It is a rather common practice that teachers prepare multiple  versions of a test for the same exam in order to reduce cheating. Can \LaTeX do this? I want to design a math test with a set of parameters that are randomly chosen from a given set to create problems that have same wording but different numbers (something that online homework systems do).   Is such a thing possible with any latex package? Is it possible at all?   A basic example is:  Produce 10 pages, each a with a copy of the following question  What is the sum $p+q$?   Where the program chooses and inserts $p$ randomly from the range 20 to 30 and $q$ from 50 to 60.
I want to create a math problem-solution sheet. The coefficients a, b, c must be assigned on the fly at random so the generated pdf will show a numeric quadratic equation rather than a symbolic quadratic equation. Note a must not be zero.  \documentclass{article} \begin{document} \section{Problem} Let \(x_1\) and \(x_2\) be the roots of \(a x^2 +bx +c=0\). Find  \(x_1x_2\).  \section{Solution} \[ x_1x_2=\frac{c}{a} \] \end{document}   Please kindly make the solution get automatically simplified. For example: \frac{c}{a}=3 when a=2 and c=6.    Actually the real case is more complex than this one. Not only the equations must be generated at random, but also the associated graphic plots that I write in PSTricks.     I chose Paulo's answer because using Maxima as the computation engine is very very great idea. Other answers are also good and creative, especially Altermundus'.
As per c99 standard, size of long long should be minimum 64 bits. How is this implemented in a 32 bit machine (eg. addition or multiplication of 2 long longs). Also, What is the equivalent of long long in C++. Can I enable the Windows 7 Start menu in Windows 10? I've upgraded from Windows 7 to Windows 10 and now I only find this new slower Start menu with all the tiles in it   (picturesource: )  Can I enable the older Windows 7 one again which suites my needs more? White regions in DensityPlot — is this a bug with ColorFunctionScaling? How to highlight (color/draw attention to) a particular snippet in Minted I'm currently doing some work on error messages in programming languages. As such, I'm showing faulty pieces of code, alongside the compiler-errors accompanying them.  I'm using minted for the code snippets, but ideally, in addition to normal syntax highlighting, I'd like to highlight the sections of the code at which the error is located, by underlining them, putting a red box around them, shading their background, etc.  Is this possible using Minted? Raising a decimal to a power of decimal? The .net framework provides in the Math class a method for powering double. But by precision requirement I need to raise a decimal to a decimal power [ Pow(decimal a, decimal b) ]. Does the framework have such a function? Does anyone know of a library with this kind of function? Will cases with front USB port support USB 3.0? Making overview with linked detailed maps in QGIS? i want to create 4-5 detailed maps, and then an overview map that has rectangles that markes the locations of the detailed maps. Best case would be if the rectangles were links to the detailed map.   I have managed to make the overview and the rectangles, and think I know how to make the detailed maps one by one. The rectangles are drawn manually on the overview map. All layers that I plan on using are in the same QGIS project.  The final product that I hope to create would be the overview map on the first page, followed by the detailed maps. The overview would have links to the detailed maps, click on the rectangles to open the right detailed map.  Is there a way to link the detailed maps to the overview in QGIS 2.8 print composer?  I'm still not sure if I'm doing something wrong, when I try to create the overview. I want it to show the extents of all of my detailed maps.   Is this possible? A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $ Sci-Fi Movie/Show Where a Soul is Captured in a Glass Vessel Chat messages should use consistent icon in iOS app It'd be nice if the chat notifications in the feed used the default Stack Exchange icon like the ones in the inbox do*:     Since items in the feed are grouped so that multiple items from the same site , the site icon helps delimit grouped items a bit less subtlely than the grey divider lines, and chat replies' lack of one causes them to sort of blend in to the previous group.  *Ideally it'd use the icon of the site the room was associated with, but I don't think that information is readily available Difference of $R^2$ between OLS with individual dummies to panel fixed effect model? Based on my understanding, panel fixed effect model is equivalent to OLS with individual dummies. However, when I ran the two models in R, the $R^2$ from the two models were quite different: 0.8 for OLS with individual dummies and 0.06 for fixed effect model.  Is it the case that in fixed effect model, the fixed effects (individual dummies) are excluded from the calculation of $R^2$? Relationship between balloon size and pressure I see numerous websites talking about how a small balloon is at higher pressure than a big balloon. This is a fun counter-intuitive factoid... unless it isn't a fact at all.  Young-Laplace gives  $$T = \Delta p \frac R2 $$  Which means that for a given tension, increasing the radius does decrease the pressure. But why would the tension be constant? A latex balloon is like a 2D spring, right? So the tension in a inflated spherical balloon should be proportional to the surface area, correct?  $$T \propto R^2 $$  But this gives  $$\Delta p \propto R$$  Which means the bigger the balloon, the higher the internal pressure. Which, again, would be the normal intuition - but it would burst the bubble of some simplified explanations. (har har) What to do with an Ubuntu disk image that appears as a WinRAR file? While proving a universal quantification, we begin by "Let ... in ..." or "Arbitrary choose ..."? I am trying to prove that if I have $f:\mathbb{R} \to \mathbb{R}$ satisfying $\forall x,y\in\mathbb{R},f(x+y) = f(x) + f(y)$. Which is assumed continuous at $0$, that $f$ is continuous on $\mathbb{R}$  I am fairly sure it is, for that property seems to be a property of polynomials, and we know polynomials are continuous where defined(all reals)  Any ideas for rigor?  $|x-a| \lt \delta \implies |f(x+a)-f(x)-f(a)| \lt \epsilon$  No idea where to go from here, this is my first time doing $\epsilon-\delta$ stuff. How would you explain covariance to someone who understands only the mean? ...assuming that I'm able to augment their knowledge about variance in an intuitive fashion (  ) or by saying: It's the average distance of the data values from the 'mean' - and since variance is in square units, we take the square root to keep the units same and that is called standard deviation.  Let's assume this much is articulated and (hopefully) understood by the 'receiver'. Now what is covariance and how would one explain it in simple English without the use of any mathematical terms/formulae? (I.e., intuitive explanation. ;)  Please note: I do know the formulae and the math behind the concept. I want to be able to 'explain' the same in an easy to understand fashion, without including the math; i.e., what does 'covariance' even mean? QGIS update from 2.14 to 2.16 failed on Ubuntu 14.04 Until yesterday my whole qgis and python-qgis worked fine with version 2.14 under Ubuntu 14.04. After a simple sudo apt-get update and sudo apt-get upgrade qgis failed to update... Several attempts to reinstall it with different versions failed.  Current error message (for version 2.14.3) goes like this:  qgis-providers (2.14.3+dfsg-2~trusty1) is configured ... /usr/lib/qgis/crssync: symbol lookup error: /usr/lib/libgdal.so.20: undefined symbol: GEOSDelaunayTriangulation_r   I also tried to reinstall all gdal libraries - not sure if I got all?!  Maybe it is somehow related to this one:  ?  UPDATE:  Trying to install version 2.16.0 it gives different but similar error:  /usr/lib/qgis/crssync: symbol lookup error: /usr/lib/libqgis_core.so.2.16.0: undefined symbol: GEOSNearestPoints_r   UPDATE Sources:  For version 2.16.0 there are these sources in /etc/apt/sources.list:  deb http://qgis.org/debian trusty main deb-src http://qgis.org/debian trusty main deb http://qgis.org/debian trusty main deb-src http://qgis.org/debian trusty main   which are all the same, right?   When I do apt-cache policy qgis it gives me:  qgis:   Installiert:           1:2.16.0+20trusty   Installationskandidat: 1:2.16.0+20trusty   Versionstabelle:  *** 1:2.16.0+20trusty 0         500 http://qgis.org/debian/ trusty/main amd64 Packages         100 /var/lib/dpkg/status      2.0.1-2build2 0         500 http://de.archive.ubuntu.com/ubuntu/ trusty/universe amd64 Packages Examples of topologies in which all open sets are regular? An open subset U of a space X is regular if it equals the interior of its closure, as we learn from the Wikipedia . Furthermore, the regular open subsets of a space (any space) form a complete Boolean algebra.  I'm coming to this from logic and algebra, with not much background in topology. I can't figure out which topologies have "interesting" collections of regular open sets. For example, in the trivial topology and the discrete topology, every open set is regular, if I'm not mistaken. Those are not "interesting" topologies. I assume there are other topologies in which the space X and the null set are the only regular open sets. If so, those aren't "interesting" either, at least not with regard to their regular open ets.  I believe what I'm looking for is topologies in which every open set is regular, other than the ones I've just described.  Thanks for any help. Object emit light distance I created an object, and I wanted it to glow. I used to just place points of light around it, and parent them to it, but using the emit option in the materials seemed so much easier.  But when I gave it an a higher emit than 0, it went only a small distance before the light stopped. I turned it up to 200, and the object was white with light, but the light didn't go any farther. Oh and I changed the color, and nothing happened. Why Does Harry Have a Scar When Avada Kedavra Leaves No Trace? Why does Harry have a scar when Avada Kedavra leaves no trace?     ‘The Muggle authorities were perplexed. As far as I am aware, they do not know to this day how the Riddles died, for the Avada Kedavra Curse does not usually leave any sign of damage ... the exception sits before me,’ Dumbledore added, with a nod to Harry’s scar.   Half-Blood Prince - page 343 - Bloomsbury - chapter 17, A Sluggish Memory   What caused Harry to retain a scar from Avada Kedavra, when no one else in know history showed any signs of cause of death when Avada Kedavra was used?  What caused Harry's scar?  I'd love an answer based in canon, such as the books, interviews with J.K. Rowling, or Pottermore.