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# SPDX-License-Identifier: GPL-2.0-or-later
# RingsForHomalg: Dictionaries of external rings
#
# Implementations
#
## Implementations for the rings provided by the ring packages
## of the Maple implementation of homalg.
####################################
#
# global variables:
#
####################################
BindGlobal( "CommonHomalgTableForMapleHomalgBestBasis",
rec(
## Can optionally be provided by the RingPackage
## (homalg functions check if these functions are defined or not)
## (homalgTable gives no default value)
BestBasis :=
function( arg )
local M, R, nargs, S, U, V;
M := arg[1];
R := HomalgRing( M );
nargs := Length( arg );
S := HomalgVoidMatrix( NumberRows( M ), NumberColumns( M ), R );
## SetIsDiagonalMatrix( S, true ); ## do not set this, it is false for Quillen-Suslin output
if nargs > 1 then
# assign U:
if IsHomalgMatrix( arg[2] ) then ## not BestBasis( M, "", V )
U := arg[2];
SetNumberRows( U, NumberRows( M ) );
SetNumberColumns( U, NumberRows( M ) );
SetIsInvertibleMatrix( U, true );
else
U := HomalgVoidMatrix( R );
fi;
# assign V:
if nargs > 2 and IsHomalgMatrix( arg[3] ) then ## not BestBasis( M, U, "" )
V := arg[3];
SetNumberRows( V, NumberColumns( M ) );
SetNumberColumns( V, NumberColumns( M ) );
SetIsInvertibleMatrix( V, true );
else
V := HomalgVoidMatrix( R );
fi;
## compute S, U and (if nargs > 2) V: S = U*M*V
homalgSendBlocking( [ S, " := ", R, "[-1][BestBasis](", M, R, "[1],", U, V, ")" ], "need_command", "BestBasis" );
else
## compute S only:
homalgSendBlocking( [ S, " := ", R, "[-1][BestBasis](", M, R, "[1])" ], "need_command", "BestBasis" );
fi;
return S;
end
)
);
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