Face making and Loop Cutting
why does loop-cut-and-slide ignore some faces but not others?
Export My Stack Overflow Data Is there a first party (or third party?) way to export just my data out of Stack Overflow?  I realize there's a massive Creative Commons data dump.  I'm interested in knowing if there's a quick and easy way for me to get my posts dumped out in some plain text file format for easy  personal archiving. The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain Let $\alpha = \frac{1+\sqrt{-19}}{2}$. Let $A = \mathbb Z[\alpha]$. Let's assume that we know that its invertibles are $\{1,-1\}$. During an exercise we proved that:     Lemma: If $(D,g)$ is a Euclidean domain such that its invertibles are $\{1,-1\}$, and $x$ is an element of minimal degree among the elements that are not invertible, then $D/(x)$ is isomorphic to $\mathbb Z/2\mathbb Z$ or $\mathbb Z/3\mathbb Z$.   Now the exercise asks:     Prove that $A$ is not a Euclidean Domain.   Everything hints to an argument by contradiction: let $(A, d)$ be a ED and $x$ an element of minimal degree among the non invertibles we'd like to show that $A/(x)$ is not isomorphic to $\mathbb Z/2\mathbb Z$ or $\mathbb Z/3\mathbb Z$.  How do we do that? My problem is that, since I don't know what this degree function looks like, I don't know how to choose this $x$!  I know that the elements of $A/(x)$ are of the form $a+(x)$, with $a$ of degree less than $x$ or zero. By minimality of $x$ this means that $a\in \{0, 1, -1\}$. Now I'm lost: how do we derive a contradiction from this? example of not surjective isometry on a bounded not closed set. I have a motherboard with a PCIexpress x16 slot.  I want to purchase a card called AMD Radeon HD 7770, which uses PCIe version 3.0.  Is that backwards compatible? Is it possible to install Ubuntu through network? I would like to install Ubuntu  for almost 120 users. But it's very difficult in using USB and drives.  Any suggestions? What does 'super' do in Python? - difference between super().__init__() and explicit superclass __init__() What's the difference between:  class Child(SomeBaseClass):     def __init__(self):         super(Child, self).__init__()   and:  class Child(SomeBaseClass):     def __init__(self):         SomeBaseClass.__init__(self)   I've seen super being used quite a lot in classes with only single inheritance. I can see why you'd use it in multiple inheritance but am unclear as to what the advantages are of using it in this kind of situation. Change the Fill Color of a cell if the value of that cell equals the value of another specific cell I want to change the fill color of cell C5 if it has the same value as cell A5.   Can this be done? I know how to format cell C5 if it has a certain value - but not when it is to be compared to the value of another cell. I would like to build a new computer (it's been 7 years since the last one). Does Windows 10 support more than one ? Can you grapple/shove with the Hunter Ranger's Whirlwind Attack? The  states:     You can use your action to make a melee attack against any number of creatures within 5 feet of you, with a separate attack roll for each target.   The rules on "" state (the rules in shoving are effectively identical):     When you want to grab a creature or wrestle with it, you can use the Attack action to make a special melee attack, a grapple. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.   I couldn't find any other features spells or abilities that allow a creature to make a flat "melee attack". If they had said "melee weapon attack" instead this would have meant the same thing but specifically have excluded grapple/shove as an option.  I am unsure whether the rules on grappling/shoving mean that the only time you can grapple/shove are when you take the Attack action, which you are not doing when using the Whirlwind Attack feature.   I would like answers to assume that the following ruling made in the  is correct:     Whirlwind Attack is unusual, in that it’s a single attack with multiple attack rolls... This is a problem from Introduction to Representation Theory by Etingof et al. I have no idea how to approach it. My friend wrote a program that uses Gaussian elimination to find a basis, which starts with x, y, [x, y], [y, [x, y]], ... but freezes once it gets to elements with 9 or more occurrences of x, y.  I expect that there is some way to characterize the nonzero elements of this Lie algebra (i.e., elements that are "immune" to being shown to be zero through repeated application of the Jacobi identity) which could be turned into a way to enumerate them. I don't see what it is, though.  It's also totally unclear to me how to show that some set we know spans the Lie algebra (proven using some criterion as described in the previous paragraph) is actually linearly independent, unless we find a faithful representation... but I have no idea how to find a faithful representation for an infinite-dimensional Lie algebra.  Hints would be greatly appreciated.  Edit: After looking at the partial output, we can form the "straightforward" conjecture that:   If $n \geq 4$ is even, then there is one basis element of grade $n$, namely $\mathrm{ad}([x, y])^{(n-4)/2}[y, [y, [y, x]]]$. If $n \geq 5$ is odd, then there are two basis elements of grade $n$, namely $[x, z]$ and $[y, z]$ where $z$ is the single basis element of grade $n-1$.   I also have a different conjecture, which is mutually exclusive with the above: that if we flatten out all nonzero elements into the form ${\rm ad}(e_1) {\rm ad}(e_2) \ldots {\rm ad}(e_{n-1}) e_n$ using the Jacobi identity, then in the sequences $e_1, \ldots, e_{n-1}, e_n$ and $e_1, \ldots, e_n, e_{n-1}$, any span containing two x's must contain at least two y's and any span containing five y's must contain at least two x's, otherwise we can use the Jacobi identity to rearrange the element somehow to show that it vanishes. If this is true, then the long-range behaviour must be:   For $n \geq 8$ there is exactly one basis element of grade $n$, namely $[... [y, [x, [y, [y, [x, y]]]]] ...]$ (the pattern $y x y$ repeats).   I still don't see an approach to proving that none of the elements in this sequence actually vanishes, though.  Edit 2: Here is the hint given by Etingof in an email:     No, there are no published solutions, since these problems are used as   a homework for classes. This is indeed a nontrivial problem.      This is the positive part of the affine Kac-Moody algebra of type   A_2^2, which is the twisted loop algebra for sl(2). So what you need   to do is to relate this Lie algebra to loops into sl(2). I see from   your post that you are on the right track. How deterministic is floating point inaccuracy? What is the difference between Newtonian and Lagrangian mechanics in a nutshell? Ring homomorphism and characteristic I've recently set up the compiz cube again, and I was very happy to find that that flickering window glitch is gone! However, the cube reflection and deformation plugins are also gone.  I am running a fresh 12.10 install, and I have every compiz plugin package installed (including compiz-plugins-extra, which supposedly contains everything that compiz-fusion-plugins-extra package used to have), but those two plugins are still missing. I haven't been able to find anyone with the same problem.   Any ideas? (thanks!) easy_install: command not found CloudPagesURL() value not showing in HTML I am trying to pass the email value from a data extension to HTML. I am using the CloudPagesURL() in my email in attempt to grab the subscriber's email.  Here is my code syntax that I am attempting to use:  Email Code:  &lt;p&gt;&lt;a title="MyPage" href="%%=RedirectTo(CloudPagesURL(505,'Email Address',@EmailAddress))=%%" alias="ThisAlias" conversion="false"&gt;Click to unsubscribe page 505&lt;/a&gt;&lt;/p&gt;   CloudPage AMPScript Code:  %%[  VAR @emailAddress  SET @emailAddress = RequestParameter("emailaddr")  ]%%   Cloudpage HTML Code:  &lt;td width='155' valign='bottom'&gt;&lt;input type='text' name='Name1' value='%%=v(@emailAddress)=%%' id='Name1' /&gt;&lt;/td&gt;   Any reason as to why this doesn't work? My syntax might just be wrong or I might be using the CloudPagesURL() function incorrectly. Suppose my speed is normally 30 feet. I get hit with a Slow spell, reducing my speed to 15 feet, and then I get knocked prone. How many feet of movement do I need to spend in order to stand back up from prone? How many feet of movement do I have left over once I've stood up?  What if I am also hit with a Ray of Frost spell while slowed, reducing my speed to 5 feet for 1 round? Am I able to stand up at all? If a thin metal plate is placed between two charges $+q$ and $+q$, will this cause a change in the electrostatic force acting on one charge due to another? What is the concept behind this? What will happen if the metal plate is thick? Word for sentences that make sense when read backwards? Is there a word for sentences that make sense when read normally or backwards (not necessarily by reversing the words)? Example:     "Are you as bored as I am?" Web colors: how to compensate for differences in monitors