how to introduce multiplication in shell scripting
How to do integer & float calculations, in bash or other languages/frameworks?
Is there such a thing as a switch that can be actuated automatically? I'm interested in a toggle switch that can be toggled without user input. That is, the physical state can be toggled electrically. It would need to incorporate some sort of motor or magnetic actuator. My google-fu is weak in this area, and I haven't been able to come up with the correct combination of search terms.  Note that I'm not talking about a relay; I'm talking about a normal toggle switch:    Except that it can be toggled without user input. As in, the lever physically moves. Like a  except that the mechanism is internal to the switch. Why is $c+q$ still a primitive root modulo $q$? Question: Let $p$ and $q$ be distinct odd prime numbers.  By considering primitive roots, we need to show $\exists c\in\mathbb{Z}$ with the property that:  $\bullet$ $c^n\equiv 1\pmod{p}$ whenever $n$ is a multiple of $p-1$, and   $\bullet$ whenever $n$ is not divisible by $q-1$, then $c^n\not\equiv 1\pmod{q}$  I am only interested with the beginning of this answer.  Answer: We let $c$ be a primitive root modulo $q$.  We are going to use Fermat's little theorem so we need $(c,p)=1$  If $(c,p)\neq 1$, then we have $p\mid c$, but then we have $(c+q, p)=1$  and since $c+q$ is a primitive root modulo $q$, we can replace $c$ with $c+q$ for $(c,p)=1$ for using Fermat's little theorem.  I understand the general method and argument, but...  Contention: Why is $c+q$ still a primitive root modulo $q$?  When is this generally true? Is there an identity for when things remain a primitive root?  Why is $(c+q)^{\phi(q)}\equiv 1\pmod{q}$? Mob Arena - Mob vs. Mob I want to make an arena where mobs will fight each other and a player can bet on one side or the other. For example: There are 2 skeletons in dyed armor; red and blue. Each color representing a team. When they spawn I want them to fight each and then when one dies I want it to announce which team is the winner and give the player the "money" due. I'm just not sure how to get the skeletons to attack each other without a player instigating it. How to change the title of ToC? I need to change default title of ToC. Is it possible with titlesec package? Here is my MWE:  \documentclass{book}  \usepackage{titlesec} \titleformat{\chapter}{\normalfont\Large\scshape}{\thechapter}{1em}{} \vspace{6pt}]  \usepackage{lipsum}   %-------------------------------------------------------------------------  \begin{document}   \newpage \thispagestyle{empty} \tableofcontents \thispagestyle{empty} \newpage \thispagestyle{empty}  \setcounter{footnote} {0}\chapter*{{\fontsize{11}{14}\selectfont\normalfont{Author1} \\ {\scshape\Large Title}}} \addcontentsline{toc}{chapter}{\normalsize\normalfont{Author1} \\ \normalfont\scshape{Title}} \thispagestyle{empty} \Author{Author1} \Title{Title} \lipsum \newpage \thispagestyle{empty}    \end{document} I am flying from Los Angeles to Bangalore. I have a flight option from LAX to Minneapolis and from there to Paris. I have only 45 minutes at Minneapolis before my next flight. Is this too risky a schedule? I am not an American, so I guess I would need to cross emigration too? Constructing the reciprocal of a segment How can one construct the reciprocal length of a line segment? For example, given any line segment a, how can $\frac{1}{a}$ be constructed?  I was told that it can be solved by creating similar triangles, but I do not get it. What are some grandiloquent, or simply better, ways of expressing "an idea/thought suddenly came to me", or "an idea/thought struck me", or "I was struck by an idea/thought"? SQL Server: Examples of PIVOTing String data Force.com IDE 35.0.0.201510211056 and Force.com IDE Debugger 35.0.0.201510211056 in eclipse but it doesn't show this option to run test class, is their any way i can see it because it show the Apex_Test_Result panel but running a test class option is missing. plz help Basic question about Merging faces I'm a beginner with blender so this is probably a very basic question.  I have this basic model below. I've ended up with a lot of unwanted geometry that I want to simplify. I wanted to start by merging the two selected faces below but no matter what I try to delete or merge it just destroys the geometry.  How can I achieve what I want to do (which is combining all of the unwanted geometry, either starting with this merge or some other way?) How can I access cloth properties via python? I want to manipulate options like Disk Cache with python:    Any Ideas? I'm talking about at least two juvenile sci-fi novels, read between second and fourth  public grades (U.S.A.) which for me places them around 1956-9.  The protagonists are a brother and sister, presumably my (then) age. They are friends  with a single man, a scientist who has built a rocket ship. The scientist is little fey,  physically; a (relatively) large, round head, balding, short in stature and striking long,  thin hands and fingers.  The rocket ship's final preparation is to slop a viscous, clear gloop over EVERYTHING, inside and out from a pail with a paintbrush. In flight, there is an encounter with the moon, and a very small planet with (non-threatening) inhabitants not physically unlike the fey rocket scientist. The planet orbits either the moon or the earth, not the sun, and strangely, some kind of mushroom(!) theme runs through the books. Really.  That's it. That's all I got (I was nine at the most, fer chrissake). My recollection tells me there was concealment from parents, a particular name for the planet and people  and flight through a spatial fog. I mention these things separately because I am less sure  of them than the previous two paragraphs. The author was blissfully unrepentant of the laws  of physics:  Earth gravity on a micro-planet, fog in space and super-gloop to ready the  ricketiest rocket. Worked for me.  I'm guessing even Richard, my previous mentor/savior might not be familiar with these.  Anybody? Author, titles? Or do you just recognize one of these? Using CSS to affect div style inside iframe Theorem:   If $x$ is a positive integer and  $x^3$ is even, then $x$ is even.   My Proof by Contrapositive:  I. Assuming that $x$ is odd, then I will show that $x^3$ is odd.  II. $x$ is odd, so $x$ can be expressed as $2k+1$  III. $(2k+1)^3$  IV. $2k(4k^2 + 6k + 3) +1$  V. Since $2k(4k^2 + 6k + 3) + 1$ is an integer, we can conclude $x^3$ is odd.  Did I go about this correctly? Should step V say "$2$ multiplied by an integer and added by $1$ is odd therefore we can conclude $x^3$ is odd"? How can I add a newline in the text of a label in WPF such as the following?  &lt;Label&gt;Lorem    ipsum&lt;/Label&gt; Can you use Uncanny Dodge against extra damage effects? I am not able to play "Half-Life-2" on Steam + Ubuntu 14.04 . Error shown in message box on screen:      Could not find required OpenGL entry pint 'glGetError'! Either your video card is unsupported, or your OpenGL driver needs to be updated.   I have a Dell Inspiron Laptop.  My OS is Ubuntu 14.04 and my graphics card is AMD Radeon HD 8600M.  I have installed AMD properietry Driver.    The partial output of "glxinfo" is as follows:      name of display: :0     libGL: screen 0 does not appear to be DRI3 capable     libGL: pci id for fd 4: 8086:0a16, driver i965     libGL: OpenDriver: trying /usr/lib/i386-linux-gnu/dri/tls/i965_dri.so     libGL: OpenDriver: trying /usr/lib/i386-linux-gnu/dri/i965_dri.so     libGL: Can't open configuration file /home/arushi/.drirc: No such file or directory.     libGL error: failed to load driver: i965     libGL: OpenDriver: trying /usr/lib/i386-linux-gnu/dri/tls/swrast_dri.so     libGL: OpenDriver: trying /usr/lib/i386-linux-gnu/dri/swrast_dri.so     libGL: driver does not expose __driDriverGetExtensions_swrast(): /usr/lib/i386- linux-gnu/dri/swrast_dri.so: undefined symbol: __driDriverGetExtensions_swrast     libGL: Can't open configuration file /home/arushi/.drirc: No such file or directory.     libGL: Can't open configuration file /home/arushi/.drirc: No such file or directory.     libGL error: failed to load driver: swrast     display: :0  screen: 0     direct rendering: No (If you want to find out why, try setting LIBGL_DEBUG=verbose) I created a thick glass bottle and duplicated the interior faces to make a new object to create the liquid inside.   I went in the edit mode, selected the faces I wanted to copy and duplicated them with ShiftD. Then I pressed P to  separate the duplicated faces.   Now I try to make a duplicate of that liquid to make it flow out of the bottle, and I simply need the duplicate of one face of it. So I go to edit mode and do as I did to make the liquid from the bottle faces... but as soon as I'm back to the object mode and I want to move the duplicated faces, every thing moves with it...   I played around and tried things, and while doing so I realized that if I dupe the liquid object in object mode using ShiftD and press 0 to place it where the original is, they move together if I duplicate it and place it somewhere else so that they are separated.   Also if I pick one of the two separated objects and make it intersect with the other one, release my left mouse button to place it there, and then try to move it again, they both move together, but not at the same speed.  I really don't understand what is going on and I'm sure it's really badly explained, so what I'll do is make a screen capture of my Outliner and record the behavior of the objects and upload those to help you understand. How to insert text before the first line of a file? Number of ring homomorphisms from $\mathbb Z_{12}$ to $\mathbb Z_{28}$. Question:      Find the number of non trivial ring homomorphisms from $\mathbb Z_{12}$ to $\mathbb Z_{28}$. ($f$ is not necessarily unitary, i.e., $f(1)$ need not be $1$.)    Suppose $f$ is a ring homomorphism from $\mathbb Z_{12}$ to $\mathbb Z_{28}$.  Consider $f$ as a additive group homomorphism.  Let $k= |\ker f|$ and  $ t = |\operatorname{im}(f)|$. Then $k\mid 12$ and $t\mid 24$ and $kt=12$, by first isomorphism  theorem of groups.  There are two possibilities $k=3$, $t=4$   and $k=6$, $t=2$.  For the first case $f$ should map $1$ to an element of the subgroup generated by $7$ as there is a unique subgroup of $\mathbb Z_{28}$ of order $4$ generated by $7$. For the second case $1$ has to map to $14$, for the same reasoning.  So there are at most two ring homomorphisms from $\mathbb Z_{12}$ to $\mathbb Z_{28}$. Question is how to check the possible maps which are ring homomorphisms.  Thanks.