beginner question: extending python types

[Uwe Mayer]

Hi,

I am totally new to python and was about to start programming when more 
and more questions upon "how to do it actually" came up. 

My problem: I want do write classes which behave like algebraic 
structures, i.e. a group, a field or vector space and then want to work 
on them.

To my first question: 
I know I can overwrite built-in operations like add with, f.e. __add__() 
methods, but can I add new f.e. postfix operators like "!" (facculty: n! 
= 1*2*3*4*...*n)?`

My second question:
I found Python lacking the type of a "set". i.e. an unordered list. I'd 
just wanted to use a normal list and pretend there was no order. Of 
course I want to iterate over them and in section 2.2.5 of the Python 
Library Reference they say that the method __iter__() must return an 
iterator object. I couldn't find a class called iterator in the Library 
and Language Reference...

To my last question for now:
I want to force certain parameters of methods to be of a specific type, 
so that when I expect a set I'll get a set or a sub-class thereoff. How 
to I controll that? Use the type() function and raise an IllegalType 
exception otherwise?

Thanks for your help
Yours
Uwe