20200309 21:34:19 0500  commented question  Unimodular matrices with additional restrictions Good point. This certainly works if the dimension is 8 e.g. the $E_8$ root lattice gram matrix: E8 lattice wiki. I edited the post. Thank you 
20200309 12:56:08 0500  asked a question  Unimodular matrices with additional restrictions I'd like to generate some unimodular matrices over ZZ with some restrictions:
Item (1) above can be addressed with the option becomes extremely inefficient, especially as the dimension grows. Is there a way to enforce items (1),(2) within the unimodular algorithm? Or another workaround? Edit: I originally also wanted the diagonal entries fixed at 2, but this is a bit too restrictive. 
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20200226 11:30:01 0500  commented answer  continuous Fourier transform Thank you! 
20200226 11:29:50 0500  commented answer  continuous Fourier transform Thank you! 
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20200219 13:38:32 0500  asked a question  continuous Fourier transform I have some basic code to plot a "nice" realvalued function and its continuous Fourier transform. For example, Like many things in Sage, I appreciate it when the code looks like the formal math. However, this code is not robust. For instance, if we change the function to Then I get an error message "Variable 'xi' not found". I'd like to improve this code to work with a wider class of functions. Thanks, 
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20180630 17:13:48 0500  commented answer  Solving a power series equation The workaround on the above thread works well. Thanks for the help! 
20180630 15:58:02 0500  commented answer  Solving a power series equation When I run this code I get the following traceback error: ValueError: rtol too small (4.5e16 < 8.88178e16) I'm not sure what this means or why it's happening. 
20180629 12:52:53 0500  asked a question  Solving a power series equation I'd like to solve the equation I've tried simply plugging in values for t and I estimate that if f(t) = 1 then t is approximately 1.51. I'd like to possibly do something like but this appears to lock sage up and I have to interrupt the process. The true f function is actually an infinite series, but I am truncating it to the first 1000 terms. I know there are methods of solving series equations such as the method of regula falsi. Does Sage have anything like this? Thanks! 
20180422 13:45:13 0500  asked a question  problem loading large file I have a file which was generated and saved from a Sage notebook worksheet:
where When I try to load this file later to do some analysis
my computer goes deep into swap memory (with python eating it all up) and basically freezes. I have done the exact same thing for smaller file sizes (<10Mb) with no issues. I've tried waiting over 30 minutes and nothing seems to happen. Is this possibly a memory issue? Something with Sage? Possible workaround? I'm running the Sage notebook in fedora linux with an older laptop with 8Gb of RAM. Thanks! 
20180401 22:13:06 0500  commented answer  3d plot, slow Great, thanks for the help! 
20180322 15:52:29 0500  commented question  3d plot, slow Also, is there a way to crank up the resolution so the spheres don't look pixelated? 
20180322 13:47:01 0500  asked a question  3d plot, slow I have some graphical objects (spheres and planes) and I'm trying to create a nice picture to export as a .png (other options?). The problem I'm having is that the interactive mode (right clicking on the graphic) is so slow that the menu options freeze up. I'd like to preview the image (rotate it around, zoom, etc.) before saving so that I can make sure I've got the right picture. What is a more efficient/ faster way to create and export a 3d picture? Thanks!
Also, if I try

20180201 09:25:51 0500  commented answer  random matrix with determinant + 1 This works. Nice simple solution. Thanks Dan. 
20180131 23:27:00 0500  commented answer  random matrix with determinant + 1 Right, that should work!...I'll let you know... 
20180131 22:15:26 0500  asked a question  random matrix with determinant + 1 I want to generate a random 4x4 matrix with integer entries and determinant either 1 or 1. I know that you can use
to generate matrices with determinant 1 (so in the special linear group). However, I'm actually more interested in the matrices with determinant 1. Is there a 'Sage' way to do this? Or are there other functions/routines out there I should look at? Thanks! 
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20171109 14:31:28 0500  commented answer  tree of vectors On the last line 
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20171107 16:18:12 0500  commented answer  tree of vectors Ok got it. In some cases, my thin_group may have loops and in other cases not. The visualization is very nice! 
20171107 15:49:01 0500  commented answer  tree of vectors Very nice code, thank you. Can I ask, in line 4, why did you use random matrices? 
20171107 15:47:21 0500  commented answer  tree of vectors Dan: very nice code. I'm still working on checking it with what I have here, but it appears to agree with my hand calculation for vectors of ht < 20. Thank you 
20171107 12:01:32 0500  asked a question  tree of vectors This is a more complicated version of apply functions iteratively I have a starting "seed" vector, say
where $T1 = \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 2 & 1 & 0 & 0 \\ 4 & 0 & 1 & 0 \\ 4 & 0 & 0 & 1 \end{array}\right), T2 = \left(\begin{array}{rrrr} 1 & 2 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 4 & 1 & 0 \\ 0 & 4 & 0 & 1 \end{array}\right), T3 = \left(\begin{array}{rrrr} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right), T4 = \left(\begin{array}{rrrr} 1 & 6 & 0 & 6 \\ 0 & 3 & 0 & 2 \\ 0 & 4 & 1 & 4 \\ 0 & 4 & 0 & 3 \end{array}\right), T5 = \left(\begin{array}{rrrr} 3 & 0 & 0 & 2 \\ 6 & 1 & 0 & 6 \\ 4 & 0 & 1 & 4 \\ 4 & 0 & 0 & 3 \end{array}\right)$ These matrices either fix
I want to develop the following procedure:
This procedure should "remember" the vectors that were counted/stored, so I'm thinking that I may be able to index each vector in the tree with a sequence (a1,a2,a3,...,an) where aj=1,2,3,4,5 to denote which matrix T1,...,T5 we applied previously. Any/all ideas or partial solutions greatly appreciated. Thanks! 
20170613 19:45:46 0500  commented answer  Help with unstable code This is a nice solution to the problem. Thanks. 
20170613 19:45:04 0500  commented answer  Help with unstable code Very nice code. I like how you made use of projective space. In doing so, you remind the user/reader that a FLT is just matrix multiplication. Thanks 
20170610 14:16:34 0500  asked a question  Help with unstable code This basically continues from a previous post: generation of certain matrices I'm trying to draw circles in the plane by using fractional linear transformations. Here is my code: Now generate circles based on 3 image points of a matrix M with entries in the ring OK via FLT: This second chunk of code throws the error "list index out of range" about 50% of the time. I thought that it may have been due to division by zero, but now I'm not so sure. I've also tried using a for loop with the exact same result. Thank you very much for the help! 