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# SPDX-License-Identifier: GPL-2.0-or-later
# RingsForHomalg: Dictionaries of external rings
#
# Implementations
#
## Implementations for commutative principal ideal rings in MAGMA.
####################################
#
# constructor functions and methods:
#
####################################
InstallMethod( CreateHomalgTable,
"for the ring of integers in MAGMA",
[ IsHomalgExternalRingObjectInMAGMARep
and IsPrincipalIdealRing ],
function( ext_ring_obj )
local RP, RP_General, RP_BestBasis, RP_specific, component;
RP := ShallowCopy( CommonHomalgTableForMAGMATools );
RP_General := ShallowCopy( CommonHomalgTableForRings );
RP_BestBasis := ShallowCopy( CommonHomalgTableForMAGMABestBasis );
RP_specific :=
rec(
## Can optionally be provided by the RingPackage
## (homalg functions check if these functions are defined or not)
## (homalgTable gives no default value)
ElementaryDivisors :=
function( M )
return homalgSendBlocking( [ "ElementaryDivisors(", M, ")" ], "need_output", "ElementaryDivisors" );
end,
RowRankOfMatrixOverDomain :=
function( M )
return Int( homalgSendBlocking( [ "Rank(", M, ")" ], "need_output" ) );
end,
## Must be defined if other functions are not defined
ReducedRowEchelonForm :=
function( arg )
local M, R, nargs, N, U;
M := arg[1];
R := HomalgRing( M );
nargs := Length( arg );
N := HomalgVoidMatrix( NumberRows( M ), NumberColumns( M ), R );
if nargs > 1 and IsHomalgMatrix( arg[2] ) then ## not ReducedRowEchelonForm( M, "" )
# assign U:
U := arg[2];
SetNumberRows( U, NumberRows( M ) );
SetNumberColumns( U, NumberRows( M ) );
SetIsInvertibleMatrix( U, true );
## compute N and U:
homalgSendBlocking( [ N, U, " := EchelonForm(", M, ")" ], "need_command", "ReducedEchelonFormC" );
else
## compute N only:
homalgSendBlocking( [ N, " := EchelonForm(", M, ")" ], "need_command", "ReducedEchelonForm" );
fi;
SetIsUpperStairCaseMatrix( N, true );
return N;
end
);
for component in NamesOfComponents( RP_General ) do
RP.(component) := RP_General.(component);
od;
for component in NamesOfComponents( RP_BestBasis ) do
RP.(component) := RP_BestBasis.(component);
od;
for component in NamesOfComponents( RP_specific ) do
RP.(component) := RP_specific.(component);
od;
Objectify( TheTypeHomalgTable, RP );
return RP;
end );
[ Dauer der Verarbeitung: 0.30 Sekunden
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