Timeline for Non-triviality of the sum of simple rational functions
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 23, 2023 at 23:32 | comment | added | yaoxiao | @fedja thanks. It seems that $m_0$, and $n_0$ appear in the sum two times indeed, while, $m_i, _i (1\leq i\leq 3)$ appear only one time. And m_0, n_0 only appear one time in the example above you mentioned. | |
| Jul 23, 2023 at 23:27 | comment | added | fedja | @yaoxiao Nope, everything is as written, i.e., $m_0=-2, n_0=-1$. If you want to exclude negative numbers, you should say so explicitly in the formulation of the problem. As I said, some more restrictions can help, but we are not guessing which ones you really need :-) | |
| Jul 23, 2023 at 23:22 | comment | added | yaoxiao | @fedja Thanks for your comment, fedja. For the last term, whether you mean $-\frac{1-z^{-2}}{1-z^{-1}}$, thanks. | |
| Jul 23, 2023 at 23:09 | comment | added | fedja | Given that $\frac{1-z^2}{1-z}-3\frac{1-z^3}{1-z}+3\frac{1-z^4}{1-z^2}-\frac{1-(-z)^2}{1-(-z)}-\frac{1-(-z)^2}{1-(-z)}\equiv -1$, you may want to revise your question and impose some more restrictions before any good answer to it can be given ;-) | |
| Jul 23, 2023 at 19:16 | review | Close votes | |||
| Sep 18, 2023 at 3:05 | |||||
| Jul 23, 2023 at 16:11 | comment | added | Michael Hardy | Remember that this software evolved ultimately from the work of the renowned software genius Donald Knuth, who explicitly intended to make attention to this kind of thing possible. | |
| Jul 23, 2023 at 16:09 | comment | added | Michael Hardy |
And that is why I edited the question as I did. The \backslash, causing you to see $\mathbb Z\backslash\{0\}$ instead of $\mathbb Z\setminus\{0\}$ will strike people who are aware of things like this about the same way a spelling error does, and others will be affected in the way noted above, about differences between appearances of different fonts.
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| Jul 23, 2023 at 16:07 | comment | added | Michael Hardy |
$$ \begin{align} & \mathbb Z \backslash\{0\} \\ {} \\ & \mathbb Z \setminus\{0\} \\ {} \\ & \mathbb Z \smallsetminus\{0\} \end{align} $$ The first line above uses \backslash, the second \setminus and the third smallsetminus. Those last two provide horizontal spacing proper to a binary operation symbol. I.e. we normally see $3+5$ and not $3{+}5$, whereas +5 with nothing before it appears as $+5$ without that horizontal space (and similarly $3+$). The thing that makes you think one font looks good and another does not consists of many little things like this. $\qquad$
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| Jul 23, 2023 at 15:58 | history | edited | Michael Hardy | CC BY-SA 4.0 |
deleted 1 character in body
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| Jul 23, 2023 at 14:47 | history | asked | yaoxiao | CC BY-SA 4.0 |