function call - default value & collecting arguments

[Primoz Skale]

Hello!

I am fairly new to Python, so I apologise if this is a 'newbie' question.

First define a simple function:

def f(a=0):
    print a

>> f(1)
1
>>f()
0

Argument a in function f() is set at default value of 0, if it is not passed 
to the function at the function call. I get this! :)

I also understand (fairly) how to collect arguments. For example, let's 
define another function:

def f(*a):
   print a

>>f(1)
(1,)
>>f(1,2)
(1,2)
>>f()
()

OK, everything allright till so fair. But! :) Now define third function as:

def f(*a):
   print a[0]

In this case, function only prints first argument in the tuple:

>>f(1,2,3)
1
>>f(3)
3
>>f()    #no arguments passed
Traceback (most recent call last):
  File "<pyshell#425>", line 1, in <module>
    f() #no arguments passed
  File "<pyshell#422>", line 2, in f
    print a[0]
IndexError: tuple index out of range

Then I tried to define the function as:

def f(*a=(0,)):
  print a[0]  #this should come next, but we get error msg instead, saying

          SyntaxError: invalid syntax

but it does not work this way. Now my 'newbie' question: Why not? :)
I wanted to write function in this way, because then we can call function 
without any arguments, and it would still print 0 (in this case).

What I wanted was something like this:

def f(*a=(0,)):
  print a[0]

>>f(1,2)
1
>>f()  #no args passed
0

but this of course does not work. Again, why not?

Thank you for your comments.

Primoz