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# SPDX-License-Identifier: GPL-2.0-or-later
# RingsForHomalg: Dictionaries of external rings
#
# Implementations
#
## Implementations for the rings provided by Sage.
####################################
#
# global variables:
#
####################################
BindGlobal( "CommonHomalgTableForSageTools",
rec(
Zero := HomalgExternalRingElement( R -> homalgSendBlocking( [ R, ".zero()" ], "Zero" ), "Sage", IsZero ),
One := HomalgExternalRingElement( R -> homalgSendBlocking( [ R, ".one()" ], "One" ), "Sage", IsOne ),
MinusOne := HomalgExternalRingElement( R -> homalgSendBlocking( [ "-", R, ".one()" ], "MinusOne" ), "Sage", IsMinusOne ),
RingElement := R -> r -> homalgSendBlocking( [ R, ".one() * (", r, ")" ], "define" ),
IsZero := r -> homalgSendBlocking( [ r, " == ", Zero( r ) ] , "need_output", "IsZero" ) = "True",
IsOne := r -> homalgSendBlocking( [ r, " == ", One( r ) ] , "need_output", "IsOne" ) = "True",
Minus :=
function( a, b )
return homalgSendBlocking( [ a, " - ( ", b, " )" ], "Minus" );
end,
Equal :=
function( A, B )
return homalgSendBlocking( [ A, "==", B ], "need_output", "AreEqualMatrices" ) = "True";
end,
ZeroMatrix :=
function( C )
return homalgSendBlocking( [ "matrix(", HomalgRing( C ), NumberRows( C ), NumberColumns( C ), ")" ], "ZeroMatrix" );
end,
IdentityMatrix :=
function( C )
local R;
R := HomalgRing( C );
return homalgSendBlocking( [ "identity_matrix(", R, NumberRows( C ), ")" ], "IdentityMatrix" );
end,
Involution :=
function( M )
return homalgSendBlocking( [ M, ".transpose()" ], "Involution" );
end,
TransposedMatrix :=
function( M )
return homalgSendBlocking( [ M, ".transpose()" ], "TransposedMatrix" );
end,
CertainRows :=
function( M, plist )
plist := plist - 1;
return homalgSendBlocking( [ M, ".matrix_from_rows(", plist, ")" ], "CertainRows" );
end,
CertainColumns :=
function( M, plist )
plist := plist - 1;
return homalgSendBlocking( [ M, ".matrix_from_columns(", plist, ")" ], "CertainColumns" );
end,
UnionOfRowsPair :=
function( A, B )
return homalgSendBlocking( [ "block_matrix([", A, B, "],ncols=2)" ], "UnionOfRows" );
end,
UnionOfColumnsPair :=
function( A, B )
return homalgSendBlocking( [ "block_matrix([", A, B, "],ncols=1)" ], "UnionOfColumns" );
end,
DiagMat :=
function( e )
local f;
f := ShallowCopy( e );
Add( f, "block_diagonal_matrix(", 1 );
Add( f, ")" );
return homalgSendBlocking( f, "DiagMat" );
end,
MulMat :=
function( a, A )
return homalgSendBlocking( [ "(", a, ")*", A ], "MulMat" );
end,
MulMatRight :=
function( A, a )
return homalgSendBlocking( [ A, "*(", a, ")" ], "MulMatRight" );
end,
AddMat :=
function( A, B )
return homalgSendBlocking( [ A, "+", B ], "AddMat" );
end,
SubMat :=
function( A, B )
return homalgSendBlocking( [ A, "-", B ], "SubMat" );
end,
Compose :=
function( A, B )
return homalgSendBlocking( [ A, "*", B ], "Compose" );
end,
NumberRows :=
function( C )
return StringToInt( homalgSendBlocking( [ C, ".nrows()" ], "need_output", "NumberRows" ) );
end,
NumberColumns :=
function( C )
return StringToInt( homalgSendBlocking( [ C, ".ncols()" ], "need_output", "NumberColumns" ) );
end,
ZeroRows :=
function( C )
return StringToIntList( homalgSendBlocking( [ "ZeroRows(", C, ")" ], "need_output", "ZeroRows" ) ) + 1;
end,
ZeroColumns :=
function( C )
return StringToIntList( homalgSendBlocking( [ "ZeroColumns(", C, ")" ], "need_output", "ZeroColumns" ) ) + 1;
end,
)
);
[ Dauer der Verarbeitung: 0.31 Sekunden
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