Identify $\mathbb{Z}[x]/(x^2-3,2x+4)$. I need help to identify $\mathbb{Z}[x]/(x^2-3,2x+4)$.  I've been solving such problems in an approach like:  $$ 2(x^2-3)=2x^2-6, x(2x+4)=2x^2+4x \\ (2x^2+4x)-(2x^2-6)=4x+6, 2(2x+4)=4x+8 \\ (4x+8)-(4x+6)=2 $$  What shall I do next, please? Thank you.  Simon
How many elements does the ring $ℤ[X]/(X^2-3,2X-4)$ have? Describe the structure of this ring. I'm making exercises to prepare for my ring theory exam:     How many elements does the ring $ℤ[X]/(X^2-3,2X-4)$ have? Describe the   structure of the this ring.   I find it always difficult if the ideal is generated by two elements.   I thought about someting like this. $X=2$ and $X^2=3$. Therefore $4=3$ therefore $1=0$. As $2=1$ then $X=0$. And then everyting seems to become $0$.   I'm not sure if I'm allowed to see it this way, but this is the first thing that comes to my mind.
App drawer icon gone from Cyanogenmod dock I have a Samsung Galaxy S2, running the latest CM10.1.  I lost the app drawer icon on my Dock; I must have deleted it. The app drawer icon lets you go to the app list, and the widget list.  How do I get the app drawer icon back? The icon looks like a circle with 6 dots inside it. Is my expansion of the state $| x \rangle$ correct? Windows 7 finding location of installed program ref to subsection number only I just recently completed a neutral run where I experimented seeing how the story would go on if I only killed certain characters (it was my second run, my first run was True Pacifist) and I ended up choosing to kill Flowey instead of letting him live. I planned to start a Genocide run after resetting the game, but Flowey was gone when i did. Flowey is basically the base for each story in undertale (pacifist and genocide) so I know I can't progress any further without him being here. I really just want to start anew and, without Flowey, I dont think I can access True Resets anymore. It may be possible if I did a genocide route, but then I'd have to fight Sans, and that would take FOREVER.  Basically, I am wondering if I can erase all my progress somehow. I heard that True Resets don't erase everything entirely, so is there another way? Please respond, Undertale is the only game I have that's any fun and I don't want to have to buy another game. Every subspace of a compact space is compact? It seems as if every subspace of a compact topological space (equipped with its relative topology) had ought to be compact as well. Is this true in general?  And in particular, I want to use the fact that every quasi-projective variety is compact with the Zariski topology - I remember having proven it for quasi-affine varieties, but the same proof does not work for quasi-projective varieties. Is every quasi-projective variety compact? How do I remove repeated elements from ArrayList? I have an ArrayList&lt;String&gt;, and I want to remove repeated strings from it. How can I do this? Invest money and get 120% back - a site says Prove $ \forall c \in \mathbb{R^{+}}, \forall B \in \mathbb{N}, \exists n \in \mathbb{N}, (n \geq B) \wedge (\sqrt{2n} > c \ln(n+2)) $? Is this group solvable? Let $G=H\times K$ (a direct product of $H , K$) where $H$ is an abelian 2-group and $K$ is a non-abelian simple group. Is $G$ solvable? why?  These three answers are true, and I thought so. But in a book I found a remark that made me confused: T.M. Gagen, Topics in Finite Groups, London Math. Soc. Lecture Note Ser., vol. 16, Cambridge Univ. Press, Cambridge, 1976, Remark, Theorem A on p. $40 $ and Definition $11.3$ on p. $39$. Please see it and say me your ideas. How do I get an Intel Wireless 3168 802.11ac wireless card to work? How can a file size be zero? Just something I ran into and couldn't think of a proper explanation. If I create an empty *.txt file on my PC and then look at its size, it shows 0. But how is that possible? I mean even if the file itself is empty, it still must have some size, just to store its own name. How can this be explained? (Non OS specific) How do I pluralize Italian foods, like pasta noodles (spaghetti, macaroni)? Possible Duplicate:             Is it proper to say spaghettis for more than one spaghetti noodle?  What about macaronis as a plural for more than one macaroni noodle? Can we divide two vector quantities? For eg., Pressure( a scalar) equals force (a vector) divided by area (a vector). What's the full-form & significance of USS & ISS prefixes in name of Star Trek starships? When would you call java's thread.run() instead of thread.start()? When would you call Java's thread.run() instead of thread.start()? I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the surroundings?  Let me explain more, Einstein proved that $E = mc^2$ and equivalently, we can say $m = \frac{E}{c^2}$ . We however know mass causes curvature in space-time (gravity well). Now that statement being completely valid we can use Quantum Fluctuation, implying energy and time can be related by the relation:  $\Delta{E}\Delta{t}\approx\frac{\hbar}{2}$ and by that simple relation we can make the following points:   As the energy increases, the time allowed to be "borrowed" decreases, before it gives it back to the universe. As time increases, the energy allowed to be "borrowed" decreases.    These are completely satisfactory points I've made, I believe.  Now, I have read that the vacuum is filled with constantly bubbling virtual particles that get created from the energy "borrowed" by the above relation and is destroyed again, which satisfies the energy conservation laws.   This seems to imply that  in the short time the virtual particle exists, they must have a very small mass which is: $m_{1} = \frac{\Delta{E}}{c^2}$ and using basic classical mechanics rather than GR (for sake of simplicity) we calculate that the gravitational force mediated by this short-lived virtual particle;  $F_{g}= G\frac{m_1 * m_x}{r^2}$   where $m_x$ is an particle\mass in question. Nevertheless since we know the force set upon an object moves the object in a direction, we can say it would increase its kinetic energy by this factor: $F_g = \frac{1}{2}mv^2$ which is equal to $G\frac{m_1 * m_x}{r^2} = \frac{1}{2}mv^2$.  Surely, this implies that every time quantum fluctuations happen, energy of real-particles\masses increases and therefore violates energy conservation, but what prevents this violation from taking place?  If virtual particles are not really present and interact with objects like I thought, how can Hawking radiation (currently a large concept in black hole physics) then be accepted in physics community? Space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable Let's consider the space $\mathcal{L}^p(X, \Sigma, \mu)$ of all functions $f\colon X \to \mathbb{R}$ (or $\mathbb{C}$) for which: $$ \int\limits_X|f|^p \mu(dx) &lt; \infty. $$ Here $X$ is a metric space, $\Sigma\subset 2^X$ — sigma-algebra on $X$ and $\mu$ — is the measure on $\Sigma$. As usual, functions that are equal almost everywhere considered to be equivalent, so technically we are dealing with classes $$[f]=\{g\in \mathcal{L}^\infty(X,\Sigma, \mu) \colon \mu \{x\in X\colon f(x)\neq g(x)\}=0\}.$$ This space is endowed with integral metric $$\rho_p(f,g)=\left(\int\limits_X|f-g|^p \mu(dx)\right)^{1/p}$$  The statement is that space $\mathcal{L}^p(X, \Sigma, \mu)$ is separable iff $(\Sigma, \rho_\Delta)$ is separable, where $\forall A,B\in\Sigma$ $$\rho_\Delta(A,B)=\mu(A\Delta B)$$ Here, again, we consider $A\in \Sigma$ as a class $[A]=\{A'\in\Sigma\colon \mu(A\Delta A')=0\}$ to have the identity of indiscernibles.  How do one prove the statement? How to Combine two Normal Maps? I made a high poly model and then baked its textures onto a low poly model. Now I want to give another normal map's details to the model. How can this be done? Quick way to subtract white outline from knotwork pattern in Illustrator? I am working with a pretty complex traced AI that I received, and I want to basically make it so that all the visually black stuff is shapes, and all the white outlines (invisible here) are removed. Most of the spaces when a line crosses over another is created by a white outline.   I know about expanding appearance and the pathfinder tool, but because there are so many lines that are crisscrossing, I haven't had an easy way of minusing the fronts away. I could expand appearance and sort every object carefully, but I feel like there may be a quicker way of doing this.  If I put it in Photoshop as a smart object in 'screen' mode, it looks right.. I could put that back in Illy and trace it, but I don't want to complicate the paths.