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Quelle OscarBasic.gi
Sprache: unbekannt
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# SPDX-License-Identifier: GPL-2.0-or-later
# RingsForHomalg: Dictionaries of external rings
#
# Implementations
#
####################################
#
# global variables:
#
####################################
BindGlobal( "CommonHomalgTableForOscarBasic",
rec(
## Must only then be provided by the RingPackage in case the default
## "service" function does not match the Ring
RowEchelonForm :=
function( M )
local ignore, N;
ignore := ValueOption( "ignore" );
if not IsInt( ignore ) then
ignore := 0;
fi;
N := HomalgVoidMatrix(
"unknown_number_of_rows",
NumberColumns( M ),
HomalgRing( M )
);
homalgSendBlocking(
[ N, " = RowEchelonForm(", M, "; ignore = ", ignore, ")" ],
"need_command",
"ReducedEchelonForm"
);
return N;
end,
ColumnEchelonForm :=
function( M )
local N;
N := HomalgVoidMatrix(
NumberRows( M ),
"unknown_number_of_rows",
HomalgRing( M )
);
homalgSendBlocking(
[ N, " = ColumnEchelonForm(", M, ")" ],
"need_command",
"ReducedEchelonForm"
);
return N;
end,
ReducedRowEchelonForm :=
function( arg )
local M, R, nargs, N, T;
M := arg[1];
R := HomalgRing( M );
nargs := Length( arg );
N := HomalgVoidMatrix( "unknown_number_of_rows", NumberColumns( M ), R );
if nargs > 1 and IsHomalgMatrix( arg[2] ) then
T := arg[2];
homalgSendBlocking(
[ N, T, " = map(transpose,hnf_with_transform(transpose(", M, ")))" ],
"need_command",
"ReducedEchelonForm"
);
else
homalgSendBlocking(
[ N, " = transpose(hnf(transpose(", M, ")))" ],
"need_command",
"ReducedEchelonForm"
);
fi;
SetIsUpperStairCaseMatrix( N, true );
return N;
end,
ReducedColumnEchelonForm :=
function( arg )
local M, R, nargs, N, T;
M := arg[1];
R := HomalgRing( M );
nargs := Length( arg );
N := HomalgVoidMatrix( NumberRows( M ), "unknown_number_of_rows", R );
if nargs > 1 and IsHomalgMatrix( arg[2] ) then
T := arg[2];
homalgSendBlocking(
[ N, T, " = hnf_with_transform(", M, ")" ],
"need_command",
"ReducedEchelonForm"
);
else
homalgSendBlocking(
[ N, " = hnf(", M, ")" ],
"need_command",
"ReducedEchelonForm"
);
fi;
return N;
end,
## <#GAPDoc Label="BasisOfRowModule:Oscar">
## <ManSection>
## <Func Arg="M" Name="BasisOfRowModule" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="BasisOfRowModule" Label="Oscar macro"/> inside the computer algebra system.
## <Listing Type="Code"><![CDATA[
BasisOfRowModule :=
function( M )
local N;
N := HomalgVoidMatrix(
"unknown_number_of_rows",
NumberColumns( M ),
HomalgRing( M )
);
homalgSendBlocking(
[ N, " = BasisOfRowModule(", M, ")" ],
"need_command",
"BasisOfModule"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="BasisOfColumnModule:Oscar">
## <ManSection>
## <Func Arg="M" Name="BasisOfColumnModule" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="BasisOfColumnModule" Label="Oscar macro"/> inside the computer algebra system.
## <Listing Type="Code"><![CDATA[
BasisOfColumnModule :=
function( M )
local N;
N := HomalgVoidMatrix(
NumberRows( M ),
"unknown_number_of_columns",
HomalgRing( M )
);
homalgSendBlocking(
[ N, " = BasisOfColumnModule(", M, ")" ],
"need_command",
"BasisOfModule"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="BasisOfRowsCoeff:Oscar">
## <ManSection>
## <Func Arg="M, T" Name="BasisOfRowsCoeff" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="BasisOfRowsCoeff" Label="Oscar macro"/> inside the computer algebra system.
## <Listing Type="Code"><![CDATA[
BasisOfRowsCoeff :=
function( M, T )
local N;
N := HomalgVoidMatrix(
"unknown_number_of_rows",
NumberColumns( M ),
HomalgRing( M )
);
homalgSendBlocking(
[ N, T, " = BasisOfRowsCoeff(", M, ")" ],
"need_command",
"BasisCoeff"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="BasisOfColumnsCoeff:Oscar">
## <ManSection>
## <Func Arg="M, T" Name="BasisOfColumnsCoeff" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="BasisOfColumnsCoeff" Label="Oscar macro"/> inside the computer algebra system.
## <Listing Type="Code"><![CDATA[
BasisOfColumnsCoeff :=
function( M, T )
local N;
N := HomalgVoidMatrix(
NumberRows( M ),
"unknown_number_of_columns",
HomalgRing( M )
);
homalgSendBlocking(
[ N, T, " = BasisOfColumnsCoeff(", M, ")" ],
"need_command",
"BasisCoeff"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="DecideZeroRows:Oscar">
## <ManSection>
## <Func Arg="A, B" Name="DecideZeroRows" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="DecideZeroRows" Label="Oscar macro"/> inside the computer algebra system. The rows of <A>B</A> must form a basis (see <Ref Func="BasisOfRowModule" Label="in the homalg table for Oscar"/>).
## <Listing Type="Code"><![CDATA[
DecideZeroRows :=
function( A, B )
local N;
N := HomalgVoidMatrix(
NumberRows( A ),
NumberColumns( A ),
HomalgRing( A )
);
homalgSendBlocking(
[ N, " = DecideZeroRows(", A, B, ")" ],
"need_command",
"DecideZero"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="DecideZeroColumns:Oscar">
## <ManSection>
## <Func Arg="A, B" Name="DecideZeroColumns" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="DecideZeroColumns" Label="Oscar macro"/> inside the computer algebra system. The columns of <A>B</A> must form a basis (see <Ref Func="BasisOfColumnModule" Label="in the homalg table for Oscar"/>).
## <Listing Type="Code"><![CDATA[
DecideZeroColumns :=
function( A, B )
local N;
N := HomalgVoidMatrix(
NumberRows( A ),
NumberColumns( A ),
HomalgRing( A )
);
homalgSendBlocking(
[ N, " = DecideZeroColumns(", A, B, ")" ],
"need_command",
"DecideZero"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="DecideZeroRowsEffectively:Oscar">
## <ManSection>
## <Func Arg="A, B, T" Name="DecideZeroRowsEffectively" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="DecideZeroRowsEffectively" Label="Oscar macro"/> inside the computer algebra system. The rows of <A>B</A> must form a basis (see <Ref Func="BasisOfRowModule" Label="in the homalg table for Oscar"/>).
## <Listing Type="Code"><![CDATA[
DecideZeroRowsEffectively :=
function( A, B, T )
local v, N;
v := homalgStream( HomalgRing( A ) )!.variable_name;
N := HomalgVoidMatrix(
NumberRows( A ),
NumberColumns( A ),
HomalgRing( A )
);
homalgSendBlocking(
[ N, T, " = DecideZeroRowsEffectively(", A, B, ");" ],
"need_command",
"DecideZeroEffectively"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="DecideZeroColumnsEffectively:Oscar">
## <ManSection>
## <Func Arg="A, B, T" Name="DecideZeroColumnsEffectively" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="DecideZeroColumnsEffectively" Label="Oscar macro"/> inside the computer algebra system. The columns of <A>B</A> must form a basis (see <Ref Func="BasisOfColumnModule" Label="in the homalg table for Oscar"/>).
## <Listing Type="Code"><![CDATA[
DecideZeroColumnsEffectively :=
function( A, B, T )
local v, N;
v := homalgStream( HomalgRing( A ) )!.variable_name;
N := HomalgVoidMatrix(
NumberRows( A ),
NumberColumns( A ),
HomalgRing( A )
);
homalgSendBlocking(
[ N, T, " = DecideZeroColumnsEffectively(", A, B, ")" ],
"need_command",
"DecideZeroEffectively"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="SyzygiesGeneratorsOfRows:Oscar">
## <ManSection>
## <Func Arg="M" Name="SyzygiesGeneratorsOfRows" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="SyzygiesGeneratorsOfRows" Label="Oscar macro"/> inside the computer algebra system.
## <Listing Type="Code"><![CDATA[
SyzygiesGeneratorsOfRows :=
function( M )
local N;
N := HomalgVoidMatrix(
"unknown_number_of_rows",
NumberRows( M ),
HomalgRing( M )
);
homalgSendBlocking(
[ N, " = SyzygiesGeneratorsOfRows(", M, ")" ],
"need_command",
"SyzygiesGenerators"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="SyzygiesGeneratorsOfColumns:Oscar">
## <ManSection>
## <Func Arg="M" Name="SyzygiesGeneratorsOfColumns" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="SyzygiesGeneratorsOfColumns" Label="Oscar macro"/> inside the computer algebra system.
## <Listing Type="Code"><![CDATA[
SyzygiesGeneratorsOfColumns :=
function( M )
local N;
N := HomalgVoidMatrix(
NumberColumns( M ),
"unknown_number_of_columns",
HomalgRing( M )
);
homalgSendBlocking(
[ N, " = SyzygiesGeneratorsOfColumns(", M, ")" ],
"need_command",
"SyzygiesGenerators"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="RelativeSyzygiesGeneratorsOfRows:Oscar">
## <ManSection>
## <Func Arg="M, M2" Name="RelativeSyzygiesGeneratorsOfRows" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="RelativeSyzygiesGeneratorsOfRows" Label="Oscar macro"/> inside the computer algebra system.
## <Listing Type="Code"><![CDATA[
RelativeSyzygiesGeneratorsOfRows :=
function( M, M2 )
local N;
N := HomalgVoidMatrix(
"unknown_number_of_rows",
NumberRows( M ),
HomalgRing( M )
);
homalgSendBlocking(
[ N, " = RelativeSyzygiesGeneratorsOfRows(", M, M2, ")" ],
"need_command",
"SyzygiesGenerators"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="RelativeSyzygiesGeneratorsOfColumns:Oscar">
## <ManSection>
## <Func Arg="M, M2" Name="RelativeSyzygiesGeneratorsOfColumns" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="RelativeSyzygiesGeneratorsOfColumns" Label="Oscar macro"/> inside the computer algebra system.
## <Listing Type="Code"><![CDATA[
RelativeSyzygiesGeneratorsOfColumns :=
function( M, M2 )
local N;
N := HomalgVoidMatrix(
NumberColumns( M ),
"unknown_number_of_columns",
HomalgRing( M )
);
homalgSendBlocking(
[ N, " = RelativeSyzygiesGeneratorsOfColumns(", M, M2, ")" ],
"need_command",
"SyzygiesGenerators"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## our fallback seems to be more efficient
X_PartiallyReducedBasisOfRowModule :=
function( M )
local N;
N := HomalgVoidMatrix( "unknown_number_of_rows", NumberColumns( M ), HomalgRing( M ) );
homalgSendBlocking( [ N, " = PartiallyReducedBasisOfRowModule(", M, ")" ], "need_command", "ReducedBasisOfModule" );
return N;
end,
## our fallback seems to be more efficient
X_PartiallyReducedBasisOfColumnModule :=
function( M )
local N;
N := HomalgVoidMatrix( NumberRows( M ), "unknown_number_of_columns", HomalgRing( M ) );
homalgSendBlocking( [ N, " = PartiallyReducedBasisOfColumnModule(", M, ")" ], "need_command", "ReducedBasisOfModule" );
return N;
end,
## <#GAPDoc Label="ReducedSyzygiesGeneratorsOfRows:Oscar">
## <ManSection>
## <Func Arg="M" Name="ReducedSyzygiesGeneratorsOfRows" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="ReducedSyzygiesGeneratorsOfRows" Label="Oscar macro"/> inside the computer algebra system.
## <Listing Type="Code"><![CDATA[
X_ReducedSyzygiesGeneratorsOfRows :=
function( M )
local N;
N := HomalgVoidMatrix(
"unknown_number_of_rows",
NumberRows( M ),
HomalgRing( M )
);
homalgSendBlocking(
[ N, " = ReducedSyzygiesGeneratorsOfRows(", M, ")" ],
"need_command",
"SyzygiesGenerators"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
## <#GAPDoc Label="ReducedSyzygiesGeneratorsOfColumns:Oscar">
## <ManSection>
## <Func Arg="M" Name="ReducedSyzygiesGeneratorsOfColumns" Label="in the homalg table for Oscar"/>
## <Returns></Returns>
## <Description>
## This is the entry of the &homalg; table, which calls the corresponding macro <Ref Func="ReducedSyzygiesGeneratorsOfColumns" Label="Oscar macro"/> inside the computer algebra system.
## <Listing Type="Code"><![CDATA[
X_ReducedSyzygiesGeneratorsOfColumns :=
function( M )
local N;
N := HomalgVoidMatrix(
NumberColumns( M ),
"unknown_number_of_columns",
HomalgRing( M )
);
homalgSendBlocking(
[ N, " = ReducedSyzygiesGeneratorsOfColumns(", M, ")" ],
"need_command",
"SyzygiesGenerators"
);
return N;
end,
## ]]></Listing>
## </Description>
## </ManSection>
## <#/GAPDoc>
)
);
[ Dauer der Verarbeitung: 0.25 Sekunden
(vorverarbeitet)
]
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2026-04-02
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