I’ve been reading Algebraic Number Theory and Fermat’s Last Theorem by Ian Stewart and David Tall in a seminar this summer holiday.

I found that ring of algebraic integers has some very nice properties, which makes it behaves like the ring of rational integers $\mathbb{Z}$. For instance, we know:

The ring of integers $\mathfrak{O}$ of a number field $K$ has the following properties:

1. It is an ingegral domain, with the field of fractions $K$.
2. It is noetherian.
3. $\forall \alpha\in K$ satisfying a monic polynomial equation with coefficients in $\mathfrak{O}$, then $\alpha\in\mathfrak{O}$.
4. Every non-zero prime ideals of $\mathfrak{O}$ is maximal.

Isn’t it nice? Such kind of large famliy of rings, where all of which shares such well properties, has been really rare.

I’ve been tinkering with something fascinating lately — a fully file-based immersive teaching system that turns a vanilla markdown directory into a living, breathing academic world with persistent characters, emotions, and memory.

What a pleasure live & learn with Togawa Sakiko & Wakaba Mutsumi! It’s just like a interactive Galgame.

The project is nearly finished as a “beta version”– I’m using it and see if there’re any bugs. If you are interested in this project, see Learning algebra in an interactive galgame

I tranplanted my nvim config file from .vim to .lua. I heard there’re some better alternatives in nvim plugins community comparing to vim community where I used to be at. Hence as I result I replaced vim-plug with lazy.nvim, auto-pairs with nvim-autopairs. I’m quite satisfied so far.

First time using AI agent!

I tried Opencode with Deepseek api to help me with my galgame developing, and it’s way more efficient than the traditional web-based chatbot AI. It has access to my specified directories, which is way more convenient than manually uploading files. It can even dispatch subagents to handle tasks on its own—a huge efficiency boost.

Also, tokens from Deepseek V4 are indeed really cheap. I’m now using it to do tedious works or those I’m not so familiar with. Let’s just hope it doesn’t crash my repo.

Now that the three core subsites (math, blogs, posts) of this domain are basically done, I’ve redesigned the whole site to go for a galgame-style reading experience.

This is my first post at my site using Hugo, kind of excited. The web configuration was easier than I thought.

I tried Tridactyl to replace Vimium C , which I’ve been using for quite a while.

It’s always a pleasure to use vim-keybindings in web browsers. I’ve already heard of Qutebrowser , but it seems to be kind of counterintuitive to use – as I’m used to nice gui-interface in my web browser. Also, I do really appreciate my current browser Zen for its elegant UI&UX as well as innovative functionalities. Therefore I was looking for a better vim-keybindings experience without leaving Zen, where Tridactyl shows up.

I’m still transforming my habits & muscle memory in Vimium C to suit Tridactyl. So far, I can say the gi behaviour (for focusing input) is being worse. h/j/k/l for moving web pages was kind of laggy, where the page will pulse for a while before continuous scrolling, as it’s not the one I’m accustomed to in Vimium C. But the native messenger was game-changing, as it enables me to use neovim in a floating terminal window to edit input in web – I’m loving it.

I’ll try Tridactyl for a while, unless I found it really not being my cup of tea.