Please add sets in Doenet

Discussion
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1

This came up in another thread: The need for “sets”.

I am proposing a new tag: <mathSet> or something like that. The current <numberList> and <mathList> don’t quite do the same things because they care about order and allow repeats.

Someone else can chime in if there is a need for multisets (unordered lists where duplicates are allowed).

I would like it to work with sets of numbers, words, letters, (and maybe even algebraic expressions?). Here is what I would like to be able to accomplish:

  1. Remove duplicates from a user provided list. This is already possible using <numberList><convertSetToList>{$user_in}</convertSetToList></numberList> but the syntax is weird and we are actually converting a list to a set, so the naming feels off.
  2. Check the cardinality of a finite set using something like $s.numComponents (again, already possible, but requires the above tag wrapping to make it happen).
  3. Check whether one set is a subset (or proper subset) of another.
  4. Find set intersections
  5. Find set unions
  6. Find set complements when a Universal set is defined and relative set complements when two sets are defined.
  7. Determine if a set is a subset of the natural numbers, whole numbers, integers, rational numbers, etc.

I’ve already manually coded a lot of this using modules, but I’d like to be able to do this with the semantic language rather than huge setup blocks at the start of my activity. I have not adapted it for a user inputted set. I’ve only tested it for very small sets, but it works so far. It feels very “hacky” though and uses a lot of RepeatForSequence which I know can be computationally expensive.

Carly’s Attempt at Sets

[7/28 CFM] Web editor improvement, a <set> component, <graph> axes
2

Thanks, Carly, for the request.

Suggestions on the name of the potential new component? Carly suggested one candidate so far <mathSet>. Other suggestions?

Other suggestions or comments on how this component should work?

3

Looking at the component source code, there is already an “unordered” property for lists. Wouldn’t we just need to also remove duplicates, and lists would act like sets?

Also, I looked but it wasn’t obvious, what does convertSetToList act on? It is doing what it says (because the outer object in Carly’s example IS a list, so the inside {$user_in} is begin treated as a set and being placed in the outer numberList, but this just seems to be a shortcut to remove duplicates?)

Either way, the question of what the component should be called and how it should work I think depends a lot on what already exists in the Doenet back-end, but without doing a deep dive into the source, I don’t have that context. Duane, could you expand on how works? That might provide some insight already.

4

This seems like a good addition. finiteSet might be another possible name. @Carly_Vollet , what kind of syntax were you envisioning for 3-7?

5

We already have elementOf, so maybe $A subsetOf $B?

For intersections and unions, maybe just tags? So

<union> $A $B </union>

Right now I’m doing it in modules. This is still a work in progress, but here is what I have: Set Operations Draft

6

We already have these operators parsed by <math>

<ul>
  <li><math>x elementof A</math></li>
  <li><math>x notelementof A</math></li>
  <li><math>A containselement x</math></li>
  <li><math>A notcontainselement x</math></li>
  <li><math>A subset B</math></li>
  <li><math>A notsubset B</math></li>
  <li><math>A subseteq B</math></li>
  <li><math>A notsubseteq B</math></li>
  <li><math>A superset B</math></li>
  <li><math>A notsuperset B</math></li>
  <li><math>A superseteq B</math></li>
  <li><math>A notsuperseteq B</math></li>
  <li><math>A union B</math></li>
  <li><math>A intersect B</math></li>
</ul>

I know that containselement does not work with boolean logic; we created an issue to fix that.

It seems like the superset/subset operators work, though superseteq is the same as superset, etc.

I couldn’t get the union to work, i.e., <boolean>x elementof {x} union {y}</boolean> returns false.

Also, Doenet turns x into {x} if needed, so <boolean>x subset {x}</boolean> is true…

If you can create scenarios on how you want to use these components, that would help me to understand what needs to be built.