# Bill Page _ again's profile - activity

 2022-12-20 10:50:03 +0100 received badge ● Notable Question (source) 2022-04-12 01:10:33 +0100 received badge ● Popular Question (source) 2022-02-14 22:45:28 +0100 received badge ● Notable Question (source) 2021-06-10 06:51:55 +0100 received badge ● Famous Question (source) 2019-03-18 04:38:52 +0100 received badge ● Popular Question (source) 2017-05-10 15:41:48 +0100 commented answer How can I specify a (possibly non-associative) algebra over a finite (small) set of generators by means of structure constants? This is nice. There is a lot of useful documentation: here but so far I could not easily find how compute the center of the algebra (elements that commute with all other elements) but perhaps this is defined in some other way? 2017-05-09 21:38:23 +0100 received badge ● Supporter (source) 2017-05-09 21:09:47 +0100 asked a question How can I specify a (possibly non-associative) algebra over a finite (small) set of generators by means of structure constants? I am looking for something similar to the Axiom/FriCAS domain AlgebraGivenByStructuralConstants which implements finite rank algebras over a commutative ring, given by the structural constants with respect to a fixed basis [a1,..,an] or equivalently in terms of generating equations of the form a_i * a_j = gamma_ij1 * a_1 + ... + gamma_ijn * a_n where gamma is a vector/list of length n of n by n matrices. In particular I would like to be able to easily compute various properties of such algebras such as the conditions for idempotents etc. For example: 2017-01-03 14:00:55 +0100 received badge ● Notable Question (source) 2016-07-26 04:18:05 +0100 received badge ● Editor (source) 2016-07-26 04:17:14 +0100 answered a question Problem in installing SAGE I had exactly the same problem on OpenSuse Leap 42.1. I downloaded the binary distribution sage-7.2-Fedora_23-x86_64.tar.bz2 from http://mirrors.mit.edu/sage/linux/64b... (since there is no OpenSuse binary). I extracted it and then ran 'make' (in spite of the fact that this was a binary distribution). Make ran for 20 minutes before giving this error. But the problem went away when I actually downloaded the source distribution instead from http://www.sagemath.org/download-sour.... Is 'make' supposed to work with the binary distribution? 2015-03-25 03:31:09 +0100 answered a question Complex analysis. Compute bar derivative http://en.wikipedia.org/wiki/Wirtinge... I would agree that this is not implemented in Sage but I would disagree that it can be defined as a "simple combination of the usual derivatives". In particular it is necessary to consider the chain-rule. I have a prototype implementation in FriCAS (Axiom) that does this. In that context I am interested in collaboration and critical review. http://axiom-wiki.newsynthesis.org/Sa... From the point of view of complex analysis you might also want to look up references to polygenic functions, e.g. Kasner http://www.ncbi.nlm.nih.gov/pmc/artic... 2014-09-03 15:29:10 +0100 commented answer Why is diff(conjugate(x),x) unevaluated? Thanks. This is cute, but as you say does not really answer the question. I am thinking of a way to make diff equivalent to your d operator, then dbar can be implemented simply by substituting a dummy variable for conjugate(x). 2014-09-03 15:24:16 +0100 received badge ● Autobiographer 2014-09-03 03:25:09 +0100 asked a question Why is diff(conjugate(x),x) unevaluated? Or, can we differentiate holomorphic functions only? Wirtinger defined two derivations in complex analysis for which we have: diff(x,conjugate(x)) = 0 and diff(conjugate(x),x) = 0. http://en.wikipedia.org/wiki/Wirtinge... Wirtinger calculus has important applications in optimization and has been extended to quaternion functions. Is there any situation in which leaving diff(conjugate(x),x) unevaluated is an advantage? 2013-05-05 23:46:43 +0100 received badge ● Popular Question (source) 2011-11-07 07:37:49 +0100 commented answer polar_plot((1/sin(theta)),(theta, pi/12, pi/2)) Ok, yes with this option I do get a reasonable looking graph but I also get the message: verbose 0 (3998: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 24999 points. verbose 0 (3998: plot.py, generate_plot_points) Last error message: '' 2011-11-04 12:52:26 +0100 received badge ● Self-Learner (source) 2011-11-04 12:52:26 +0100 received badge ● Teacher (source) 2011-11-04 11:08:55 +0100 answered a question polar_plot((1/sin(theta)),(theta, pi/12, pi/2)) Thanks for the trac ticket. Here is another one with a problem: polar_plot(3*sqrt(cos(2*theta)),(theta, 0, 2*pi))  gives the follow graph: > ![image description](http://) > > Sorry, file uploading requires karma > 60  Arrrgh! Well, ok try it yourslf. On my v.4.6.1 worksheet I see a plot with some weird discontinuity near the origin. 2011-11-01 22:03:23 +0100 received badge ● Student (source) 2011-11-01 20:57:13 +0100 asked a question polar_plot((1/sin(theta)),(theta, pi/12, pi/2)) In Sage notebook v 4.6.1 I wrote: var('theta') polar_plot((1/sin(theta)),(theta, pi/12, pi/2))  I got libpng error: Image width or height is zero in IHDR Traceback (click to the left of this block for traceback) ... RuntimeError: Error building image  What am I doing wrong? 2011-11-01 20:56:02 +0100 asked a question polar_plot((1/sin(theta)),(theta, pi/12, pi/2)) In Sage notebook v 4.6.1 I wrote: var('theta') polar_plot((1/sin(theta)),(theta, pi/12, pi/2))  I got libpng error: Image width or height is zero in IHDR Traceback (click to the left of this block for traceback) ... RuntimeError: Error building image  What am I doing wrong?