What is the best source to learn how to use tensor operations (exterior algebra) in Mathematica?

I’m specifically interested in the TensorProduct,TensorWedge, HodgeDual and certain build in functions to do tensor arithmetic like TensorReduce, TensorExpand.

I would like to do exterior algebra calculations where I can choose to work with basis vectors as symbolic objects (and where I can choose to work without basis vectors).

To be explicit, I would like mathematica to do this input:

v = {v1, v2}; w = {w1, w2}; v\[TensorWedge]w  

desired output:

(v1 w2 - v2 v1) e1 \[TensorWedge] e2 

actual output (in normal form):

{{0, -v2 w1 + v1 w2}, {v2 w1 - v1 w2, 0}} 

If this is not possible what source gives the best advice on how to use mathematica to deal with exterior algebra related differential geometry topics ? A simple example code, video, guide or tutorial on the wolfram site would be optimal.

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handling primary key with large tree, best way to get root id from child table X

I always used database design using this pattern;

root table with PK id1  child1 table with PK id2 FK id1 child2 table with PK id3 FK id2 child3 table with PK id4 FK id3 etc... 

so if i have to get id1 from child5 table I need to traverse all child tables up to the root one (multiple join)

ex;

select root.id from root    inner join child1 ...    inner join child2 ...    inner join child3 ...    inner join child4 ...    inner join child5 ... where child5.id = X 

is that "ok" as a design or there is way to optimize it?

I could see a few way to do it;

  1. bring the idX as a FK in the table that I expect, so I could modified (add the proper FK) down the line to any childX table as needed
  2. just add the FK as I create new table, this seem wasteful, ex; child5 table would have at mininum 4 FK (id1, id2, id3, id4)

with these options i could simply do;

select child5.rootid from child5 where child5.id = X 

questions

  1. is any of my option above is a good thing to do or there is a better way of doing this?
  2. is there any name given to this pattern (so i can search online, i can’t think of any)

Getting Back Int WP Dev – Best Approach for custom post widgets (drag/drop)

At one point I was a fairly solid WP dev (at least I thought I was), but have not done a lot with the platform in about 6 years.

An old work friend has a job and was asking me to help out. I downloaded WP today and boy, was I shocked at the changes.

Here is what I am trying to do.

The project my friend has designed is pretty straightforward, outside of the home page.

On the HP, he wants to have dedicated areas where the client can drag and drop posts from various categories, BUT they all have custom layouts – ie in one section a post widget looks different than another, additionally, inside that section there needs to be some conditional logic – ie if the post has no image, don’t have the image tag etc.

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To illustrate: Here is an example from his design:

enter image description here

All items here are standard posts, albeit in different categories.

What he would be looking to do is have a template where these posts can be dragged in. And be styled according to the section.

Back when I was building WP, it would have been a little more rigid, the sections would be hardcoded into the HP template and I would pull the posts in based on a query result (most recent, have a custom field checked etc etc). However, it would have been fool-proof and the content would simply flow.

I know the Gutenberg block editor allegedly will eventually allow this I would ideally be able to build a template with editable areas that the user could just drag items onto, BUT THEY NEED TO LOOK LIKE THEY DO IN EACH SECTION! Ie, could I build a template with those areas hardcoded in, and then have the user drag/remove custom post widgets into each, one at a time? Based on what I am seeing with the current state of the block editor, this is not doable.

Questions:

Can this be achieved with Elementor, Divi, or any of the other new editor tools – ie a completely custom single post element?

Ideally, can this be done with the current block editor – seems like it is still a bit off.

One more thing to add: this is not a new site, I actually built the original version in 2013, and it currently has 4k posts, so we’re kind of stuck wp here.

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