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How would I solve for a variable in this ugly equation?

Posted 10 years ago
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Hi,
The following is the ugly equation that I am trying to solve. As you can see, the right hand side is a function of alpha and five other variables (theta_l, theta_h, i_h, i_l and delta) and the left hand side is just alpha. All I need is to solve for alpha in this equation (which will be in terms of the variables) but I'm finding that Mathematica cannot do this (I have used Solve and Reduce and Mathematica just hangs on me). Is this because of the multiple variables in the equation? Any suggestions in finding a solution is greatly appreciated. Thanks!


POSTED BY: Mel N
2 Replies
Posted 10 years ago
Thank you Bruce! With 
{\[Alpha] -> a, \[Delta] -> d, Subscript[\[Theta], L] -> TL, Subscript[\[Theta], H] -> TH}

we have:
(ih ((-1+d) d+\[Sqrt](d^2 (1-d^2+d (a^2 d TH^2-2 a TH (-1+d+a d TL+Sqrt[1-d^2+d ((-1+a) a d TH^2-2 a TH (-1+d+(-1+a) d TL)+(-1+a) TL (-2+2 d+a d TL))])+TL (2 (-1+a) (-1+d)+a (a d TL+2 Sqrt[1-d^2+d ((-1+a) a d TH^2-2 a TH (-1+d+(-1+a) d TL)+(-1+a) TL (-2+2 d+a d TL))])))))))/(d il (-1+d+Sqrt[1-d^2+d ((-1+a) a d TH^2-2 a TH (-1+d+(-1+a) d TL)+(-1+a) TL (-2+2 d+a d TL))])+ih ((-1+d) d+\[Sqrt](d^2 (1-d^2+d (a^2 d TH^2-2 a TH (-1+d+a d TL+Sqrt[1-d^2+d ((-1+a) a d TH^2-2 a TH (-1+d+(-1+a) d TL)+(-1+a) TL (-2+2 d+a d TL))])+TL (2 (-1+a) (-1+d)+a (a d TL+2 Sqrt[1-d^2+d ((-1+a) a d TH^2-2 a TH (-1+d+(-1+a) d TL)+(-1+a) TL (-2+2 d+a d TL))])))))))==a
POSTED BY: Mel N
Solve and Reduce are happiest with polynomial equations.  The nested square roots are hard for them to digest.

It would be helpful for potential helpers if the code could be posted in machine-readable form.
My suggestion:
- select (click once) the cell bracket for the cell,
- go to Edit menu, Copy As, and pick Cell Expression,
- in a reply to this thread, click the spikey in the top of the reply area,
- paste the Cell Expression for your input cell into the reply area.

The result can be copied and pasted into a Mathematica notebook for experimenting.
Simpler methods of copying and pasting are likely to loose typesetting.
POSTED BY: Bruce Miller
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