How do I get the creation date of a MySQL table?
How to display all the tables with more information (create date, size,...) in a MySQL database?
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$ I have to show that the ring $\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$.    I know that $(\mathbb{Z}\times\mathbb{Z})^*=\{(\pm1,\pm1)\}$, so I thought I should be looking for elements which have inverses in $\mathbb{Z}[X]/(X^2-1)$ and hopefully find more or less than 4. But I didnt succeed, so I need hints. Thanks. Are large data sets inappropriate for hypothesis testing? Cardinality of the set of bijective functions on $\mathbb{N}$? Defining scalable "white curly brackets" {| and |} (⦃ and ⦄) I would like to construct what Unicode calls "white curly brackets" that are in addition scalable. They look like ⦃ (≈{|) and ⦄ (≈|}) and have Unicode codepoints U+2983 and U+2984.  unicode-math has them as \lBrace and \rBrace, but (1) I don't presently use XeTeX or LuaTeX and (2) their design (shown in  on pages 3-4) is not to my liking: the brace part is too fat for my taste, and I would like the vertical bar to not leave any protrusions. I am trying to have them visually match the parentheses \llparenthesis, \rrparenthesis, \llbracket, and \rrbracket from stmaryrd.  Right now I am using a makeshift definition, which is sufficient for now, but the symbols don't scale (in general or with \left/\right). Here is sample code:  \documentclass{article} \usepackage{amsmath} \usepackage[only,llbracket,rrbracket,llparenthesis,rrparenthesis]{stmaryrd} % for comparison with 4 similar parenthesis symbols \usepackage{accsupp} % for ensuring the right Unicode codepoint upon pasting  \newcommand*{\llbrace}{%   \BeginAccSupp{method=hex,unicode,ActualText=2983}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char102}%     \mathchoice{\mkern-4.05mu}{\mkern-4.05mu}{\mkern-4.3mu}{\mkern-4.8mu}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char106}%   \EndAccSupp{}% } \newcommand*{\rrbrace}{%   \BeginAccSupp{method=hex,unicode,ActualText=2984}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char106}%     \mathchoice{\mkern-4.05mu}{\mkern-4.05mu}{\mkern-4.3mu}{\mkern-4.8mu}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char103}%   \EndAccSupp{}% }   \begin{document}  \noindent ok: \(\displaystyle\llbrace abc \rrbrace\) \(\textstyle\llbrace abc \rrbrace\) \(\scriptstyle\llbrace abc \rrbrace\) \(\scriptscriptstyle\llbrace abc \rrbrace\)  \noindent ok: \(\displaystyle \llbrace \frac{a}{b} \rrbrace\) \(\textstyle\llbrace \frac{a}{b} \rrbrace\) \(\scriptstyle\llbrace \frac{a}{b} \rrbrace\) \(\scriptscriptstyle\llbrace \frac{a}{b} \rrbrace\)  \noindent incorrectly scaled (\verb|\scriptsize|): {\scriptsize\(\llbrace abc \rrbrace\)} (large magnification required)  \noindent incorrectly scaled (\verb|\tiny|): {\tiny\(\llbrace abc \rrbrace\)}  \noindent \verb|\left| and \verb|\right| not possible before \verb|\llbrace| and \verb|\rrbrace|: \\ \indent \(\llbrace \left\llbracket\left\{\left[(a) \cdot bc^{2^3}\right]^4\right\}^5\right\rrbracket \rrbrace\) % Note: This is also not possible with \llparenthesis and \rrparenthesis from stmaryrd.  \noindent for comparison: \(\llparenthesis x \rrparenthesis, \llbracket x \rrbracket, \llbrace x \rrbrace; (x), [x], \{x\}\)  \end{document}   Lines 1 and 2 look just right with the present setup. Lines 3 and 4 demonstrate that my definitions don't scale. Lines 5a/b gives an example of where I would like to be able to use \left and \right. Line 6 juxtaposes different types of parentheses for visual comparison.  Is there an easy way to scale the glyphs I have constructed myself? Or is designing new glyphs the only way? While the vertical part of my glyphs doesn't leave any protrusions, the "brace part being too fat" part of my problem isn't being addressed by my code. With this in mind: I recognize that it might not be that easy to make the brace part of the glyph thinner (though if you can, more power to you), but I think that any solution that addresses the scaling problem for any manually constructed glyph cluster will be a valuable contribution to the community.    For a slightly different setup (original example code) with  \RequirePackage{fix-cm} \documentclass[12pt]{memoir} \usepackage{fixltx2e}[2006/09/13] \usepackage{amsmath} \usepackage{txfonts} \usepackage[only,llbracket,rrbracket,llparenthesis,rrparenthesis]{stmaryrd} \usepackage{accsupp}   in the preamble, one needs \mkern-5.7mu in the fourth argument to \mathchoice for "correct" scaling. To see what goes wrong in that case, it's best to include a line such as discontinuous small symbols in a footnote\footnote{\(\scriptscriptstyle\llbrace \frac{a}{b} \rrbrace\)}. This might help a potential answerer test things out. Why does my Nikon D3100 give the error "Lens not attached" with a Vivitar 200 telephoto lens? I have a Nikon D3100 camera, and am trying to use an "Automatic Fixed Mount Vivitar 200mm lens" with it. When I attach the lens, I get the message "Lens not attached". and nothing works. HELP!  I can't easily take it to a camera shop, as I live in the Mojave Desert, about 200 miles away from any camera shop. This is a new lens, and a new camera. Removing phone number from iMessage I'd like to remove my phone number from my iMessage account, but still have my phone enabled to receive messages sent to my email address (also used on iPad, Mac). Is there a way of doing this? TikZ is undergoing lots of development with new features being added, but the versions distributed with standard TeX releases are often a little old. How do I get the latest version? If I want to be sure that I get the latest stable version, how do I do that?    Note: I'm not asking this question for myself, but because a question like this seems to be useful for pointing to it when a new feature of TikZ is mentioned in an answer to some other question. Feel free to post answers for any operating system/TeX distribution combination. Usage of "shall we?" What does it mean and where would I use it? Understanding the length extension attack I have been trying to understand exactly how a length extension attack works on SHA-1. I'll detail below what I've understood so far, so that I can convey my understanding of the same and hopefully get advice on where I'm going wrong.  Lets assume that for a message $m$, a secret $s$ is appended to it and the SHA-1 hash is calculated. If $\textrm{len}(m) + \textrm{len}(s)$ is not a multiple of the block size, a certain amount of padding is added to it to make it a multiple, and the hash is generated using what is essentially $s || m || \textrm{padding}$.  Now SHA-1 internally uses 5 registers — it takes in an block, generates new register values, turns the crank, takes in another block, generates new register values, turns the crank ... and so on till the end. When all blocks are exhausted, the register values are concatenated and spit out.  Assume that an attacker knows a certain value of $m$, for which he also knows the hashed key. In such a case, he knows the state of the 5 registers when $(s || m || \textrm{padding}$ was processed. Lets also assume that the attacker knows the length of $s$, so that he can predict how much padding was added.  Here is where I get confused. From what I've read so far, the attack involves taking the known hash, adding a certain amount of padding and then the value that we want. However, isn't the padding already used up in creating the hash? Why are we using padding in our attack? Use of comma separating two adjectives When you watch a video in YouTube, you can seek it with the thumbnail preview. Many Windows' and MacOS' video players have this feature, but what about Linux's? I've already read , but the information in it seems out-of-date.  is still alive but the project is neglected (see ), and actually the player doesn't work on the latest Ubuntu or Linux Mint.  Is there any video player which has the feature and works on the latest linux distributions? Or must I use Windows' one with VirtualBox? If only VLC would implement this feature, but it seems that won't happen as far as I read .  YouTube's seek preview: What happens if a person can't die of a heart attack? I have a Lenovo T570 with Xubuntu 18.04 LTS. My current issue is that my cpu speed stepping is kind of going nuts and does what ever it thinks its best.  Sample: when I run my IDE and cpu load increases during build time, the governor changes automatically. I caught the moment during compiling my project with the following call:  martin@martin-ThinkPad-T570:~$ while cat /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor; do sleep 1; done powersave powersave performance performance   cpufreq-info tells me this:  martin@martin-ThinkPad-T570:~$ cpufreq-info  cpufrequtils 008: cpufreq-info (C) Dominik Brodowski 2004-2009 Report errors and bugs to cpufreq@vger.kernel.org, please. analyzing CPU 0:   driver: intel_pstate   CPUs which run at the same hardware frequency: 0   CPUs which need to have their frequency coordinated by software: 0   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.25 GHz. analyzing CPU 1:   driver: intel_pstate   CPUs which run at the same hardware frequency: 1   CPUs which need to have their frequency coordinated by software: 1   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.36 GHz. analyzing CPU 2:   driver: intel_pstate   CPUs which run at the same hardware frequency: 2   CPUs which need to have their frequency coordinated by software: 2   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.26 GHz. analyzing CPU 3:   driver: intel_pstate   CPUs which run at the same hardware frequency: 3   CPUs which need to have their frequency coordinated by software: 3   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.36 GHz.   Please take a look at     current policy: frequency should be within 3.50 GHz and 3.50 GHz.       The governor "performance" may decide which speed to use   Afterwards to go back to powersave I use my little script:  martin@martin-ThinkPad-T570:~$ cat cpu_freq_save.sh  #!/bin/bash sudo cpufreq-set -g powersave -c 0 --min 400MHz sudo cpufreq-set -g powersave -c 1 --min 400MHz sudo cpufreq-set -g powersave -c 2 --min 400MHz sudo cpufreq-set -g powersave -c 3 --min 400MHz   Which resets the min frequency and the governor but as soon as I compile again with my IDE every time the governor and the min frequency changes again.  Any idea how I can disable that automatic change?  PS: If you need more details, just tell me where to find them and I will provide them Why we don't use gamma rays, x-rays or ultraviolet to transmit data? The greater the frequency range of a transmission medium, the greater the number of bits per second it can transmit. In other words, the bigger the bandwidth in hertz available, the bigger the bandwidth in bits per second that can be transmitted.  Given that, why we don't use gamma rays, x-rays or ultraviolet to transmit data instead of e.g. visible(light) in optical fiber or microwaves(cell phones)? Notification for reviews shows way too many Since a , I see more than I should:    I see no reason to see 134 posts are awaiting review, when there is literally nothing I can do about them. I think it is a bug, because notification is meant as something that will make me act. When I know I usually can't, obviously I will start to ignore it.  If it's not a bug, please remove bug tag and explain how it is supposed to be useful, or how can I switch to only seeing notifications about things I can act on.  Note that apaprently there are no flags for me, neither. I see only stats, migrated, close, delete, there, as if there was no flags waiting:    If you expect us to click on it every few minutes  just to see personalized numbers next to queues, why don't you simply query for personalized numbers every few minutes and cache them for us? It should cost you similar, in database usage, and will save us a lot of clicking and frustration.  If all this number means is "there might be reviews, or not" or "for sure there are none"  it would be simpler just to hide "review" link in the second case. We don't need two links with the same function next to each other, thank you, one is enough, and meaningless numbers are only irritating. Existence of irreducible polynomials over finite field Let $F$ be a finite field. How do we prove that for each $n \in \mathbb{N}$ there is an irreducible polynomial of degree $n$?  One can assume that $F = \mathbb{F}_{p^m}$ where $p$ is prime. If $n \ge |F|$ then I can construct an irreducible polynomial, namely  $ p(x) = 1 + \prod_{j=1}^{|F|} ( x - a_j )$  where $a_j$ are all the field elements. It is clear that $p(x)$ has no roots in $F$.  This trick doesn't work for $n &lt; |F|$. A counter-example: Let $F = \mathbb{F}_3$ and $p(x) = 1 + (x-1)(x-2)$, then $p(1) = 1$, $p(2) = 1$, $p(0) = 1 + (-1)(-2) = 1 + 2 = 3 = 0 \pmod 3$.  I know there is a way to count them using the Möbius function $\mu(n)$ but I want a proof without it that just shows existence. Can I use apt-get or aptitude to install software to non standard location? prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer Prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer.      For clarity: the denominator is the only part being squared.   My thought process:   The numerator is the product of the first $n$ even numbers and the product of the first $n$ odd numbers.   That is, $(2n!) = (2n)(2n-2)(2n-4)\cdots(2n-1)(2n-3)(2n-5).$ In effect, the product of even numbers can be cancelled out with $n!$ resulting in the following quotient:  $$ \frac{(2^n)(2n-1)(2n-3)}{(n!)}\;.$$  To me this looks even thanks to the powers of $2$. But I am not convinced for some reason.   Was this approach to naive?   Sorry for the poor notation, I don't know any coding languages, my apologies. What's wrong with this demonstration?:  $$A \iff 1 = 1^1$$ $$A \implies 1 = 1^\frac{2}{2}$$ $$A \implies 1 = (1^2)^\frac{1}{2}$$ $$A \implies 1 = ((-1)^2)^\frac{1}{2}$$ $$A \implies 1 = (-1)^\frac{2}{2}$$ $$A \implies 1 = (-1)^1 = -1$$  So finaly we get  $$1 = -1$$ vertical spacing in nested fraction I have complicated math expression:    Vertical spacing between text and fraction line is too small. I tried to define new \frac command (with amsmath package) with adjustable vertical spaces. As you can see, the result is not satisfying:    \documentclass[a4paper,fleqn,leqno]{article} \usepackage{polyglossia} \usepackage{color,pifont,fontspec} \usepackage[top=2.54cm,bottom=2.54cm,left=2.54cm,right=2.54cm]{geometry} \usepackage{tikz,tikz-3dplot,graphicx} \usepackage{mathtools,breqn,amsmath} \usepackage[fontsize=12]{scrextend} \usepackage{array,multirow} \usepackage{pgfplots} \DeclareMathSizes{12}{14}{14}{10} \newcommand{\myfrac}[3][0pt]{\genfrac{}{}{}{}{\raisebox{#1}{$#2$}}{\raisebox{-#1}{$#3$}}} \begin{document} \begin{dmath*}[breakdepth={0},style={\mathindent=0pt},spread={10pt}] {n=\myfrac[3pt]{\myfrac[3pt]{0,0625N+0,0215}{2}-0,043}{\myfrac[3pt]{\myfrac[3pt]{\scriptstyle 0,0625N+0,0215}{\scriptstyle 2}-0,043}{\myfrac[3pt]{\scriptstyle N}{\scriptstyle 2}-1}+0,0215}} \end{dmath*} \end{document}   How can I enlarge verticall spacing in whole fraction?