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Laveling solution in package. Problems with context


I have a package such as the follow (it is an easy example of the real package).

BeginPackage["Test`Test`"]

fTest::"usage" = "fTest gives solution."

Options[q] = {AI1 -> 0.3 AI, AI2 -> 0.6 AI, AI3 -> 0.1 AI};

Begin["`Private`"]

fTest[int_List, t_, t1_, opts___Rule] := Module[{ic, sol}, 
      ic = {AI1, AI2} /.{opts} /. Options[q];
      sol = Dot[ic, int];
      Thread[{q1[t1], q2[t1]} -> sol]];

End[]

Protect[fTest];

EndPackage[]

I test the package

in[]:=fTest[{a1 Exp[-b1 t], a2 Exp[-b2 t]}, t, t1, AI3 -> 0.9 AI]

out[]:={Test`Test`Private`q1[t1] -> (0.3*a1*AI)/E^(b1*t) + (0.6*a2*AI)/E^
(b2*t), Test`Test`Private`q2[t1] -> (0.3*a1*AI)/E^(b1*t) + (0.6*a2*AI)/E^(b2*t)}

Of course, I receive the message that q1[t], q2[t] are defined in a private 
context. How can I fix this problem?.

I know that using fTest[int_List, t_, t1_, q1_, q2_, opts___Rule] the problem 
is solved but I can avoid write q1 and q2 in  fTest.


 

But I wish that the solution will be labeled with q1[t],
q2[t].

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