simple Mathematica function that will let me rewrite the
>equation as x=A+By+Cy^2 and obtain values for A, B and C?
>


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