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Fix scalar normalization in ClassicalForms_GeneratorsWithBetterScalarsSesquilinear #84

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Merged
fingolfin merged 2 commits into from
May 17, 2026
Merged

Fix scalar normalization in ClassicalForms_GeneratorsWithBetterScalarsSesquilinear #84

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251bafd
Fix scalars normalization in sesquilinear form detection
chseeger Apr 9, 2026
c4f244d
Remove unused variable 'root'
chseeger May 6, 2026
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14 changes: 5 additions & 9 deletions lib/recognition_new.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -90,7 +90,7 @@ InstallGlobalFunction( ClassicalForms_PossibleScalarsSesquilinear,
##
InstallGlobalFunction( ClassicalForms_GeneratorsWithBetterScalarsSesquilinear,
function( grp, frob )
local tries, gens, field, m1, a1, new, i, scalars, root, improvegenerator, res, newgens, champion, len, qq, q;
local tries, gens, field, m1, a1, new, i, scalars, improvegenerator, res, newgens, champion, len, qq, q;

# the aim of this function is to replace the matrix m1 by a
# matrix that has as few solutions to the scalar equation
Expand All @@ -114,7 +114,7 @@ InstallGlobalFunction( ClassicalForms_GeneratorsWithBetterScalarsSesquilinear,
# if it is possible to change the matrix to multiple that preserves up to scalar one, this is achieved.

improvegenerator := function(m1,i,count,len)
local a1, s, j, k, scalars, root; #I think root should be declare locally here!
local a1, s, j, k, scalars;

a1 := ClassicalForms_PossibleScalarsSesquilinear(field,m1,frob);
#Recall that the scalars satisfy the equation lambda^a[1] = a[2]
Expand All @@ -123,15 +123,11 @@ InstallGlobalFunction( ClassicalForms_GeneratorsWithBetterScalarsSesquilinear,
fi;

if IsList(a1) then
root := NthRoot(field,a1[2],a1[1]);
if a1[1] = 1 then # the matrix m1 has scalar a1[2]
#if a1[2] has a square root, we can replace m1 with m1*sqrt{a1[2]};
if LogFFE(a1[2],PrimitiveRoot(field)) mod 2 = 0 then
return [m1/NthRoot(field,a1[2],2),[One(field)]];
if LogFFE(a1[2],PrimitiveRoot(field)) mod (q+1) = 0 then
return [m1/NthRoot(field,a1[2],q+1),[One(field)]];
fi;
return [m1,[a1[2]]]; #originally, the three lines above this return were not there. Those three lines make sure scalar becomes 1 if possible (basicaly if there is a sqrt).
elif LogFFE(root,PrimitiveRoot(field)) mod (q+1) = 0 then
return [m1/NthRoot(field,root,q+1),[One(field)]]; #either frob = id, then q+1 = 2, or frob is not trivial, then we take q+1-st root. In both cases, modify m1 to a matrix that has scalar one.
return [m1,[a1[2]]]; #originally, the three lines above this return were not there. Those three lines make sure scalar becomes 1 if possible (basically if there is a q+1-st root).
else
scalars := AsList(Group(NthRoot(field,a1[2],a1[1]))); # add all possible scalars for m1
if count = 0 then
Expand Down
81 changes: 81 additions & 0 deletions tst/adv/test_pres_sesforms3.tst
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@@ -0,0 +1,81 @@
gap> START_TEST("Forms: test_pres_sesforms3.tst");

# Regression tests for issue #83:
# examples where sesquilinear forms preserved up to scalars
# were not detected due to scalar normalization issues.
gap> grp := Group([
> [ [ Z(3^2)^3, Z(3^2)^6, Z(3^2)^7 ],
> [ Z(3^2)^7, Z(3^2)^2, Z(3)^0 ],
> [ Z(3^2)^7, Z(3^2)^7, 0*Z(3) ] ],
> [ [ 0*Z(3), 0*Z(3), Z(3) ],
> [ Z(3^2)^7, Z(3)^0, Z(3^2)^7 ],
> [ Z(3), Z(3^2), Z(3) ] ],
> [ [ Z(3^2), 0*Z(3), 0*Z(3) ],
> [ 0*Z(3), Z(3^2), 0*Z(3) ],
> [ 0*Z(3), 0*Z(3), Z(3^2) ] ]
> ]);;
gap> forms := PreservedSesquilinearForms(grp);
[ < hermitian form > ]
gap> TestPreservedSesquilinearForms(grp, forms);
true
gap> grp := Group(Z(3)^0*[
> [ [ 0, 1, 2, 2, 0, 1, 1, 0 ],
> [ 0, 1, 0, 2, 0, 1, 0, 2 ],
> [ 1, 2, 2, 0, 0, 0, 2, 2 ],
> [ 0, 0, 0, 1, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 1, 0, 1, 1 ],
> [ 0, 0, 0, 0, 0, 0, 0, 1 ],
> [ 0, 0, 0, 0, 0, 1, 1, 2 ],
> [ 0, 0, 0, 0, 0, 2, 0, 2 ] ],
> [ [ 2, 1, 0, 2, 2, 2, 0, 1 ],
> [ 0, 0, 0, 1, 0, 2, 2, 1 ],
> [ 1, 2, 0, 0, 1, 0, 2, 2 ],
> [ 0, 0, 0, 1, 0, 1, 2, 1 ],
> [ 1, 0, 2, 1, 1, 1, 0, 0 ],
> [ 0, 1, 0, 2, 1, 1, 1, 1 ],
> [ 1, 2, 1, 0, 0, 0, 2, 2 ],
> [ 0, 1, 0, 1, 1, 1, 2, 2 ] ],
> [ [ 0, 2, 0, 1, 1, 2, 1, 0 ],
> [ 2, 0, 1, 2, 2, 1, 0, 2 ],
> [ 2, 2, 0, 0, 0, 0, 2, 1 ],
> [ 1, 1, 1, 1, 0, 0, 1, 2 ],
> [ 1, 1, 2, 0, 2, 0, 1, 2 ],
> [ 0, 2, 0, 1, 2, 0, 2, 0 ],
> [ 1, 0, 1, 2, 2, 1, 0, 1 ],
> [ 0, 2, 0, 2, 2, 1, 1, 0 ] ]
> ]);;
gap> forms := PreservedSesquilinearForms(grp);
[ < bilinear form > ]
gap> TestPreservedSesquilinearForms(grp, forms);
true
gap> grp := Group(Z(5)^0*[
> [ [ 0, 1, 0, 0, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 1, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0, 0, 1 ],
> [ 2, 3, 4, 3, 1, 3, 2, 4 ],
> [ 1, 4, 0, 0, 1, 0, 0, 0 ],
> [ 0, 2, 2, 2, 4, 4, 2, 1 ],
> [ 2, 3, 4, 2, 1, 3, 3, 4 ],
> [ 2, 2, 3, 0, 1, 0, 0, 3 ] ],
> [ [ 0, 0, 1, 0, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 1, 0, 0 ],
> [ 2, 4, 0, 3, 2, 1, 2, 2 ],
> [ 2, 4, 0, 2, 4, 4, 4, 4 ],
> [ 4, 4, 1, 0, 1, 0, 3, 2 ],
> [ 1, 1, 2, 3, 2, 4, 1, 3 ],
> [ 3, 2, 0, 3, 1, 4, 1, 4 ],
> [ 3, 3, 1, 4, 0, 3, 4, 3 ] ],
> [ [ 0, 0, 0, 1, 0, 0, 0, 0 ],
> [ 0, 0, 0, 0, 0, 0, 1, 0 ],
> [ 2, 2, 3, 1, 3, 3, 2, 4 ],
> [ 3, 0, 0, 0, 0, 0, 0, 0 ],
> [ 1, 0, 2, 1, 0, 3, 2, 1 ],
> [ 1, 3, 2, 4, 3, 1, 2, 2 ],
> [ 0, 3, 0, 0, 0, 0, 0, 0 ],
> [ 0, 1, 3, 0, 3, 1, 0, 1 ] ]
> ]);;
gap> forms := PreservedSesquilinearForms(grp);
[ < bilinear form > ]
gap> TestPreservedSesquilinearForms(grp, forms);
true
gap> STOP_TEST("test_pres_sesforms3.tst", 10000 );
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