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# SPDX-License-Identifier: GPL-2.0-or-later
# RingsForHomalg: Dictionaries of external rings
#
# Implementations
#
## Implementations for the external rings provided by the by the ring packages
## of the Maple implementation of homalg.
####################################
#
# global variables:
#
####################################
BindGlobal( "CommonHomalgTableForMapleHomalgBasic",
rec(
## Must only then be provided by the RingPackage in case the default
## "service" function does not match the Ring
RowEchelonForm :=
function( M )
local R, N;
R := HomalgRing( M );
N := HomalgVoidMatrix( "unknown_number_of_rows", NumberColumns( M ), R );
homalgSendBlocking( [ N, " := ", R, "[-1][matrix](LinearAlgebra[GaussianElimination](Matrix(", M, ")))" ], "need_command", "ReducedEchelonForm" );
return N;
end,
BasisOfRowModule :=
function( M )
local R, N;
R := HomalgRing( M );
N := HomalgVoidMatrix( "unknown_number_of_rows", NumberColumns( M ), R );
homalgSendBlocking( [ N, " := `homalg/BasisOfRowModule`(", M, R, ")" ], "need_command", "BasisOfModule" );
return N;
end,
BasisOfColumnModule :=
function( M )
local R, N;
R := HomalgRing( M );
N := HomalgVoidMatrix( NumberRows( M ), "unknown_number_of_columns", R );
homalgSendBlocking( [ N, " := `homalg/BasisOfColumnModule`(", M, R, ")" ], "need_command", "BasisOfModule" );
return N;
end,
BasisOfRowsCoeff :=
function( M, T )
local R, N;
R := HomalgRing( M );
N := HomalgVoidMatrix( "unknown_number_of_rows", NumberColumns( M ), R );
homalgSendBlocking( [ N, " := `homalg/BasisOfRowsCoeff`(", M, R, "[1],", T, R, "[-1])" ], "need_command", "BasisCoeff" );
return N;
end,
BasisOfColumnsCoeff :=
function( M, T )
local R, N;
R := HomalgRing( M );
N := HomalgVoidMatrix( NumberRows( M ), "unknown_number_of_columns", R );
homalgSendBlocking( [ N, " := `homalg/BasisOfColumnsCoeff`(", M, R, "[1],", T, R, "[-1])" ], "need_command", "BasisCoeff" );
return N;
end,
DecideZeroRows :=
function( A, B )
local R, N;
R := HomalgRing( A );
N := HomalgVoidMatrix( NumberRows( A ), NumberColumns( A ), R );
homalgSendBlocking( [ N, " := `homalg/DecideZeroRows`(", A, B, R, ")" ], "need_command", "DecideZero" );
return N;
end,
DecideZeroColumns :=
function( A, B )
local R, N;
R := HomalgRing( A );
N := HomalgVoidMatrix( NumberRows( A ), NumberColumns( A ), R );
homalgSendBlocking( [ N, " := `homalg/DecideZeroColumns`(", A, B, R, ")" ], "need_command", "DecideZero" );
return N;
end,
DecideZeroRowsEffectively :=
function( A, B, T )
local R, N;
R := HomalgRing( A );
N := HomalgVoidMatrix( NumberRows( A ), NumberColumns( A ), R );
homalgSendBlocking( [ N, " := `homalg/DecideZeroRowsEffectively`(", A, B, R, "[1],", T, R, "[-1])" ], "need_command", "DecideZeroEffectively" );
return N;
end,
DecideZeroColumnsEffectively :=
function( A, B, T )
local R, N;
R := HomalgRing( A );
N := HomalgVoidMatrix( NumberRows( A ), NumberColumns( A ), R );
homalgSendBlocking( [ N, " := `homalg/DecideZeroColumnsEffectively`(", A, B, R, "[1],", T, R, "[-1])" ], "need_command", "DecideZeroEffectively" );
return N;
end,
SyzygiesGeneratorsOfRows :=
function( M )
local R, N;
R := HomalgRing( M );
N := HomalgVoidMatrix( "unknown_number_of_rows", NumberRows( M ), R );
homalgSendBlocking( [ N, " := `homalg/SyzygiesGeneratorsOfRows`(", M, ",[],", R, ")" ], "need_command", "SyzygiesGenerators" );
return N;
end,
SyzygiesGeneratorsOfColumns :=
function( M )
local R, N;
R := HomalgRing( M );
N := HomalgVoidMatrix( NumberColumns( M ), "unknown_number_of_columns", R );
homalgSendBlocking( [ N, " := `homalg/SyzygiesGeneratorsOfColumns`(", M, ",[],", R, ")" ], "need_command", "SyzygiesGenerators" );
return N;
end,
RelativeSyzygiesGeneratorsOfRows :=
function( M, M2 )
local R, N;
R := HomalgRing( M );
N := HomalgVoidMatrix( "unknown_number_of_rows", NumberRows( M ), R );
homalgSendBlocking( [ N, " := `homalg/SyzygiesGeneratorsOfRows`(", M, M2, R, ")" ], "need_command", "SyzygiesGenerators" );
return N;
end,
RelativeSyzygiesGeneratorsOfColumns :=
function( M, M2 )
local R, N;
R := HomalgRing( M );
N := HomalgVoidMatrix( NumberColumns( M ), "unknown_number_of_columns", R );
homalgSendBlocking( [ N, " := `homalg/SyzygiesGeneratorsOfColumns`(", M, M2, R, ")" ], "need_command", "SyzygiesGenerators" );
return N;
end,
)
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