Add wedge and vee duplicates of and and or

[T0mstone]

Currently, ∧ and ∨ are only addressable as and and or.

Though that usage is very common, these symbols have various other uses in different fields of math.

Two that I know of are:

• exterior and regressive product in geometry
• infimum and supremum in order theory

Therefore, like xor with plus.circle, I think these deserve a name that reflects their shape.

I took the names from LaTeX, though I'm not too happy about "vee". Maybe having the same names as LaTeX here is a benefit in and of itself, but I'd also like to hear some other suggestions if you have any.

Side-note: I didn't know where to put them in the source file, so I just went with "Shapes". Feel free to offer a better suggestion.

[MDLC01]

They are also used for GCD and LCM in France.

like xor with plus.circle

Wouldn't that be like plus.circle for xor?

I took the names from LaTeX, though I'm not too happy about "vee".

We already have ell for ℓ, and are considering adding pee for ℘. With this in mind, I agree vee is not a very good name because I would expect it to be a somewhat rounded "v."

[dccsillag]

+1.

They are also more generally used for meets and joins in a lattice (related to the order theory example given by @T0mstone).

Also agree that vee is unsatisfying, but I don't have any suggestions at the moment.

[MDLC01]

@T0mstone note that you would also need to add sect.wedge for sect.and, and union.vee for union.or.

Also agree that vee is unsatisfying, but I don't have any suggestions at the moment.

To be fair, I don't really like wedge either (although this is more a matter of taste). But at least it probably cannot be confused with anything else, and is well known by people coming from LaTeX.

An alternative to vee that I don't really like, but feels worth mentioning, is wedge.inv. Or wedge.t and wedge.b, with wedge.t being the default.

[laurmaedje]

At first glance, I'm not a big fan of this. Let's discuss it more before any merge. (Next week.)

[T0mstone]

I've added sect.wedge and union.vee for now.

As for the discussion, I personally think this is a very reasonable request and if we don't have this, then we should take away xor, which I judge as about the same level of niche as the applications mentioned above.

[laurmaedje]

What I mainly dislike about this is the following: For the meaning of "and" and "or", and and or are, in my opinion, much better than wedge and vee. However, by introducing these two aliases, people coming from LaTeX will just stay with wedge and vee because it's what they are used to. In an attempt of making math markup more semantically correct, we'd likely reduce the average semantic correctness of documents in the wild. This is of course a more general problem, but it's especially pronounced here.

People that use these operators for other meanings than "and" and "or" should probably define their own binding. I can agree that defining let meet = sym.and is a bit less clean than let meet = sym.wedge (though there's always let meet = "\u{2227}"), but I'm not sure that outweighs the downside of hurting the visibility of and and or.

[dccsillag]

I agree with @laurmaedje's point.

However, the use of these symbols for meets and joins are also exceptionally common, so I'm inclined to say that we should perhaps also have them as meet and join -- in fact, these terms subsume their use in logic (and can be seen as a meet, and or can be seen as a join).

I'm unfamiliar with the original motivating example of exterior and regressive products, but a quick search seems to reveal that they are also special cases of meets and joins in the sense of lattices (and are even sometimes called meet and join). So I think my current vote right now is to just also include these as meet and join, and avoid 'non-descriptive' and LaTeX names (though wedge does actually seem to be occasionally used in geometric algebra).

[T0mstone]

If "people coming from LaTeX" is the issue, how about just using different names? Then, if people ask, we can direct them to and and or first.

For example, they could be angle.t and angle.b.

Edit: Didn't see @dccsillag's point above before writing this. I'd also be fine with meet and join.

[laurmaedje]

There is a problem because join already exists as ⨝

[MDLC01]

Some more context about the current join symbol and bowties, from the Symbol Proposals document.

In summary, the difference between bowties and the current join symbol is the math class, and (roughly) there is not enough symbols in Unicode for it to make sense to have two different symbols (bowtie and join) with their variants. If we really want to use join for the logical or symbol, the current join could be renamed to bowtie.big.

[dccsillag]

As far as I'm aware, meets and joins are way more common than bowties, and more commonly referred to as simply 'join'. So my personal vote is to change join, and have the bowtie as bowtie or similar (possibly also accessible with a dot under join, e.g. join.nat [for 'natural join'], but I don't think this is crucial).

[T0mstone]

Converting this to a draft since it would ideally be done with the changes from #27 instead.