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# SPDX-License-Identifier: GPL-2.0-or-later
# GradedRingForHomalg: Endow Commutative Rings with an Abelian Grading
#
# Implementations
#
####################################
#
# global variables:
#
####################################
##
InstallValue( GradedRingMacrosForOscar,
rec(
_CAS_name := "Oscar",
_Identifier := "GradedRingForHomalg",
Degree := """
function Degree(pol, weights)
if iszero(pol)
return -1
end
exponents = collect(exponent_vectors(pol))
l = length(weights)
f = e -> sum(i->e[i] * weights[i], 1:l)
d = map(f, exponents)
max(d...)
end
""",
)
);
##
UpdateMacrosOfCAS( GradedRingMacrosForOscar, OscarMacros );
UpdateMacrosOfLaunchedCASs( GradedRingMacrosForOscar );
##
InstallValue( GradedRingTableForOscarTools,
rec(
WeightedDegreeOfRingElement :=
function( r, weights, R )
return Int( homalgSendBlocking( [ "Degree(", r, ", ", weights, ")" ], "need_output", HOMALG_IO.Pictograms.DegreeOfRingElement ) );
end,
MultiWeightedDegreeOfRingElement :=
function( r, weights, R )
if IsList( weights ) then
weights := MatrixOfWeightsOfIndeterminates( R, weights );
fi;
return StringToIntList( homalgSendBlocking( [ "MultiDeg(", r, weights, ")" ], "need_output", HOMALG_IO.Pictograms.DegreeOfRingElement ) );
end,
DegreesOfEntries :=
function( M )
local list_string, L;
list_string := homalgSendBlocking( [ "DegreesOfEntries( ", M, " )" ], "need_output", HOMALG_IO.Pictograms.DegreesOfEntries );
L := StringToIntList( list_string );
return ListToListList( L, NumberRows( M ), NumberColumns( M ) );
end,
WeightedDegreesOfEntries :=
function( M, weights )
local list_string, L;
list_string := homalgSendBlocking( [ "WeightedDegreesOfEntries(", M, ",intvec(", weights, "))" ], "need_output", HOMALG_IO.Pictograms.DegreesOfEntries );
L := StringToIntList( list_string );
return ListToListList( L, NumberRows( M ), NumberColumns( M ) );
end,
# MultiWeightedDegreesOfEntries :=
# function( M, weights, R )
# local nr_rows, nr_cols, i, j, deg_mat;
#
# nr_rows := NumberRows( M );
# nr_cols := NumberColumns( M );
#
# deg_mat := NullMat( nr_rows, nr_cols );
#
# for i in [ 1 .. nr_rows ] do
# for j in [ 1 .. nr_cols ] do
# deg_mat[ i ][ j ] := StringToIntList( homalgSendBlocking( [ "MultiDegOfMatrixEntry(", M, weights, j, i, ")" ], "need_output", HOMALG_IO.Pictograms.DegreeOfRingElement ) );
# od;
# od;
#
# return deg_mat;
#
# end,
NonTrivialDegreePerRowWithColPosition :=
function( M )
local L;
L := homalgSendBlocking( [ "NonTrivialDegreePerRowWithColPosition( ", M, " )" ], "need_output", HOMALG_IO.Pictograms.NonTrivialDegreePerRow );
L := StringToIntList( L );
return ListToListList( L, 2, NumberRows( M ) );
end,
NonTrivialWeightedDegreePerRowWithColPosition :=
function( M, weights )
local L;
L := homalgSendBlocking( [ "NonTrivialWeightedDegreePerRowWithColPosition(", M, ",intvec(", weights, "))" ], "need_output", HOMALG_IO.Pictograms.NonTrivialDegreePerRow );
L := StringToIntList( L );
return ListToListList( L, 2, NumberRows( M ) );
end,
NonTrivialDegreePerColumnWithRowPosition :=
function( M )
local L;
L := homalgSendBlocking( [ "NonTrivialDegreePerColumnWithRowPosition( ", M, " )" ], "need_output", HOMALG_IO.Pictograms.NonTrivialDegreePerColumn );
L := StringToIntList( L );
return ListToListList( L, 2, NumberColumns( M ) );
end,
NonTrivialWeightedDegreePerColumnWithRowPosition :=
function( M, weights )
local L;
L := homalgSendBlocking( [ "NonTrivialWeightedDegreePerColumnWithRowPosition(", M, ",intvec(", weights, "))" ], "need_output", HOMALG_IO.Pictograms.NonTrivialDegreePerColumn );
L := StringToIntList( L );
return ListToListList( L, 2, NumberColumns( M ) );
end,
LinearSyzygiesGeneratorsOfRows :=
function( M )
local N;
N := HomalgVoidMatrix(
"unknown_number_of_rows",
NumberRows( M ),
HomalgRing( M )
);
homalgSendBlocking(
[ "matrix ", N, " = LinearSyzygiesGeneratorsOfRows(", M, ")" ],
"need_command",
HOMALG_IO.Pictograms.LinearSyzygiesGenerators
);
return N;
end,
LinearSyzygiesGeneratorsOfColumns :=
function( M )
local N;
N := HomalgVoidMatrix(
NumberColumns( M ),
"unknown_number_of_columns",
HomalgRing( M )
);
homalgSendBlocking(
[ "matrix ", N, " = LinearSyzygiesGeneratorsOfColumns(", M, ")" ],
"need_command",
HOMALG_IO.Pictograms.LinearSyzygiesGenerators
);
return N;
end,
)
);
## enrich the global and the created homalg tables for Oscar:
AppendToAhomalgTable( CommonHomalgTableForOscarTools, GradedRingTableForOscarTools );
AppendTohomalgTablesOfCreatedExternalRings( GradedRingTableForOscarTools, IsHomalgExternalRingInOscarRep );
####################################
#
# methods for operations:
#
####################################
##
InstallMethod( MatrixOfWeightsOfIndeterminates,
"for external rings in Oscar",
[ IsHomalgExternalRingInOscarRep, IsList ],
function( R, weights )
local n, m, ext_obj;
if IsHomalgElement( weights[1] ) then
## this should be handled with care, as it will eventually fail if the module is not over the ring of integers
weights := List( weights, UnderlyingListOfRingElementsInCurrentPresentation );
fi;
n := Length( weights );
if n > 0 and IsList( weights[1] ) then
m := Length( weights[1] );
weights := Flat( TransposedMat( weights ) );
else
m := 1;
fi;
ext_obj := homalgSendBlocking( [ "CreateListListOfIntegers(", weights, ",", m, n, ")" ], R, HOMALG_IO.Pictograms.CreateList );
## CAUTION: ext_obj is not a pointer to a matrix in Oscar but to an intvec;
## use with care
return HomalgMatrix( ext_obj, m, n, R );
end );
##
InstallMethod( AreLinearSyzygiesAvailable,
"for homalg rings in Oscar",
[ IsHomalgExternalRingInOscarRep and IsExteriorRing ],
function( R )
return homalgSendBlocking( "isdefined(Base, LinSyzForHomalgExterior)",
"need_output", R, HOMALG_IO.Pictograms.initialize ) = "true";
end );
