Source code -matrix_mutation-

Source code (Requires SageMath; optimized for Jupyter Notebook; SymPy dependency)

• matrix_mutation.sage

Notice 

• This code is free to download and modify. Use of this code is at your own risk; the author holds no responsibility for any damages or issues resulting from its use.

A plain-text version of the code is available at the bottom of this page for quick reference. 

Background

 To prove the sign-coherence of C-patterns of type H3 and type H4 in this paper, I temporarily used the computer. (I believe we should give an alternative and beautiful proof of this fact sooner or later.)

 Since nice and useful programs have already been served by Dylan Rupel and Salvatore Stella (see this page in SageMath) and by Bernhard Keller (see this page), most people will not have to use my program. However, I would like to put this program on this page since I wrote it on the paper.

If you find any errors or have suggestions for improvement, please feel free to contact me via email (adress: akagi.ryota.303 at gmail.com or ryota.akagi.e6 at math.nagoya-u.ac.jp).

How to use

This program provides the following functions to explore cluster algebra mutations: 

Functions:

• B_pattern(B0,l)

• C_pattern(B0,l)

• G_pattern(B0,l)

• BC_pattern(B0,l)

• BG_pattern(B0,l)

• CG_pattern(B0,l)

• BCG_pattern(B0,l)

Arguments:

• B0 is a square matrix representing the initial exchange matrix.

•  l is a positive integer denoting the maximum mutation depth.

After loading the sage file, you can call function_list() to display the list of available functions. 

Each function computes and lists all distinct matrices obtained through mutation up to permutation.

Notice 

• Please be aware that setting l to a large value may result in significant computation time. This is because the program performs a comprehensive comparison of each new matrix against all previously obtained matrices to eliminate duplicates, which becomes computationally expensive as the mutation tree grows.