My computer Plato is having a technical issue.

One of the main computers which I’ve been using, that is named ‘Plato’, that was running Debian / Stretch, has experienced a major technical problem. When I got home this afternoon, I found it was not running. And, when I pushed the power button, it did not turn on.

A basic, automatic idea which would pop into people’s heads is, ‘The power-supply burned out.’ If the only task which lies ahead really was, to replace the power supply, I’d have it easy. This is a tower-computer from the year 2011, with a Sabertooth X58 motherboard.

  • The correct power-supplies for this old MB may have become hard to find,
  • Even if I had a replacement power-supply, it would be very cumbersome to replace because the harnesses of the present one loops behind too many recessed compartments, within the case.

The only thing I’ve done so far, is to perform a diagnostic test. I disconnected all the jacks between the power-supply and the MB, and retried the power button. My purpose behind that was, the idea that modern power supplies will refuse to turn on, if they sense a short-circuit between their load, and ground. Thus, if the power supply had been able to resume, with the MB disconnected, I’d know it was the MB, and I’d also know there’s no point in replacing the power-supply. But thankfully, the power-supply also did not power up like that. So I reconnected the power-supply to the MB.

So as it stands, I don’t know the best way to proceed, but am without the use of that trusty computer for now.

(Update 2/7/2019, 14h15 : )

One reason this apparent loss is unfortunate is the fact that, being my only Debian / Stretch computer, that computer was also the only one, which had “SageMath” installed and working on it. So my available Computer Algebra Systems are reduced to “Maxima” and “Yacas” for now.

(Update 2/9/2019, 18h50 : )

Actually, I’ve learned that my so-called diagnostic test was pointless. The power button these days, does not have a direct connection to the power-supply, to signal that the power-supply should turn on. The power button has its connection to the M.B., which tells the power-supply to turn on. Therefore, with the M.B. disconnected from the power-supply, there was no way for the power-supply even to get the signal, to turn on.

A personal friend of mine has lent me a power-supply tester, so that I’ll next be able to test that more properly. And, hoping that it is just the power-supply which is faulty, I’ll look into replacing it.

(As of 2/7/2019, 14h15 … )

Continue reading My computer Plato is having a technical issue.

Noticing when SageMath is using IPython, instead of Maxima.

One of the subjects of my recent postings, has been a Computer Algebra System called “SageMath”, which I was able to install on my Debian / Stretch (Debian 9) computer named ‘Plato’. One of the distinctions which I left slightly blurred about this, is the distinction between Computer Algebra, and Numerical Tools. The former refers to the ability of a computer to manipulate symbols, in the way Algebra manipulates them, but to solve equations which Humans might just find tedious or too time-consuming to solve. This can lead to answers that are theoretically exact, but which can sometimes be useless because the numerical equivalent is only available indirectly.

Numerical Tools are more numerous under Linux, and offer theoretically inexact solutions to equations, simply because the numerical answers have a limited number of decimal places after the point or comma. Yet, the numerical answers can sometimes be much more useful than Algebraic answers, for reasons that I think are self-explanatory.

SageMath offers both. In order to do Algebra, SageMath uses “Maxima” as its back-end. And under Debian Linux, installing SageMath actually installs a separate version of Maxima, which users are not supposed to use directly.

Continue reading Noticing when SageMath is using IPython, instead of Maxima.

A Hypothetical Algorithm…

One of the ideas which I’ve written about often is, that when certain Computer Algebra Software needs to compute the root of an equation, such as of a polynomial, an exact Algebraic solution, which is also referred to as the analytical solution, or symbolic Math, may not be at hand, and that therefore, the software uses numerical approximation, in a way that never churned out the Algebraic solution in the first place. And while it might sound disappointing, often, the numerical solution is what Engineers really need.

But one subject which I haven’t analyzed in-depth before, was, how this art might work. This is a subject which some people may study in University, and I never studied that. I can see that in certain cases, an obvious pathway suggests itself. For example, if somebody knows an interval for (x), and if the polynomial function of (x), that being (y), happens to be positive at one end of the interval, and negative at the other end, then it becomes feasible to keep bisecting the interval, so that if (y) is positive at the point of bisection, its value of (x) replaces the ‘positive’ value of (x) for the interval, while if at that new point, (y) is negative, its value for (x) replaces the ‘negative’ value of (x) for the interval. This can be repeated until the interval has become smaller than some amount, by which the root is allowed to be inaccurate.

But there exist certain cases in which the path forward is not as obvious, such as what one should do, if one was given a polynomial of an even degree, that only has complex roots, yet, if these complex roots nevertheless needed to be found. Granted, in practical terms such a problem may never present itself in the lifetime of the reader. But if it does, I just had lots of idle time, and have contemplated an answer.

(Updated 1/30/2019, 13h00 … )

Continue reading A Hypothetical Algorithm…

Exploring the newer GUI front-end, for use with SageMath.

One of the subjects which I had written about only yesterday, is that the Computer Algebra / Numerical Tool System called ‘SageMath‘ was available in the repositories, for Debian / Stretch – which is in itself news – and that additionally, the default way to use it under Debian is through a Web-interface called ‘SageNB’. Well what I’ve now learned is that the SageMath developers no longer support SageNB, and are continuing their work with the graphical front-end called ‘Jupyter‘.

But, installing Jupyter under Debian is a bit of a chore, because unlike how it is with custom-compiles, Debian package maintainers tend to break major software down into little bits and pieces. At one point, I had Jupyter running, but with no awareness of the existence of SageMath. What finally did the trick for me today, was to install the following packages:

  • python-notebook
  • jupyter-nbextension-jupyter-js-widgets
  • sage-math-jupyter

Needless to say, that last package out of the three is the most important, and may even pull in enough of the other packages, to be selected by itself. It’s just that I did not know immediately, to install that last package.

So this is what SageMath 7.4 looks like, through Jupyter:

screenshot_20180916_165217

(Corrected 09/18/2018, 3h50 … )

(Updated 09/18/2018, 5h40 … )

(As of 09/16/2018, 20h10 : )

Frankly, I was a bit disappointed at first. My main disappointment seemed to be with the fact, that this GUI did not offer to typeset the Math. It does allow us to ‘download’ our Notebooks as PDF-Files, but when we do, we simply get the same, highlighted text, and graphics, only as a PDF – in code – or with whatever appearance the browser-view is already showing us. Also, the support for 3D plots is lackluster, as the plot above is non-interactive. At least with SageNB, I was able to select the ‘canvas3d’ viewer, which allowed the plot to be rotated. Also, if we use SageMath from the command-line, it defaults to using ‘JMol’ as its viewer, which is full-featured.

But as it turns out, I have discovered ‘the trick’, to getting Jupyter to typeset the users’ Math…

Continue reading Exploring the newer GUI front-end, for use with SageMath.