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# SPDX-License-Identifier: GPL-2.0-or-later
# MatricesForHomalg: Matrices for the homalg project
#
# Implementations
#
## LIMAT = Logical Implications for homalg MATrices
####################################
#
# logical implications methods:
#
####################################
InstallLogicalImplicationsForHomalgBasicObjects( LogicalImplicationsForHomalgMatrices, IsHomalgMatrix );
InstallLogicalImplicationsForHomalgBasicObjects( LogicalImplicationsForHomalgMatricesOverSpecialRings, IsHomalgMatrix, IsHomalgRing );
####################################
#
# immediate methods for properties:
#
####################################
##
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( IsOne,
IsHomalgMatrix and HasNumberRows and HasNumberColumns, 0,
function( M )
if NumberRows( M ) = 0 or NumberColumns( M ) = 0 then
return NumberRows( M ) = NumberColumns( M );
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( IsOne,
IsHomalgMatrix and HasNumberRows and HasNumberColumns, 0,
function( M )
if NumberRows( M ) <> NumberColumns( M ) then
return false;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( IsOne,
IsHomalgMatrix and IsPermutationMatrix and HasPositionOfFirstNonZeroEntryPerRow and HasNumberRows, 0,
function( M )
return PositionOfFirstNonZeroEntryPerRow( M ) = [ 1 .. NumberRows( M ) ];
end );
##
InstallImmediateMethod( IsOne,
IsHomalgMatrix and IsPermutationMatrix and HasPositionOfFirstNonZeroEntryPerColumn and HasNumberColumns, 0,
function( M )
return PositionOfFirstNonZeroEntryPerColumn( M ) = [ 1 .. NumberColumns( M ) ];
end );
##
InstallImmediateMethod( IsZero,
IsHomalgMatrix and HasPositionOfFirstNonZeroEntryPerRow, 0,
function( M )
return ForAll( PositionOfFirstNonZeroEntryPerRow( M ), IsZero );
end );
##
InstallImmediateMethod( IsZero,
IsHomalgMatrix and HasPositionOfFirstNonZeroEntryPerColumn, 0,
function( M )
return ForAll( PositionOfFirstNonZeroEntryPerColumn( M ), IsZero );
end );
##
InstallImmediateMethod( IsZero,
IsHomalgMatrix and HasIsRightRegular and HasIsEmptyMatrix, 0,
function( M )
if not IsEmptyMatrix( M ) and IsRightRegular( M ) then
return false;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( IsZero,
IsHomalgMatrix and HasIsLeftRegular and HasIsEmptyMatrix, 0,
function( M )
if not IsEmptyMatrix( M ) and IsLeftRegular( M ) then
return false;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( IsZero,
IsHomalgMatrix and HasZeroRows and HasNumberRows, 0,
function( M )
return Length( ZeroRows( M ) ) = NumberRows( M );
end );
##
InstallImmediateMethod( IsZero,
IsHomalgMatrix and HasZeroColumns and HasNumberColumns, 0,
function( M )
return Length( ZeroColumns( M ) ) = NumberColumns( M );
end );
##
InstallImmediateMethod( IsRightInvertibleMatrix,
IsHomalgMatrix and IsSubidentityMatrix, 0,
function( M )
return NumberRows( M ) <= NumberColumns( M );
end );
##
InstallImmediateMethod( IsRightInvertibleMatrix,
IsHomalgMatrix and HasNumberRows, 0,
function( M )
if NumberRows( M ) = 0 then
return true;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( IsLeftInvertibleMatrix,
IsHomalgMatrix and IsSubidentityMatrix, 0,
function( M )
return NumberColumns( M ) <= NumberRows( M );
end );
##
InstallImmediateMethod( IsLeftInvertibleMatrix,
IsHomalgMatrix and HasNumberColumns, 0,
function( M )
if NumberColumns( M ) = 0 then
return true;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( IsRightRegular,
IsHomalgMatrix and IsLowerStairCaseMatrix and HasZeroColumns, 0,
function( M )
local R;
R := HomalgRing( M );
if not ( HasIsIntegralDomain( R ) and IsIntegralDomain( R ) ) then
TryNextMethod( );
fi;
return ZeroColumns( M ) = [ ];
end );
##
InstallImmediateMethod( IsRightRegular,
IsHomalgMatrix and HasNumberColumns and HasIsZero, 0,
function( M )
local R;
R := HomalgRing( M );
if NumberColumns( M ) = 1 and not IsZero( M ) and HasIsIntegralDomain( R ) and IsIntegralDomain( R ) then
return true;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( IsLeftRegular,
IsHomalgMatrix and IsUpperStairCaseMatrix and HasZeroRows, 0,
function( M )
local R;
R := HomalgRing( M );
if not ( HasIsIntegralDomain( R ) and IsIntegralDomain( R ) ) then
TryNextMethod( );
fi;
return ZeroRows( M ) = [ ];
end );
##
InstallImmediateMethod( IsLeftRegular,
IsHomalgMatrix and HasNumberRows and HasIsZero, 0,
function( M )
local R;
R := HomalgRing( M );
if NumberRows( M ) = 1 and not IsZero( M ) and HasIsIntegralDomain( R ) and IsIntegralDomain( R ) then
return true;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( IsUpperStairCaseMatrix,
IsHomalgMatrix and HasNumberRows, 0,
function( M )
if NumberRows( M ) = 1 then
return true;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( IsLowerStairCaseMatrix,
IsHomalgMatrix and HasNumberColumns, 0,
function( M )
if NumberColumns( M ) = 1 then
return true;
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( RowRankOfMatrix,
IsHomalgMatrix and IsUpperStairCaseMatrix and HasNonZeroRows, 0,
function( M )
local R;
R := HomalgRing( M );
if not ( HasIsIntegralDomain( R ) and IsIntegralDomain( R ) ) then
TryNextMethod( );
fi;
return Length( NonZeroRows( M ) );
end );
##
InstallImmediateMethod( ColumnRankOfMatrix,
IsHomalgMatrix and IsLowerStairCaseMatrix and HasNonZeroColumns, 0,
function( M )
local R;
R := HomalgRing( M );
if not ( HasIsIntegralDomain( R ) and IsIntegralDomain( R ) ) then
TryNextMethod( );
fi;
return Length( NonZeroColumns( M ) );
end );
####################################
#
# immediate methods for attributes:
#
####################################
##
InstallImmediateMethod( NumberRows,
IsHomalgMatrix and HasPositionOfFirstNonZeroEntryPerRow, 0,
function( M )
return Length( PositionOfFirstNonZeroEntryPerRow( M ) );
end );
##
InstallImmediateMethod( NumberColumns,
IsHomalgMatrix and HasPositionOfFirstNonZeroEntryPerColumn, 0,
function( M )
return Length( PositionOfFirstNonZeroEntryPerColumn( M ) );
end );
##
InstallImmediateMethod( RowRankOfMatrix,
IsHomalgMatrix and IsOne and HasNumberRows, 0,
function( M )
return NumberRows( M );
end );
##
InstallImmediateMethod( ColumnRankOfMatrix,
IsHomalgMatrix and IsOne and HasNumberColumns, 0,
function( M )
return NumberColumns( M );
end );
##
InstallImmediateMethod( RowRankOfMatrix,
IsHomalgMatrix and IsZero, 0,
function( M )
return 0;
end );
##
InstallImmediateMethod( ColumnRankOfMatrix,
IsHomalgMatrix and IsZero, 0,
function( M )
return 0;
end );
##
InstallImmediateMethod( RowRankOfMatrix,
IsHomalgMatrix and HasIsLeftRegular and HasNumberRows, 0,
function( M )
if IsLeftRegular( M ) then
return NumberRows( M );
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( ColumnRankOfMatrix,
IsHomalgMatrix and HasIsRightRegular and HasNumberColumns, 0,
function( M )
if IsRightRegular( M ) then
return NumberColumns( M );
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( RowRankOfMatrix,
IsHomalgMatrix and HasColumnRankOfMatrix, 0,
function( M )
local R;
R := HomalgRing( M );
if HasIsFieldForHomalg( R ) and IsFieldForHomalg( R ) then ## FIXME: make me more general!
return ColumnRankOfMatrix( M );
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( ColumnRankOfMatrix,
IsHomalgMatrix and HasRowRankOfMatrix, 0,
function( M )
local R;
R := HomalgRing( M );
if HasIsFieldForHomalg( R ) and IsFieldForHomalg( R ) then ## FIXME: make me more general!
return RowRankOfMatrix( M );
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( ZeroRows,
IsHomalgMatrix and HasIsZero and HasNumberRows, 0,
function( M )
if not IsZero( M ) and NumberRows( M ) = 1 then
return [ ];
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( ZeroRows,
IsHomalgMatrix and IsOne, 0,
function( M )
return [ ];
end );
##
InstallImmediateMethod( ZeroRows,
IsHomalgMatrix and IsZero and HasNumberRows, 0,
function( M )
return [ 1 .. NumberRows( M ) ];
end );
##
InstallImmediateMethod( ZeroRows,
IsHomalgMatrix and HasPositionOfFirstNonZeroEntryPerRow and HasNumberRows, 0,
function( M )
local pos;
pos := PositionOfFirstNonZeroEntryPerRow( M );
return Filtered( [ 1 .. NumberRows( M ) ], i -> pos[i] = 0 );
end );
##
InstallImmediateMethod( ZeroRows,
IsHomalgMatrix and HasPositionOfFirstNonZeroEntryPerColumn and IsSubidentityMatrix and HasNumberRows, 0,
function( M )
local pos;
pos := PositionOfFirstNonZeroEntryPerColumn( M );
return Filtered( [ 1 .. NumberRows( M ) ], i -> not i in pos );
end );
##
InstallImmediateMethod( ZeroRows,
IsHomalgMatrix and HasEvalCertainRows, 0,
function( M )
local e;
e := EvalCertainRows( M );
if not HasZeroRows( e[1] ) then
TryNextMethod( );
fi;
return SortedList( List( Intersection2( ZeroRows( e[1] ), e[2] ), i -> Position( e[2], i ) ) );
end );
##
InstallImmediateMethod( ZeroColumns,
IsHomalgMatrix and HasIsZero and HasNumberColumns, 0,
function( M )
if not IsZero( M ) and NumberColumns( M ) = 1 then
return [ ];
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( ZeroColumns,
IsHomalgMatrix and IsOne, 0,
function( M )
return [ ];
end );
##
InstallImmediateMethod( ZeroColumns,
IsHomalgMatrix and IsZero and HasNumberColumns, 0,
function( M )
return [ 1 .. NumberColumns( M ) ];
end );
##
InstallImmediateMethod( ZeroColumns,
IsHomalgMatrix and HasPositionOfFirstNonZeroEntryPerColumn and HasNumberColumns, 0,
function( M )
local pos;
pos := PositionOfFirstNonZeroEntryPerColumn( M );
return Filtered( [ 1 .. NumberColumns( M ) ], i -> pos[i] = 0 );
end );
##
InstallImmediateMethod( ZeroColumns,
IsHomalgMatrix and HasPositionOfFirstNonZeroEntryPerRow and IsSubidentityMatrix and HasNumberColumns, 0,
function( M )
local pos;
pos := PositionOfFirstNonZeroEntryPerRow( M );
return Filtered( [ 1 .. NumberColumns( M ) ], i -> not i in pos );
end );
##
InstallImmediateMethod( ZeroColumns,
IsHomalgMatrix and HasEvalCertainColumns, 0,
function( M )
local e;
e := EvalCertainColumns( M );
if not HasZeroColumns( e[1] ) then
TryNextMethod( );
fi;
return SortedList( List( Intersection2( ZeroColumns( e[1] ), e[2] ), i -> Position( e[2], i ) ) );
end );
##
InstallImmediateMethod( NonZeroRows,
IsHomalgMatrix and HasZeroRows and HasNumberRows, 0,
function( M )
return Filtered( [ 1 .. NumberRows( M ) ], a -> not a in ZeroRows( M ) );
end );
##
InstallImmediateMethod( NonZeroRows,
IsHomalgMatrix and IsOne and HasNumberRows, 0,
function( M )
return [ 1 .. NumberRows( M ) ];
end );
##
InstallImmediateMethod( NonZeroRows,
IsHomalgMatrix and IsZero, 0,
function( M )
return [ ];
end );
##
InstallImmediateMethod( NonZeroColumns,
IsHomalgMatrix and HasZeroColumns and HasNumberColumns, 0,
function( M )
return Filtered( [ 1 .. NumberColumns( M ) ], a -> not a in ZeroColumns( M ) );
end );
##
InstallImmediateMethod( NonZeroColumns,
IsHomalgMatrix and IsOne and HasNumberColumns, 0,
function( M )
return [ 1 .. NumberColumns( M ) ];
end );
##
InstallImmediateMethod( NonZeroColumns,
IsHomalgMatrix and IsZero, 0,
function( M )
return [ ];
end );
##
InstallImmediateMethod( PositionOfFirstNonZeroEntryPerRow,
IsHomalgMatrix and IsOne and HasNumberRows, 0,
function( M )
if not ( HasIsZero( M ) and IsZero( M ) ) then
return [ 1 .. NumberRows( M ) ];
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( PositionOfFirstNonZeroEntryPerRow,
IsHomalgMatrix and IsZero and HasNumberRows, 0,
function( M )
return ListWithIdenticalEntries( NumberRows( M ), 0 );
end );
##
InstallImmediateMethod( PositionOfFirstNonZeroEntryPerColumn,
IsHomalgMatrix and IsOne and HasNumberColumns, 0,
function( M )
if not ( HasIsZero( M ) and IsZero( M ) ) then
return [ 1 .. NumberColumns( M ) ];
fi;
TryNextMethod( );
end );
##
InstallImmediateMethod( PositionOfFirstNonZeroEntryPerColumn,
IsHomalgMatrix and IsZero and HasNumberColumns, 0,
function( M )
return ListWithIdenticalEntries( NumberColumns( M ), 0 );
end );
####################################
#
# methods for attributes:
#
####################################
#-----------------------------------
# RowRankOfMatrix
#-----------------------------------
##
InstallMethod( RowRankOfMatrix,
"LIMAT: for homalg matrices",
[ IsHomalgMatrix ],
function( M )
local R, B;
R := HomalgRing( M );
if HasIsDivisionRingForHomalg( R ) and
IsDivisionRingForHomalg( R ) then
return Length( NonZeroRows( BasisOfRows( M ) ) );
fi;
TryNextMethod( );
end );
##
InstallMethod( RowRankOfMatrix,
"LIMAT: for homalg matrices",
[ IsHomalgMatrix ],
function( M )
local RP, B;
RP := homalgTable( HomalgRing( M ) );
if IsBound( RP!.RowRankOfMatrix ) then
return RP!.RowRankOfMatrix( M );
elif IsBound( RP!.RowEchelonForm ) then
B := RP!.RowEchelonForm( M );
if HasRowRankOfMatrix( B ) then
return RowRankOfMatrix( B );
fi;
elif IsBound( RP!.ReducedRowEchelonForm ) then
B := RP!.ReducedRowEchelonForm( M );
if HasRowRankOfMatrix( B ) then
return RowRankOfMatrix( B );
fi;
else
BasisOfRowModule( M );
if HasRowRankOfMatrix( M ) then
return RowRankOfMatrix( M );
fi;
fi;
TryNextMethod( );
end );
#-----------------------------------
# ColumnRankOfMatrix
#-----------------------------------
##
InstallMethod( ColumnRankOfMatrix,
"LIMAT: for homalg matrices",
[ IsHomalgMatrix ],
function( M )
local R, B;
R := HomalgRing( M );
if HasIsDivisionRingForHomalg( R ) and
IsDivisionRingForHomalg( R ) then
return Length( NonZeroColumns( BasisOfColumns( M ) ) );
fi;
TryNextMethod( );
end );
##
InstallMethod( ColumnRankOfMatrix,
"LIMAT: for homalg matrices",
[ IsHomalgMatrix ],
function( M )
local RP, B, N;
RP := homalgTable( HomalgRing( M ) );
if IsBound( RP!.ColumnRankOfMatrix ) then
return RP!.ColumnRankOfMatrix( M );
elif IsBound( RP!.RowRankOfMatrix ) then
return RP!.RowRankOfMatrix( Involution( M ) ); ## in most cases Involution is obsolete
elif IsBound( RP!.ColumnEchelonForm ) then
B := RP!.ColumnEchelonForm( M );
if HasColumnRankOfMatrix( B ) then
return ColumnRankOfMatrix( B );
fi;
elif IsBound( RP!.ReducedColumnEchelonForm ) then
B := RP!.ReducedColumnEchelonForm( M );
if HasColumnRankOfMatrix( B ) then
return ColumnRankOfMatrix( B );
fi;
elif IsBound( RP!.ReducedRowEchelonForm ) then
N := Involution( M );
B := RP!.ReducedRowEchelonForm( N );
if HasRowRankOfMatrix( B ) then
return RowRankOfMatrix( B );
fi;
elif IsBound( RP!.RowEchelonForm ) then
N := Involution( M );
B := RP!.RowEchelonForm( N );
if HasRowRankOfMatrix( B ) then
return RowRankOfMatrix( B );
fi;
else
BasisOfColumnModule( M );
if HasColumnRankOfMatrix( M ) then
return ColumnRankOfMatrix( M );
fi;
fi;
TryNextMethod( );
end );
##
InstallMethod( IndicatorMatrixOfNonZeroEntries,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
function( mat )
local result;
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IndicatorMatrixOfNonZeroEntries(IsZero(Matrix))", "\033[0m" );
result := ListWithIdenticalEntries( NumberColumns( mat ), 0 );
result := List( [ 1 .. NumberRows( mat ) ], a -> ShallowCopy( result ) );
return result;
end );
##
InstallMethod( IndicatorMatrixOfNonZeroEntries,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( mat )
local result, i;
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IndicatorMatrixOfNonZeroEntries(IsOne(Matrix))", "\033[0m" );
result := ListWithIdenticalEntries( NumberColumns( mat ), 0 );
result := List( [ 1 .. NumberRows( mat ) ], a -> ShallowCopy( result ) );
for i in [ 1 .. NumberRows( mat ) ] do
result[i][i] := 1;
od;
return result;
end );
####################################
#
# methods for properties:
#
####################################
##
InstallMethod( IsEmptyMatrix,
"LIMAT: for homalg matrices",
[ IsHomalgMatrix ],
function( M )
return NumberRows( M ) = 0 or NumberColumns( M ) = 0;
end );
##
InstallMethod( IsRightRegular,
"LIMAT: for homalg matrices",
[ IsHomalgMatrix ],
function( M )
return NumberColumns( SyzygiesGeneratorsOfColumns( M ) ) = 0;
end );
##
InstallMethod( IsLeftRegular,
"LIMAT: for homalg matrices",
[ IsHomalgMatrix ],
function( M )
return NumberRows( SyzygiesGeneratorsOfRows( M ) ) = 0;
end );
##
InstallMethod( IsSpecialSubidentityMatrix,
"LIMAT: for homalg matrices",
[ IsHomalgMatrix ],
function( M )
local r, c, nz, l;
r := NumberRows( M );
c := NumberColumns( M );
if r = 0 or c = 0 then
return true;
elif r = c then
return IsOne( M );
elif r < c then
nz := NonZeroColumns( M );
l := Length( nz );
if not ( l = 0 or l <> r or nz <> [ nz[1] .. nz[l] ] ) then
l := IsOne( CertainColumns( M, nz ) );
if l then
SetZeroRows( M, [ ] );
return true;
fi;
fi;
else
nz := NonZeroRows( M );
l := Length( nz );
if not ( l = 0 or l <> r or nz <> [ nz[1] .. nz[l] ] ) then
l := IsOne( CertainRows( M, nz ) );
if l then
SetZeroColumns( M, [ ] );
return true;
fi;
fi;
fi;
return false;
end );
##
InstallMethod( IsUnitFree,
"LIMAT: for homalg matrices",
[ IsHomalgMatrix ],
function( M )
return GetUnitPosition( M ) = fail;
end );
####################################
#
# methods for operations:
#
####################################
#-----------------------------------
# \=
#-----------------------------------
##
InstallMethod( \=,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero, IsHomalgMatrix and IsZero ],
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( \=,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne, IsHomalgMatrix and IsOne ],
function( M1, M2 )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsOne(Matrix) = IsOne(Matrix)", "\033[0m" );
return AreComparableMatrices( M1, M2 );
end );
#-----------------------------------
# Involution
#-----------------------------------
##
InstallMethod( Involution,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "Involution( IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( NumberColumns( M ), NumberRows( M ), HomalgRing( M ) );
end );
##
InstallMethod( Involution,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "Involution( IsOne(Matrix) )", "\033[0m" );
return M;
end );
#-----------------------------------
# TransposedMatrix
#-----------------------------------
##
InstallMethod( TransposedMatrix,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "TransposedMatrix( IsZero(Matrix) )", "\033[0m" );
return HomalgZeroMatrix( NumberColumns( M ), NumberRows( M ), HomalgRing( M ) );
end );
##
InstallMethod( TransposedMatrix,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "TransposedMatrix( IsOne(Matrix) )", "\033[0m" );
return M;
end );
#-----------------------------------
# CertainRows
#-----------------------------------
##
InstallMethod( CertainRows,
"LIMAT: for homalg matrices (check input and trivial cases)",
[ IsHomalgMatrix, IsList ], 10001,
function( M, plist )
if not IsSubset( [ 1 .. NumberRows( M ) ], plist ) then
Error( "the list of row positions ", plist, " must be in the range [ 1 .. ", NumberRows( M ), " ]\n" );
fi;
if NumberRows( M ) = 0 or plist = [ 1 .. NumberRows( M ) ] then
return M;
elif plist = [ ] then
return HomalgZeroMatrix( 0, NumberColumns( M ), HomalgRing( M ) );
fi;
TryNextMethod( );
end );
#-----------------------------------
# CertainColumns
#-----------------------------------
##
InstallMethod( CertainColumns,
"LIMAT: for homalg matrices (check input and trivial cases)",
[ IsHomalgMatrix, IsList ], 10001,
function( M, plist )
if not IsSubset( [ 1 .. NumberColumns( M ) ], plist ) then
Error( "the list of column positions ", plist, " must be in the range [ 1 .. ", NumberColumns( M ), " ]\n" );
fi;
if NumberColumns( M ) = 0 or plist = [ 1 .. NumberColumns( M ) ] then
return M;
elif plist = [ ] then
return HomalgZeroMatrix( NumberRows( M ), 0, HomalgRing( M ) );
fi;
TryNextMethod( );
end );
#-----------------------------------
# UnionOfRows
#-----------------------------------
##
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 );
#-----------------------------------
# UnionOfColumns
#-----------------------------------
##
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 );
#-----------------------------------
# DiagMat
#-----------------------------------
##
InstallMethod( DiagMat,
"LIMAT: of a homalg ring and a list of homalg matrices (check input)",
[ IsHomalgRing, IsHomogeneousList ], 10001,
function( R, l )
if not ForAll( l, IsHomalgMatrix ) then
Error( "at least one of the matrices in the list is not a homalg matrix\n" );
fi;
if Length( l ) = 1 then
return l[1];
fi;
if not ForAll( l, a -> IsIdenticalObj( HomalgRing( a ), R ) ) then
Error( "the matrices are not defined over identically the same ring\n" );
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, HasIsOne and IsOne ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DiagMat( [ identity matrices ] )", "\033[0m" );
return HomalgIdentityMatrix( Sum( List( l, NumberRows ) ), Sum( List( l, NumberColumns ) ), R );
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 IsZero ) 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 );
#-----------------------------------
# KroneckerMat
#-----------------------------------
##
InstallMethod( KroneckerMat,
"LIMAT: for homalg matrices (check input)",
[ IsHomalgMatrix, IsHomalgMatrix ], 10001,
function( A, B )
if not IsIdenticalObj( HomalgRing( A ), HomalgRing( B ) ) then
Error( "the two matrices are not defined over identically the same ring\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( KroneckerMat,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne, IsHomalgMatrix ],
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "KroneckerMat( IsOne(Matrix), IsHomalgMatrix )", "\033[0m" );
return DiagMat( HomalgRing( A ), ListWithIdenticalEntries( NumberRows( A ), B ) );
end );
##
InstallMethod( KroneckerMat,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero, 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 (IsOne)",
[ IsHomalgMatrix, IsHomalgMatrix and IsOne ],
function( A, B )
local R;
R := HomalgRing( A );
if ( HasNumberRows( B ) and NumberRows( B ) = 1 )
or ( HasNumberColumns( B ) and NumberColumns( B ) = 1 ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "KroneckerMat( IsHomalgMatrix, (1) )", "\033[0m" );
return A;
fi;
TryNextMethod( );
end );
##
InstallMethod( KroneckerMat,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix, IsHomalgMatrix and IsZero ],
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 );
#-----------------------------------
# DualKroneckerMat
#-----------------------------------
##
InstallMethod( DualKroneckerMat,
"LIMAT: for homalg matrices (check input)",
[ IsHomalgMatrix, IsHomalgMatrix ], 10001,
function( A, B )
if not IsIdenticalObj( HomalgRing( A ), HomalgRing( B ) ) then
Error( "the two matrices are not defined over identically the same ring\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( DualKroneckerMat,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne, IsHomalgMatrix ],
function( A, B )
local R;
R := HomalgRing( A );
if ( HasNumberRows( A ) and NumberRows( A ) = 1 )
or ( HasNumberColumns( A ) and NumberColumns( A ) = 1 ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DualKroneckerMat( (1), IsHomalgMatrix )", "\033[0m" );
return B;
fi;
TryNextMethod( );
end );
##
InstallMethod( DualKroneckerMat,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero, 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 (IsOne)",
[ IsHomalgMatrix, IsHomalgMatrix and IsOne ],
function( A, B )
local R;
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "DualKroneckerMat( IsHomalgMatrix, IsOne(Matrix) )", "\033[0m" );
return DiagMat( HomalgRing( A ), ListWithIdenticalEntries( NumberRows( B ), A ) );
end );
##
InstallMethod( DualKroneckerMat,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix, IsHomalgMatrix and IsZero ],
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 );
#-----------------------------------
# MulMatRight
#-----------------------------------
##
InstallMethod( \*,
"LIMAT: for a homalg matrix and a ring element (check input)",
[ IsHomalgMatrix, IsHomalgRingElement ], 12001,
function( A, a )
local R;
R := HomalgRing( a );
if R <> fail and not IsIdenticalObj( R, HomalgRing( A ) ) then
Error( "the ring element and the matrix are not defined over identically the same ring\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( \*,
"LIMAT: for homalg matrices with ring elements",
[ IsHomalgMatrix, IsRingElement and IsZero ], 10001,
function( A, a )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsHomalgMatrix * IsZero", "\033[0m" );
return HomalgZeroMatrix( NumberRows( A ), NumberColumns( A ), HomalgRing( A ) );
end );
##
InstallMethod( \*,
"LIMAT: for homalg matrices with ring elements",
[ IsHomalgMatrix, IsRingElement and IsOne ], 10001,
function( A, a )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsHomalgMatrix * IsOne(Matrix)", "\033[0m" );
return A;
end );
##
InstallMethod( \*,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero, IsRingElement ], 10001,
function( A, a )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsZero(Matrix) * IsRingElement", "\033[0m" );
return A;
end );
#-----------------------------------
# MulMat
#-----------------------------------
##
InstallMethod( \*,
"LIMAT: for a ring element and a homalg matrix (check input)",
[ IsHomalgRingElement, IsHomalgMatrix ], 12001,
function( a, A )
local R;
R := HomalgRing( a );
if R <> fail and not IsIdenticalObj( R, HomalgRing( A ) ) then
Error( "the ring element and the matrix are not defined over identically the same ring\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( \*,
"LIMAT: for homalg matrices with ring elements",
[ IsRingElement and IsZero, IsHomalgMatrix ], 10001,
function( a, A )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsZero * IsHomalgMatrix", "\033[0m" );
return HomalgZeroMatrix( NumberRows( A ), NumberColumns( A ), HomalgRing( A ) );
end );
##
InstallMethod( \*,
"LIMAT: for homalg matrices with ring elements",
[ IsRingElement and IsOne, IsHomalgMatrix ], 10001,
function( a, A )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsOne(Matrix) * IsHomalgMatrix", "\033[0m" );
return A;
end );
##
InstallMethod( \*,
"LIMAT: for homalg matrices (IsZero)",
[ IsRingElement, IsHomalgMatrix and IsZero ], 10001,
function( a, A )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsRingElement * IsZero(Matrix)", "\033[0m" );
return A;
end );
#-----------------------------------
# AddMat
#-----------------------------------
##
InstallMethod( \+,
"LIMAT: for two homalg matrices (check input)",
[ IsHomalgMatrix, IsHomalgMatrix ], 10001,
function( A, B )
if not IsIdenticalObj( HomalgRing( A ), HomalgRing( B ) ) then
Error( "the two matrices are not defined over identically the same ring\n" );
fi;
if NumberRows( A ) <> NumberRows( B ) then
Error( "the two matrices are not summable, since the first one has ", NumberRows( A ), " row(s), while the second ", NumberRows( B ), "\n" );
fi;
if NumberColumns( A ) <> NumberColumns( B ) then
Error( "the two matrices are not summable, since the first one has ", NumberColumns( A ), " column(s), while the second ", NumberColumns( B ), "\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( \+,
"LIMAT: for two homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero, 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 (IsZero)",
[ IsHomalgMatrix, IsHomalgMatrix and IsZero ],
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 );
#-----------------------------------
# AdditiveInverseMutable
#-----------------------------------
## a synonym of `-<elm>':
InstallMethod( AdditiveInverseMutable,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
function( A )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "-IsZero(Matrix)", "\033[0m" );
return A;
end );
#-----------------------------------
# SubMat
#-----------------------------------
##
InstallMethod( \-,
"LIMAT: for two homalg matrices (check input)",
[ IsHomalgMatrix, IsHomalgMatrix ], 10001,
function( A, B )
if not IsIdenticalObj( HomalgRing( A ), HomalgRing( B ) ) then
Error( "the two matrices are not defined over identically the same ring\n" );
fi;
if NumberRows( A ) <> NumberRows( B ) then
Error( "the two matrices are not subtractable, since the first one has ", NumberRows( A ), " row(s), while the second ", NumberRows( B ), "\n" );
fi;
if NumberColumns( A ) <> NumberColumns( B ) then
Error( "the two matrices are not subtractable, since the first one has ", NumberColumns( A ), " column(s), while the second ", NumberColumns( B ), "\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( \-,
"LIMAT: for two homalg matrices",
[ IsHomalgMatrix, IsHomalgMatrix ], 1000,
function( A, B )
if IsIdenticalObj( A, B ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "M - M", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ) );
return 0 * A;
fi;
TryNextMethod( );
end );
##
InstallMethod( \-,
"LIMAT: for two homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero, 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 (IsZero)",
[ IsHomalgMatrix, IsHomalgMatrix and IsZero ],
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 );
#-----------------------------------
# Compose
#-----------------------------------
##
InstallMethod( \*,
"LIMAT: for two homalg matrices (check input)",
[ IsHomalgMatrix, IsHomalgMatrix ], 20001,
function( A, B )
if not IsIdenticalObj( HomalgRing( A ), HomalgRing( B ) ) then
Error( "the two matrices are not defined over identically the same ring\n" );
fi;
if NumberColumns( A ) <> NumberRows( B ) then
Error( "the two matrices are not composable, since the first one has ", NumberColumns( A ), " column(s), while the second ", NumberRows( B ), " row(s)\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( \*,
"LIMAT: for two homalg matrices (IsSubidentityMatrix)",
[ IsHomalgMatrix and IsSubidentityMatrix and HasEvalCertainRows and IsRightInvertibleMatrix, IsHomalgMatrix ], 16001,
function( A, B )
local id;
id := EvalCertainRows( A )[1];
if not ( HasIsOne( id ) and IsOne( id ) ) then
TryNextMethod( );
fi;
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "CertainRows(IsOne(Matrix)) * IsHomalgMatrix", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ), " x ", NumberColumns( B ) );
return CertainRows( B, EvalCertainRows( A )[2] );
end );
##
InstallMethod( \*,
"LIMAT: for two homalg matrices (IsSubidentityMatrix)",
[ IsHomalgMatrix, IsHomalgMatrix and IsSubidentityMatrix and HasEvalCertainColumns and IsLeftInvertibleMatrix ], 16001,
function( A, B )
local id;
id := EvalCertainColumns( B )[1];
if not ( HasIsOne( id ) and IsOne( id ) ) then
TryNextMethod( );
fi;
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsHomalgMatrix * CertainColumns(IsOne(Matrix))", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ), " x ", NumberColumns( B ) );
return CertainColumns( A, EvalCertainColumns( B )[2] );
end );
##
InstallMethod( \*,
"LIMAT: for two homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne, IsHomalgMatrix ], 17001,
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsOne(Matrix) * IsHomalgMatrix", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ), " x ", NumberColumns( B ) );
return B;
end );
##
InstallMethod( \*,
"LIMAT: for two homalg matrices (IsOne)",
[ IsHomalgMatrix, IsHomalgMatrix and IsOne ], 17001,
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "IsHomalgMatrix * IsOne(Matrix)", "\033[0m", " ", NumberRows( A ), " x ", NumberColumns( A ), " x ", NumberColumns( B ) );
return A;
end );
##
InstallMethod( \*,
"LIMAT: for two homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero, 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 (IsZero)",
[ IsHomalgMatrix, IsHomalgMatrix and IsZero ], 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 );
#-----------------------------------
# RightDivide
#-----------------------------------
##
InstallMethod( RightDivide,
"LIMAT: for homalg matrices (check input)",
[ IsHomalgMatrix, IsHomalgMatrix ], 10001,
function( B, A )
if NumberColumns( A ) <> NumberColumns( B ) then
Error( "the first and the second matrix must have the same number of columns\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( RightDivide,
"LIMAT: for homalg matrices (IsIdenticalObj)",
[ IsHomalgMatrix, IsHomalgMatrix ],
function( B, A )
if IsIdenticalObj( B, A ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RightDivide( A, A )", "\033[0m" );
return HomalgIdentityMatrix( NumberRows( A ), HomalgRing( A ) );
fi;
TryNextMethod( );
end );
##
InstallMethod( RightDivide,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix, IsHomalgMatrix and IsOne ],
function( B, A )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RightDivide( IsHomalgMatrix, IsOne(Matrix) )", "\033[0m" );
return B;
end );
##
InstallMethod( RightDivide,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero, 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 (check input)",
[ IsHomalgMatrix, IsHomalgMatrix, IsHomalgMatrix ], 10001,
function( B, A, L )
if NumberColumns( A ) <> NumberColumns( B ) then
Error( "the first and the second matrix must have the same number of columns\n" );
fi;
if NumberColumns( A ) <> NumberColumns( L ) then
Error( "the first and the third matrix must have the same number of columns\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( RightDivide,
"LIMAT: for homalg matrices (IsIdenticalObj)",
[ IsHomalgMatrix, IsHomalgMatrix, IsHomalgMatrix ],
function( B, A, L )
if IsIdenticalObj( B, A ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RightDivide( A, A, IsHomalgMatrix )", "\033[0m" );
return HomalgIdentityMatrix( NumberRows( A ), HomalgRing( A ) );
fi;
TryNextMethod( );
end );
##
InstallMethod( RightDivide,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix, IsHomalgMatrix and IsOne, IsHomalgMatrix ],
function( B, A, L )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RightDivide( IsHomalgMatrix, IsOne(Matrix), IsHomalgMatrix )", "\033[0m" );
return B;
end );
##
InstallMethod( RightDivide,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero, 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 );
#-----------------------------------
# LeftDivide
#-----------------------------------
##
InstallMethod( LeftDivide,
"LIMAT: for homalg matrices (check input)",
[ IsHomalgMatrix, IsHomalgMatrix ], 10001,
function( A, B )
if NumberRows( A ) <> NumberRows( B ) then
Error( "the first and the second matrix must have the same number of rows\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( LeftDivide,
"LIMAT: for homalg matrices (IsIdenticalObj)",
[ IsHomalgMatrix, IsHomalgMatrix ],
function( A, B )
if IsIdenticalObj( A, B ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "LeftDivide( A, A )", "\033[0m" );
return HomalgIdentityMatrix( NumberColumns( A ), HomalgRing( A ) );
fi;
TryNextMethod( );
end );
##
InstallMethod( LeftDivide,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne, IsHomalgMatrix ],
function( A, B )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "LeftDivide( IsOne(Matrix), IsHomalgMatrix )", "\033[0m" );
return B;
end );
##
InstallMethod( LeftDivide,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix, IsHomalgMatrix and IsZero ],
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 (check input)",
[ IsHomalgMatrix, IsHomalgMatrix, IsHomalgMatrix ], 10001,
function( A, B, L )
if NumberRows( A ) <> NumberRows( B ) then
Error( "the first and the second matrix must have the same number of rows\n" );
fi;
if NumberRows( A ) <> NumberRows( L ) then
Error( "the first and the third matrix must have the same number of rows\n" );
fi;
TryNextMethod( );
end );
##
InstallMethod( LeftDivide,
"LIMAT: for homalg matrices (IsIdenticalObj)",
[ IsHomalgMatrix, IsHomalgMatrix, IsHomalgMatrix ],
function( A, B, L )
if IsIdenticalObj( A, B ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "LeftDivide( A, A, IsHomalgMatrix )", "\033[0m" );
return HomalgIdentityMatrix( NumberColumns( A ), HomalgRing( A ) );
fi;
TryNextMethod( );
end );
##
InstallMethod( LeftDivide,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne, IsHomalgMatrix, IsHomalgMatrix ],
function( A, B, L )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "LeftDivide( IsOne(Matrix), IsHomalgMatrix, IsHomalgMatrix )", "\033[0m" );
return B;
end );
##
InstallMethod( LeftDivide,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix, IsHomalgMatrix and IsZero, 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 );
#-----------------------------------
# LeftInverse
#-----------------------------------
##
InstallMethod( LeftInverse,
"LIMAT: for homalg matrices (check input)",
[ IsHomalgMatrix ], 10001,
function( M )
if NumberRows( M ) < NumberColumns( M ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "LeftInverse( NumberRows < NumberColumns )", "\033[0m" );
return false;
fi;
TryNextMethod( );
end );
##
InstallMethod( LeftInverse,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "LeftInverse( IsOne(Matrix) )", "\033[0m" );
return M;
end );
##
InstallMethod( LeftInverse,
"LIMAT: for homalg matrices (IsSubidentityMatrix)",
[ IsHomalgMatrix and IsSubidentityMatrix and HasEvalCertainColumns ],
function( M )
local C;
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "LeftInverse( CertainColumns(IsOne(Matrix)) )", "\033[0m" );
## the consistency test is performed by a high rank method above
C := EvalCertainColumns( M );
C := CertainRows( Involution( C[1] ), C[2] ); ## Involution( Id ) = Id;
SetRightInverse( M, C );
return C;
end );
##
InstallMethod( LeftInverse,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
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 );
#-----------------------------------
# RightInverse
#-----------------------------------
##
InstallMethod( RightInverse,
"LIMAT: for homalg matrices (check input)",
[ IsHomalgMatrix ], 10001,
function( M )
if NumberColumns( M ) < NumberRows( M ) then
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RightInverse( NumberColumns < NumberRows )", "\033[0m" );
return false;
fi;
TryNextMethod( );
end );
##
InstallMethod( RightInverse,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RightInverse( IsOne(Matrix) )", "\033[0m" );
return M;
end );
##
InstallMethod( RightInverse,
"LIMAT: for homalg matrices (IsSubidentityMatrix)",
[ IsHomalgMatrix and IsSubidentityMatrix and HasEvalCertainRows ],
function( M )
local C;
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RightInverse( CertainRows(IsOne(Matrix)) )", "\033[0m" );
## the consistency test is performed by a high rank method above
C := EvalCertainRows( M );
C := CertainColumns( Involution( C[1] ), C[2] ); ## Involution( Id ) = Id;
SetLeftInverse( M, C );
return C;
end );
##
InstallMethod( RightInverse,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
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 );
#-----------------------------------
# RowRankOfMatrix
#-----------------------------------
##
InstallMethod( RowRankOfMatrix, ## FIXME: make an extra InstallImmediateMethod when NonZeroRows( M ) is set
"LIMAT: for homalg matrices (IsUpperStairCaseMatrix)",
[ IsHomalgMatrix and IsUpperStairCaseMatrix ],
function( M )
local R;
R := HomalgRing( M );
if not ( HasIsIntegralDomain( R ) and IsIntegralDomain( R ) ) then
TryNextMethod( );
fi;
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RowRankOfMatrix( IsTriangularMatrix over domain )", "\033[0m" );
return Length( NonZeroRows( M ) );
end );
#-----------------------------------
# ColumnRankOfMatrix
#-----------------------------------
##
InstallMethod( ColumnRankOfMatrix, ## FIXME: make an extra InstallImmediateMethod when NonZeroColumns( M ) is set
"LIMAT: for homalg matrices (IsLowerStairCaseMatrix)",
[ IsHomalgMatrix and IsLowerStairCaseMatrix ],
function( M )
local R;
R := HomalgRing( M );
if not ( HasIsIntegralDomain( R ) and IsIntegralDomain( R ) ) then
TryNextMethod( );
fi;
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ColumnRankOfMatrix( IsTriangularMatrix over domain )", "\033[0m" );
return Length( NonZeroColumns( M ) );
end );
#-----------------------------------
# RowEchelonForm
#-----------------------------------
##
InstallMethod( RowEchelonForm,
"LIMAT: for homalg matrices (IsBasisOfRowsMatrix)",
[ IsHomalgMatrix and IsBasisOfRowsMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RowEchelonForm( IsBasisOfRowsMatrix )", "\033[0m" );
return M;
end );
##
InstallMethod( RowEchelonForm,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RowEchelonForm( IsOne(Matrix) )", "\033[0m" );
return M;
end );
##
InstallMethod( RowEchelonForm,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "RowEchelonForm( IsZero(Matrix) )", "\033[0m" );
return M;
end );
#-----------------------------------
# ColumnEchelonForm
#-----------------------------------
##
InstallMethod( ColumnEchelonForm,
"LIMAT: for homalg matrices (IsBasisOfColumnsMatrix)",
[ IsHomalgMatrix and IsBasisOfColumnsMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ColumnEchelonForm( IsBasisOfColumnsMatrix )", "\033[0m" );
return M;
end );
##
InstallMethod( ColumnEchelonForm,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ColumnEchelonForm( IsOne(Matrix) )", "\033[0m" );
return M;
end );
##
InstallMethod( ColumnEchelonForm,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ColumnEchelonForm( IsZero(Matrix) )", "\033[0m" );
return M;
end );
#-----------------------------------
# ReducedRowEchelonForm
#-----------------------------------
##
InstallMethod( ReducedRowEchelonForm,
"LIMAT: for homalg matrices (IsReducedBasisOfRowsMatrix)",
[ IsHomalgMatrix and IsReducedBasisOfRowsMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedRowEchelonForm( IsReducedBasisOfRowsMatrix )", "\033[0m" );
return M;
end );
##
InstallMethod( ReducedRowEchelonForm,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedRowEchelonForm( IsOne(Matrix) )", "\033[0m" );
return M;
end );
##
InstallMethod( ReducedRowEchelonForm,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedRowEchelonForm( IsZero(Matrix) )", "\033[0m" );
return M;
end );
#-----------------------------------
# ReducedColumnEchelonForm
#-----------------------------------
##
InstallMethod( ReducedColumnEchelonForm,
"LIMAT: for homalg matrices (IsReducedBasisOfColumnsMatrix)",
[ IsHomalgMatrix and IsReducedBasisOfColumnsMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedColumnEchelonForm( IsReducedBasisOfColumnsMatrix )", "\033[0m" );
return M;
end );
##
InstallMethod( ReducedColumnEchelonForm,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedColumnEchelonForm( IsOne(Matrix) )", "\033[0m" );
return M;
end );
##
InstallMethod( ReducedColumnEchelonForm,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedColumnEchelonForm( IsZero(Matrix) )", "\033[0m" );
return M;
end );
#-----------------------------------
# BasisOfRowModule
#-----------------------------------
##
InstallMethod( BasisOfRowModule,
"LIMAT: for homalg matrices (IsBasisOfRowsMatrix)",
[ IsHomalgMatrix and IsBasisOfRowsMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "BasisOfRowModule( IsBasisOfRowsMatrix )", "\033[0m" );
return M;
end );
##
InstallMethod( BasisOfRowModule,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "BasisOfRowModule( IsOne(Matrix) )", "\033[0m" );
return M;
end );
##
InstallMethod( BasisOfRowModule,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
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 );
#-----------------------------------
# BasisOfColumnModule
#-----------------------------------
##
InstallMethod( BasisOfColumnModule,
"LIMAT: for homalg matrices (IsBasisOfColumnsMatrix)",
[ IsHomalgMatrix and IsBasisOfColumnsMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "BasisOfColumnModule( IsBasisOfColumnsMatrix )", "\033[0m" );
return M;
end );
##
InstallMethod( BasisOfColumnModule,
"LIMAT: for homalg matrices (IsOne)",
[ IsHomalgMatrix and IsOne ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "BasisOfColumnModule( IsOne(Matrix) )", "\033[0m" );
return M;
end );
##
InstallMethod( BasisOfColumnModule,
"LIMAT: for homalg matrices (IsZero)",
[ IsHomalgMatrix and IsZero ],
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 );
#-----------------------------------
# ReducedBasisOfRowModule
#-----------------------------------
##
InstallMethod( ReducedBasisOfRowModule,
"LIMAT: for homalg matrices (IsReducedBasisOfRowsMatrix)",
[ IsHomalgMatrix and IsReducedBasisOfRowsMatrix ],
function( M )
Info( InfoLIMAT, 2, LIMAT.color, "\033[01mLIMAT\033[0m ", LIMAT.color, "ReducedBasisOfRowModule( IsReducedBasisOfRowsMatrix )", "\033[0m" );
return M;
end );
##
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