Can someone explain how to find inverses in truncated polynomial rings manually (i.e. on pen and paper)? As an example from the tutorial:     Example. Take $N=7$, $q=11$, $a=3+2X^2-3X^4+X^6$. The inverse of $a \bmod 11$ is   $a^{-1}=-2+4X+2X^2+4X^3-4X^4+2X^5-2X^6$, since      $(3+2X^2-3X^4+X^6)*(-2+4^X+2X^2+4X^3-4X^4+2X^5-2X^6) \equiv -10+22X+22X^3-22X^6 \equiv 1 \mod 11$.   How to find $a^{-1} = -2+4X+2X^2+4X^3-4X^4+2X^5-2X^6$, manually, not using the pseudocode?
It's using Euclidian inverse. Can you show it step by step?   $$N=7, q=11, a = 3+2X^2 -3X^4 +X^6$$  the inverse of $a \pmod {11}$ is  $$A=-2+4X+2X^2 +4X^3 -4X^4 +2X^5 -2X^6$$  How do we compute $A$?
Using headset controls like a smart phone Is there a closed formula for this summation? I have the summation  $$\sum\limits_{i=1}^n \frac{1}{i^2}$$  And I don't know how to find a closed formula for it. Any ideas? How should an educational institute woo good faculty? What steps must an educational institution wanting to recruit good faculty take? There is a cycle in the academia:    Good doctorates from top universities invariably join other top universities as faculty members.  Good students aspire to study in top universities under excellent faculty members.   Suppose a new educational institution or department springs up and desires to set up a top-quality group, how does it break into this cycle? I suppose this could take some years, but is money-power the only thing that could be wielded by the institute to achieve its end? Why can a 1 element set be a member of another set but not a subset of it? Has any Dark Force user/ally ever said "May the Force be with you"? UV coordinates on a deformed plane I added a plane to a scene, subdivided it, and deformed it with proportional editing:    I'd like to UV unwrap this plane, making the mapping what the would have been without the edit mode deformations. In other words, I'd like my UV map to look like a square grid.  Is it possible to UV map this deformed plane to a square grid? Or do I need to start from scratch, and make sure I unwrap it before I do the edits? Sharepoint REST API - Using caml query and select/expand to get lookup data I have a solid understanding of most OOP theory but the one thing that confuses me a lot is virtual destructors. I thought that the destructor always gets called no matter what and for every object in the chain. When are you meant to make them virtual and why? Incorrect query filter according to the requirement My requirement wholly depends on the QUERY.  I am filtering my gridview on the basis of three parameters.   Project_name (Always required) Date (Not always) Vehicle_No (Not always)   So, what my requirement is,      With project_name either any one can be used for filtering my gridview.   Currently my debugged query works exactly fine for any two parameters.  Below is my debugged query:-  SELECT DISTINCT sv.mkey, vehicle_no,                TO_CHAR (date_in, 'dd-MM-yyyy')             || ' &amp; '             || time_in vehicleindate_time,                TO_CHAR (date_out, 'dd-MM-yyyy')             || ' &amp; '             || time_out vehicleoutdate_time,             gate_no_in || ' &amp; ' || gate_no_out ingate_outgateno,             gd.good_type goods_type, net_weight netweight,                TO_CHAR (challan_date, 'dd-MM-yyyy')             || ' &amp; '             || challan_no challandate_no,             remark_in remarkin, NULL receipt_no, date_in        FROM xxcus.xxgid_supinv sv,             xxcus.xx_supinv_goodtype gd,             xxcus.xxacl_xxgid_user_mst ms       WHERE (gd.good_type_code(+) = sv.good_type)         AND (       sv.project_id = '1368'                 AND TO_CHAR (date_in, 'dd-MM-yyyy') = '26-11-2015'              OR vehicle_no = '0'             )         AND sv.delete_flag = 'N'    ORDER BY date_in DESC, vehicle_no   The above query shows me the exact result for project_name and Date which I entered.  But when I add the third parameter say Vehicle_no it doesn't show the data for that exact vehicle_no it still shows me the same data which I looked for 2 parameters.  I am using Oracle for the database.  LATEST UPDATE WHICH IS NOT WORKING  I am confused as how to deal with the query, as Balazs' solution was working fine when I selected, Project_name, Date and then vehicle_no (not necessary). But it was not fetching proper result when I took first as Project_name, and Vehicle_no. Any guesses why?     The issue  is when I only filter with Project_name and Vehicle_no the date_column value comes as 0 so it doesn't show me any row, which is incorrect as I have data for that Project_name and Vehicle_no.   I have used Balaz's second query for the solution which is below  WHERE (gd.good_type_code(+) = sv.good_type)     AND (       sv.project_id = '1368'             AND TO_CHAR (date_in, 'dd-MM-yyyy') = '26-11-2015'          AND vehicle_no = decode(:vehicle_no, '0', vehicle_no, :vehicle_no)         ) How to properly typeset multiletter quantities, e.g. Re or Nu (Reynolds, Nusselt numbers) Is there a canonical way to typeset such quantities in equations and inline math?  \documentclass{article} \begin{document} $Re$, $Nu$ are clearly not an option. $\mathit{Re}$, $\mathit{Nu}$ appear ok to me. \end{document} I'm wondering if it's possible to hide a folder without renaming it with a dot on the Desktop.  Ubuntu 12.04  Thanks What is a good use case for static import of methods? Just got a review comment that my static import of the method was not a good idea. The static import was of a method from a DA class, which has mostly static methods. So in middle of the business logic I had a da activity that apparently seemed to belong to the current class:  import static some.package.DA.*; class BusinessObject {   void someMethod() {     ....     save(this);   } }    The reviewer was not keen that I change the code and I didn't but I do kind of agree with him. One reason given for not static-importing was it was confusing where the method was defined, it wasn't in the current class and not in any superclass so it too some time to identify its definition (the web based review system does not have clickable links like IDE :-) I don't really think this matters, static-imports are still quite new and soon we will all get used to locating them.  But the other reason, the one I agree with, is that an unqualified method call seems to belong to current object and should not jump contexts. But if it really did belong, it would make sense to extend that super class.  So, when does it make sense to static import methods? When have you done it? Did/do you like the way the unqualified calls look?  EDIT: The popular opinion seems to be that static-import methods if nobody is going to confuse them as methods of the current class. For example methods from java.lang.Math and java.awt.Color. But if abs and getAlpha are not ambiguous I don't see why readEmployee is. As in lot of programming choices, I think this too is a personal preference thing.   Thanks for your response guys, I am closing the question. Gparted: move extended partition on the left You should choose your Display Name when signing up Why does the command shuf file > file leave an empty file, but similar commands do not? I know this is sort of a duplicate of another question () but I wanted to expand on the question in response to the answers given.  The command  shuf example.txt &gt; example.txt  Returns a blank file, because the shell truncates the file before shuffling it, leaving only a blank file to shuffle. However,  cat example.txt | shuf &gt; example.txt  will produce a shuffled file as expected.  Why does the pipeline method work when the simple redirection doesn't? If the file is truncated before the commands are run, shouldn't the second method also leave an empty file? Why $9$ & $11$ are special in divisibility tests using decimal digit sums? (casting out nines & elevens) As a 8th grader I am still a newbie at science and I have problems understanding the forces that I can not imagine and one of these "forces" is the moment.  We are told that,  $$\text{moment}= Nm$$ but how can a certain force (i.e. $N$) be applied when there is $m$? How does it depend on the length of the considered object?  And how can 1 moment be defined on the basis of that representation?  And what would be the effect if the moment value is increased by the newton part as opposed to the effect when the value is increased by the length part.  Or is the result the same in both cases? How to use combinatorial proof instead of induction? Let k ≥ 1 be an integer and consider a sequence $n_1, n_2, . . . , n_k$ of positive integers. Use a combinatorial proof to show that  $\binom{n_1}{2}$ + $\binom{n_2}{2}$ +...+ $\binom{n_k}{2}$ $\le$ $\binom{n_1 + n_2 + ...+ n_k}{2}$ Summing Up A 2D Array Problem: Let $X$ and $Y$ be independent and suppose that each has a $\text{Uniform}(0,1)$ distribution. Let $Z = \min\{X, Y\}$. Find the density $f_Z(z)$ for $Z$. Hint: It might be easier to first find $\mathbb{P}(Z &gt; z)$.  Attempted Solution:  Given that $X, Y \sim \text{Uniform}(0,1)$, how do we not just have the following?  $$ f_Z(t) = f_X(t) = f_Y(t) = \begin{cases} 1 &amp; \text{if } 0 \le t \le 1 \\                                           0 &amp; \text{otherwise}                             \end{cases} $$  Of course I'm highly suspicious of this answer because it's not making use of the fact that $X$ and $Y$ are independent, nor is it making use of the provided hint.