Talk:S-expression: Difference between revisions

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So we see for ''k'' = 4''n'', 4''n'' + 1, and 4''n'' - 2, a coefficient of 22 is canceled out, whereas for the ''k'' = 4''n'' - 1, a coefficient of 2 is canceled out. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:31, 7 February 2022 (UTC)

: I figured something like this would be possible but I sometimes get lost in how to simplify and group stuff in intermediate steps when I do it that way or I make mistakes simplifying/expanding so I tried to use the most intuitive approach I could think of. The observation that k=2n leads to a factor of 4 I think is a relatively intuitive explanation of why ~~its~~ superparticular for those cases. Also, it took me a little while but I believe S(k)/S(k+2) = (k+3)/(k-1) * k2/(k+2)2 is the equation you substituted into for the four cases? (Just arranged as one single fraction.) --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:45, 7 February 2022 (UTC)

: I figured something like this would be possible but I sometimes get lost in how to simplify and group stuff in intermediate steps when I do it that way or I make mistakes simplifying/expanding so I tried to use the most intuitive approach I could think of. The observation that k=2n leads to a factor of 4 I think is a relatively intuitive explanation of why it's superparticular for those cases. Also, it took me a little while but I believe S(k)/S(k+2) = (k+3)/(k-1) * k2/(k+2)2 is the equation you substituted into for the four cases? (Just arranged as one single fraction.) --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:45, 7 February 2022 (UTC)

:: Yup that's the equation I started from. We may go even more primitive if we want, such as from the definitions. It doesn't matter in the end. I consider the elementary algebraic operations an easy problem, i.e. the solution is guaranteed by a known routine. All the tricks on the other hand involve observation and intuition. I mean, it's totally reasonable for one to apply them to instantly gain the insight, but I take the liberty of assuming the readers' expectation here is a solid and sound presentation of the result. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 00:55, 8 February 2022 (UTC)

@@ Line 50: / Line 50: @@
 So we see for ''k'' = 4''n'', 4''n'' + 1, and 4''n'' - 2, a coefficient of 2<sup>2</sup> is canceled out, whereas for the ''k'' = 4''n'' - 1, a coefficient of 2 is canceled out. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:31, 7 February 2022 (UTC)
-: I figured something like this would be possible but I sometimes get lost in how to simplify and group stuff in intermediate steps when I do it that way or I make mistakes simplifying/expanding so I tried to use the most intuitive approach I could think of. The observation that k=2n leads to a factor of 4 I think is a relatively intuitive explanation of why its superparticular for those cases. Also, it took me a little while but I believe S(k)/S(k+2) = (k+3)/(k-1) * k<sup>2</sup>/(k+2)<sup>2</sup> is the equation you substituted into for the four cases? (Just arranged as one single fraction.) --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:45, 7 February 2022 (UTC)
+: I figured something like this would be possible but I sometimes get lost in how to simplify and group stuff in intermediate steps when I do it that way or I make mistakes simplifying/expanding so I tried to use the most intuitive approach I could think of. The observation that k=2n leads to a factor of 4 I think is a relatively intuitive explanation of why it's superparticular for those cases. Also, it took me a little while but I believe S(k)/S(k+2) = (k+3)/(k-1) * k<sup>2</sup>/(k+2)<sup>2</sup> is the equation you substituted into for the four cases? (Just arranged as one single fraction.) --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:45, 7 February 2022 (UTC)
 :: Yup that's the equation I started from. We may go even more primitive if we want, such as from the definitions. It doesn't matter in the end. I consider the elementary algebraic operations an easy problem, i.e. the solution is guaranteed by a known routine. All the tricks on the other hand involve observation and intuition. I mean, it's totally reasonable for one to apply them to instantly gain the insight, but I take the liberty of assuming the readers' expectation here is a solid and sound presentation of the result. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 00:55, 8 February 2022 (UTC)