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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346#############################################################################
##
## MapleHomalgTools.gi GradedRingForHomalg package
##
## Copyright 2009-2011, Mohamed Barakat, University of Kaiserslautern
## Markus Lange-Hegermann, RWTH-Aachen University
##
## Implementations for the rings provided by the Maple implementation of homalg.
##
#############################################################################
####################################
#
# global variables:
#
####################################
##
InstallValue( GradedRingMacrosForMaple,
rec(
_CAS_name := "Maple",
_Identifier := "GradedRingForHomalg",
DegreesOfEntries := "\n\
DegreesOfEntries := proc(M)\n\
local m;\n\
m := convert(M,listlist);\n\
m := map(op,m);\n\
m := map(degree,m);\n\
m := map(a->if a = -infinity then -1 else a fi,m);\n\
RETURN(m);\n\
end:\n\n",
WeightedDegreesOfEntries := "\n\
WeightedDegreesOfEntries := proc(M, var)\n\
local m;\n\
m := convert(M,listlist);\n\
m := map(op,m);\n\
m := map(r->degree(r,var),m);\n\
m := map(a->if a = -infinity then -1 else a fi,m);\n\
RETURN(m);\n\
end:\n\n",
NonTrivialDegreePerRowWithColPosition := "\n\
NonTrivialDegreePerRowWithColPosition := proc(M,r,c)\n\
local m,i,j,e;\n\
m := matrix(2,r,0);\n\
for i in [$1..r] do\n\
for j in [$1..c] do\n\
e := M[i,j];\n\
if e <> 0 then\n\
m[1,i] := degree(e); m[2,i] := j; break;\n\
fi;\n\
od;\n\
od;\n\
RETURN(map(op,convert(m,listlist)));\n\
end:\n\n",
NonTrivialWeightedDegreePerRowWithColPosition := "\n\
NonTrivialWeightedDegreePerRowWithColPosition := proc(M,r,c,var)\n\
local m,i,j,e;\n\
m := matrix(2,r,0);\n\
for i in [$1..r] do\n\
for j in [$1..c] do\n\
e := M[i,j];\n\
if e <> 0 then\n\
m[1,i] := degree(e,var); m[2,i] := j; break;\n\
fi;\n\
od;\n\
od;\n\
RETURN(map(op,convert(m,listlist)));\n\
end:\n\n",
NonTrivialDegreePerColumnWithRowPosition := "\n\
NonTrivialDegreePerColumnWithRowPosition := proc(M,r,c)\n\
local m,i,j,e;\n\
m := matrix(2,c,0);\n\
for j in [$1..c] do\n\
for i in [$1..r] do\n\
e := M[i,j];\n\
if e <> 0 then\n\
m[1,j] := degree(e); m[2,j] := i; break;\n\
fi;\n\
od;\n\
od;\n\
RETURN(map(op,convert(m,listlist)));\n\
end:\n\n",
NonTrivialWeightedDegreePerColumnWithRowPosition := "\n\
NonTrivialWeightedDegreePerColumnWithRowPosition := proc(M,r,c,var)\n\
local m,i,j,e;\n\
m := matrix(2,c,0);\n\
for j in [$1..c] do\n\
for i in [$1..r] do\n\
e := M[i,j];\n\
if e <> 0 then\n\
m[1,j] := degree(e,var); m[2,j] := i; break;\n\
fi;\n\
od;\n\
od;\n\
RETURN(map(op,convert(m,listlist)));\n\
end:\n\n",
)
);
##
UpdateMacrosOfCAS( GradedRingMacrosForMaple, MapleMacros );
UpdateMacrosOfLaunchedCASs( GradedRingMacrosForMaple );
##
InstallValue( GradedRingTableForMapleHomalgTools,
rec(
WeightedDegreeOfRingElement :=
function( r, weights, R )
local deg, var;
if Set( weights ) <> [ 0, 1 ] then
Error( "there is no direct way to compute the weighted degree in Maple\n" );
fi;
var := Indeterminates( R );
var := var{Filtered( [ 1 .. Length( var ) ], p -> weights[p] = 1 )};
deg := Int( homalgSendBlocking( [ "degree(", r, var, ")" ], "need_output", HOMALG_IO.Pictograms.DegreeOfRingElement ) );
if deg <> fail then
return deg;
fi;
return -1;
end,
DegreesOfEntries :=
function( M )
local R, list_string, L;
R := HomalgRing( M );
list_string := homalgSendBlocking( [ "DegreesOfEntries(`homalg/ReduceRingElements`(", M, R, "))" ], "need_output", HOMALG_IO.Pictograms.DegreesOfEntries );
L := StringToIntList( list_string );
return ListToListList( L, NrRows( M ), NrColumns( M ) );
end,
WeightedDegreesOfEntries :=
function( M, weights )
local R, var, list_string, L;
if Set( weights ) <> [ 0, 1 ] then
Error( "there is no direct way to compute the weighted degree in Maple\n" );
fi;
R := HomalgRing( M );
var := Indeterminates( R );
var := var{Filtered( [ 1 .. Length( var ) ], p -> weights[p] = 1 )};
list_string := homalgSendBlocking( [ "WeightedDegreesOfEntries(`homalg/ReduceRingElements`(", M, R, "),", var, ")" ], "need_output", HOMALG_IO.Pictograms.DegreesOfEntries );
L := StringToIntList( list_string );
return ListToListList( L, NrRows( M ), NrColumns( M ) );
end,
NonTrivialDegreePerRowWithColPosition :=
function( M )
local R, L;
R := HomalgRing( M );
L := homalgSendBlocking( [ "NonTrivialDegreePerRowWithColPosition(`homalg/ReduceRingElements`(", M, R, "),", NrRows( M ), NrColumns( M ), ")" ], "need_output", HOMALG_IO.Pictograms.NonTrivialDegreePerRow );
L := StringToIntList( L );
return ListToListList( L, 2, NrRows( M ) );
end,
NonTrivialWeightedDegreePerRowWithColPosition :=
function( M, weights )
local R, var, L;
if Set( weights ) <> [ 0, 1 ] then
Error( "there is no direct way to compute the weighted degree in Maple\n" );
fi;
R := HomalgRing( M );
var := Indeterminates( R );
var := var{Filtered( [ 1 .. Length( var ) ], p -> weights[p] = 1 )};
L := homalgSendBlocking( [ "NonTrivialWeightedDegreePerRowWithColPosition(`homalg/ReduceRingElements`(", M, R, "),", NrRows( M ), NrColumns( M ), var, ")" ], "need_output", HOMALG_IO.Pictograms.NonTrivialDegreePerRow );
L := StringToIntList( L );
return ListToListList( L, 2, NrRows( M ) );
end,
NonTrivialDegreePerColumnWithRowPosition :=
function( M )
local R, L;
R := HomalgRing( M );
L := homalgSendBlocking( [ "NonTrivialDegreePerColumnWithRowPosition(`homalg/ReduceRingElements`(", M, R, "),", NrRows( M ), NrColumns( M ), ")" ], "need_output", HOMALG_IO.Pictograms.NonTrivialDegreePerColumn );
L := StringToIntList( L );
return ListToListList( L, 2, NrColumns( M ) );
end,
NonTrivialWeightedDegreePerColumnWithRowPosition :=
function( M, weights )
local R, L, var;
if Set( weights ) <> [ 0, 1 ] then
Error( "there is no direct way to compute the weighted degree in Maple\n" );
fi;
R := HomalgRing( M );
var := Indeterminates( R );
var := var{Filtered( [ 1 .. Length( var ) ], p -> weights[p] = 1 )};
L := homalgSendBlocking( [ "NonTrivialWeightedDegreePerColumnWithRowPosition(`homalg/ReduceRingElements`(", M, R, "),", NrRows( M ), NrColumns( M ), var, ")" ], "need_output", HOMALG_IO.Pictograms.NonTrivialDegreePerColumn );
L := StringToIntList( L );
return ListToListList( L, 2, NrColumns( M ) );
end,
)
);
## enrich the global and the created homalg tables for MapleHomalg:
AppendToAhomalgTable( CommonHomalgTableForMapleHomalgTools, GradedRingTableForMapleHomalgTools );
AppendTohomalgTablesOfCreatedExternalRings( GradedRingTableForMapleHomalgTools, IsHomalgExternalRingInMapleRep );