Nice. 

He closes his eyes and naps for real. 

The mouse is sitting on El's shoulder in Kareen's third class, arcanism.

In the game, El's skill level is one of the things controlled by the difficulty slider. By default she is good, best save the player character in this specific class though not best in the entire school (not that anyone in the school who lacks plot relevance ever matters or sits to the player character's immediate left), but not hard to outperform by applying non-computer-program talent to the applicable minigames. But you can turn it up so high that it's actually mathematically impossible to beat her without supernatural luck with the RNG; that doesn't make the romance route impossible to win, just debuffs you a bit for some relevant plot flags, and it unlocks a pretty cool cutscene where she casts eight spells at once. (The player character can kinda do that but only if they add additional controllers of some kind to their machine; no normal input system will allow it alone and the fact that Roses of Villarosa not only supports keyboard, mouse, Playstation, and dance pad spellcasting, but supports all of those things at once, is much memed upon. Normally you would only start eight spells at the same time to then immediately drop whichever four of them you got the worse RNG on and Ultra Punishing Difficulty El can just do it.)

This might or might not be Ultra Punishing Difficulty El. That one looks the same as Normal Difficulty El, when they're just petting Precious, sitting to Kareen's immediate left.

Precious is adorable. 

Kareen hopes this is Ultra Punishing Difficulty El. Kareen is better at magic than the game lets you be, although obviously that's less to her credit than it is to El's since Kareen literally customized the magic system for her to be good at it. Even if Kareen doesn't succeed at not making an enemy of El, she is just actually in favor of people being good at magic, once the magic isn't evil fearmurder stuff.

"Your familiar is so cute," Kareen whispers. 

El is not programmed destined to take a dislike to Kareen until Kareen moves in on her fiancé! "Her name is Precious," she murmurs back.

"That's a good name! My familiar is named Macula. Because I got him when I was a child."

"...ah, yes, Macula, right up there with Stripes and Doggie."

"You know, I bet Doggie would be a pretty funny name for a cat."

"It's been done, I'm sure."

"I'm sure everything's been done somewhere."

"She says she met a cat today."

"It could be mine! He's around here somewhere. He prefers to talk in person, most of the time, so I wouldn't expect to know yet." 

"Missing an ear?" El asks, tickling Precious under the chin.

"That's him! Unless someone else here has an equally-battered kitty, which I wouldn't expect. He was a stray for a while before I found him."

"Well, she appreciates that he didn't pounce."

"He can tell a familiar from a normal animal!"

"Huh, how?"

"...Inquiry powers leaking down the familiar bond, basically."

"Huh."

And then the teacher wants them to pay attention to their magic class. In the game this is about how to play the spellcasting minigame but here it's more interesting.

Oh, magic is wonderful. Kareen "remembers" being good at the spellcasting minigame but real magic is so much better. Kareen takes extremely dense notes. 

El takes a lot of notes too.

Her charms on her wrist become visible when she pushes up her sleeve to do so: diligence, integrity, magic.

That is pretty unsurprising considering what Kareen knows about her. Diligence avatar, daughter of a heavy-hitter Integrity avatar, really good at magic. Really Kareen could stand to wear a Magic charm more often herself, it's just. Eye Eye Eye.

If you're speaking formally, here it's Inquiry Inquiry Inquiry!

The game didn't want to spend too much time in school, so the classes were just history (for lore infodump), foreign language (content almost completely elided, teacher a huge softie about chattering with your love interest as long as you "say it in High Wisachian"), and magic (for minigame purposes), but of course now it's real life and Kareen also has grammar and composition, religion, music theory, rhetoric, and mathematics and logic to occupy her days, all the things a young lady moving in high places in Villarosa ought to know.

Kareen is not speaking formally inside her own head, and also is specifically emphasizing the fact that she is so Eye that she will deliberately throw herself down the Beholding pit if Inquiry is not available. 

Magic is the best class, obviously, but any chance to soak up knowledge is an excellent thing. She is having much much less trouble catching up than most of her peers and some of her teachers are expecting. Mostly because of autodidactic tendencies, but also because she was in college in her first life, even the advanced classes here haven't caught up with what she knows about math. 

Zalor is in religion class with her!

Good for her!

Religion is a class she has some edge in, on account of having, you know, designed the gods, but the worldbuilding team filled in a lot of details, so she's still learning things!

Actually she has more of an edge from having grown up in a temple than from having designed the gods. That does in fact help a lot. 

Fingers crossed that the teacher doesn't say anything insensitive about Fairness in front of Zalor.