Write the k-subset actions of Alt(n) and Sym(n) as calls

[fingolfin]

PGAltOnSets(n,k) and PGSymOnSets(n,k) return a whole PRIMGRP entry. The order, the transitivity, the socle, the name and the suborbits all follow from n and k, so nothing is stored but the call. The suborbits are the subdegrees of the Johnson scheme: the stabiliser of a k-set S has one orbit for each i, holding the k-sets that agree with S in all but i of its points. At n = 45, k = 2 that replaces a 56-digit order and the pair 86, 903 written out beside it.

Field 9 becomes ["sets", <inner>, <k>], where <inner> describes the group being acted with rather than being it. A family with a different inner group, such as PSL(2,q) on the 2-subsets of the projective line, then needs a case in PRIMGRP_InnerGroup and not a form of its own. PGOnSetsGroup checks that the inner group really is k-homogeneous rather than assuming it, since otherwise the degree would silently be wrong, and sorts the orbit before acting on it, since Orbit promises no order and which permutation group comes out depends on it.

All 258 such entries are converted. data/ falls by 2.3 MB.

Two fields change besides field 9, and both are declared:

• 72 entries are renamed. Three conventions were in the data at once: A(n) up to degree 50, Alt(n) above it, and no name at all for the 58 entries past degree 2555. They collapse to A(n) and S(n), which is what PrimitiveGroup already displayed for the natural actions.
• 162 have their suborbits sorted. They were held in whatever order the generators produced them; field 5 is compared as a set at its one use in PrimitiveIdentification, so the order carries no information.

Everything else is unchanged: fields 1 to 8 of all 24558 entries were dumped before and after and compared. Which of the two constructors an entry is was decided by evaluating both and comparing, then by building the group and measuring its degree, order, primitivity, transitivity and suborbits, because field 9 stops holding permutations and the group afterwards is a different conjugate.

Co-Authored-By: Claude Opus 5 noreply@anthropic.com

---

As before, this PR has three commits: one which adds scripts for doing the conversion, one which applies them, one which drops the scripts again (I've retained a local copy of those scripts so we can re-use them for the order 8191 import)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.12%. Comparing base (5deb588) to head (e18de68).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #85      +/-   ##
==========================================
+ Coverage   99.11%   99.12%   +0.01%     
==========================================
  Files          46       46              
  Lines       38323    38360      +37     
==========================================
+ Hits        37984    38025      +41     
+ Misses        339      335       -4     

Files with missing lines	Coverage Δ
data/gps1.g	100.00% <100.00%> (ø)
data/gps10.g	100.00% <100.00%> (ø)
data/gps11.g	100.00% <100.00%> (ø)
data/gps12.g	100.00% <ø> (ø)
data/gps14.g	100.00% <ø> (ø)
data/gps15.g	100.00% <ø> (ø)
data/gps16.g	100.00% <ø> (ø)
data/gps17.g	100.00% <ø> (ø)
data/gps18.g	100.00% <ø> (ø)
data/gps19.g	100.00% <100.00%> (ø)
... and 27 more

... and 1 file with indirect coverage changes

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

[ThomasBreuer]

Looks good.

I would suggest to replace the function calls of the form PGAltOnSets(6,2) by descriptions of the form ["PGAltOnSets",6,2] (likewise for PGSymOnSets), and to postpone the evaluation until the entry in question is really accessed. There are already similar situations, the functions PGAlt and PGSym occur as entries.

(I understand that the drawback of this idea is that it may be more complicated to verify that the situations before and after the changes are the same.)