This page includes more examples of the matrix reduction in Section 8 - 10 of the paper Jung, Lee, and Moon. At the end of this page, there is an online calculator evaluating the matrix \star W_{r,m} for various g.

Examples for the invertibility computation for r = 3

We include a few small cases showing the invertibility computation algorithm in Section 8 - 10 of the paper. The documents were generated by ChatGPT 5.6 Sol Pro. 

• g = 3
  m = 1
  m = 2

• g = 5
  m = 1
  m = 2
  m = 3

• g = 7
  m = 1
  m = 2
  m = 3
  m = 4

Matrix Calculator

The following app is the computation of the matrix W_{r,m} and its numerical invariants including the determinant and rank. The original python code was made by Jiwan Jung, and was converted into an online app using Chat-GPT 5.6 Sol Pro.