How Can Fortran Be Used to Manipulate Permutation Groups?

[kevek]

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.

 

[lippyka]

5. Create a subroutine that determines whether two permutations are conjugate.6. Create a subroutine that calculates the order of a permutation.7. Create a subroutine that generates all permutations of N elements.8. Create a subroutine that determines whether two permutations are equal.9. Create a subroutine that implements the disjoint cycle notation.10. Discuss how to implement the Sylow theorems.Resources: 1. The Fortran Wiki website provides an extensive range of resources and tutorials for learning Fortran programming. 2. "Fortran 90/95 Programming Manual" by Ian Chivers and Jane Sleightholme is an excellent resource for learning Fortran programming. 3. "Modern Fortran in Practice" by Metcalf, Reid and Cohen is another great resource for learning Fortran. 4. You can also find some online resources such as tutorials and video lectures for learning Fortran programming.