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Fix FieldOfMatrixGroup calls, analogous to the GAP library #82

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Fix FieldOfMatrixGroup calls, analogous to the GAP library #82

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81 changes: 63 additions & 18 deletions lib/classic.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -43,18 +43,39 @@ BindGlobal( "_IsEqualModScalars",
return IsZero( mat2 );
end );

# The following helper function provides compatibility
# with older GAP versions.
# Before gap-system/gap/pull/6203, 'FieldOfMatrixGroup( G )' was interpreted
# as the field of definition of the invariant forms stored in 'G'.
# This was not always correct, hence we decided to add a component
# 'baseDomain' to the records that describe the invariant forms created with
# 'InvariantBilinearForm' etc.
BindGlobal("Forms_FieldOfDefinition", function( form_record, G )
if IsBound( form_record.baseDomain ) then
return form_record.baseDomain;
else
return FieldOfMatrixGroup( G );
fi;
end );

BindGlobal("Forms_OrthogonalGroup",
function( g, form )
local stored, gf, d, wanted, mat1, mat2, mat, matinv, gens, gg;

stored:= InvariantQuadraticForm( g ).matrix;
stored:= InvariantQuadraticForm( g );
gf:= Forms_FieldOfDefinition( stored, g );
stored:= stored.matrix;

# Check that 'form' lives over the intended field.
if not IsSubset( gf, form!.basefield ) then
Error( "the defining field of <form> does not fit to <gf>" );
fi;

# If the prescribed form fits then just return.
if stored = form!.matrix then
return g;
fi;

gf:= FieldOfMatrixGroup( g );
d:= DimensionOfMatrixGroup( g );

# Compute a base change matrix.
Expand All @@ -80,7 +101,8 @@ BindGlobal("Forms_OrthogonalGroup",
SetName( gg, Name( g ) );
fi;

SetInvariantQuadraticForm( gg, rec( matrix:= form!.matrix ) );
SetInvariantQuadraticForm( gg, rec( matrix:= form!.matrix,
baseDomain:= gf ) );
if HasIsFullSubgroupGLorSLRespectingQuadraticForm( g ) then
SetIsFullSubgroupGLorSLRespectingQuadraticForm( gg,
IsFullSubgroupGLorSLRespectingQuadraticForm( g ) );
Expand Down Expand Up @@ -138,7 +160,7 @@ InstallMethod( GeneralOrthogonalGroupCons,
{ filt, G } -> GeneralOrthogonalGroupCons( filt,
QuadraticFormByMatrix(
InvariantQuadraticForm( G ).matrix,
FieldOfMatrixGroup( G ) ) ) );
Forms_FieldOfDefinition( InvariantQuadraticForm( G ), G ) ) ) );

InstallMethod( GeneralOrthogonalGroupCons,
"matrix group for form",
Expand Down Expand Up @@ -278,7 +300,7 @@ InstallMethod( SpecialOrthogonalGroupCons,
{ filt, G } -> SpecialOrthogonalGroupCons( filt,
QuadraticFormByMatrix(
InvariantQuadraticForm( G ).matrix,
FieldOfMatrixGroup( G ) ) ) );
Forms_FieldOfDefinition( InvariantQuadraticForm( G ), G ) ) ) );

InstallMethod( SpecialOrthogonalGroupCons,
"matrix group for form",
Expand Down Expand Up @@ -455,7 +477,7 @@ InstallMethod( OmegaCons,
{ filt, G } -> OmegaCons( filt,
QuadraticFormByMatrix(
InvariantQuadraticForm( G ).matrix,
FieldOfMatrixGroup( G ) ) ) );
Forms_FieldOfDefinition( InvariantQuadraticForm( G ), G ) ) ) );

InstallMethod( OmegaCons,
"matrix group for form",
Expand Down Expand Up @@ -563,7 +585,7 @@ InstallMethod( GeneralUnitaryGroupCons,
{ filt, G } -> GeneralUnitaryGroupCons( filt,
HermitianFormByMatrix(
InvariantSesquilinearForm( G ).matrix,
FieldOfMatrixGroup( G ) ) ) );
Forms_FieldOfDefinition( InvariantSesquilinearForm( G ), G ) ) ) );

InstallMethod( GeneralUnitaryGroupCons,
"matrix group for form",
Expand Down Expand Up @@ -619,20 +641,26 @@ InstallMethod( GeneralUnitaryGroupCons,
IsPosInt,
IsHermitianForm ],
function( filt, d, q, form )
local g, stored, wanted, mat1, mat2, mat, matinv, gens, gg;
local g, stored, F, wanted, mat1, mat2, mat, matinv, gens, gg;

# Create the default generators and form.
g:= GeneralUnitaryGroupCons( filt, d, q );
stored:= InvariantSesquilinearForm( g ).matrix;

# Check that 'form' lives over the intended field.
F:= GF(q^2);
if not IsSubset( F, form!.basefield ) then
Error( "the defining field of <form> does not fit to <q>" );
fi;

# If the prescribed form fits then just return.
if stored = form!.matrix then
return g;
fi;

# Compute a base change matrix.
# (Check that the canonical forms are equal.)
wanted:= HermitianFormByMatrix( stored, GF(q^2) );
wanted:= HermitianFormByMatrix( stored, F );
mat1:= BaseChangeToCanonical( form );
mat2:= BaseChangeToCanonical( wanted );
if mat1 * form!.matrix * TransposedFrobeniusMat( mat1, q ) <>
Expand All @@ -652,7 +680,9 @@ InstallMethod( GeneralUnitaryGroupCons,
SetName( gg, Name( g ) );
fi;

SetInvariantSesquilinearForm( gg, rec( matrix:= form!.matrix ) );
SetInvariantSesquilinearForm( gg, rec( matrix:= form!.matrix,
baseDomain:= F ) );

if HasIsFullSubgroupGLorSLRespectingSesquilinearForm( g ) then
SetIsFullSubgroupGLorSLRespectingSesquilinearForm( gg,
IsFullSubgroupGLorSLRespectingSesquilinearForm( g ) );
Expand Down Expand Up @@ -708,7 +738,7 @@ InstallMethod( SpecialUnitaryGroupCons,
{ filt, G } -> SpecialUnitaryGroupCons( filt,
HermitianFormByMatrix(
InvariantSesquilinearForm( G ).matrix,
FieldOfMatrixGroup( G ) ) ) );
Forms_FieldOfDefinition( InvariantSesquilinearForm( G ), G ) ) ) );

InstallMethod( SpecialUnitaryGroupCons,
"matrix group for form",
Expand Down Expand Up @@ -748,7 +778,7 @@ InstallMethod( SpecialUnitaryGroupCons,
IsPosInt,
IsHermitianForm ],
function( filt, d, q, form )
local g, stored, wanted, mat1, mat2, mat, matinv, gens, gg;
local g, stored, F, wanted, mat1, mat2, mat, matinv, gens, gg;

# Create the default generators and form.
g:= SpecialUnitaryGroupCons( filt, d, q );
Expand All @@ -759,9 +789,15 @@ InstallMethod( SpecialUnitaryGroupCons,
return g;
fi;

# Check that 'form' lives over the intended field.
F:= GF(q^2);
if not IsSubset( F, form!.basefield ) then
Error( "the defining field of <form> does not fit to <q>" );
fi;

# Compute a base change matrix.
# (Check that the canonical forms are equal.)
wanted:= HermitianFormByMatrix( stored, GF(q^2) );
wanted:= HermitianFormByMatrix( stored, F );
mat1:= BaseChangeToCanonical( form );
mat2:= BaseChangeToCanonical( wanted );
if mat1 * form!.matrix * TransposedFrobeniusMat( mat1, q ) <>
Expand All @@ -781,7 +817,9 @@ InstallMethod( SpecialUnitaryGroupCons,
SetName( gg, Name( g ) );
fi;

SetInvariantSesquilinearForm( gg, rec( matrix:= form!.matrix ) );
SetInvariantSesquilinearForm( gg, rec( matrix:= form!.matrix,
baseDomain:= F ) );

if HasIsFullSubgroupGLorSLRespectingSesquilinearForm( g ) then
SetIsFullSubgroupGLorSLRespectingSesquilinearForm( gg,
IsFullSubgroupGLorSLRespectingSesquilinearForm( g ) );
Expand Down Expand Up @@ -830,7 +868,7 @@ InstallMethod( SymplecticGroupCons,
{ filt, G } -> SymplecticGroupCons( filt,
BilinearFormByMatrix(
InvariantBilinearForm( G ).matrix,
FieldOfMatrixGroup( G ) ) ) );
Forms_FieldOfDefinition( InvariantBilinearForm( G ), G ) ) ) );

InstallMethod( SymplecticGroupCons,
"matrix group for form",
Expand Down Expand Up @@ -870,7 +908,7 @@ InstallMethod( SymplecticGroupCons,
IsPosInt,
IsBilinearForm ],
function( filt, d, q, form )
local g, stored, wanted, mat1, mat2, mat, matinv, gens, gg;
local g, stored, F, wanted, mat1, mat2, mat, matinv, gens, gg;

# Create the default generators and form.
g:= SymplecticGroupCons( filt, d, q );
Expand All @@ -881,9 +919,15 @@ InstallMethod( SymplecticGroupCons,
return g;
fi;

# Check that 'form' lives over the intended field.
F:= GF(q);
if not IsSubset( F, form!.basefield ) then
Error( "the defining field of <form> does not fit to <q>" );
fi;

# Compute a base change matrix.
# (Check that the canonical forms are equal.)
wanted:= BilinearFormByMatrix( stored, GF(q) );
wanted:= BilinearFormByMatrix( stored, F );
mat1:= BaseChangeToCanonical( form );
mat2:= BaseChangeToCanonical( wanted );
if mat1 * form!.matrix * TransposedMat( mat1 ) <>
Expand All @@ -903,7 +947,8 @@ InstallMethod( SymplecticGroupCons,
SetName( gg, Name( g ) );
fi;

SetInvariantBilinearForm( gg, rec( matrix:= form!.matrix ) );
SetInvariantBilinearForm( gg, rec( matrix:= form!.matrix,
baseDomain:= F ) );
if HasIsFullSubgroupGLorSLRespectingBilinearForm( g ) then
SetIsFullSubgroupGLorSLRespectingBilinearForm( gg,
IsFullSubgroupGLorSLRespectingBilinearForm( g ) );
Expand Down
17 changes: 17 additions & 0 deletions tst/adv/classic.tst
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Original file line number Diff line number Diff line change
Expand Up @@ -201,6 +201,23 @@ gap> g:= GO( 3, 257, mat );;
gap> InvariantQuadraticForm( g ).matrix = mat;
true

# Test inconsistent fields of definition.
gap> g:= GeneralOrthogonalGroup( 5, GF(3) );;
gap> mat:= InvariantQuadraticForm( g ).matrix;;
gap> form:= QuadraticFormByMatrix( mat, GF(9) );;
gap> GeneralOrthogonalGroup( 5, GF(3), form );;
Error, the defining field of <form> does not fit to <gf>
gap> g:= GeneralUnitaryGroup( 4, 2 );;
gap> mat:= InvariantSesquilinearForm( g ).matrix;;
gap> form:= HermitianFormByMatrix( mat, GF(16) );;
gap> GeneralUnitaryGroup( 4, 2, form );
Error, the defining field of <form> does not fit to <q>
gap> g:= SymplecticGroup( 4, GF(2) );;
gap> mat:= InvariantBilinearForm( g ).matrix;;
gap> form:= BilinearFormByMatrix( mat, GF(4) );;
gap> SymplecticGroup( 4, GF(2), form );
Error, the defining field of <form> does not fit to <q>

# Increase the code coverage.
gap> mat:= IdentityMat( 3, GF(5) );;
gap> _IsEqualModScalars( mat, Z(5) * mat );
Expand Down