> sage: x = "this is x"
> sage: y = "this is y"
> sage: z = "this is z"
> sage: def f():
> ....:     print x
> ....:     y = "new value"
> ....:     print y
> ....:     global z
> ....:     z = "new value"
> ....:     print z
> ....:
>
> sage: f()
> this is x
> new value
> new value
>
> sage: x, y, z
> ('this is x', 'this is y', 'new value')

Yes it's true, that's the behavior I was referring to. My problem was
actually that I couldn't print a global variable inside a function
before I made an assignment to it; the error was something like
"Cannot istantiate a local variable before assigning it." and I didn't
understand why I had to assign locally a global variable which had
already been assigned globally. Anyway the keyword "global" solved my
problem.

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