Dear all,

Motivated by problems about modular forms, we want to find the ring 
structure of Hecke algebra. Therefore, I have written some codes in Sage to 
compute the finite-dimensional algebra by a list of commuting matrices and 
I want to contribute it to Sage. Here is the idea of my codes.

1. We can construct the algebra as a quotient of a polynomial ring(by using 
the homomorphism which sends each x_i to t_i, where t_1,...,t_n is the n 
matrices generate the algebra), we can also get the basis by doing this.

2. With the basis of the algebra, we can also compute the multiplication 
table then use the finite-dimensional algebra command in Sage to get a 
description to this algebra.

Once we have done with these things above, we can get the ring structure of 
the algebra. This is very useful in dealing with some problems about 
modular forms since we can further study the prime ideals or maximal ideals 
of Hecke algebra by using its ring structure.

I'm an undergraduate student and this is part of my research project and I 
want to contribute my code to Sage. I have put my code on my GitHub page so 
that you can clearly  see the code. If you have some questions or comments 
on this(or you find some bugs in this code), we can discuss about it here.

Here's a link of my code in GiHub(see the code called "Finite generated 
algebra as a ring")
Dongulas/Dongulas: Config files for my GitHub profile. 
<https://github.com/Dongulas/Dongulas/tree/main>

(I have posted a similar discussion on Sage-devel before, but I think it's 
better to add the link of my code here to make the idea more clear.)

Thanks in advance!


Best wishes,
Li Yingdong

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