Some Observations about Roots with Multiplicities.

One of the subjects which I had visited in my past, was to write a C++ program that approximates the roots of polynomials, but that needed to deal with ‘Doubled Roots’ in a special way, just because the search algorithm within that program, which searches for the roots, cannot deal with doubled roots. And what I found was, roots cannot only be doubled, but can have multiplicities higher than (2). After not having pondered that programming project from the past, for some time, I now come back to rethink it, and find that it can be given a lecture of sorts, all to itself.

So, this is a link to a work-sheet, in which I try to explain Roots with Multiplicities, maybe to people with limited knowledge in Calculus:

Link to Letter-Sized PDF

Link to EPUB File, for viewing on Mobile Devices

And as those two documents mention, the following is a link to the earlier blog posting, from which readers can download the C++ program, as well as to find instructions on how to compile it, on Linux computers:

Link to Earlier Blog Posting

Hence, the C++ program linked to in the earlier blog posting, needed to make use of the subject, that the two PDF Files describe.

N.B.:

(Updated 5/06/2019, 13h15 … )

Continue reading Some Observations about Roots with Multiplicities.

I’ve just received my 13.3″ Onyx BOOX Max2 e-Reader.

And so far I’m happy with it.

There exists an underlying issue with Android-based e-Readers, where these e-Readers are 4 years in the making, and where the issue is something I’m just learning about in recent weeks. As a security precaution, Google has toughened the requirements on the Google Play Store app, and on the Google Services app, which made numerous e-Readers, that were once proud to offer a working Google Play app, unable to connect to Google Play in the short term. This measure became effective as of March in 2018. However, certain manufacturers of such devices have been struggling to make their devices compliant with the new Google Store, and as far as I know, the BOOX Max2 which I just received, may be able to connect to the Google Play store fully.

(This posting has been revised, as of 4/14/2019, 10h15 : )

Out-of-the-box, the Max2 had a firmware version from April in 2018. But the latest Firmware update is from December in 2018.

  • I am glad to say that I found out how to set a PIN Code for this device because if there had truly been no way, then the cloud resources that I’m logged in to would be just as vulnerable, as an unlocked tablet. With the latest firmware, I found this setting under ‘Settings -> (Arrow to the Right) -> Screen Lock PIN Code’.
  • Apparently, the way to activate Google Play on this device, is now to go into “Settings -> Application” and to check “Activate Google Play”.

Instead of activating the Google Play Store, I have been focusing on using the Onyx app store for the time being. In days gone by, their in-house app store had a reputation of only offering apps in Chinese. But what the users of the Max2 can now do, is download e-Ink optimized apps in English. Those apps include the Amazon Kindle Android app.

This is a huge find for me because it also implies less of a security compromise, than what I’d have, if I was just to log the Max2 into Google Play.

I can side-load Free APK-Files to install software, and can install some additional proprietary, non-free apps from Onyx. APKs include the ‘OverDrive’ app, which allows me to check out books from my public library, in e-Book format. And what installs from the Onyx app store includes the ‘Kindle’ Android app, optimized for e-Ink.

I’ve tested both apps, and they seem to work fine.

But then again, speaking of side-loading… This can imply that files need to be transferred via USB-cable from a PC, to the device, and the device uses MTP as its protocol. There are some reports of issues in getting this to work from the Linux GUI, and I just ran in to such an issue…

(Updated 6/21/2019, 7h35 … )

Continue reading I’ve just received my 13.3″ Onyx BOOX Max2 e-Reader.