I have reinstalled the O/S on an existing computer.

According to an earlier posting of mine, the computer which I named ‘Plato’ was experiencing technical issues. Its power-supply was dead.

Technically, I succeeded in replacing the power supply. But unfortunately it also turned out, that its main hard-drive was dead. Therefore, it is now using a different hard-drive as well, which means that I needed to reinstall the O/S. I installed the latest build of Kanotix, and all is well again with that computer.


That computer has now been renamed ‘Phosphene’.

I suppose that one question which now remains unanswered, is whether I should switch ‘Phosphene’ to the proprietary NVIDIA drivers, as I had done with ‘Plato’, or whether I should keep it with the open-source ‘Mesa’ drivers, that include the ‘Nouveau’ drivers.

Continue reading I have reinstalled the O/S on an existing computer.

Debian WordPress recently received an update.

One of the facts which I’ve blogged about before, is exactly, what blogging platform I’m presently using. I subscribe more to ‘WordPress.org’, and less to ‘WordPress.com’.

This synopsis is a bit over-simplified. The actual WordPress version I have installed is the one that ships with Debian / Jessie, aka Debian 8, from the package manager. But that doesn’t mean we don’t receive security updates. I actually tend to trust the Debian Maintainers more, than WordPress.org, to keep the platform secure. They’ll downright snub features, if they find the feature poses any sort of security threat.

And in recent days, this Debian build of WordPress did receive such a routine update. The main reason I take notice of such things is, the fact that my personal WordPress installation is modified somewhat, from what the package maintainers build. This still allows me to download a modest set of plug-ins from WordPress.org, as well as one plug-in from WordPress.com.

I’m happy to say that no snarl took place, between the recent Debian-based update, and my custom-configured blogging platform. Service was never disrupted.



Secondary Polishing

When the project is undertaken to write programs, that would be sub-components to Computer Algebra Systems, but that produce floating-point numerical outputs, then an unwanted side effect of how those work is, they can be output in place of integers (whole numbers), but may differ from those integers by some very small fractional amount. Thus, instead of outputting (1) exactly, such a program might output:


The problem is that such output can be visually misleading, and confusing because a Human user wants to know that the answer to a problem was (1). And so a possible step in the refinement of such programs is “Secondary Polishing”, which does not change the actual computations, but which makes the output ‘look nicer’.

I recently completed a project that approximates the roots of arbitrary polynomials, and also looked in to the need for secondary polishing. There was one specific situation in which this was not required: The root’s real or imaginary component could have an absolute of (1/10) or greater. In this case, the simple fact that I had set the precision of the printed output to (14), but that the roots found are more precise than to be within (10^-14), at least after the actual, primary polishing, that affects computed values, together with the way the standard output functions work in C++, will cause the example above to be output as a single-digit (1), even though what was stored internally might be different from that, by less than (10^-14). But a special case exists within the norms of C++, if the absolute of the numerical term to be output is less than (1/10).

(Updated 2/11/2019, 19h35 … )

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How an exact solution can sometimes be found, without using the general solution.

One of the facts which I’ve been writing about is, that the general solution to a polynomial of a degree higher than (4), that is expected to produce Algebraically exact results, cannot be used because none exists. At the same time, I make a distinction between an exact solution, and the general solution. This distinction can also be explained in greater detail…

We are sometimes given a polynomial, which has at least one “rational root”, meaning a root that can be stated either as a whole number, which is actually referred to as an “integer”, or as a fraction. The following is an example:

x^3 -3*x^2 -2*x + 6 = 0

In this case it can be observed, that the coefficient of (x^3), which is not stated, corresponds to a (1), and that the constant term, which is visible as (+6), is an integer. What can be done here, is that all the factors of (6) can be used positively and negatively – not only the prime factors – and plugged in to see whether they do in fact constitute one root. Again, they do if and only if the equation is satisfied as resulting in zero.

Thus, as potential candidates, ±1, ±2, ±3, ±6 can all be tried.

(Updated 2/9/2019, 19h40 … )

Continue reading How an exact solution can sometimes be found, without using the general solution.