Implement IsBetweenCoverAndLattice

[ThatOtherAndrew]

Prompted by conversation in #714, I believe this is a functional implementation of the IsBetweenCoverAndLattice function. My implementation is based on the three-step outline given by @Joseph-Edwards and also implements DIGRAPHS_MeetJoinTableBetweenCover (as a slightly modified/generalised version of DIGRAPHS_MeetJoinTable) in order to make this possible. I've thrown in some tests as well (due to my limited understanding of the maths I'm unsure how comprehensive they are though!) and they do appear to pass when building and running locally. (hopefully CI/CD can validate if they still work!)

[ThatOtherAndrew]

gaplint should be satisfied now :>

[Copilot]

Pull request overview

Adds a new predicate to determine whether a digraph lies between the cover relation of some lattice and a lattice digraph (without constructing the reflexive transitive closure), motivated by #714.

Changes:

• Introduces IsBetweenCoverAndLattice as a declared property and implements its method in gap/prop.gi.
• Adds DIGRAPHS_MeetJoinTableBetweenCover, a meet/join table builder that avoids relying on transitive edges being present.
• Adds standard tests covering basic positive/negative cases for IsBetweenCoverAndLattice.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 3 comments.

File	Description
gap/prop.gi	Implements IsBetweenCoverAndLattice and adds the new meet/join table helper used by it.
gap/prop.gd	Declares the IsBetweenCoverAndLattice property and installs a trivial-true implication for lattice digraphs.
tst/standard/prop.tst	Adds regression tests for IsBetweenCoverAndLattice across several small digraph examples.

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[codecov]

Codecov Report

❌ Patch coverage is 95.23810% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 97.37%. Comparing base (1f56fb0) to head (d2c54bc).
⚠️ Report is 10 commits behind head on main.

Files with missing lines	Patch %	Lines
gap/prop.gi	95.08%	3 Missing ⚠️

❌ Your patch check has failed because the patch coverage (95.23%) is below the target coverage (100.00%). You can increase the patch coverage or adjust the target coverage.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #920      +/-   ##
==========================================
+ Coverage   97.35%   97.37%   +0.02%     
==========================================
  Files          50       50              
  Lines       21045    21256     +211     
  Branches      639      639              
==========================================
+ Hits        20489    20699     +210     
- Misses        491      492       +1     
  Partials       65       65              

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[reiniscirpons]

Thanks for the commit! I have suggested some changes. One larger change I would like is for you to modify DIGRAPHS_MeetJoinTable to have the behavior of DIGRAPHS_MeetJoinTableBetweenCover depending on a switch.

One other thing: The function is currently missing documentation. To add this you should modify the doc/prop.xml file and add an entry to this file for the IsBetweenCoverAndLattice function, see the doc for IsMeetSemilatticeDigraph function doc for an example:

Digraphs/doc/prop.xml

Lines 1295 to 1349 in 313228b

	<#GAPDoc Label="IsMeetSemilatticeDigraph">
	<ManSection>
	<Prop Name="IsMeetSemilatticeDigraph" Arg="digraph"/>
	<Prop Name="IsJoinSemilatticeDigraph" Arg="digraph"/>
	<Prop Name="IsLatticeDigraph" Arg="digraph"/>
	<Returns><K>true</K> or <K>false</K>.</Returns>
	<Description>
	<C>IsMeetSemilatticeDigraph</C> returns <K>true</K> if the digraph
	<A>digraph</A> is a meet semilattice; <C>IsJoinSemilatticeDigraph</C>
	returns <K>true</K> if the digraph <A>digraph</A> is a join semilattice;
	and <C>IsLatticeDigraph</C> returns <K>true</K> if the digraph
	<A>digraph</A> is both a meet and a join semilattice.
	<P/>
	For a partial order digraph <Ref Prop="IsPartialOrderDigraph"/> the
	corresponding partial order is the relation <M>\leq</M>, defined by
	<M>x \leq y</M> if and only if <C>[x, y]</C> is an edge.
	A digraph is a <E>meet semilattice</E> if it is a partial order and every
	pair of vertices has a greatest lower bound (meet) with respect to the
	aforementioned relation. A <E>join semilattice</E> is a partial order where
	every pair of vertices has a least upper bound (join) with respect to
	the relation.
	<P/>
	&MUTABLE_RECOMPUTED_PROP;
	<Example><![CDATA[
	gap> D := Digraph([[1, 3], [2, 3], [3]]);
	<immutable digraph with 3 vertices, 5 edges>
	gap> IsMeetSemilatticeDigraph(D);
	false
	gap> IsJoinSemilatticeDigraph(D);
	true
	gap> IsLatticeDigraph(D);
	false
	gap> D := Digraph([[1], [2], [1 .. 3]]);
	<immutable digraph with 3 vertices, 5 edges>
	gap> IsJoinSemilatticeDigraph(D);
	false
	gap> IsMeetSemilatticeDigraph(D);
	true
	gap> IsLatticeDigraph(D);
	false
	gap> D := Digraph([[1 .. 4], [2, 4], [3, 4], [4]]);
	<immutable digraph with 4 vertices, 9 edges>
	gap> IsMeetSemilatticeDigraph(D);
	true
	gap> IsJoinSemilatticeDigraph(D);
	true
	gap> IsLatticeDigraph(D);
	true
	]]></Example>
	</Description>
	</ManSection>
	<#/GAPDoc>

You then want to include the function doc in the manual, the doc/z-chap5.xml file in the orders section after IsMeetSemilatticeDigraph is probably the right place for this:

Digraphs/doc/z-chap5.xml

Lines 41 to 51 in 313228b

	<Section><Heading>Orders</Heading>
	<#Include Label="IsPreorderDigraph">
	<#Include Label="IsPartialOrderDigraph">
	<#Include Label="IsMeetSemilatticeDigraph">
	<#Include Label="DigraphMeetTable">
	<#Include Label="IsOrderIdeal">
	<#Include Label="IsOrderFilter">
	<#Include Label="IsUpperSemimodularDigraph">
	<#Include Label="IsDistributiveLatticeDigraph">
	<#Include Label="IsModularLatticeDigraph">
	</Section>

Otherwise looks good in the first instance!

[reiniscirpons]

Given that this is the only difference, would it be feasible to modify DIGRAPHS_MeetJoinTable to have both functionalities e.g. by adding an extra boolean parameter check_edges, which makes the DIGRAPHS_MeetJoinTable behave the same as before if set to true and otherwise make it behave like DIGRAPHS_MeetJoinTableBetweenCover?

[ThatOtherAndrew]

On it! Would doing a text search for "DIGRAPHS_MeetJoinTable" be sufficient to ensure that all places affected by the function signature breaking change are covered?

[reiniscirpons]

Yes I think so! It would also be nice if you could add a comment describing what each of the input parameters D, P, U, join and the new one you add is expected to be, and how using them affects the output. The DIGRAPHS_ prefix functions are for internal use only, so they don't get an official documentation entry, but it might be useful for the next person who touches the code.

[reiniscirpons]

A few more things I noticed. We should discuss next meeting, but overall looks good.

[reiniscirpons]

Given the similarity of this line to the previous one, would it might make more sense to have two functions IsBetweenCoverAndMeetSemilattice and IsBetweenCoverAndJoinSemilattice which to this check with the meet and join table respectively and then make IsBetweenCoverAndLattice to simply return true when both IsBetweenCoverAndMeetSemilattice and IsBetweenCoverAndJoinSemilattice are true, like we do for IsLatticeDigraph.

[reiniscirpons]

Suggested change

	if IsImmutableDigraph(D) then
	SetDigraphMeetTable(D, tab);
	fi;

We can save the result as the meet table here, since we already did all that work to compute it. The same should be done for the join table below.