# Exercise

## range

Write an iterable class like range, but without returning a whole list, but storing only the actual element.

``` class Range:
def __init__( ... ):
...
def __iter__( ... ):
...
def __next__( ... ):
...```
• Its constructor should have one parameter: a number or a string. The iteration should go up that number, from 0 with 1 steps.
• If the number is not positive, then the iteration should take 0 steps.
• If you get a string then try to convert it to a number. If it cannot be converted, then raise a ValueError exception.
• If it is a valid integer, then calculate with that.
• If you get the string "inf" then make the iteration go endless (infinite loop)!

## Shapes

Write a class called Shape.

• Let it have two members: x and y, the coordinates of the shape on the plane (center of mass).
• Define a move method, with one parameter v: a list of length 2, a vector to translate the shape with. After this method the coordinates should be changed.

Define the following classes as children of Shape:

• Ellipse with additional parameters (except the (x, y) coordinates): a and b the x and y axes radii
• Rectangle with additional parameters (except the (x, y) coordinates) a and b the length of the sides

Write an area method for both, which calculates the area!

Define an equation method for printing the equation of the Ellipse! Something like:

```   ((x-1)/2)^2 + ((y-2)/3)^2 = 1
```

## Palindrome

Write a function, called Palindrome, with one parameter which is a string. The function should check whether the string is a palindrome or not. The function should return "True" if the string is a palindrome, otherwise It returns "False".

## Mersenne Prime

Write a function, called Mersenne, with one parameter which is an integer. The function should check whether the number is a Mersenne Prime or not. The function should return "True" if the number is a Mersenne prime number, otherwise It returns "False".

## Average

Use variadic function strategy to write a function average which gives the average of all numbers from the parameters. For example:

``` average(2, 3, 4) --> 3
average(2, 3, 4, 5, 6) --> 4
average(2, 3, 4, 5, 6, ...)
```

## Union Sets

Use variadic function strategy to write a function which gives the union of any number of sets. For example:

``` union({1, 2, 3 }, {2, 3, 4}, {3, 4, 5}) --> {1, 2, 3, 4, 5}
```

Hint: use .update() method to add a new element to a set.