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Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$ I know that $\mathbb Z[\sqrt{7}]$ is a UFD, and I can write the equation $(2 + \sqrt{7})(3 - 2\sqrt{7}) = (5 - 2\sqrt{7})(18 + 7\sqrt{7}) $. So clearly these are not all irreducibles. How do I determine which of these aren't irreducible? How do I factor those into irreducibles?  It seems difficult when dealing with $\mathbb Z [\sqrt{d}] $ with $d$ positive, since the norm map isn't as nice (it's not always positive).  Thanks 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 $A$? Some time ago, I baked a cake (Sachertorte to be exact). The taste and texture was fine, so my recipe is okay.  My biggest issue was the shape. In the middle it was really a lot higher than on the sides. I would like to redo it in the near future, but preferably with a flat(ter) surface. (Especially since I put icing on top and I don't want it to drip off this time.)  Anyone knows the cause of my problem, or even better a solution? I think I put enough butter on the side of my springform pan, in case this is an option. How to make a good glow effect around a sun? I flagged a post and (choose one)   my flag was marked as helpful, yet nothing was done my flag was marked as declined, yet the post was deleted/edited/closed   Why? If someone could help me with the proposed change of variables, it would be greatly appreciated. Consider Euler's equation:  $$z^2w'' + \alpha zw' + \beta w = 0$$  where $w$ is a function of $z$ and $\alpha, \beta$ are constants. How would the change of variables $t =\ln(z)$ transform this equation? subsurf splits the mirrored model into two objects I tried to subsurf this model that I mirrored but when I use subsurf it splits the model into two objects.  Before Subsurf:   After Subsurf:   Any help would be appreciated. Would a backpack or cargo rack be better for commuting? Right now I use a backpack to hold all of my supplies including spare tubes, pump, patch kits, tools, my change of clothes for work, etc.  This is the backpack I use:    It's about as comfortable as a backpack can get without getting into the hiking backpacks with frames. Altogether I would say it weighs no more than 10 lbs max. The muscles in my back get slightly irritated during my commute.  Would it be more comfortable to use a rear cargo rack on my bike instead? Will adding more weight to the bike change how the bike rides and feels?  EDIT: After doing some research I came across  that explains the different methods of carrying your gear on commutes and how it affects your body. It's worth a look.  EDIT #2: Having tried both for a couple of weeks now, I can say that (for me personally) the backpack is the better way to go given the relatively light weight I have to carry.  If you do use a backpack, make sure that the straps are tightened enough so that it's positioned higher up on your back and to the point to where there is little to no movement on your back. This makes a world of difference when it comes to comfort. In the simple linear regression model, $\hat{\beta}$ is the sum of independent normally distributed random variables.  Is it false because in linear regression there is $\beta$ and not $\hat{\beta}$? In what order do multiple readied actions with the same trigger resolve? My players have been scheming with rapid entry tactics for the megadungeon I've recently started running. Unfortunately, the monsters are aware of the adventurers, and this has lead to a weird question of priority. Given the following situation (which I'm pretty sure is going to happen next session in some form or another) what happens?     Alice the adventurer readies an action; if her teammate Carlos opens   the door, she's going to throw the alchemists fire through the door,   which should do enough damage to kill any goblins hiding there.      Meanwhile, on the other side of the door, Bob the goblin is lying in   wait. He readies an action; if the door opens, he's going to hit the   switch to open the trapdoor in the next room, which should drop any    pesky adventurers into a pit with spikes at the bottom.      Carlos opens the door.   I know what happens when , but what happens when multiple readied actions get triggered at the same time? My guess would be an opposed reflex save or initiative check of some kind to see who goes first, but that's entirely just intuition speaking. The rulebook doesn't seem to speak to the issue. OpenLayers Plugin Error: latitude or longitude exceeded limits I'm aware the 'traceback' OpenLayers plugin error has been dealt with before, so apologies for raising the issue once again. Unfortunately for me, the solutions posted were way over my head, e.g. using workarounds and code posted on github, etc. I find it all mind-boggling.  If anyone could post a step by step answer for an absolute beginner like me I would be eternally grateful! Thank you. I hope that one day I can contribute something.  The error message reads:   An error has occured while executing Python code:  Traceback (most recent call last):   File "C:/Users/MCMA1580/.qgis//python/plugins\openlayers_plugin\openlayers_plugin.py", line 48, in addLayer     self.__plugin.addLayer(self)   File "C:/Users/MCMA1580/.qgis//python/plugins\openlayers_plugin\openlayers_plugin.py", line 190, in addLayer     self.__setMapSrsGoogle()   File "C:/Users/MCMA1580/.qgis//python/plugins\openlayers_plugin\openlayers_plugin.py", line 249, in __setMapSrsGoogle     extMap = coodTrans.transform(extMap, QgsCoordinateTransform.ForwardTransform) QgsCsException: forward transform of (0.884883, 2.549197) PROJ.4: +proj=longlat +datum=WGS84 +no_defs +to +proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +wktext  +no_defs Error: latitude or longitude exceeded limits Are any of these verb phrases grammatical?        allows the user of modeling and resolving     allows the user to model and resolve      Which version of the following sentence is correct/better?        In particular, it allows to acquire a signal using a sample rate significantly lower than the one dictated by the Nyquist criterion.   In particular, it allows acquiring a signal using a sample rate   significantly lower than the one dictated by the Nyquist criterion.      I searched Google Scholar for "" and "", and it seems people use both more or less with the same frequency. Car accident, put in park or neutral? Before I start, YES, I have done my own research - I know how annoying a repeat question is. Yet each answer is so specific to others...  When I tried the beta 2.8 64 bit, it says "Blender requires a driver with at least OpenGL 3.3 support. The program will now close."    The question: I know that it is true that 2.8 requires OpenGL 3.3. But does my PC not have it, doesn't support it, or do I have it and blender won't detect it? I'm not sure what info to include or what to look for, so here's my PC's specs:  Windows 10 (64 bit) Core -        Intel Core i5-2400 CPU @ 3.10GHz RAM -         8GB (7.89GB usable) System type - 64-bit Operating System, x64-based processor  Thanks!  EDIT: Graphics properties: I don't know how to integrate $\displaystyle \int\frac{1}{x^{4}+1}\mathrm dx$. Do I have to use trigonometric substitution? What is special about square numbers here? How can I use Bengali script in an English document? So, in my physics textbook it's written that the kinetic energy possessed by a body is equal to the amount of work done by an opposing force to stop the body, now that got me thinking that when a ball hits a wall, the wall which is the opposing force does no work  because there is no displacement, so to say isn't the kinetic energy possessed by the ball zero? How do I declare and initialize an array in Java? How to get BSD FTP and Telnet back in 10.13 (High Sierra)? There are  with not having ftp and telnet present in 10.13 now as per Apple's dictate.  Has anyone found a solid way to bring BSD ftp and telnet back to macOS vs using inetutils?