$k[x,y,z]$ and modules.

My professor gave us this example on modules(he started this by saying what is a basis? what is the meaning of linearly independent?):

" $R = k(x,y,z)$ where $k$ is a field. $I = xyR + yz R + xz R ,$ take $u = xy, v = yz, w = xz$ then $I = uR + vR + wR.$ So, $$z.u – xv = 0, xv – yw = 0, zu – yw = 0.$$ Hence, $$begin{bmatrix}
z & -x & 0\
0 & x & -y\
z & 0 & -y
u \
v \
end{bmatrix} = begin{bmatrix}
end{bmatrix}, $$

$det A = 0.$

The span of $u,v,w$ is $Ru + Rv + Rw = I$ so $I$ can not be spanned by $2$ elements.

Upshot: $I ncong_R R^2 = R(1,0) oplus R(0,1)$"

And I am for my life do not understand the idea my professor wanted to convey, could someone help me in trying to understand my professor’s mind?

settings – how to configure a recent Android image with Mesa DRM / KMS support and virtio-gpu modules

I would like to understand how to emulate a recent version of Android on my jetson nano with qemu / kvm. I already have some experience with linux,with the jetson nano and with the arm64 platform,but a very little one with Android. But I have already asked some crucial informations about the most important requisites that Android should have to run with qemu-kvm. Basically these :

  1. An Android image with Mesa DRM/KMS support.
  2. Android kernel with the appropriate Virtio-gpu modules enabled.
  3. Modified Jetson nano kernel to add support for KVM
  4. compiled Virgilrender and qemu with virgilrender support

I have already configured point 3 and 4. Point 1 and 2 are missing ’cause I have a little Android knowledge. Someone said to me “It needs to be one targeted for Qemu with virtio-gpu support enabled. There are images around with it configured but don’t have ones that I can share”. Ok. for me its better to understand how to configure Android from the beginning like it should be,but I’m pragmatic,so I don’t say no if someone wants to give me a recent Android image already configured :]. In any case,since I don’t know where to start,I would like to get some detailed documentation from you,because I want to learn the workflow. Thanks in advance.

architecture – Monorepo, or how to handle two application modules in one project

The problem:
There are two application, which have many common parts.

Desire: reuse common code between application.

Question: what is the best way to achieve this?

Simply create two application modules in project and share common code between them in lib modules?

Monorepo? What is monorepo for Android projects?

linux – Unable to load signed modules on a signed custom kernel

I’m using Fedora 33. In order to boot a custom kernel, I had to generate an X.509 certificate to sign the kernel. This part works just fine.

I can also sign a custom kernel module with the same certificate and I can load the module while the Fedora kernel is loaded.

But when I compile a vanilla mainline kernel with the same config as the Fedora kernel and boot it, I’m unable to load the load the custom module, even though it’s signed with the same kernel.

While the .builtin_trusted_keys keyring doesn’t list my certificate (same on Fedora kernel), the output of dmesg shows that the certificate has been loaded from MOK.

Am I missing something?

Cannot load files as modules

Here’s my app directories structure

This is my "excel_import_tests.py" code

import unittest
import pandas
from nasdaq_info import nasdaq_loading

class MyTestCase(unittest.TestCase):
    def test_import_excel(self):
        nasdaq_dataframe = nasdaq_loading.loading_nasdaq_info_from_spreadsheet()

        self.assertEqual(nasdaq_dataframe.loc('ZVO', 'Sector'), 'ConsumerServices')
        self.assertEqual(nasdaq_dataframe.loc('STT', 'Name'), 'StateStreetCorporationCommonStock')
        self.assertEqual(nasdaq_dataframe('Name')('ZVO'), 'ZovioInc.CommonStock')
        self.assertEqual(nasdaq_dataframe('AEG')('Industry'), 'LifeInsurance')
        self.assertEqual(nasdaq_dataframe('AIN')('Sector'), 'BasicIndustries')

if __name__ == '__main__':

When I’m trying to run him i got

No module named ‘nasdaq_info’

What’s going wrong?

fa.functional analysis – Functional calculus for “pre-linear” regular operators on a Hilbert modules

Let $E$ be a Hilbert module over a $C^*$-algebra $A$. Let $Tcolon Eto E$ be a densely defined, unbounded $A$-linear operator. (In particular, the initial domain of $T$ is an $A$-submodule of $E$.) If the operators $Tpm i$ each has dense range, then $T$ is an essentially self-adjoint, regular operator on $E$, and there is a continuous functional calculus

$$F_Tcolon C_b(mathbb{R})tomathcal{B}_A(E),$$

where $C_b(mathbb{R})$ denotes the bounded continuous $mathbb{C}$-valued functions on $mathbb{R}$, and $mathcal{B}_A(E)$ denotes the $C^*$-algebra of bounded adjointable $A$-linear operators on $E$.

Question: Suppose $D(T)$ is not an $A$-submodule of $E$, but only an $A_0$-submodule, where $A_0$ is a (metrically) dense $*$-subalgebra of $A$. Then, still assuming that $Tpm i$ each has dense range, is it possible to construct a continuous functional calculus for $T$?

9 – Step by step on how to add Javascript dependencies for modules as Blazy or Slick using Composer

Because my project is deployed to a remote server I need to reduce human access to that server, this is Why I add a composer extra repositories to manage javascript dependencies and then add those dependencies to mi theme library.

  1. Add repositories.
    Blazy and Slick require external libraries that according to the authors it must be done manually. But, you could do it automatically. In the composer.json file add this code in the repositories area.
            "type": "package",
            "package": {
                "name": "kenwheeler/slick",
                "version": "1.8.1",
                "type": "drupal-library",
                "dist": {
                    "url": "https://github.com/kenwheeler/slick/archive/v1.8.1.zip",
                    "type": "zip"
            "type": "package",
            "package": {
                "name": "dinbror/blazy",
                "version": "1.8.2",
                "type": "drupal-library",
                "source": {
                    "url": "https://github.com/dinbror/blazy",
                    "type": "git",
                    "reference": "tags/1.8.2"

Note: that we are using the latest versions for both libraries, but you could fix the text to connect your required version.

  1. Install modules
    Using composer commands to install the modules.
composer require dinbror/blazy
composer require kenwheeler/slick

Note: Because we are setting both packages with type “drupal-library”, they will be installed according to extra params in composer on the propper “installer-paths” folder found in the composer file too.

  1. Add dependencies to your THEME libraries file
    In your custom THEME in the file YOUR_THEME.libraries.yml and the below lines taking care of identation.
    /libraries/blazy/blazy.min.js: {}
    /libraries/blazy/blazy.js: {}
    /libraries/slick/slick/slick.min.js: {}
    /libraries/slick/slick/slick.css: {}
  1. Rebuild your cache
    This way your new changes will take effect. (Drush required)
drush cr

How can I prevent importing unnecessary modules from my own submodule using __all__ in Python?

So here’s the case,
I want to import a module, say a.py. However I don’t want other modules which is imported by a.py in it.
my a.py looks like this:

__all__ = ("fuc")

import os

def fuc():
    return 1

then, in the same dir i create a file called b.py, which is simply prints out the modules in a:

import a

Simply running b.py gives me the output:
('__all__', '__builtins__', '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__spec__', 'fuc', 'os'), which ‘os’ is still in there.

Why is __all__ not working here?