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

Adjust ConformalSymplecticGroup to matrix object changes #86

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a4bf198
adjust `ConformalSymplecticGroup` to matrix object changes
ThomasBreuer May 15, 2026
a1107dd
revisit the `ConformalSymplecticGroup` tests
ThomasBreuer May 15, 2026
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22 changes: 14 additions & 8 deletions lib/conformal.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -115,32 +115,38 @@ InstallMethod( ConformalSymplecticGroupCons,
"IsField and IsFinite",
"IsBilinearForm" ],
function( filt, d, F, form )
local g, stored, wanted, mat1, mat2, mat, matinv, gens, gg;
local g, stored, matrix_filt, form_matrix, wanted, mat1, mat2, mat, matinv,
gens, gg;

# Create the default generators and form.
g:= ConformalSymplecticGroupCons( filt, d, F );
stored:= InvariantBilinearFormUpToScalars( g ).matrix;
matrix_filt:= ConstructingFilter( stored );
Assert( 1, ForAll( GeneratorsOfGroup( g ),
x -> ConstructingFilter( x ) = matrix_filt ) );

# If the prescribed form fits then just return.
if stored = form!.matrix then
# We do not require that 'form!.matrix' is in 'matrix_filt',
# only its entries describe the desired form.
form_matrix:= Matrix( matrix_filt, F, form!.matrix );
if stored = form_matrix then
return g;
fi;

# Compute a base change matrix.
# (Check that the canonical forms are equal.)
wanted:= BilinearFormByMatrix( stored, F );
mat1:= BaseChangeToCanonical( form );
mat2:= BaseChangeToCanonical( wanted );
if mat1 * form!.matrix * TransposedMat( mat1 ) <>
mat1:= Matrix( matrix_filt, F, BaseChangeToCanonical( form ) );
mat2:= Matrix( matrix_filt, F, BaseChangeToCanonical( wanted ) );
if mat1 * form_matrix * TransposedMat( mat1 ) <>
mat2 * stored * TransposedMat( mat2 ) then
Error( "canonical forms of <form> and <wanted> differ" );
fi;
mat:= mat2^-1 * mat1;
matinv:= mat^-1;

# Create the group w.r.t. the prescribed form.
gens:= List( GeneratorsOfGroup( g ),
x -> Matrix( matinv * x * mat, stored ) );
gens:= List( GeneratorsOfGroup( g ), x -> matinv * x * mat );
gg:= GroupWithGenerators( gens );

UseIsomorphismRelation( g, gg );
Expand All @@ -150,7 +156,7 @@ InstallMethod( ConformalSymplecticGroupCons,
fi;

SetInvariantBilinearFormUpToScalars( gg,
rec( matrix:= Matrix( form!.matrix, stored ), baseDomain:= F ) );
rec( matrix:= form_matrix, baseDomain:= F ) );

if HasIsFullSubgroupGLRespectingBilinearFormUpToScalars( g ) then
SetIsFullSubgroupGLRespectingBilinearFormUpToScalars( gg,
Expand Down
42 changes: 20 additions & 22 deletions tst/adv/conformal.tst
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Original file line number Diff line number Diff line change
@@ -1,18 +1,18 @@
#@local is_equal, q, F, d, filt, g, stored, pi, permmat, form, gg, pg, sp
#@local q, F, d, filts, filt, g, stored, pi, permmat, form, gg, pg, sp

gap> START_TEST( "Forms: conformal.tst" );

# Provide an auxiliary function (until GAP's '=' gets fast).
gap> is_equal:= function( G1, G2 )
> return IsSubset( G1, GeneratorsOfGroup( G2 ) ) and
> IsSubset( G2, GeneratorsOfGroup( G1 ) );
> end;;

# Test the creation of conformal symplectic groups.
gap> for q in [ 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25 ] do
> F:= GF(q);
> for d in [ 2, 4 .. 8 ] do
> for filt in [ IsPlistRep, IsPlistMatrixRep ] do
> filts:= [ IsPlistRep, IsPlistMatrixRep ];
> if q = 2 then
> Add( filts, IsGF2MatrixRep );
> elif q <= 256 then
> Add( filts, Is8BitMatrixRep );
> fi;
> for filt in filts do
> PushOptions( rec( ConstructingFilter:= filt ) );
>
> g:= ConformalSymplecticGroup( d, F );
Expand All @@ -30,24 +30,23 @@ gap> for q in [ 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25 ] do
> if filt <> IsPlistRep and not filt( One( gg ) ) then
> Error( "wrong repres. of matrices" );
> fi;
> if not ( is_equal( g, ConformalSymplecticGroup( g ) ) and
> ( is_equal( g, ConformalSymplecticGroup( stored ) ) or
> if not ( g = ConformalSymplecticGroup( g ) and
> ( g = ConformalSymplecticGroup( stored ) or
> BaseDomain( stored ) <> F ) and
> is_equal( g, ConformalSymplecticGroup( d, q ) ) and
> is_equal( g, ConformalSymplecticGroup( form ) ) and
> is_equal( g, ConformalSymplecticGroup( d, q, g ) ) and
> is_equal( g, ConformalSymplecticGroup( d, q, stored ) ) and
> is_equal( g, ConformalSymplecticGroup( d, q, form ) ) and
> is_equal( g, ConformalSymplecticGroup( d, F, g ) ) and
> is_equal( g, ConformalSymplecticGroup( d, F, stored ) ) and
> is_equal( g, ConformalSymplecticGroup( d, F, form ) ) and
> g = ConformalSymplecticGroup( d, q ) and
> g = ConformalSymplecticGroup( form ) and
> g = ConformalSymplecticGroup( d, q, g ) and
> g = ConformalSymplecticGroup( d, q, stored ) and
> g = ConformalSymplecticGroup( d, q, form ) and
> g = ConformalSymplecticGroup( d, F, g ) and
> g = ConformalSymplecticGroup( d, F, stored ) and
> g = ConformalSymplecticGroup( d, F, form ) and
> IsSubset( gg, GeneratorsOfGroup( gg ) ) and
> IsSubset( g, List( GeneratorsOfGroup( gg ), x -> x^pi ) ) ) then
> Error( "problem with CSp(", d, ",", q, ")" );
> fi;
>
> if Size( g ) < 10^7 and filt = IsPlistRep then
> # Change this as soon as also `IsPlistMatrixRep` works!
> if Size( g ) < 10^7 then
> pg:= ConformalSymplecticGroup( IsPermGroup, d, q );
> if Size( g ) <> Size( pg ) then
> Error( "problem with CSp(IsPermGroup, ", d, ",", q, ")" );
Expand All @@ -59,8 +58,7 @@ gap> for q in [ 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25 ] do
> Error( "wrong repres. of matrices" );
> fi;
> g:= ConformalSymplecticGroup( sp );
> # if not IsSubset( g, sp ) then # make this fast in the GAP library
> if ForAny( GeneratorsOfGroup( sp ), x -> not x in g ) then
> if not IsSubset( g, sp ) then
> Error( "problem with CSp(", d, ",", q, ")" );
> fi;
>
Expand Down