I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra computations. Also, I would like this package to be able to do wedge and hodge dual, and other computation relating to forms. Can anyone suggest a specific one? I looked for atlas2, but it seems I have to pay to use it without a trial version.
Already the early papers on supergravity were written using computer algebra software to do some calculations. What modern packages do people normally use for doing such calculations? Of course Mathematica and presumable a lot of other programs can be made to do such calculations, I am wondering if there are special packages or tutorials how to do such calculations in them.
Multicollinearity when individual regressions are significant, but VIFs are low I have 6 variables ($x_{1}...x_{6}$) that I am using to predict $y$. When performing my data analysis, I first tried a multiple linear regression. From this, only two variables were significant. However, when I ran a linear regression comparing each variable individually to $y$, all but one were significant ($p$ anywhere from less than 0.01 to less than 0.001). It was suggested that this was due to multicollinearity.  My initial research on this suggests checking for multicollinearity by using . I downloaded the appropriate package from R, and ended up with the resulting VIFs: 3.35, 3.59, 2.64, 2.24, and 5.56. According to various sources online, the point you should be worried about multicollinearity with your VIFs is either at 4 or 5.   I am now stumped about what this means for my data. Do I or do I not have a multicollinearity problem? If I do, then how should I proceed? (I cannot collect more data, and the variables are parts of a model that aren't obviously related) If I don't have this problem, then what should I be taking from my data, particularly the fact that these variables are highly significant individually, but not significant at all when combined.  Edit: Some questions have been asked regarding the dataset, and so I would like to expand...  In this particular case, we're looking to understand how specific social cues (gesture, gaze, etc) affect the likelihood of someone producing some other cue. We would like our model to include all significant attributes, so I am uncomfortable removing some that seem redundant.  There are not any hypotheses with this right now. Rather, the problem is unstudied, and we are looking to gain a better understanding of what attributes are important. As far as I can tell, these attributes should be relatively independent of one another (you can't just say gaze and gestures are the same, or one the subset of another). It would be nice to be able to report p values for everything, since we would like other researchers to understand what has been looked at.  Edit 2: Since it came up somewhere below, my $n$ is 24. I was trying to understand the internal structure of AES (Advanced Encryption Standard)  The Standard order of steps within a round:   Substitute Bytes Shift Rows Mix Columns Add Round Key   Substitute Bytes, Shift Rows &amp; Mix Columns satisfies the two most important properties required for a secure cipher i.e confusion and diffusion   Substitute Bytes provides Confusion i.e. that each binary digit (bit) of the ciphertext should depend on several parts of the key.  Shift Rows along with Mix Column provides Diffusion i.e. if we change a single bit of the plaintext, then (statistically) half of the bits in the ciphertext should change  Changing the order of Step 1 and Step 2 won't have any effect. But to what extent can we change the order of other steps? Does it weakens the security of AES, and if so, how? Trying to understand what happens with a brokerage firm's customers when it goes bankrupt (case of study: Lehman Brothers) I'm trying to understand how secure it is to own mutual funds/ETFs, not in terms of market volatility etc., but in terms of judicial security (i.e. what happens to your holdings if the firm goes bankrupt). To understand it, I have read this article about the bankruptcy of Lehman Brothers:  Note: From now on, I'm always referring to investors who own funds/ETFs managed by Lehman Brothers, not by investors who invested in Lehman Brothers or subprime mortgages (e.g. S&amp;P 500 ETF investors). From the above article, what I have understood is that the funds/ETFs managed by Lehman Bros. were shifted to other brokerage firms to be managed by them. Is this what actually happened? Still, what happens with the investors if, hypothetically, no brokerage firm in the world wants to manage these financial products? To better describe the above problem, whenever I start up my Ubuntu/Windows 10 Machine and select Ubuntu, whenever the machine tries to start the GNOME Desktop Environment, it says it started it successfully. however, I never get a graphical desktop environment to use. I can fix this by logging into tty3 and typing gnome-session but I don't really want to do that as, for some reason, that skips login. Can anyone help? Upper bound and lower bound of an integral I have this problem and I don't know where to start. Can you give me some hint, please?  Suppose that $f:[a,b]\to [0,\infty]$ is a lebesgue integrable function. Let $B=\int_a^b fd\mu.$ Prove that $\sqrt{1+B^2}\leq \int_a^b\sqrt{1+f^2}d\mu\leq 1+B$. This appears to be a css bug which (I think) has recently been introduced. It's most visible when viewing questions on Stack Exchange sites using mobile devices (the full site with responsiveness, not the mobile site) but can easily be reproduced by resizing a browser window on a question where the combined width of the tags is large. A couple of example questions show this behaviour:  On Meta Stack Overflow:   On Meta Stack Exchange:     Using the Meta Stack Overflow question to demonstrate (as the total width of the tags is larger):  At 1100px, the tags just about fit into their containing div.     At 800px, the tags appear on top of related questions:     At 450px, the tags are now wider than the view (the last tag is completely off the screen), causing scroll bars to appear:      This doesn't happen to lists of questions - the tags flow onto multiple lines:     Reproduced on: { Firefox 81, Chrome 84, Edge 84 } on Windows 10, and Chrome 85 on Android 11. How can I edit/create new launcher items in Unity by hand? Will Unity allow making custom launcher icons from .desktop files or via menu editing system? (Right now the launcher doesn't give the option to "keep in launcher" on all programs.  For some programs I use, I have to make custom launchers or .desktop files.  For instance, daily blender builds are generally just folders with an executable.  In basic Gnome or KDE, I can make a new menu entry with the menu editing system. Then, I can also add it to Docky either from the menu or by dragging a .desktop file to it. Unity launcher doesn't support drag and drop, so thats not a bug or anything, but when I open a .desktop file, it has unpredictable results. Most time it will not have "keep in launcher". Sometime it will have a pinnable item without the .desktop's icon, and if I pin the item to the launcher, it will not call upon the program again after closing it. I've also gotten it to just work with a .desktop file for celtx. Saving memoization to disk Indefinite articles used with plural nouns: It was AN amazing TWO DAYS Changing deleted partition back to NTFS without having to recover to another drive Recently, I accidentally deleted a partition off of my external hard disk. I had a copy of Minitool Power Data Recovery left over when the same drive had become RAW about a year ago. When I selected lost partition recovery, it immediately identified my deleted partition and allowed me to access and recover the files that were there.  My question is this. Is there any way to change the deleted partition back to NTFS without having to have a drive that you need to recover the files to and then move them back after formatting, as I don’t have any space left on either the computer or on my other external hard drive, so that I don’t need to buy a new one. The files on the disk were really important.  I am using Windows 7 Home Premium.  I appreciate any help in solving this crisis. I play with some serious board gamers, but we have neglected Monopoly for a number of years, so our knowledge is mostly based on high school &amp; house rules.  We played last week and enjoyed it, but there was a piece of contention. There are times where we decide that we don't like one of our friends for some reason and don't want them to win (i.e. we landed on their property a bunch, or they refused to make a deal, etc.).  So when player 1 has some property and player 2 lands on it and cannot pay the rent their assets (houses/hotels get liquidated), their property gets transferred to the other player. (Please correct me if I'm wrong.) In this case, though, player 3 "traded" the amount of money owing for a piece of property (way overpaid). In this case they did it so that player 1 would not get the properties. Player 2 had no chance of winning the game (all properties mortgaged, no cash to speak of and many of the other properties with 3+ houses/hotels on them).  To summarize: Is it OK for a third player to purchase/trade property or cash to/from a player who is about to lose? How do I opt-out of the new Reply in Gmail? Today, when trying to reply to a message in Gmail, I was told that there is a new reply mode and then it was automatically enabled. I find it difficult to use, and it doesn't let you reply to the message in accordance with the netiquette I'm used to.  How do I opt-out of this brand new reply mode? It wasn't there yesterday. Does 'fight' involve combat? TOC entries and labels for included PDF pages I am embedding full pages from another PDF document (using the pdfpages package), but I would like to be able to declare my own section headings before each embedded document (for e.g. hyperlinking / TOC purposes). pdfpages has an experimental feature which lets me do this, but the problem is that I want to put all of these embedded documents inside a section, so I need to insert a section heading and a subsection heading on the first document I embed. Unfortunately pdfpages doesn't seem to be able to do this. Is there a way for me to do this?  Edit: Thank you for the suggestions. I am also in need of something similar for general labels — at the moment I am abusing the addtolist option of \includePDF but the objects I'm labelling aren't really figures or tables. A great Python IDE for Ubuntu Possible Duplicate:          I want to develop Python apps in Ubuntu, and I'm tired of working with gedit one time and another.  So I'm trying to find a great Python IDE (a true IDE, not just a syntax-highlighting editor) on the Ubuntu repositories. Which one do you recommend me? I know and have observed that the the division algorithm can be used to convert any number in the decimal system to the binary system. However, I have tried searching for an intuition of why this method works, and I just can't seem to see anything, although I know what type of intuition I am trying to make out.   So, my question is why we can use the division algorithm to convert between the decimal bases and any other number bases?   An example from the decimal system to binary would be appreciated. I have come across this .  Has anyone tried anything similar or does it work for you? Can you tell if an email customer / user enters is correct &amp; exists? How to reset evolution settings to defaults? I have not used Evolution for long time now and I would like to reset all the settings and start from scratch. How would I be able to do this? Which package to use for presentations? Beamer, Prosper, or Other How can I swap or replace multiple strings in code at the same time?