Implement IsJoinIrreducible and IsMeetIrreducible

[ThatOtherAndrew]

Adds two new operations to section 10 (Operations for vertices) of oper.gi/oper.gd:

• IsJoinIrreducible(D, v) — returns true if vertex v is not the join of any two distinct smaller nodes in D
• IsMeetIrreducible(D, v) — returns true if vertex v is not the meet of any two distinct larger nodes in D

Both were originally implemented by building the full O(N²) join/meet table, but then optimised to use DigraphReflexiveTransitiveReduction, a function producing a Hasse diagram which allows for a computational shortcut (see SageMath docs below):

https://doc.sagemath.org/html/en/reference/combinat/sage/combinat/posets/hasse_diagram.html#sage.combinat.posets.hasse_diagram.HasseDiagram.find_nontrivial_congruence

Tests are merged into tst/standard/oper.tst, covering N5, a chain, B2, M3, and error handling (two test case sets written by myself and the rest with LLM assistance because I do not think my mathematical knowledge of the underlying concepts is strong enough to come up with reasonably comprehensive/diverse test cases).

---

Closes #400

[ThatOtherAndrew]

Requesting a review from @james-d-mitchell please - how does this look? Is the PR description sufficiently detailed and mathematically accurate?

[james-d-mitchell]

Looks good to me! If you also resolve #714, then this PR (or the code if merged first) should be updated to check for that rather than IsPartialOrderDigraph. Otherwise, this looks good to me!

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.36%. Comparing base (1f56fb0) to head (8ae6cba).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #910   +/-   ##
=======================================
  Coverage   97.35%   97.36%           
=======================================
  Files          50       50           
  Lines       21045    21069   +24     
  Branches      639      639           
=======================================
+ Hits        20489    20513   +24     
  Misses        491      491           
  Partials       65       65           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[james-d-mitchell]

Suggested change

	return InDegreeOfVertexNC(hasse, v) <= 1;
	return InDegrees(hasse)[v] <= 1;

Turns out InDegreeOfVertexNC is rather slow if called repeatedly, in one example I have before this suggested change:

gap> D := DigraphReflexiveTransitiveClosure(DigraphRemoveAllMultipleEdges(D));
<immutable preorder digraph with 8146 vertices, 1768801 edges>
gap> Filtered(DigraphVertices(D), x-> IsJoinIrreducible(D, x)); time;
[ 1, 110, 111, 112, 113, 130, 163, 164, 210, 213, 218, 222, 225, 227, 230, 231, 232, 236, 237, 241, 242, 244, 246, 269, 270,
  273, 274, 275, 276, 277, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314,
  315, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331 ]
2180
gap> Filtered(DigraphVertices(D), x-> IsJoinIrreducible(D, x)); time;
[ 1, 110, 111, 112, 113, 130, 163, 164, 210, 213, 218, 222, 225, 227, 230, 231, 232, 236, 237, 241, 242, 244, 246, 269, 270,
  273, 274, 275, 276, 277, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314,
  315, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331 ]
1813
gap> Filtered(DigraphVertices(D), x-> IsJoinIrreducible(D, x)); time;
[ 1, 110, 111, 112, 113, 130, 163, 164, 210, 213, 218, 222, 225, 227, 230, 231, 232, 236, 237, 241, 242, 244, 246, 269, 270,
  273, 274, 275, 276, 277, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314,
  315, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331 ]
1799
gap> Filtered(DigraphVertices(D), x-> IsJoinIrreducible(D, x)); time;
[ 1, 110, 111, 112, 113, 130, 163, 164, 210, 213, 218, 222, 225, 227, 230, 231, 232, 236, 237, 241, 242, 244, 246, 269, 270,
  273, 274, 275, 276, 277, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314,
  315, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331 ]
1805

and after:

gap> Filtered(DigraphVertices(D), x-> IsJoinIrreducible(D, x)); time;
[ 1, 110, 111, 112, 113, 130, 163, 164, 210, 213, 218, 222, 225, 227, 230, 231, 232, 236, 237, 241, 242, 244, 246, 269, 270,
  273, 274, 275, 276, 277, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314,
  315, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331 ]
373
gap> Filtered(DigraphVertices(D), x-> IsJoinIrreducible(D, x)); time;
[ 1, 110, 111, 112, 113, 130, 163, 164, 210, 213, 218, 222, 225, 227, 230, 231, 232, 236, 237, 241, 242, 244, 246, 269, 270,
  273, 274, 275, 276, 277, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314,
  315, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331 ]
1
gap> Filtered(DigraphVertices(D), x-> IsJoinIrreducible(D, x)); time;
[ 1, 110, 111, 112, 113, 130, 163, 164, 210, 213, 218, 222, 225, 227, 230, 231, 232, 236, 237, 241, 242, 244, 246, 269, 270,
  273, 274, 275, 276, 277, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314,
  315, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331 ]
3
gap> Filtered(DigraphVertices(D), x-> IsJoinIrreducible(D, x)); time;
[ 1, 110, 111, 112, 113, 130, 163, 164, 210, 213, 218, 222, 225, 227, 230, 231, 232, 236, 237, 241, 242, 244, 246, 269, 270,
  273, 274, 275, 276, 277, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314,
  315, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331 ]
2
gap> Filtered(DigraphVertices(D), x-> IsJoinIrreducible(D, x)); time;
[ 1, 110, 111, 112, 113, 130, 163, 164, 210, 213, 218, 222, 225, 227, 230, 231, 232, 236, 237, 241, 242, 244, 246, 269, 270,
  273, 274, 275, 276, 277, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314,
  315, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331 ]
2
gap>

[james-d-mitchell]

This doesn't suffer in the same way as InDegree so no change suggested here.