Add EnumeratorOfCombinations( mset, k ) and speed up orbits of permutation groups on sets and tuples

[fingolfin]

EnumeratorOfCombinations takes an optional k, like IteratorOfCombinations. With k it lists the combinations in lexicographic order; for a set it ranks a combination with k binomial coefficients.

DomainForAction for permutations on lists of integers returned the placeholder ["BoundedTuples", [1..m], k] for OnSets, which SparseIntKey recognised by comparing strings. It now returns EnumeratorOfCombinations([1..m], k) for OnSets and EnumeratorOfTuples([1..m], k) for OnTuples and OnPairs, which had no domain and fell back to a sort dictionary. Dictionaries index these enumerators by position, or above blistlimit hash them with HashKeyBag. The old hash read the length word and dropped the last entry, so k-sets that differed only in their largest point collided. EnumeratorOfTuples no longer allocates a list in NumberElement.

A position dictionary keeps its values in a list indexed by domain position, which grows to the largest position used, so a small orbit in a domain of up to 2^25 points would allocate hundreds of MB. The orbit has at most Size(G) points, so OrbitStabilizer now hashes domains with more than 8*Size(G) points, including vector spaces for matrix groups.

Before:

gap> G:=SymmetricGroup(100);;
gap> Orbit(G,[1,2,3],OnSets);; time;
3461
gap> Orbit(G,[1,2,3],OnTuples);; time;
40960
gap> OrbitStabilizer(G,[1,2,3],OnTuples);; time;
45121

After:

gap> G:=SymmetricGroup(100);;
gap> Orbit(G,[1,2,3],OnSets);; time;
257
gap> Orbit(G,[1,2,3],OnTuples);; time;
1281
gap> OrbitStabilizer(G,[1,2,3],OnTuples);; time;
4294

Assisted-by: Generative AI

[codecov]

Codecov Report

❌ Patch coverage is 99.39394% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 79.70%. Comparing base (856aeeb) to head (9184750).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
lib/combinat.gi	99.31%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6756      +/-   ##
==========================================
+ Coverage   79.67%   79.70%   +0.02%     
==========================================
  Files         684      684              
  Lines      295460   295609     +149     
  Branches     8656     8656              
==========================================
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+ Misses      58215    58176      -39     
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[hulpke]

This is nice.

[hulpke]

Maybe indicate how this number arose? Is it 2^17 bytes, i.e. 130kB?

[james-d-mitchell]

I also think this is really good but should probably have a bit more robust checks on the additional arguments as indicated.

[james-d-mitchell]

Shouldn't we give an error or something if arg is of length >1?

[james-d-mitchell]

Also shouldn't there be some checks that if arg[1] is present then it is a non-negative integer? At the moment I can do stupid things like:

gap> EnumeratorOfCombinations([1 .. 3], infinity);
[  ]
gap> EnumeratorOfCombinations([1 .. 3], -infinity);
Error, Binomial: <k> must be an integer (not a positional object)
Stack trace:
*[1] Binomial( Length( els ), k )
   @ /Users/jdm3/gap/lib/combinat.gi:329
 [2] EnumeratorOfCombinations_k( mset, arg[1] )
   @ /Users/jdm3/gap/lib/combinat.gi:366
<function "EnumeratorOfCombinations">( <arguments> )
 called from read-eval loop at *stdin*:2
you can enter 'quit;' to quit to outer loop
brk>
gap> EnumeratorOfCombinations([1 .. 3], "a");
[  ]
gap> EnumeratorOfCombinations([1 .. 3], "a", "b");
[  ]

[james-d-mitchell]

Suggested change

	Error("Index ", num, " not bound.");
	Error("Index ", num, " not bound, expected at most ", enum!.size);

Might be a bit more helpful.