Comp Sci Computional Methods Problem with Fortran programming

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Fortran programming can be utilized to represent permutation groups through a data structure, focusing on N elements, ideally N=9 or less. The project involves creating a module that includes type definitions, functions, and subroutines, with operator overloading for multiplication and exponentiation of permutations. Key functionalities to implement include inverting permutations, converting to cycle notation, and determining if a permutation is even or odd. While some programmers may view operator overloading as poor practice, numerous resources are available for guidance. Exploring algebraic structures beyond permutations could also enhance the project.
kevek
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Is there anyone familiar with Fortran programming, who can give me some simple ideas or resources how can I strart this project? Many thanks


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.
 
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