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I have the following code which sets up a Reduce function call:

xX = List[x[0, 0], x[0, 1], x[1, 0], x[1, 1]]
yY = List[y[0, 0], y[0, 1], y[1, 0], y[1, 1]]

psiTarget = 
 List[Sin[δ], 0, Cos[δ] Cos[γ], 
  Cos[δ] Sin[γ]]

sqrtlambdaPlus := 
 Sqrt[(1/2) (1 + Sqrt[1 - ((Sin[2 δ])^2) (Sin[γ])^2])]
sqrtlambdaMinus := 
 Sqrt[(1/2) (1 - Sqrt[1 - ((Sin[2 δ])^2) (Sin[γ])^2])]

varsList = Join[xX , yY]

Reduce[psiTarget == sqrtlambdaPlus*xX + sqrtlambdaMinus*yY  && 
  xX.yY== 0 && xX.xX== 1 && yY.yY== 1, Flatten[varsList]]

I am unable to get a solution for the Reduce function however, as it keeps running for a very long time. I do expect there to be a solution, but unfortunately I do not get one with this method. The Solve function returns empty brackets, but I don't expect it to. What could be the issue?

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  • 3
    $\begingroup$ Welcome to MSE. Please post code that can be copied/pasted and evaluated. $\endgroup$ Aug 3, 2021 at 18:39
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    $\begingroup$ Please edit your question to include copy and paste-able code rather than images of code. $\endgroup$
    – Bob Hanlon
    Aug 3, 2021 at 18:40
  • $\begingroup$ Never use upper-case letters to start your variables or functions (e.g., X, Y, VarsList, ...) as they can conflict with internal function names. $\endgroup$ Aug 3, 2021 at 20:29
  • $\begingroup$ Thanks for the suggestions, I have edited the question. $\endgroup$ Aug 4, 2021 at 0:55
  • $\begingroup$ If you remove the extra conditions on the xX and yY (i.e., the orthogonality and the normalization) then Solve gives an answer for y[0,0] in terms of x[0,0], for y[0,1] in terms of x[0,1], for y[1,0] in terms of x[1,0] and for y[1,1] in terms of x[1,1]. Moreover, the terms multiplying the x[i,j] are identical in all four equations. You could clearly normalize the ys but the other two constraints might be problematic. $\endgroup$
    – bill s
    Aug 4, 2021 at 2:31

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