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# SPDX-License-Identifier: GPL-2.0-or-later
# MatricesForHomalg: Matrices for the homalg project
#
# Implementations
#
##
InstallImmediateMethod( IsOne,
IsHomalgMatrix and HasNumberRows and HasNumberColumns, 0,
function( M )
if NumberRows( M ) = 0 and NumberColumns( M ) = 0 then
return true;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( IsEmptyMatrix,
IsHomalgMatrix and HasNumberRows and HasNumberColumns, 0,
function( M )
if NumberRows( M ) = 0 or NumberColumns( M ) = 0 then
return true;
else
return false;
fi;
end );
##
InstallImmediateMethod( IsZero,
IsHomalgMatrix and HasIsEmptyMatrix and IsEmptyMatrix, 0,
function( M )
return true;
end );
##
InstallImmediateMethod( IsLeftInvertibleMatrix,
IsHomalgMatrix and HasNumberColumns, 0,
function( M )
if NumberColumns( M ) = 0 then
return true;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( ZeroRows,
IsHomalgMatrix and IsEmptyMatrix and HasNumberRows, 0,
function( M )
return [ 1 .. NumberRows( M ) ];
end );
##
InstallImmediateMethod( ZeroColumns,
IsHomalgMatrix and IsEmptyMatrix and HasNumberColumns, 0,
function( M )
return [ 1 .. NumberColumns( M ) ];
end );
##
InstallMethod( UnionOfRowsOp,
"LIMAT: of a homalg ring, an integer and a list of homalg matrices (check input, drop empty matrices)",
[ IsHomalgRing, IsInt, IsList ], 10001,
function( R, nr_cols, L )
local c, filtered_L;
if not ForAll( L, IsHomalgMatrix ) then
Error( "L must be a list of homalg matrices" );
fi;
c := nr_cols;
if Length( L ) = 1 then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "UnionOfRows( [ single matrix ] )", "\033[0m" );
return L[1];
fi;
if not ForAll( L, x -> IsIdenticalObj( HomalgRing( x ), R ) ) then
Error( "the matrices are not defined over identically the same ring\n" );
fi;
if not ForAll( L, x -> NumberColumns( x ) = c ) then
Error( "the matrices are not stackable, since they do not all have the same number of columns\n" );
fi;
filtered_L := Filtered( L, x -> not IsEmptyMatrix( x ) );
if Length( filtered_L ) = 0 then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "UnionOfRows( [ empty matrices ] )", "\033[0m" );
return HomalgZeroMatrix( Sum( List( L, NumberRows ) ), c, R );
elif Length( filtered_L ) <> Length( L ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "UnionOfRows( <dropped empty matrices> )", "\033[0m" );
return UnionOfRowsOp( R, nr_cols, filtered_L );
fi;
TryNextMethod( );
end );
##
InstallMethod( \=,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix and IsEmptyMatrix ],
function( M1, M2 )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsZero(Matrix) = IsZero(Matrix)", "\033[0m" );
return AreComparableMatrices( M1, M2 );
end );
##
InstallMethod( UnionOfColumnsOp,
"LIMAT: of a homalg ring, an integer and a list of homalg matrices (check input, drop empty matrices)",
[ IsHomalgRing, IsInt, IsList ], 10001,
function( R, nr_rows, L )
local r, filtered_L;
if not ForAll( L, IsHomalgMatrix ) then
Error( "L must be a list of homalg matrices" );
fi;
r := nr_rows;
if Length( L ) = 1 then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "UnionOfColumns( [ single matrix ] )", "\033[0m" );
return L[1];
fi;
if not ForAll( L, x -> IsIdenticalObj( HomalgRing( x ), R ) ) then
Error( "the matrices are not defined over identically the same ring\n" );
fi;
if not ForAll( L, x -> NumberRows( x ) = r ) then
Error( "the matrices are not augmentable, since they do not all have the same number of rows\n" );
fi;
filtered_L := Filtered( L, x -> not IsEmptyMatrix( x ) );
if Length( filtered_L ) = 0 then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "UnionOfColumns( [ empty matrices ] )", "\033[0m" );
return HomalgZeroMatrix( r, Sum( List( L, NumberColumns ) ), R );
elif Length( filtered_L ) <> Length( L ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "UnionOfColumns( <dropped empty matrices> )", "\033[0m" );
return UnionOfColumnsOp( R, nr_rows, filtered_L );
fi;
TryNextMethod( );
end );
##
InstallMethod( DiagMat,
"LIMAT: of a homalg ring and a list of homalg matrices",
[ IsHomalgRing, IsHomogeneousList ], 2,
function( R, l )
if ForAll( l, HasIsZero and IsEmptyMatrix ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DiagMat( [ zero matrices ] )", "\033[0m" );
return HomalgZeroMatrix( Sum( List( l, NumberRows ) ), Sum( List( l, NumberColumns ) ), R );
fi;
TryNextMethod( );
end );
##
InstallMethod( KroneckerMat,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ], 1001, ## FIXME: this must be ranked higher than the "KroneckerMat( IsOne, IsHomalgMatrix )", why?
function( A, B )
local R;
R := HomalgRing( A );
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "KroneckerMat( IsZero(Matrix), IsHomalgMatrix )", "\033[0m" );
return HomalgZeroMatrix( NumberRows( A ) * NumberRows( B ), NumberColumns( A ) * NumberColumns( B ), R );
end );
##
InstallMethod( KroneckerMat,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix ],
function( A, B )
local R;
R := HomalgRing( A );
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "KroneckerMat( IsHomalgMatrix, IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( NumberRows( A ) * NumberRows( B ), NumberColumns( A ) * NumberColumns( B ), R );
end );
##
InstallMethod( DualKroneckerMat,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ], 1001, ## FIXME: this must be ranked higher than the "DualKroneckerMat( IsOne, IsHomalgMatrix )", why?
function( A, B )
local R;
R := HomalgRing( A );
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DualKroneckerMat( IsZero(Matrix), IsHomalgMatrix )", "\033[0m" );
return HomalgZeroMatrix( NumberRows( A ) * NumberRows( B ), NumberColumns( A ) * NumberColumns( B ), R );
end );
##
InstallMethod( DualKroneckerMat,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix ],
function( A, B )
local R;
R := HomalgRing( A );
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DualKroneckerMat( IsHomalgMatrix, IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( NumberRows( A ) * NumberRows( B ), NumberColumns( A ) * NumberColumns( B ), R );
end );
##
InstallMethod( \*,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsRingElement, IsHomalgMatrix and IsEmptyMatrix ], 10001,
function( a, A )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsRingElement * IsZero(Matrix)", "\033[0m" );
return A;
end );
##
InstallMethod( \+,
"LIMAT: for two homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ],
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsZero(Matrix) + IsHomalgMatrix", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ) );
return B;
end );
##
InstallMethod( \+,
"LIMAT: for two homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix ],
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsHomalgMatrix + IsZero(Matrix)", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ) );
return A;
end );
## a synonym of `-<elm>':
InstallMethod( AdditiveInverseMutable,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( A )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "-IsZero(Matrix)", "\033[0m" );
return A;
end );
##
InstallMethod( \-,
"LIMAT: for two homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ],
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsZero(Matrix) - IsHomalgMatrix", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ) );
return -B;
end );
##
InstallMethod( \-,
"LIMAT: for two homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix ],
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsHomalgMatrix - IsZero(Matrix)", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ) );
return A;
end );
##
InstallMethod( \*,
"LIMAT: for two homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ], 17001,
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsZero(Matrix) * IsHomalgMatrix", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ), " x ", NumberColumns( B ) );
if NumberRows( B ) = NumberColumns( B ) then
return A;
else
return HomalgZeroMatrix( NumberRows( A ), NumberColumns( B ), HomalgRing( A ) );
fi;
end );
##
InstallMethod( \*,
"LIMAT: for two homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix ], 17001,
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsHomalgMatrix * IsZero(Matrix)", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ), " x ", NumberColumns( B ) );
if NumberRows( A ) = NumberColumns( A ) then
return B;
else
return HomalgZeroMatrix( NumberRows( A ), NumberColumns( B ), HomalgRing( B ) );
fi;
end );
##
InstallMethod( RightDivide,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ],
function( B, A )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RightDivide( IsZero(Matrix), IsHomalgMatrix )", "\033[0m" );
return HomalgZeroMatrix( NumberRows( B ), NumberRows( A ), HomalgRing( B ) );
end );
##
InstallMethod( RightDivide,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix, IsHomalgMatrix ],
function( B, A, L )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RightDivide( IsZero(Matrix), IsHomalgMatrix, IsHomalgMatrix )", "\033[0m" );
return HomalgZeroMatrix( NumberRows( B ), NumberRows( A ), HomalgRing( B ) );
end );
##
InstallMethod( LeftDivide,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix ],
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "LeftDivide( IsHomalgMatrix, IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( NumberColumns( A ), NumberColumns( B ), HomalgRing( B ) );
end );
##
InstallMethod( LeftDivide,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ],
function( A, B, L )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "LeftDivide( IsHomalgMatrix, IsZero(Matrix), IsHomalgMatrix )", "\033[0m" );
return HomalgZeroMatrix( NumberColumns( A ), NumberColumns( B ), HomalgRing( B ) );
end );
##
InstallMethod( LeftInverse,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
if NumberColumns( M ) = 0 then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "LeftInverse( ? x 0 -- IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( 0, NumberRows( M ), HomalgRing( M ) );
else
Error( "a zero matrix with positive number of columns has no left inverse!\n" );
fi;
end );
##
InstallMethod( RightInverse,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
if NumberRows( M ) = 0 then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RightInverse( 0 x ? -- IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( NumberColumns( M ), 0, HomalgRing( M ) );
else
Error( "a zero matrix with positive number of rows has no left inverse!\n" );
fi;
end );
##
InstallMethod( BasisOfRowModule,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "BasisOfRowModule( IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( 0, NumberColumns( M ), HomalgRing( M ) );
end );
##
InstallMethod( BasisOfColumnModule,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "BasisOfColumnModule( IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( NumberRows( M ), 0, HomalgRing( M ) );
end );
##
InstallMethod( ReducedBasisOfRowModule,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedBasisOfRowModule( IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( 0, NumberColumns( M ), HomalgRing( M ) );
end );
##
InstallMethod( ReducedBasisOfColumnModule,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedBasisOfColumnModule( IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( NumberRows( M ), 0, HomalgRing( M ) );
end );
##
InstallMethod( BasisOfRowsCoeff,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix and IsVoidMatrix ],
function( M, T )
local R;
R := HomalgRing( M );
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "BasisOfRowsCoeff( IsZero(Matrix), T )", "\033[0m" );
SetPreEval( T, HomalgZeroMatrix( 0, NumberRows( M ), R ) ); ResetFilterObj( T, IsVoidMatrix );
return HomalgZeroMatrix( 0, NumberColumns( M ), R );
end );
##
InstallMethod( BasisOfColumnsCoeff,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix and IsVoidMatrix ],
function( M, T )
local R;
R := HomalgRing( M );
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "BasisOfColumnsCoeff( IsZero(Matrix), T )", "\033[0m" );
SetPreEval( T, HomalgZeroMatrix( NumberColumns( M ), 0, R ) ); ResetFilterObj( T, IsVoidMatrix );
return HomalgZeroMatrix( NumberRows( M ), 0, R );
end );
##
InstallMethod( DecideZeroRows,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix ],
function( L, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DecideZeroRows( IsHomalgMatrix, IsZero(Matrix) )", "\033[0m" );
## calling IsZero( L ) causes too much unnecessary trafic
#IsZero( L );
return L;
end );
##
InstallMethod( DecideZeroRows,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ],
function( L, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DecideZeroRows( IsZero(Matrix), IsHomalgMatrix )", "\033[0m" );
return L;
end );
##
InstallMethod( DecideZeroColumns,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix ],
function( L, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DecideZeroColumns( IsHomalgMatrix, IsZero(Matrix) )", "\033[0m" );
## calling IsZero( L ) causes too much unnecessary trafic
#IsZero( L );
return L;
end );
##
InstallMethod( DecideZeroColumns,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ],
function( L, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DecideZeroColumns( IsZero(Matrix), IsHomalgMatrix )", "\033[0m" );
return L;
end );
##
InstallMethod( DecideZeroRowsEffectively,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix, IsVoidMatrix ],
function( A, B, T )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DecideZeroRowsEffectively( IsHomalgMatrix, IsZero(Matrix), T )", "\033[0m" );
SetPreEval( T, HomalgZeroMatrix( NumberRows( A ), NumberRows( B ), HomalgRing( A ) ) ); ResetFilterObj( T, IsVoidMatrix );
return A;
end );
##
InstallMethod( DecideZeroRowsEffectively,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix, IsVoidMatrix ],
function( A, B, T )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DecideZeroRowsEffectively( IsZero(Matrix), IsHomalgMatrix, T )", "\033[0m" );
SetPreEval( T, HomalgZeroMatrix( NumberRows( A ), NumberRows( B ), HomalgRing( A ) ) ); ResetFilterObj( T, IsVoidMatrix );
return A;
end );
##
InstallMethod( DecideZeroColumnsEffectively,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix, IsVoidMatrix ],
function( A, B, T )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DecideZeroColumnsEffectively( IsHomalgMatrix, IsZero(Matrix), T )", "\033[0m" );
SetPreEval( T, HomalgZeroMatrix( NumberColumns( B ), NumberColumns( A ), HomalgRing( A ) ) ); ResetFilterObj( T, IsVoidMatrix );
return A;
end );
##
InstallMethod( DecideZeroColumnsEffectively,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix, IsVoidMatrix ],
function( A, B, T )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DecideZeroColumnsEffectively( IsZero(Matrix), IsHomalgMatrix, T )", "\033[0m" );
SetPreEval( T, HomalgZeroMatrix( NumberColumns( B ), NumberColumns( A ), HomalgRing( A ) ) ); ResetFilterObj( T, IsVoidMatrix );
return A;
end );
##
InstallMethod( SyzygiesGeneratorsOfRows,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsEmptyMatrix and HasNumberRows and HasNumberColumns, IsHomalgMatrix ],
function( M1, M2 )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "SyzygiesGeneratorsOfRows(IsOne(Matrix),IsHomalgMatrix)", "\033[0m" );
if NumberRows( M1 ) = NumberRows( M2 ) then
return M2;
fi;
TryNextMethod( );
end );
##
InstallMethod( SyzygiesGeneratorsOfRows,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix ],
function( M1, M2 )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "SyzygiesGeneratorsOfRows(IsHomalgMatrix,IsZero(Matrix))", "\033[0m" );
return SyzygiesGeneratorsOfRows( M1 );
end );
##
InstallMethod( SyzygiesGeneratorsOfRows,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "SyzygiesGeneratorsOfRows( IsZero(Matrix) )", "\033[0m" );
return HomalgIdentityMatrix( NumberRows( M ), HomalgRing( M ) );
end );
##
InstallMethod( SyzygiesGeneratorsOfRows,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ],
function( M1, M2 )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "SyzygiesGeneratorsOfRows(IsZero(Matrix),IsHomalgMatrix)", "\033[0m" );
return HomalgIdentityMatrix( NumberRows( M1 ), HomalgRing( M1 ) );
end );
##
InstallMethod( SyzygiesGeneratorsOfColumns,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsEmptyMatrix and HasNumberRows and HasNumberColumns, IsHomalgMatrix ],
function( M1, M2 )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "SyzygiesGeneratorsOfColumns(IsOne(Matrix),IsHomalgMatrix)", "\033[0m" );
if NumberRows( M1 ) = NumberColumns( M1 ) then
return M2;
fi;
TryNextMethod( );
end );
##
InstallMethod( SyzygiesGeneratorsOfColumns,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsEmptyMatrix ],
function( M1, M2 )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "SyzygiesGeneratorsOfColumns(IsHomalgMatrix,IsZero(Matrix))", "\033[0m" );
return SyzygiesGeneratorsOfColumns( M1 );
end );
##
InstallMethod( SyzygiesGeneratorsOfColumns,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "SyzygiesGeneratorsOfColumns( IsZero(Matrix) )", "\033[0m" );
return HomalgIdentityMatrix( NumberColumns( M ), HomalgRing( M ) );
end );
##
InstallMethod( SyzygiesGeneratorsOfColumns,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomalgMatrix ],
function( M1, M2 )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "SyzygiesGeneratorsOfColumns(IsZero(Matrix),IsHomalgMatrix)", "\033[0m" );
return HomalgIdentityMatrix( NumberColumns( M1 ), HomalgRing( M1 ) );
end );
##
InstallMethod( ReducedSyzygiesGeneratorsOfRows,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedSyzygiesGeneratorsOfRows( IsZero(Matrix) )", "\033[0m" );
return HomalgIdentityMatrix( NumberRows( M ), HomalgRing( M ) );
end );
##
InstallMethod( ReducedSyzygiesGeneratorsOfColumns,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedSyzygiesGeneratorsOfColumns( IsZero(Matrix) )", "\033[0m" );
return HomalgIdentityMatrix( NumberColumns( M ), HomalgRing( M ) );
end );
##
InstallMethod( GetUnitPosition,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "GetUnitPosition( IsZero(Matrix) )", "\033[0m" );
return fail;
end );
##
InstallMethod( GetUnitPosition,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsHomogeneousList ],
function( M, poslist )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "GetUnitPosition( IsZero(Matrix), poslist )", "\033[0m" );
return fail;
end );
##
InstallMethod( GetColumnIndependentUnitPositions,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsList ],
function( M, pos_list )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "GetColumnIndependentUnitPositions( IsZero(Matrix) )", "\033[0m" );
return [ ];
end );
##
InstallMethod( GetRowIndependentUnitPositions,
"LIMAT: for homalg matrices (IsEmptyMatrix)",
[ IsHomalgMatrix and IsEmptyMatrix, IsList ],
function( M, pos_list )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "GetRowIndependentUnitPositions( IsZero(Matrix) )", "\033[0m" );
return [ ];
end );
[ Dauer der Verarbeitung: 0.57 Sekunden
(vorverarbeitet)
]
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