How to create a block for related products based on their taxonomy term?

I want to create a block for related products.. all the solutions I found are not working on drupal 8/9 with commerce 2 , for a content you can just specify a contextual filter for (has taxonomy term) but for products that’s not an available option .. is there anyway to accomplish this ?

custom taxonomy – List hierarchy of taxonomies related to posts from current query

I have a custom post type that has two taxonomies related to it.

Think a Post of “Equipment” and taxonomies of “Manufacturer” and “region”. Region is a hierarchy and a Post can be in more then one. Manufacturer is 1:1 relation to the Post.

I have a template that will lists custom posts based on a selected ‘manufacturer’ taxonomy. This is working fine but I want on the same page list the Taxonomy ‘region’ items – but only those that the selected items are linked too.

When looping through the posts I can get the Taxonomy details .. but the order and hierarchy is missing as the posts can come in any order.

So a list I’m wanting to produce would be something like this (a reduced but structured list of all the possible ones)

 - Italy (1)
 - Spain (3)

- California (1)

I’m totally lost on a way to create this. I’m thinking I will need to query the Taxonomy (Regions) to get all, then get my Equipment Post list based on the selected Manufacturers Taxonomy, and then as I loop the post list, tally the Region for each, then once done with the loop remove those Manufacturers with a 0 tally and no children in an iterative manner.

It just seems inefficient and that I’m missing something? I feel like there should be a function where I can provide an array of post IDs and get a specific list of taxonomies items back.

Get related custom post by specifics custom post ID

I created two custom posts, one is formations and the other is Technologie.
The relation between both is one formation have one or many technologies.

After that, i have created a form where i select one to three technologies.
I know that to display the list of custom post type is like this :

$args = array(
        //'post__in' => array(8136),
        'post_type' => 'categories',
        'posts_per_page' => 20

    $loop = new WP_Query( $args );
    while ( $loop->have_posts() ) : $loop->the_post();
        print '<strong>' . the_title().'</strong> <br>';


So my question is how to display this list only for the custom post id ‘1234’ ?
PS : the custom post ‘1234’ have multiple technologie and not all !


django – How can I go about creating a web app for people to reserve a duration of time(1hr) in a day for a gym related website

So I have been studying python for a good amount of time and am learning django. I have also learned basics of html/css/javascirpt. Here is my idea:

I want to create a web application for a local gym where subscribers are able to login, and because of covid, people are required to reserve the time they want to workout at, so how can I go about doing the following things:

  1. How can I make the logic for people to be able to reserve a duration of time and of course there should be a limit of people that can workout during the same time, say 30 people in a given hour, so the website should disable allowing other users to reserve that time.

  2. I am not sure how to implement the logic of RESERVATION if anyone has any idea, so should there be a model containing all the days of the year or what. This part is a big confusion of mine

  3. How can i make it possible to make that users are given a username and password to login as there shouldn’t be a sign up page, because only paid subscribers should be able to login and reserve, so that if someone’s subscription is finished they shouldn’t be able to login.

I am currently brain storming and if anyone could give me a heads up, I would be appreciative of it.

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I need some quality backlinks related with pet site

Very nice site, you could do with getting a nice logo though, but ye its very professional, straight in with the content, I like it a lot.

What you need to do is go around all the directories finding pet related blogs and commenting on them, the second step for you then is to do some link exchanges, pet niche is very tough so link exchange, especially with lets say a dog one because then people will go to that one for dogs and yours for cats so definitely worth link exchanging.

Maybe do some article marketing, getting your voice heard on the big article directories will get you some traffic too.


Lie Groups and Lie algebras related to Jordan algebras

Let $J$ be a Jordan algebra. I knew three relative Lie groups/Lie algebras to $J$.

In the paper “The Capelli Identity, Tube Domains, and the Generalized Laplace Transform

Jacobson (J) has associated two Lie algebras to $J$. For any $x in J$, let $L(x)$ denote the operator of left multiplication by $x$. Let
$mathfrak{p} = {L(x): xin J}$ and let $mathfrak{t} = (mathfrak{p}, mathfrak{p})$. Then $mathfrak{t}$ is the Lie algebra of the “automorphism
group” of $J$. Let $$mathfrak{g}=mathfrak{t}+mathfrak{p}$$
Then $mathfrak{g}$ is a reductive Lie algebra and above is the Cartan decomposition
of $mathfrak{g}$.

The paper (J) mentioned is “Some groups of Transformations defined by Jordan Algebras I.

In the note “Lecture notes in mathematics: an elementary approach to bounded symmetric domains“.

  1. The binary Lie algebras and symmetric Lie algebras were defined on Page 9 and Page 35.

  2. The Meyberg theorem on the relation to Jordan algebra was proved on Page 19.

  3. The construction of Lie algebras can be found in Page 80 and Page 46.

As far as I see, the resulting Lie algebra $mathfrak{g}=mathfrak{T}oplus Joplus J$ has two copies of $J$.

In the book “Jordan algebras and algebraic groups“.

  1. The $J$-structure was introduced in section 1 (it is equivalent to a Jordan algebra structure for characteristics $neq 2$, section 6). There is a structure group $G$ associated to it.

  2. In section 11, we pick some idempotent $a$ to define $S_a$ and give the classification of simple $J$.-structure. It seems to be related to the exceptional group $E_6$ on Page 115.

My question is,

what is the relation between them? Do we have a list of computation of $mathfrak{g}$ for real simple $J$‘s? Besides, what is the geometry of it? For example, is it the isotopic group of the symmetric domain?

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nt.number theory – Strange lacunary Lambert series related to the Liouville function

Although I have my own interest for the Liouville function, I will suppress it here as the question seems to be interesting in its own right.

It occurred to me when I saw an answer by GH from MO to Normal numbers, Liouville function, and the Riemann Hypothesis. That answer mentions the paper by Borwein and Coons where it is proved (among other things) that the functions $f_lambda(z)=sum_{ngeqslant1}lambda(n)z^n$ and $f_mu(z)=sum_{ngeqslant1}mu(n)z^n$ are both transcendental (here $lambda$ is the Liouville function and $mu$ is the Möbius function; just in case, let me recall that $lambda(n)=(-1)^{Omega(n)}$ where $Omega(n)$ is the number of prime factors of $n$ counted with multiplicities, while $mu(n)=(-1)^{omega(n)}$ when $n$ is the product of $omega(n)$ distinct primes and zero otherwise).

Initially I became curious whether these series have the unit circle as the analyticity boundary and, if yes, what can be said about their radial limit values at roots of unity. One natural thing to look at in this respect are the Lambert series for these functions. Although this is not directly related to the question, it is still related, so let me just say without proof, that$$f_lambda(z)=sum_{ngeqslant1}frac{tildelambda(n)z^n}{1-z^n},qquad f_mu(z)=sum_{ngeqslant1}frac{tildemu(n)z^n}{1-z^n}$$where $tildelambda$ and $tildemu$ are multiplicative with, for $p$ a prime, $tildelambda(p^k)$ is $(-1)^ktimes2$ while $tildemu(p^k)$ is $-2$ for $k=1$, $1$ for $k=2$ and $0$ for $k>2$.

What happened next was that I thought about representing these functions as logarithmic derivatives of some functions with nice infinite product expansions, and then modified them slightly thinking about obtaining sort of nicer infinite products. Doing that I stumbled upon the following:begin{multline*}z(1+f_lambda(z))=z+z^2-z^3-z^4+z^5+…+lambda(n)z^{n+1}+…\=frac z{1-z}-frac{2z^3}{1-z^3}-frac{2z^4}{1-z^4}+frac{2z^{12}}{1-z^{12}}-frac{2z^{13}}{1-z^{13}}+…end{multline*}

Surprised by this strange “jump” from 4 to 12 I looked at the exponents in this Lambert series and found that there are several other jumps of this length (from $n$ to $n+8$), many shorter jumps, as well as at least one still longer jump, from 4450 to 4459. Note that there are no jumps at all for $tildelambda$. So my question is,

is there any explanation for these strange jumps? Are their lengths bounded?

Some considerations around it. Certainly there are lots of jumps for $tildemu$, since it is zero on any number divisible by a cube; but they are much shorter: no longer than $4$ up to $n=5000$. The analogous “shift” for $mu$, that is, the Lambert series for $z(1+f_mu(z))$ has slightly longer jumps but still, it seems, essentially smaller than the shift for $lambda$ — for example, up to $n=5000$ it does not have jumps longer than 6. Maybe all this changes for larger $n$, I don’t know.

Another thing: the Wikipedia page on Lambert series that I link to above contains some recent additions about some Factorization theorems that seem to exhibit new exciting links between Lambert series and partition functions. In principle these theorems provide explicit expressions between the Maclaurin and Lambert series in very general situations. However I don’t readily see how to use them to explain these strange jumps.

I found two related questions on MO: Ordinary Generating Function for Mobius where the answers indicate that most likely there are no radial limits at all for $f_mu$ (so maybe I will ask a separate question about the other functions that appear here), and Lambert series identity with an answer that might be useful here, maybe also related to those factorization theorems.

php – Display related posts without a plugin

I’m trying to display the related posts using functions.php:

function posts_related($related){ if (is_single()) {
global $post;
// Build basic custom query arguments
$custom_query = new WP_Query( array( 
       'posts_per_page' => 8, // Number of related posts to display
       'post__not_in' => array($post->ID), // Ensure that the current post is not displayed
       'orderby' => 'rand', // Randomize the results

// Run the loop and output data for the results
if ( $custom_query->have_posts() ) : while ( $custom_query->have_posts() ) : $custom_query->the_post(); 
 if ( has_post_thumbnail()
  ) { 
                 $permalink = the_permalink();
                 $post_thumbnail = the_post_thumbnail('medium');
                 $title = the_title();                       
                 $related .= '<a href="' . $permalink .  '"><img src="' . $post_thumbnail . '/></a>';             
           $related .=  '<a href="' .  $permalink . '"><b>' . $title . '</b></a>';
 else : 
    $related .= '<p>Nothing to show.</p>';
// Reset postdata
         echo '<pre>'; var_dump( has_post_thumbnail() ); echo '</pre>'; 

    return $related;

}    //wp_reset_postdata();

add_filter( "the_content", "posts_related", 99 );
add_theme_support( 'post-thumbnails' );
set_post_thumbnail_size( 100, 50, true );

But I’m not being able to handle the output properly. I need it to display below the post (single post).