純粋・応用数学・数学隣接分野（含むガロア理論）12

[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）12 (1002ﾚｽ)
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764: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2023/01/15(日) 14:08:22.48 ID:fdSQKtbP

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”CYCLOTOMIC FIELDS
WITH APPLICATIONS” 188ページものPDF
リンク貼る

そこそこ纏まっている気がする
あと、2018と新しいのが良い

FFTとDFT（離散フーリエ）にも触れているが
CYCLOTOMIC FIELDSが、FFTとDFTの基礎になっているみたいなニュアンスと読んだ

file:///C:/Users/seta/Downloads/cyclotomic_fields2018.pdf
CYCLOTOMIC FIELDS
WITH APPLICATIONS 188ページもの
Lecture Notes for Math 5590
Fall 2018
G. Eric Moorhouse
University of Wyoming

P44
The Fast Fourier Transform
The Fast Fourier Transform (FFT) was known to Gauss at least as early as 1805
(predating Fourier, after whom the transform has been named). More recently, it was
rediscovered by many others, notably Cooley and Tukey (1965). The point is that the
Discrete Fourier Transform (DFT) over a large finite group, viewed as a square matrix,
may appear quite large, requiring extensive time (presumably by a computer) in its computation. However due to the highly structured nature of this matrix, this computation
can be performed in fewer steps than one might at first suppose. It is this faster approach
to computing the DFT that accounts for the name FFT. The importance of this speedup is
due to the vast number of problems requiring DFT for their solution, and where computational time required would otherwise be expensive or prohibitive. We begin by describing
how the FFT works. We then give an application to fast multiplication for polynomials
and for integer
略
P46
略
This is the idea of the FFT. Its applications are far too ubiquitous to be summarized here.
We content ourselves with describing two of the many applications of FFT
Fast Polynomial Multiplicatio
(FFTの応用 以下P49まで)

http://rio2016.5ch.net/test/read.cgi/math/1671460269/764

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