Thricegreat's Webpage
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>the_quintic_problem By the way historically the origin was the quintic problem. But that era has ended and Galois theory is used in number theory the most. I could even say that it is basically linear algebra for number theory. So study hard if you were interested in number theory.
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>the_quintic_problem Therefore an equation of degree n has general solutions if and only if Sn is solvable. And since Sn is a finite group, it means whether Sn has a composition series in which all factor groups are Zp. This corresponds to that by adding the primitive p-th root of unity, you can extend the base field to the field that factorizes the polynomial. But for n>4, An is simple so that Sn is not solvable.
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>the_quintic_problem I will not explain long. The solutions for a cubic equation depend on a+bw+gw^2 (Lagrange resolvent) and the permutations of {1,w,w^2}. Because in the end those permutations form the Galois group which fixes the base field. So it all depends on the structure of S3. Similarily for a quartic equation, {1,i,i^2,i^3} and its permutations S4. And so on.
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>diary By the way, speaking of Katawa Shoujo I like Emi route the most. 幽玄. A singularity and its monodromy group. It's really insightful. Especially Mutou in that route is my favorite.
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>diary Katawa Shoujo came as the first example. Interesting. Could you explain why? Besides Hanako route, I haven't thought that loneliness is a main theme of it.
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danielstrawb
1 year ago
Personally, i completed only Rin's route, and i see her route really depressing. Now i'm writing Rin's character analysis, but busy now....
>Analogy Analogy is just how a visual thinker tries to explain the image in own mind. If you have to "understand" or consider it a "tool", you are definitely not a visual thinker and analogy is not for you.
>mika.html After the long time, I came Neocities again and the first webpage I saw was this; Well Mika kawaii :). Though my oshi in blue archive is Noa.
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It seems that Neocities blocking Tor has been fixed. So I'll reuse this Neocities page for a clearnet mirror. I don't know. If Neocities blocks Tor again, it will be gone again.
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Oh, that's cool! :D