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Data Structures - The Permutation Group

In this project, the group of permutations on N elements (where N is probably fairly small, perhaps N= 9 or less) is represented as a data structure. The main program employs the USE command to access a module containing the declarations, type definitions, functions and subroutines.

The module should use operator overloading to make * the multiplication operator between permutations, and ** a permutation taken to some ower. The module should also have a function or subroutine that determines the order of the permutation.

Options

1. Create a subroutine that inverts a permutation.

2. Create a subroutine that converts a permutation to cycle notation.

3. Create a subroutine that determines whether a permutation is even or odd.

4. Discuss how other algebraic structures could be represented and calculated.