Any algorithm or theorem to decide whether two functions that are polynomials,rationals and analytic over $\mathbb{N}$ or $\mathbb{Q}$ or $\mathbb{R}$ or $\mathbb{C}$ are equivalent ?
Let's say you have a few expressions like the following:  $$\begin{array}((x+17)^2 \\ x^2 + 34x + 289 \end{array} \\ 288 + \frac{x^2}{2} + \frac{x^2}{2} + 34x + 1 \\ [...] $$  You get the idea: there's an infinite number of ways of representing the same expression. The challenge is that my application is validating answers to math problems, input by math students practicing a certain concept. I'd like to make sure that whenever they submit an answer, the checker is completely insensitive to the issues of ordering, simplification, formatting etc. which would be plain frustrating. I'd also ideally like to support more than one variable such as x, y, z in the same expression.  What's a reliable way to check that two expressions are the same? The most brute force way I can think of would be to just plug a number into each variable of each expression and see what the result is.  I have a hunch however that there might be ways of getting false positives this way. That, and I might be either missing something really obvious about this, or there might be a better way of doing the comparison.  Would love to hear what you think.
How do I include lines in resolv.conf that won't get lost on reboot? What uses are there for "placement new"? Has anyone here ever used C++'s "placement new"? If so, what for? It looks to me like it would only be useful on memory-mapped hardware. How does a cell phone charger work? Seeking GeoServer tutorials? What are sources where I can learn how to use GeoServer?  I know of these two sites:    - which in fact is not working (at least at the moment)  - not only (tutorials) for GeoServer   But I am interested in more complex information, and not to read only documentation. I often need to view on the canvas the (selected or not) features from the current active vector layer.  In this situation, I only need to view something on the canvas, without doing anything on the canvas itself (so, the active window is always the Attribute Table).  This is what I usually do:   Open the Attribute Table for the current active layer; Select the first feature; Press Ctrl+P button (i.e. the "Pan map to the selected row" button); Minimize the Attribute Table; View something on the canvas for the current feature; Go to the first step until needed.   Is there a way (a method, a shortcut) for directly browsing every feature on the canvas without the needing of going backwards and forwards with the Attribute Table? I mean, something like a "next" button?  (I may use the workaround of splitting the windows of the Attribute Table and of the canvas within the monitor, or also docking the Atrribute Table, but I would like to work on the full QGIS window).    EDIT I saw that my question was casted as a duplicate of  question. The two questions are very similiar, but I think it should be left as open for two reasons:   the related duplicated question doesn't have an accepted answer; my question is slightly different because I'm looking for the possibility of displaying only the selected features (and the @Joseph's , that I marked as accepted, answers well to my request). Search for singleton tags on questions Is there any way to search for questions that have a specific tag and only that lonely tag?  In other words, I'd like to be able to do something like the following to find questions that have a single tag and no other:  [mytag] tagcount:1   This would be very useful for tag cleanup situations to be able to do house-cleaning before nuking a tag. Who uses Dual_EC_DRBG? Recent news articles have suggested that the NSA may be involved in trying to influence the cryptography in public standards or commercially deployed software, to enable the NSA to decrypt the encrypted traffic.  For example, .  The New York Times article specifically mentions a 2006 NIST standard, where two Microsoft engineers later discovered a serious problem in the scheme.  The New York Times article explains how the standard was written by the NSA, who pushed the scheme hard:     Simultaneously, the N.S.A. has been deliberately weakening the international encryption standards adopted by developers. One goal in the agency’s 2013 budget request was to “influence policies, standards and specifications for commercial public key technologies,” the most common encryption method.      Cryptographers have long suspected that the agency planted vulnerabilities in a standard adopted in 2006 by the National Institute of Standards and Technology, the United States’ encryption standards body, and later by the International Organization for Standardization, which has 163 countries as members.      Classified N.S.A. memos appear to confirm that the fatal weakness, discovered by two Microsoft cryptographers in 2007, was engineered by the agency. The N.S.A. wrote the standard and aggressively pushed it on the international group, privately calling the effort “a challenge in finesse.”    After some sleuthing, I'm pretty certain this is a reference to the  pseudorandom number generator scheme described in NIST SP 800-90.  The weakness is that Dual_EC_DRBG appears to contain a backdoor, and anyone who knows the backdoor can totally break the PRNG.  The weakness was first described in  and was subsequently .  As a consequence, there are now good reasons to suspect that Dual_EC_DRBG contains a NSA backdoor, and the NSA might be able to spy on anyone who is using Dual_EC_DRBG.  My questions:   Who uses Dual_EC_DRBG? Do any commercial products use Dual_EC_DRBG? Does anyone use it? how to achieve the journal style shown in the screenshot? Means help me i want to write these all things with perfect setting.. What are the English laws on bringing pets into the country? How to install XAMPP? If $f$ is continuous, nonnegative on $[a, b]$, show that $\int_{a}^{b} f(x) dx = 0$ iff $f(x) = 0$  "$\Rightarrow$" Assume by contradiction that $f(x) \neq 0$ for some $x_0 \in [a, b]$. Without loss of generality, assume that $f(x_0) &gt; 0$. Since $f$ is continuous, $\exists \delta &gt; 0$ such that $f(x) &gt; 0,  \forall x \in (x_0 - \delta, x_0 + \delta)$. Since $f$ is continuous on $[a, b]$, then it is Riemann integrable. Therefore $\int_{a}^{b} f(x) dx = \sup L(f, p)$ for some partition $p$. Now what I want to do is to show that the lower sum, $L(f, p) &gt; 0$, in that case its supremum is $&gt;0$, and that contradicts the condition that $\int_{a}^{b} f(x) dx = 0$. However, I don't know how to articulate it.  "$\Leftarrow$" If $f(x) = 0, \forall x \in [a, b]$, then $\int_{a}^{b} f(x) dx = \int_{a}^{b} 0 dx = 0$ fast saving single field value Is it always better to use the whole dataset to train the final model? A common technique after training, validating and testing the Machine Learning model of preference is to use the complete dataset, including the testing subset, to train a final model to deploy it on, e.g. a product.      My question is: Is it always for the best to do so? What if the   performance actually deteriorates?   For example, let us assume a case where the model scores around 65% in classifying the testing subset. This could mean that either the model is trained insufficiently OR that the testing subset consists of outliers. In the latter case, training the final model with them would decrease its performance and you find out only after deploying it.   Re-phrasing my initial question:     If you had a one-time demonstration of a model, such as deploying it   on embedded electronics on-board an expensive rocket experiment, would you trust a   model that has been re-trained with the test subset in the final step without being   re-tested on its new performance? Why does Sass change the format of my colors? How to override Drupal.ajax.prototype.beforeSend? I need to add my own little if's and checks in 3 functions inside   misc/ajax.js (   Drupal.ajax.prototype.beforeSend,   Drupal.ajax.prototype.success,   Drupal.ajax.prototype.error )   How can I override them in my module? I can't find a manual and it's not in Examples for Developers. Sorry if it seems a dumb question, but I'm a php developer - I can work with js, but I'm not so fluent with it.   Can I simply write it in my module's js file? If 2 or 3 modules needs to modify them, how to avoid conflicts? Number of solutions of an arithmetic function's equation Say, an equation is given below \begin{equation} 2\pi(x) - \pi(2x)=\omega(x) \end{equation}  where $x$ is a positive integer, $\pi(x)$ is the prime-counting function, and $\omega(x)$ is the number of distinct prime factors of $x$.  I would like to know if this equation holds for finitely many values of $x$ or infinitely many.  If one uses asymptotic formula (from number theory) it can be written that \begin{equation} \omega(x) \sim \ln x / \ln \ln(x) \end{equation} (from )  and  \begin{equation} \pi(x) \sim x/\ln(x), \end{equation} so the above equation can be rewritten (after simplification) as \begin{equation} 2x\ln(2)=\ln(x)\ln\ln(x)\ln(2x) +f(x) \end{equation}  where $f(x)$ is an error term.  If  I plot left side (which is linear, supposed to be a straight line) and right side(a curve),assuming $ f(x) $ is 100% accurate, then the equation implies(?!) that the right will intersect left side. Since line can intersect a curve ($ln  $ function) finite times, so there are finite intersection point. So, can I say that there are only finitely many values of $x$?  graph example-   here f(x) is assumed as x + sinx  without the f(x)- I am already dual booting windows 10 with Linux Mint, and I am trying to replace Mint with Ubuntu. I have already created a bootable usb for Ubuntu.  When I try to install Ubuntu, I don't see any option to install Ubuntu alongside windows 10. Rather, I see "install Ubuntu alongside Linux Mint". I didn't find any option to keep my windows 10. How can I replace Mint with Ubuntu in this dual boot system? Mint is installed on an ext4 partition and I have a Linux swap partition. Make square image Using Python to convert from more than one CRS I have a Python function which converts Eastings and Northings to Latitude and Longitude if line_count == 0:                     keys = row                     print('keys', keys)                     line_count += 1                 else:                     inProj = Proj(init='epsg:27700') # British National Grid                     outProj = Proj(init='epsg:4326') # WGS84                     x1, y1 = row[1], row[2]  # easting, northing                     x2, y2 = transform(inProj, outProj, x1, y1)                     row[1], row[2] = y2, x2                                          json_doc = {}  At the moment it converts from epsg:27700 (British National Grid) to WGS84, however there is a possibility I will get TM75 Irish Grid too. Is there any way I can get Python to recognised which CRS is applicable for the conversion? Show that $(1+\frac{x}{n})^n \rightarrow e^x$ uniformly on any bounded interval of the real line. Show that $(1+\frac{x}{n})^n \rightarrow e^x$ uniformly on any bounded interval of the real line.   I am trying to argue from the definition of uniform convergence for a sequence of real-valued functions, but am struggling quite a lot. My efforts so far have concentrated on trying to find a sequences, ${a_n}$ which tends to zero, such that   $$|(1+\frac{x}{n})^n -e^x |\leq a_n$$ for all $n$. But I have been unsuccessful thus far. All help is greatly appreciated.