I need to find all parts of a mesh which are separated by seams, or which are unconnected sub meshes. As an illustration see the following image:  I need to get the sets of faces for each of the 5 shown mesh areas. How can i do that in a convenient way with Python?  I found this operator:  bpy.ops.mesh.select_linked(limit=True)   But maybe bmesh could provide a better way to go here ?
Is there a fast way (without looping over all edges/faces/verts) using ops.mesh or bmesh to get the lists of indices associated with mesh islands as shown below? These islands are part of one mesh but are disjoint from each other.    I know how to select the boundaries by running the operator Select boundary Loop or calling bpy.ops.mesh.region_to_loop() but can't find any API calls to return the vert/edge/face indices associated with the individual islands.
Going through the spells, I see the phrase "Willing creature" used to determine who you can cast some spells on. I don't ever see a proper definition of what a willing creature is, but I would assume that it would go something like if you asked them "Can I perform this spell on you" they would answer yes. Is there a more formal definition of what makes a target willing in 5e?  What are the ways I could make an otherwise unwilling creature willing? Suggestion spells, for instance, should probably work but what other options do I have? For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$ Well I attempted to try this but I failed to solve it: So $$\Phi_{p^{n}}(x)= \frac{x^{p^{n}} - 1}{\Phi_{1}(x) \Phi_{p^{2}}(x) \dots \Phi_{p^{n-1}}(x)}$$  Now I'm just stuck here. I saw a result somewhere on the net that said $\Phi_{p^n}(x) = \Phi_p(x^{p^{n-1}})$. I would just use that, but I don't see why that result is true or know how to show that's true.  How do I approach this? Based on , I figured that there might be multiple questions for distinct locales. Why do the most common transactions to or from bank accounts in the US require waiting one or more days before they are completed? In the information age, it seems like we should be able to transfer money instantly (or nearly so). Finding an isomorphic subring of matrices How to decide whether to replace or repair? First post review queue: answers are questions, questions are answers I believe there is a typo in the  review queue. When reviewing a question, the information message asks the user to review the answer. Take a look at the image below.    Similarly, when an answer is posted in the queue, the description box calls it a question instead. Has anyone else noticed this? How to insert pipe symbol in (La)TeX? How to insert pipe symbol | in TeX (LaTeX)?  I have tried this sample with pdflatex tmp.tex  \documentclass{extarticle} \begin{document} \textpipe \end{document}   And it give undefined control sequence error  This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) restricted \write18 enabled. entering extended mode (./tmp.tex LaTeX2e &lt;2009/09/24&gt; Babel &lt;v3.8l&gt; and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, loaded. (/usr/share/texmf-texlive/tex/latex/extsizes/extarticle.cls Document Class: extarticle 1996/10/08 v1.0 Non Standard LaTeX document class (/usr/share/texmf-texlive/tex/latex/base/size10.clo) (/usr/share/texmf-texlive/tex/latex/base/exscale.sty)) No file tmp.aux. ! Undefined control sequence. l.3 \textpipe For which $f,g \in k[t]$, $k[f,g]$ is integrally closed? Let $f,g \in k[t]$, $k$ is a field of characteristic zero, $\deg(f)=n \geq 2$, $\deg(g)=m \geq 2$.     Is it possible to characterize all such $f$ and $g$ for which $k[f,g]$ is integrally closed in its field of fractions $k(f,g)$?   I do not mind to further assume that $k(f,g)=k(t)$ (but I do not want to assume that $k[f,g]=k[t]$, which makes my question trivial).  Thank you very much!  Edit: (i)  is relevant.  (ii) If also $k(f,g)=k(t)$, then being integrally closed is equivalent to $k[f,g]=k[t]$. Indeed: (a) If $k[f,g]=k[t]$ then $k[f,g]$ is integrally closed (since $k[t]$ is). (b) If $k[f,g]$ is integrally closed then, in particular, since $t \in k(t)=k(f,g)$ (= the field of fractions of $k[f,g]$) and obviously $t$ is integral over $k[f,g]$ (for example, $t$ is a root of $f(T)-f \in k[f,g][T]$) hence $t \in k[f,g]$, so $k[f,g]=k[t]$.  For example: $f(t)=t^2+1$, $g(t)=t^3-4t$. We have, $t= \frac{t(t^2-4)}{t^2+1-5}=\frac{g}{f-5}$, so $k(f,g)=k(t)$. By Abhyankar-Moh-Suzuki theorem, $k[f,g] \neq k[t]$, so $k[f,g]$ is not integrally closed. Similarly, for every $f,g$ such that $k(f,g)=k(t)$ and one of the degrees does not divides the other, then $k[f,g]$ is not integrally closed.  (iii) If also $k(f,g)=k(t)$ and $k$ is algebraically closed, then being integrally closed is equivalent to $H(t)=(f(t),g(t))$ is injective and $H'(t)=(f'(t),g'(t)) \neq (0,0)$ for every $t \in k$. Indeed, $k[f,g]=k[t]$ is equivalent to the new conditions (it is important that $k$ is algebraically closed!!).  Edit: What if we replace $k$ by an integral domain $D$ (which is a $k$-algebra)? See also  question. Prove that $i^i$ is a real number File has different name in terminal and Finder I've just downloaded the driver for my preferred trackball from Logitech. In the Finder, the Installer's filename is Logitech Control Center Installer.app. In the Terminal, ls shows LCC Installer.app. How did this happen? Product of Non-Disjoint Cycles I am trying to learn how to find the product of non-disjoint cycles, as you may have guessed from the title. I have the basic idea, but I do not understand it entirely.  I am trying to find $(1352)(256)$ and $(1634)(1352)$, multiplying from right to left.  Please give me some hints/suggestions.  Thank you. What causes Nova's Triple Tap to go on a short cooldown? This isn't about the level 20 ultimate talent.  There is a brief "arming phase" where Nova locks onto her target before shooting three bullets.  When something happens to her target during that phase (allied Devouring Maw, Divine Shield, etc.), sometimes Triple Tap is placed on the full 100 second cooldown, other times it is placed on a much shorter 10 second cooldown.  What triggers this 10 second cooldown?   Is this a timing issue?  I believe if she is interrupted after the shots start going out, Triple Tap is always put on the full cooldown.  Maybe I'm just seeing the ability get blocked right as the first shot goes out? Is this ability-specific?  Does stunning Nova have a different effect than a Devouring Maw or Void Prison on her target?  And is that different from a Divine Shield/Sanctification on the target? Is this determined by whether the line to the target was interrupted by an ally or an enemy hero?  For example, is there a difference between an allied Void Prison and an enemy Void Prison on the target? Is product of two closed sets closed? If $A$ is closed in $X$ and $B$ is closed in $Y$,   does it follow that $A \times B$ is closed in $X \times Y$ ? Overriding public virtual functions with private functions in C++ In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.   I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it.        I strongly believe in the following quote:     You do not really understand something unless you can explain it to your grandmother. -- Albert Einstein   Well, I can't explain these concepts to a layman or grandma.   Why PCA, eigenvectors &amp; eigenvalues? What was the need for these concepts? How would you explain these to a layman? Travelling from India to canada via Dubai and London. Do I need a transit visa Do we have different badges in different SE sites The usual Schrodinger Lagrangian is $$ \tag 1 i(\psi^{*}\partial_{t}\psi ) + \frac{1}{2m} \psi^{*}(\nabla^2)\psi, $$ which gives the correct equations of motion, with conjugate momentum for $\psi^{*}$ vanishing. This Lagrangian density is not real but differs from a real Lagrangian density  $$ \tag 2 \frac{i}{2}(\psi^{*}\partial_{t}\psi -\psi \partial_{t}\psi^{*} ) + \frac{1}{2m} \psi^{*}(\nabla^2)\psi $$ by a total derivative.  My trouble is that these two lagrangian densities lead to different conjugate momenta and hence when setting equal time commutation relations, I am getting different results (a factor of 2 is causing the problem). I can rescale the fields but then my Hamiltonian also changes. Then applying Heisenberg equation of motion, I don't get the operator Schrodinger equation.   Is it possible to work with the real Lagrangian density and somehow get the correct commutation relations? I would have expected two Lagrangians differing by total derivative terms to give identical commutation relations (since canonical transformations preserve them). But perhaps I am making some very simple error. Unless all conjugate momenta are equivalent for two Lagrangians differing by total derivatives, how does one choose the correct one?   I guess the same thing happens for other first order systems like Dirac Lagrangian also. Catch multiple exceptions at once? It is discouraged to simply catch System.Exception. Instead, only the &quot;known&quot; exceptions should be caught. Now, this sometimes leads to unnecessary repetitive code, for example: try {     WebId = new Guid(queryString[&quot;web&quot;]); } catch (FormatException) {     WebId = Guid.Empty; } catch (OverflowException) {     WebId = Guid.Empty; }  I wonder: Is there a way to catch both exceptions and only call the WebId = Guid.Empty call once? The given example is rather simple, as it's only a . But imagine code where you modify an object multiple times, and if one of the manipulations fails expectedly, you want to &quot;reset&quot; the object. However, if there is an unexpected exception, I still want to throw that higher. Does low disk space affect SSD performance? I was wondering if having less than 5-10GB of free space on an SSD would affect performance. Is it specific to SSD or is it more of an operating system aspect?  For example, on an Intel X-25 G2 that has TRIM support (on Windows 7).