Hello everyone,

I am trying to solve the following implementation problem in Mathematica 7.0 for some days now and I do not understand exactly what is happening so I hope someone can give me some hints. I have 3 functions that I implemented in Mathematica in a source file with extension *.nb. They are working okay to all the examples. Now I want to put these functions into 3 different packages. So I created three different packages with extension .*m in which I put all the desired Mathematica function. An example in the "stereographic.m" package which contain the code:

BeginPackage["stereographic`"]

stereographic::usage="The package stereographic...."
formEqs::usage="The function formEqs[complexBivPolyEqn..."
makePoly::usage="The function makePoly[algebraicEqn] ..."
getFixPolys::usage="The function..."
milnorFibration::usage="The function..."

Begin["Private`"]
Share[];

formEqs[complex_,{m_,n_}]:=Block[{complexnew,complexnew1, realeq, imageq, expreal, 
expimag, polyrealF, polyimagF,s,t,u,v,a,b,c,epsilon,x,y,z},
complexnew:=complex/.{m->s+I*t,n->u+I*v};
complexnew1:=complexnew/.{s->(2 a epsilon)/(1+a^2+b^2+c^2),t->(2 b 
epsilon)/(1+a^2+b^2+c^2),u->(2 c epsilon)/(1+a^2+b^2+c^2),v->(-
epsilon+a^2 epsilon+b^2 epsilon+c^2 
epsilon)/(1+a^2+b^2+c^2)};
realeq:=ComplexExpand[Re[complexnew1]];
imageq:=ComplexExpand[Im[complexnew1]];
expreal:=makePoly[realeq];
expimag:=makePoly[imageq];
polyrealF:=expreal/.{a->x,b->y,c->z};
polyimagF:=expimag/.{a->x,b->y,c->z};

{polyrealF,polyimagF}
]

End[]
EndPackage[]

Now to test the function I load the package

Needs["stereographic`"]

everything is okay. But when I test the function for example with

formEqs[x^2-y^2,{x,y}]

I get the following ouput:

{Private`epsilon^2 + 2 Private`x^2 Private`epsilon^2 + 
 Private`x^4 Private`epsilon^2 - 
 6 Private`y^2 Private`epsilon^2 + 
 2 Private`x^2 Private`y^2 Private`epsilon^2 + 
 Private`y^4 Private`epsilon^2 - 
 6 Private`z^2 Private`epsilon^2 + 
 2 Private`x^2 Private`z^2 Private`epsilon^2 + 
 2 Private`y^2 Private`z^2 Private`epsilon^2 + 
 Private`z^4 Private`epsilon^2, 
 8 Private`x Private`y Private`epsilon^2 + 
 4 Private`z Private`epsilon^2 - 
 4 Private`x^2 Private`z Private`epsilon^2 - 
 4 Private`y^2 Private`z Private`epsilon^2 - 
 4 Private`z^3 Private`epsilon^2}

Of course I do not understand why Private` appears in front of any local variable which I returned in the final result. I would want not to have this Private` in the computed output. Any idea or better explanations which could indicate me why this happens?

Thank you very much for your help.

Best wishes, madalina