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by PreInternet01 2y ago
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- ogogmad 2y agoI don't think this is Galois theory. Galois theory is about "The Fundamental Theorem of Galois Theory", which states that there is a nice mapping from field-extensions to group-extensions, where the resulting groups are usually finite. When the resulting groups are finite (as they usually are), many problems involving field extensions can be solved using brute-force search. Galois fields happen to be something else named in honour of Galois.
- koolala 2y agoGalois Fields yeah. Being able to store Rational Numbers in a computer. "Originally, the theory had been developed for algebraic equations whose coefficients are rational numbers."
- matt-noonan 2y agoThat is definitely not what Galois Fields are about.
- koolala 2y agohttps://en.m.wikipedia.org/wiki/Galois_theory#Permutation_group_approach https://en.m.wikipedia.org/wiki/Galois_theory#Permutation_gr... That quote about equations with rational numbers was from here. Galois didn't have a computer of course. Rational Numbers and trisecting an angle sound related.
- wging 2y agoThe quote is followed immediately by this: "It extends naturally to equations with coefficients *in any field*, but this will not be considered in the simple examples below." Emphasis on 'in any field' is mine. Among the other fields that can be considered include the Galois fields, which are another name for finite fields. (There are also infinite fields other than the rationals, so 'in any field' does not just mean Galois fields/finite fields.) https://en.wikipedia.org/wiki/Finite_field https://en.wikipedia.org/wiki/Finite_field Galois fields have nothing to do with being able to represent rational numbers in a computer: elements of a finite field aren't even rational numbers.
- koolala 2y agoI can see how the idea extends naturally and also how it doesn't extend naturally. Thanks for explaining, I wonder what Galois would do if alive today with computers.
- graemep 2y agoPatent threats can be used to stop something being taught, rather than being used? That is awful.
- koolala 2y agoMy memory of the story was they got some research funding from the troll company and were naive about human greed.
- koolala 2y agoI had no idea Plank's work connected to Galois. I wish a University was able to publish free open information but money decides research.