Cayley Transformation Matrix and Weierstrass Quadratic Form

A moment later, the class bell rang. Zhang Wanbang walked into the classroom with a stack of test papers. It was his math class.

"Yesterday's in-class math test was quite difficult," Zhang Wanbang said with a cold expression. "I've graded all the papers, and I'm disappointed, very disappointed!"

"Even if it was difficult, it's unacceptable that only five students scored above 120!"

"What's going on with you all? Do you even want to go to college anymore!"

"Hopeless!"

Bang bang bang!

Zhang Wanbang habitually slammed the podium. Fortunately, the wooden podium was of good quality. Otherwise, after years of abuse from Zhang Wanbang, it would have rotted away long ago.

Silence fell over the students below, so quiet it was oppressive.

"Only one person surprised me." Zhang Wanbang looked towards Shen Qi's seat and suddenly said, "Shen Qi."

"Huh!?" Shen Qi jolted and stood up. He was used to it; he stood up whenever the teacher called his name.

"Who told you to stand up? Sit down!" Zhang Wanbang said to Shen Qi.

"Oh." Shen Qi sat back down.

"I've been teaching for seventeen years and have taught countless students. Of course, I've seen perfect scores on tests, but in the last three years, no one has gotten a perfect score on my exams." Zhang Wanbang pulled out a paper from the stack on the podium and walked to Shen Qi's desk. "Shen Qi, you did it. You got a perfect score of 150."

"Really!" Shen Qi saw that the paper in Zhang Wanbang's hand was his. The score section of the test clearly had a red number: 150.

"150?"

"Perfect score?"

"Shen Qi?"

The classroom erupted. If Huang Zikun had scored 150, the classmates might have understood.

But for Shen Qi, who was usually at the bottom of the rankings, to get a perfect score in math seemed incredibly surreal.

Huang Zikun smiled and shook his head. "I couldn't get a perfect score on Teacher Zhang's papers. Shen Qi is amazing. One should look at him with new eyes after a few days apart."

Chen Xiaoting: "What do you mean 'a few days apart'? We see each other every day. We only rest one day a week. Shen Qi, you said you've been listening carefully in class and doing practice problems at home. I've put in just as much effort in math as you have, so why can't I get a perfect score? You must have obtained some supreme secret technique. Quick, teach me!"

Chen Xiaoting was Shen Qi's deskmate. She wasn't stunningly beautiful, but she had fair skin and a tall, slender figure.

"Xiaoting, I completely understand your eagerness to learn. Don't be anxious, don't panic. We have plenty of time, let's take it slow," Shen Qi said.

"Mhm, don't just get rich yourself and forget about others. A man's word should count!" Chen Xiaoting was convinced that Shen Qi must have gotten some math cheat sheet or guidance from an expert, otherwise his math scores wouldn't have improved so dramatically in such a short period.

Xu Rui watched this unfold, feeling increasingly dejected. People nowadays were too pragmatic. Good grades meant you could have a girl? Good grades meant you could be arrogant? How vulgar!

After a brief period of commotion, the class returned to its normal teaching order, and Zhang Wanbang began explaining the math test.

Shen Qi's perfect score of 150 stunned everyone, making both his teacher and classmates see him in a new light. He earned the respect of a girl, and studying made him feel happy.

Good news kept coming. The system suddenly chimed: "Congratulations, Host, on achieving your first achievement in the real world: First place in the math exam in the entire class! Reward: 2000 scholar points."

The system information changed:

Host's remaining scholar points: 3143 points

"Awesome!" Shen Qi maintained a calm exterior, but inside he was ecstatic. It turned out that achieving things could earn a large amount of scholar points. It would have taken him months of grinding to earn 2000 scholar points.

So, achieving goals was a shortcut. The in-class test was just a small exam. If he could get first place in major exams like midterms or finals, he'd be raking it in. Shen Qi eagerly anticipated the next big exam.

After class, Shen Qi was called to Teacher Zhang's office alone.

This wasn't Shen Qi's first time in Zhang Wanbang's office. He had been there more than ten times before, and each time he had been severely scolded.

This time, Zhang Wanbang didn't scold Shen Qi. Instead, he took out Shen Qi's phone. "I've kept your phone for over ten days. The battery is dead. Take it back and charge it yourself."

Shen Qi took his phone. "Thank you, Teacher Zhang."

"In this day and age, it's not just high school students, even elementary school kids have phones. This is the reality of society. The school can only advocate against bringing phones, but it's hard to eliminate them completely. Shen Qi, I have only one request: from now on, don't play with your phone right under my nose." Zhang Wanbang had already gone above and beyond by saying this much.

"Absolutely, absolutely." Shen Qi nodded repeatedly.

"I've noticed you've been quite diligent lately," Zhang Wanbang praised him.

In Shen Qi's memory, ever since he started high school, Zhang Wanbang had never praised him. This was the first time, a truly unprecedented event.

"Teacher Zhang, for a long time, I've had a dream, which is to study hard for the great rejuvenation of the Chinese nation." Shen Qi said earnestly.

"Don't give me that empty talk. Did getting a perfect score make your tail go to your head?" Zhang Wanbang frowned. He preferred students who were down-to-earth.

"I don't want to be a loser my whole life. I heard that losers can't find wives." Shen Qi spoke the truth.

"Talking nonsense with a straight face! How old are you to be thinking about finding a wife?" Zhang Wanbang mentally filtered out the latter half of Shen Qi's sentence, but the first part was spoken sincerely. Zhang Wanbang chose to believe it. "In less than two weeks, you went from a math level of over 60 to a perfect score of 150. Shen Qi, don't tell me it was just luck. Math never relies on luck."

"About one or two weeks ago, on the day you confiscated my phone, a golden light suddenly descended from the sky and enveloped me. It was like a sudden awakening, a moment of enlightenment. I developed a strong interest in math, and I couldn't stop. Teacher Zhang, you often say that interest is the best teacher, and I firmly believe that. That's the whole story," Shen Qi said frankly and sincerely.

Smash!

Zhang Wanbang slammed his desk, scattering files everywhere. "Shen Qi, are you telling me a single true word? Are you insulting my intelligence?"

"I mean, I received some kind of mysterious power..." Shen Qi was being very honest.

"Why don't you just say you're Superman?" This goes to show that trust between people is more precious than gold. Shen Qi was telling the complete truth, but Zhang Wanbang didn't believe a word of it.

"Alright, you can go back to the classroom now." Zhang Wanbang waved his hand, dismissing Shen Qi.

As Shen Qi turned, Zhang Wanbang asked again, "For the last question on this math test, you used Cardano's formula theory. I never taught you Cardano's formula theory. Did you self-study it, or did a tutor teach you?"

"I self-studied it," Shen Qi replied.

"How far have you gotten?" Zhang Wanbang pressed. The Italian scholar Cardano's theory on low-degree equations is discussed in the elective textbooks for high school mathematics.

Shen Qi answered, "The application of the Cayley transformation matrix and Weierstrass quadratic form theory to bilinear determinants."

Zhang Wanbang was stunned. "Shen Qi, are you self-studying Advanced Algebra?"

"Yes, but Cayley's and Weierstrass's theories are too difficult to understand. I feel like I've hit a bottleneck and am struggling to grasp the core principles of matrix algebra and composite determinants. I'm so despairing, Teacher Zhang. What should I do?" Shen Qi poured out his heart, as Zhang Wanbang was the only person he could confide in.