Add a test to compare names and structure descriptions

[olexandr-konovalov]

This is a start of working over #31.

With it, #30 could have been detected as follows:

gap> checkname(1600);
[ 1600, 17 ] : PSU(4, 3) is PSU(3,4)
[ 1600, 18 ] : PSU(4, 3):2 is PSU(3,4) : C2
[ 1600, 19 ] : PSU(4, 3):4 is PSU(3,4) : C4

It filters some obvious cases, but because names and structure descriptions are not guaranteed to match, that's not always the case. One still needs to check manually a lot, e.g.

gap> checkname(100);
[ 100, 1 ] : J_2 is HJ
[ 100, 2 ] : J_2.2 is HJ : C2
[ 100, 5 ] : Alt(5) wreath Sym(2) is (A5 x A5) : C2
[ 100, 6 ] : Alt(5)^2.2^2 is (A5 x A5) : (C2 x C2)
[ 100, 7 ] : Alt(5)^2.4 is (A5 x A5) : C4
[ 100, 8 ] : Sym(5) wreath Sym(2) is (A5 x A5) : D8
[ 100, 9 ] : Alt(10) wreath Sym(2) is (A10 x A10) : C2
[ 100, 10 ] : Alt(10)^2.2^2 is (A10 x A10) : (C2 x C2)
[ 100, 11 ] : Alt(10)^2.4 is (A10 x A10) : C4
[ 100, 12 ] : Sym(10) wreath Sym(2) is (A10 x A10) : D8
[ 100, 13 ] : Alt(6) wreath Sym(2) is (A6 x A6) : C2
[ 100, 14 ] : Alt(6)^2.2^2 is (A6 x A6) : C4
[ 100, 15 ] : Alt(6)^2.2^2 is (A6 x A6) : (C2 x C2)
[ 100, 16 ] : Alt(6)^2.4 is (A6 x A6) : C4
[ 100, 17 ] : Alt(6)^2.2^2 is ((A6 x A6) : C2) : C2
[ 100, 18 ] : Alt(6)^2.4 is (A6 x A6) . C4
[ 100, 19 ] : Alt(6)^2.2^2 is (A6 x A6) : (C2 x C2)
[ 100, 20 ] : Alt(6)^2.D_8 is ((A6 x A6) : C4) : C2
[ 100, 21 ] : Alt(6)^2.2^3 is ((A6 x A6) : C2) : (C2 x C2)
[ 100, 22 ] : Alt(6)^2.D_8 is (A6 x A6) : D8
[ 100, 23 ] : Alt(6)^2.D_8 is (A6 x A6) : D8
[ 100, 24 ] : Alt(6)^2.D_8 is ((A6 x A6) . C4) : C2
[ 100, 25 ] : Alt(6)^2.D_8 is ((A6 x A6) . C4) : C2
[ 100, 26 ] : Alt(6)^2.(2 x 4) is ((A6 x A6) . C4) : C2
[ 100, 27 ] : Alt(6)^2.D_8 is ((A6 x A6) : C4) : C2
[ 100, 28 ] : Alt(6)^2.(2 x 4) is (A6 : (A6 : C2)) : C4
[ 100, 29 ] : Alt(6)^2.(2 x 4) is (A6 : (A6 . C2)) : C4
[ 100, 30 ] : Alt(6)^2.2^2:4 is ((A6 : S6) : C2) : C4
[ 100, 31 ] : Alt(6)^2.(2 x D_8) is (A6 : (A6 . C2)) : D8
[ 100, 32 ] : Alt(6)^2.2^2:4 is ((A6 : (A6 . C2)) : C2) : C4
[ 100, 33 ] : Alt(6)^2.(2 x D_8) is ((A6 x A6) . C4) : (C2 x C2)
[ 100, 34 ] : Alt(6)^2.(2 x D_8) is (A6 : (A6 : C2)) : D8
[ 100, 35 ] : Alt(6)^2.2^2:4 is ((A6 : (A6 . C2)) : C2) : C4
[ 100, 36 ] : PGammaL(2, 9) wreath Sym(2) is ((A6 : (A6 . C2)) : C2) : D8

Above, I've noticed the line

[ 100, 14 ] : Alt(6)^2.2^2 is (A6 x A6) : C4

• shouldn't that by any chance be Alt(6)^2.4, @hulpke and @colva ?

[olexandr-konovalov]

A fix for PrimitiveGroup(289, 35) and also for PrimitiveGroup(100,14) submitted in #36.

[codecov]

Codecov Report

Merging #34 (6d63375) into master (a4e2d7f) will decrease coverage by 0.01%.
The diff coverage is 74.15%.

@@            Coverage Diff             @@
##           master      #34      +/-   ##
==========================================
- Coverage   99.92%   99.90%   -0.02%     
==========================================
  Files          46       47       +1     
  Lines      382938   383100     +162     
==========================================
+ Hits       382633   382748     +115     
- Misses        305      352      +47     

Impacted Files	Coverage Δ
lib/testutils.g	74.15% <74.15%> (ø)
lib/primitiv.gi	53.72% <0.00%> (-1.35%)	⬇️
lib/irredsol.gi	61.45% <0.00%> (-0.44%)	⬇️
lib/cohorts.grp	100.00% <0.00%> (ø)
lib/primitiv.grp	100.00% <0.00%> (ø)

[fingolfin]

@alex-konovalov the name for [ 100, 14 ] is also definitely wrong. You can verify this even by "brute force": there is no quotient isomorphic to C_2^2 here:

gap> G:=PrimitiveGroup( 100, 14 );
Alt(6)^2.2^2
gap> StructureDescription(G/Socle(G));
"C4"
gap> List(NormalSubgroups(G), N -> StructureDescription(G/N));
[ "(A6 x A6) : C4", "C4", "C2", "1" ]

[olexandr-konovalov]

@fingolfin thanks, [100,14] already in #36.

[olexandr-konovalov]

Rebased after merging #36.

[olexandr-konovalov]

This PR is unfinished, but at least issues detected with its help were merged and could be released.

[olexandr-konovalov]

After rebase, I see this in stable-4.11,-4.10 but not in master:

########> Diff in /tmp/gaproot/pkg/primgrp/tst/testinstall/testutils.tst:12
# Input is:
for d in [1,2,3,4] do
  for q in [2,3,4,5,7,8,9] do
    facs := Factors(q);
    p := facs[1];
    e := Length(facs);
    Assert(0, Size(SL(d,q)) * q^d = Size(ASL(d,q)));
    Assert(0, Size(GL(d,q)) * q^d = Size(AGL(d,q)));
    Assert(0, Size(SigmaL(d,q)) * q^d = Size(ASigmaL(d,q)));
    Assert(0, Size(GammaL(d,q)) * q^d = Size(AGammaL(d,q)));
    if d > 1 then
        Assert(0, Size(PSL(d,q)) * e = Size(PSigmaL(d,q)));
        Assert(0, Size(PGL(d,q)) * e = Size(PGammaL(d,q)));
    fi;
  od;
od;
# Expected output:
# But found:
Error, Variable: 'PGammaL' must have an assigned value
########

[olexandr-konovalov]

Cool @fingolfin! I see that this PR might be worth revisiting!

[olexandr-konovalov]

I have rebased this, and this is why the tests fail in tst/testinstall/duplicates.tst when calling PrimGrpNamesDuplicates to report duplicated names of primitive groups (more precisely, this tests searches for primitive groups which are non-isomorphic, and have different structure descriptions, but have the same name):

$ diff expected.txt found.txt 
22,23c22,23
< PGL(2, 11) : [ [ 12, 4 ], [ 55, 2 ], [ 55, 3 ] ]
< PGL(2, 7) : [ [ 8, 5 ], [ 21, 1 ], [ 28, 1 ] ]
---
> PGL(2, 11) : [ [ 55, 2 ], [ 55, 3 ] ]
> PGL(2, 7) : [ [ 21, 1 ], [ 28, 1 ] ]
25c25
< PGammaL(2, 8) : [ [ 9, 9 ], [ 28, 3 ], [ 36, 2 ] ]
---
> PGammaL(2, 8) : [ [ 28, 3 ], [ 36, 2 ] ]
28,29c28
< PSL(2, 11) : [ [ 12, 3 ], [ 55, 1 ] ]
< PSL(2, 8) : [ [ 9, 8 ], [ 28, 2 ], [ 36, 1 ] ]
---
> PSL(2, 8) : [ [ 28, 2 ], [ 36, 1 ] ]

[olexandr-konovalov]

@fingolfin and I found why:

gap> List([ [ 12, 4 ], [ 55, 2 ], [ 55, 3 ] ], t -> PrimitiveGroup(t[1],t[2]));
[ PGL(2,11), PGL(2, 11), PGL(2, 11) ]
gap> List(  [ [ 8, 5 ], [ 21, 1 ], [ 28, 1 ] ], t -> PrimitiveGroup(t[1],t[2]));
[ PGL(2,7), PGL(2, 7), PGL(2, 7) ]
gap> List([ [ 9, 9 ], [ 28, 3 ], [ 36, 2 ] ], t -> PrimitiveGroup(t[1],t[2]));
[ PGammaL(2,8), PGammaL(2, 8), PGammaL(2, 8) ]
gap> List( [ [ 12, 3 ], [ 55, 1 ] ], t -> PrimitiveGroup(t[1],t[2]));
[ PSL(2,11), PSL(2, 11) ]
gap> List( [ [ 9, 8 ], [ 28, 2 ], [ 36, 1 ] ], t -> PrimitiveGroup(t[1],t[2]));
[ PSL(2,8), PSL(2, 8), PSL(2, 8) ]

Observe the extra space in the name, e.g.

gap> PrimitiveGroup(12,4);
PGL(2,11)
gap> PrimitiveGroup(55,2);
PGL(2, 11)

[fingolfin]

Thanks @olexandr-konovalov but this not the best time: I am still in the middle of importing the groups of degree < 8192 and in that process, more things will be "aligned"

[olexandr-konovalov]

Ok, can wait - at least I have rebased it and glad to see that it's not yet completely out of sync (and also I have updated my details in commit signatures).