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Fix SL godown eigenspace dimension check #516

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fingolfin merged 2 commits into from
Jul 14, 2026
+17 −3
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Fix SL godown eigenspace dimension check #516

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ab75b53
Fix SL godown eigenspace dimension check
fingolfin Jul 9, 2026
607d771
Apply suggestion from @TWiedemann
fingolfin Jul 14, 2026
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9 changes: 6 additions & 3 deletions gap/projective/sl.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -265,7 +265,7 @@ end;
RECOG.SLn_godownfromd:=function(g,q,d,dim)
local y,yy,ready,order,es,dims,subsp,z,x,a,b,c,h,vec,vec2,
pol,factors,degrees,comm1,comm2,comm3,image,basis,action,vs,readyqpl1,
readyqm1,count,u,orderu;
readyqm1,count,u,orderu,expecteddims;

repeat
ready:=false;
Expand All @@ -283,8 +283,11 @@ RECOG.SLn_godownfromd:=function(g,q,d,dim)
if not IsOne(yy) then
es:= Eigenspaces(GF(q),yy);
dims:=List(es,Dimension);
if IsSubset(Set([1,d-1,dim-d]),Set(dims)) and
(1 in Set(dims)) then
# Since yy^(q-1)=1, yy is semisimple over GF(q). We want
# one 1-space, one (d-1)-space, and the fixed outside space
# of dimension dim-d; the last one is absent when dim=d.
expecteddims:=Filtered([1,d-1,dim-d], x -> x > 0);
if AsSortedList(dims)=AsSortedList(expecteddims) then
es:=Filtered(es,x->Dimension(x)=1);
vec:=Basis(es[1])[1];
if vec*yy=vec then
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11 changes: 11 additions & 0 deletions tst/working/slow/bugfix.tst
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Expand Up @@ -26,6 +26,17 @@ gap> for i in [1..50] do
> ri := RECOG.TestGroup(GL(8,27), false, Size(GL(8,27)));
> od;

# The following test used to run into an error because SLn_godownfromd
# accepted eigenspace dimensions which did not include the expected
# fixed-space dimension.
gap> seed:=1;;
gap> Reset(GlobalMersenneTwister, seed);;
gap> Reset(GlobalRandomSource, seed);;
gap> h := GL(6,8);;

@Till-Eisen Till-Eisen Jul 10, 2026 •
edited
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I could see the case $d-1 = dim-d$ as a problem in the previous code. In this case there might have been "to many" eigenspaces of dimension 1.
Perhaps $GL(7,8)$ instead of $GL(6,8)$ would be a good test as well, since then $dim=7, d= 4$ and thereby $dim-d=d-1$?

@fingolfin fingolfin Jul 14, 2026

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In fact also $dim=5$ is of interest, too, as then $dim-d=1$

gap> gens := List([1..10], x -> PseudoRandom(h));;
gap> g := GroupWithGenerators(gens);;
gap> ri := RECOG.TestGroup(g, false, Size(h));;

#
gap> SetInfoLevel(InfoRecog, oldInfoLevel);
gap> STOP_TEST("bugfix.tst");