鼻水🍶🌖 retweeted
#数楽 これは興味深い。
プロンプトの問題中の多項式はp=53でのみ分岐する有理数体のPGL₂(𝔽₇)-Galois拡大(PGL₂(𝔽₇)-53 field)を与える8次の多項式。
文献:
* hobbes.la.asu.edu/papers/One…
* pdfs.semanticscholar.org/7e7…
Repeating the same experiment but one year later. GPT 5.6 Pro cannot be used vanilla for this prompt because it immediately fires the right CAS command to compute the Galois group. So instead I used a very restrictive prompt. One year has passed since GPT 5 Pro premiere, GPT Pro 5.6 is now able to compute the result from first principles, including the resolvent construction. This is like seeing a model building a whole Galois theory course live. It's so nice to learn from this output, very detailed!
chatgpt.com/share/6a7728bd-f…
Prompt:
Compute the Galois of the polynomial
x^8-x^7+3*x^6-3*x^5+2*x^4-2*x^3+5*x^2+5*x+1
Don't look up the result in the internet nor any specialized database. Don't use ready made commands from SymPy or any other program. Develop a full resolvent computation. Do it all the way down to the definitions, no excuses, like there is no tomorrow.
鼻水🍶🌖 retweeted
Repeating the same experiment but one year later. GPT 5.6 Pro cannot be used vanilla for this prompt because it immediately fires the right CAS command to compute the Galois group. So instead I used a very restrictive prompt. One year has passed since GPT 5 Pro premiere, GPT Pro 5.6 is now able to compute the result from first principles, including the resolvent construction. This is like seeing a model building a whole Galois theory course live. It's so nice to learn from this output, very detailed!
chatgpt.com/share/6a7728bd-f…
Prompt:
Compute the Galois of the polynomial
x^8-x^7+3*x^6-3*x^5+2*x^4-2*x^3+5*x^2+5*x+1
Don't look up the result in the internet nor any specialized database. Don't use ready made commands from SymPy or any other program. Develop a full resolvent computation. Do it all the way down to the definitions, no excuses, like there is no tomorrow.
鼻水🍶🌖 retweeted
aの値を次々変えていくと、 x1^(x2+a)-x2^(x1+a) は正負ほぼ半々で出現するように見える。
そこで s(a)= sgn(x1^(x2+a)-x2^(x1+a)) として、
S(n)= Σ_{a=1}^n s(a) を考える。 ±1 が等確率で出るならS(n) は0を中心に振動するはずだが n=2000までのグラフは次のようになり、正がやや多め（続く）
鼻水🍶🌖 retweeted
This isn't science fiction anymore. 🧲
The Chinese University of Hong Kong researchers developed a magnetic slime robot that can be remotely controlled to move, squeeze through tight spaces, and even grasp objects.
One potential application? Removing objects accidentally swallowed inside the human body without traditional surgery.
Soft robotics is opening doors that rigid robots simply can't.
Would you trust a robot made of slime inside your body?
🎥 Media: @newscientist , Li Zhang and The Chinese University of Hong Kong
⚠️ This content is shared for informational purposes only. CTO Robotics Media is a media platform and does not own or develop the technology shown. Credit belongs to the original creators.
#Robotics #SoftRobotics #MedicalRobotics #Engineering #Innovation #FutureTech #Science
鼻水🍶🌖 retweeted
Gallium based liquid metal that squirms due to an electron transfer reaction that changes the surface tension of the alloy.
