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Add IsSquareMat and IsAntisymmetricMat #6268

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2 changes: 2 additions & 0 deletions doc/ref/matrix.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -310,7 +310,9 @@ see&nbsp;<Ref Sect="Mutability and Copyability"/>.
<#Include Label="IsDiagonalMat">
<#Include Label="IsUpperTriangularMat">
<#Include Label="IsLowerTriangularMat">
<#Include Label="IsSquareMat">
<#Include Label="IsSymmetricMat">
<#Include Label="IsAntisymmetricMat">

</Section>

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68 changes: 68 additions & 0 deletions lib/matrix.gd
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Expand Up @@ -152,6 +152,36 @@ DeclareProperty( "IsLowerTriangularMatrix", IsMatrixOrMatrixObj );
DeclareSynonym( "IsLowerTriangularMat", IsLowerTriangularMatrix );


#############################################################################
##
#P IsSquareMatrix( <mat> )
#P IsSquareMat( <mat> )
##
## <#GAPDoc Label="IsSquareMat">
## <ManSection>
## <Prop Name="IsSquareMatrix" Arg='mat'/>
## <Prop Name="IsSquareMat" Arg='mat'/>
##
## <Description>
## return <K>true</K> if the matrix <A>mat</A> has the same number of rows
## and columns, and <K>false</K> otherwise.
## <Example><![CDATA[
## gap> IsSquareMatrix( [ [ 1 ] ] );
## true
## gap> IsSquareMatrix( [ [ 1, 2 ], [ 3, 4 ] ] );
## true
## gap> IsSquareMatrix( [ [ 1, 2, 3 ], [ 4, 5, 6 ] ] );
## false
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsSquareMatrix", IsMatrixOrMatrixObj );

DeclareSynonym( "IsSquareMat", IsSquareMatrix );


#############################################################################
##
#P IsSymmetricMatrix( <mat> )
Expand Down Expand Up @@ -184,6 +214,44 @@ DeclareProperty( "IsSymmetricMatrix", IsMatrixOrMatrixObj );

DeclareSynonym( "IsSymmetricMat", IsSymmetricMatrix );

InstallTrueMethod( IsSquareMatrix, IsSymmetricMatrix );


#############################################################################
##
#P IsAntisymmetricMatrix( <mat> )
#P IsAntisymmetricMat( <mat> )
##
## <#GAPDoc Label="IsAntisymmetricMat">
## <ManSection>
## <Prop Name="IsAntisymmetricMatrix" Arg='mat'/>
## <Prop Name="IsAntisymmetricMat" Arg='mat'/>
##
## <Description>
## return <K>true</K> if the matrix <A>mat</A> is a square matrix and
## satisfies <C><A>mat</A>[i,j] = -<A>mat</A>[j,i]</C> for all
## <M>i, j</M>, and <K>false</K> otherwise.
## (In particular, the diagonal entries must be zero.)
## <Example><![CDATA[
## gap> IsAntisymmetricMatrix( [ [ 0 ] ] );
## true
## gap> IsAntisymmetricMatrix( [ [ 0, 1 ], [ -1, 0 ] ] );
## true
## gap> IsAntisymmetricMatrix( [ [ 0, 1 ], [ 1, 0 ] ] );
## false
## gap> IsAntisymmetricMatrix( [ [ 1, 2, 3 ], [ 4, 5, 6 ] ] );
## false
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsAntisymmetricMatrix", IsMatrixOrMatrixObj );

DeclareSynonym( "IsAntisymmetricMat", IsAntisymmetricMatrix );

InstallTrueMethod( IsSquareMatrix, IsAntisymmetricMatrix );


#############################################################################
##
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45 changes: 44 additions & 1 deletion lib/matrix.gi
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Expand Up @@ -249,6 +249,20 @@ InstallMethod( IsLowerTriangularMatrix,
end);


#############################################################################
##
#M IsSquareMatrix(<mat>)
##
InstallMethod( IsSquareMatrix,
"for a matrix",
[ IsMatrixOrMatrixObj ],
function( mat )
return NrRows( mat ) = NrCols( mat );
end );

InstallTrueMethod( IsSquareMatrix, IsMatrixOrMatrixObj and IsEmptyMatrix );
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@fingolfin fingolfin Mar 18, 2026

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Hmm... is a $0\times 2$ matrix square?



#############################################################################
##
#M IsSymmetricMatrix(<mat>)
Expand All @@ -258,7 +272,7 @@ InstallMethod( IsSymmetricMatrix,
[ IsMatrixOrMatrixObj ],
function( mat )
local i, j;
if NrRows( mat ) <> NrCols( mat ) then
if not IsSquareMatrix( mat ) then
return false;
fi;
for i in [ 1 .. NrRows( mat ) ] do
Expand All @@ -274,6 +288,35 @@ InstallMethod( IsSymmetricMatrix,
InstallTrueMethod( IsSymmetricMatrix, IsMatrixOrMatrixObj and IsEmptyMatrix );


#############################################################################
##
#M IsAntisymmetricMatrix(<mat>)
##
InstallMethod( IsAntisymmetricMatrix,
"for a matrix",
[ IsMatrixOrMatrixObj ],
function( mat )
local i, j, zero;
if not IsSquareMatrix( mat ) then
return false;
fi;
zero := ZeroOfBaseDomain( mat );
for i in [ 1 .. NrRows( mat ) ] do
if mat[i,i] <> zero then
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@fingolfin fingolfin Mar 18, 2026

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This is the wrong condition in characteristic 0, isn't it?

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@Stefan-Kohl Stefan-Kohl Mar 19, 2026

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In characteristic 2, you mean?

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@fingolfin fingolfin Mar 19, 2026

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argh, yes (actually: in even positive characteristic, not just 2.

But the solution is the same: just remove this special case

return false;
fi;
for j in [ i+1 .. NrCols( mat ) ] do
if mat[i,j] <> -mat[j,i] then
return false;
fi;
od;
od;
return true;
end );

InstallTrueMethod( IsAntisymmetricMatrix, IsMatrixOrMatrixObj and IsEmptyMatrix );


#############################################################################
##
#M DiagonalOfMatrix(<mat>) . . . . . . . . . . . . . . . diagonal of matrix
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36 changes: 36 additions & 0 deletions tst/testinstall/matrix.tst
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Expand Up @@ -88,6 +88,22 @@ true
gap> IsLowerTriangularMat([[1,0],[1,1],[1,1]]);
true

#
gap> IsSquareMat(NullMat(3, 3));
true
gap> IsSquareMat(IdentityMat(3));
true
gap> IsSquareMat([[1]]);
true
gap> IsSquareMat([[1,2],[3,4]]);
true
gap> IsSquareMat(NullMat(2, 3));
false
gap> IsSquareMat(NullMat(3, 2));
false
gap> IsSquareMat([[1,2,3],[4,5,6]]);
false

#
gap> IsSymmetricMat(NullMat(3, 3));
true
Expand All @@ -112,6 +128,26 @@ false
gap> IsSymmetricMat([[1,2],[3,4],[5,6]]);
false

#
gap> IsAntisymmetricMat(NullMat(3, 3));
true
gap> IsAntisymmetricMat([[0]]);
true
gap> IsAntisymmetricMat([[0,1],[-1,0]]);
true
gap> IsAntisymmetricMat([[0,2,3],[-2,0,5],[-3,-5,0]]);
true
gap> IsAntisymmetricMat([[0,1],[1,0]]);
false
gap> IsAntisymmetricMat([[1,0],[0,1]]);
false
gap> IsAntisymmetricMat(NullMat(2, 3));
false
gap> IsAntisymmetricMat(NullMat(3, 2));
false
gap> IsAntisymmetricMat([[1,2,3],[4,5,6]]);
false

#
gap> m := Z(5)^0 * [[0, 1], [1, 0]];;
gap> m := GeneratorsWithMemory([m])[1];;
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