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How to obtain explicit symbolic output?

Posted 1 month ago
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I want Mathematica to give a symbolic output, actually, the last cell of the attached notebook, is a real number which has to be written out as an explicit function of the declared real parameters, defined at the beginning of the notebook. However, I do not succeed in Mathematica giving the result. May someone help me?

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I think what you have found is an explicit symbolic output. Perhaps what you want is an expression that does not involve Im and I? For that kind of purposes you can use ComplexExpand. However, in your special case you have square roots that make things complicated, as ComplexExpand works in the geneal case of a complex-valued square root. In the assumption that those square roots have real values (that may or may not be your situation), you can bypass the roots with a trick and get a formula that is not too complicated:

sost1 = {Sqrt[(2 + (-1 + g) m1^2)/(1 - g + 2 g m1^2)] -> root1,
   1/Sqrt[((2 + (-1 + g) m1^2)/(1 - g + 2 g m1^2))] -> 1/root1,
   Sqrt[1 - z^2] -> root2};
sost2 = {root1 -> Sqrt[(2 + (-1 + g) m1^2)/(1 - g + 2 g m1^2)],
   root2 -> Sqrt[1 - z^2]};
Simplify[ComplexExpand[Im[prigid0[-I z]] /.
    sost1]] /. sost2
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