|
# SPDX-License-Identifier: GPL-2.0-or-later
# RingsForHomalg: Dictionaries of external rings
#
# Implementations
#
## Implementation stuff for the external computer algebra system Maple.
####################################
#
# global variables:
#
####################################
BindGlobal( "HOMALG_IO_Maple",
rec(
cas := "maple", ## normalized name on which the user should have no control
name := "Maple",
executable := [ "maple_for_homalg", "maple14", "maple13", "maple12", "maple11", "maple10", "maple9", "maple" ], ## this list is processed from left to right
options := [ "-q" ],
BUFSIZE := 1024,
READY := "!$%&/(",
CUT_POS_BEGIN := 1, ## these are the most
CUT_POS_END := 4, ## delicate values!
eoc_verbose := ";",
eoc_quiet := ":",
error_stdout := "Error, ", ## a Maple specific
normalized_white_space := NormalizedWhitespace, ## a Maple specific
trim_display := function( str ) return str{ [ 1 .. Length( str ) - 36 ] }; end, ## a Maple specific
setring := _MapleHomalg_SetRing, ## a MapleHomalg specific
define := ":=",
delete := function( var, stream ) homalgSendBlocking( [ var, " := '", var, "'" ], "need_command", stream, "delete" ); end,
multiple_delete := _Maple_multiple_delete,
garbage_collector := function( stream ) homalgSendBlocking( [ "gc()" ], "need_command", stream, "garbage_collector" ); end,
prompt := "\033[01mmaple>\033[0m ",
output_prompt := "\033[1;34;47m<maple\033[0m ",
display_color := "\033[0;34m",
#banner := function( s ) Print( s.lines{ [ 1 .. Length( s.lines ) - 36 ] } ); end, ## this line is commented since we must start Maple using the -q option, which unfortunately also suppresses the Maple banner
banner := "\
|\\^/| Launching Maple\n\
._|\\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc.\n\
\\ MAPLE / All rights reserved. Maple is a trademark of\n\
<____ ____> Waterloo Maple Inc.\n\
| ",
InitializeCASMacros := InitializeMapleMacros,
UseJacobsonNormalForm := false,
time := function( stream, t ) return Int( homalgSendBlocking( [ "floor(time() * 1000)" ], "need_output", stream, "time" ) ) - t; end,
)
);
HOMALG_IO_Maple.READY_LENGTH := Length( HOMALG_IO_Maple.READY );
####################################
#
# families and types:
#
####################################
# five new types:
BindGlobal( "TheTypeHomalgExternalRingObjectInMapleUsingPIR",
NewType( TheFamilyOfHomalgRings,
IsHomalgExternalRingObjectInMapleUsingPIRRep ) );
BindGlobal( "TheTypeHomalgExternalRingObjectInMapleUsingInvolutive",
NewType( TheFamilyOfHomalgRings,
IsHomalgExternalRingObjectInMapleUsingInvolutiveRep ) );
BindGlobal( "TheTypeHomalgExternalRingObjectInMapleUsingJanet",
NewType( TheFamilyOfHomalgRings,
IsHomalgExternalRingObjectInMapleUsingJanetRep ) );
BindGlobal( "TheTypeHomalgExternalRingObjectInMapleUsingJanetOre",
NewType( TheFamilyOfHomalgRings,
IsHomalgExternalRingObjectInMapleUsingJanetOreRep ) );
BindGlobal( "TheTypeHomalgExternalRingObjectInMapleUsingOreModules",
NewType( TheFamilyOfHomalgRings,
IsHomalgExternalRingObjectInMapleUsingOreModulesRep ) );
# a new types:
BindGlobal( "TheTypeHomalgExternalRingInMaple",
NewType( TheFamilyOfHomalgRings,
IsHomalgExternalRingInMapleRep ) );
####################################
#
# methods for operations:
#
####################################
##
InstallMethod( homalgLaTeX,
"for external objects",
[ IsHomalgExternalMatrixRep ],
function( o )
local R;
R := HomalgRing( o );
if IsHomalgExternalRingInMapleRep( R ) then
Print( homalgSendBlocking( [ "latex(", o, ")" ], "need_display", "homalgLaTeX" ) );
else
TryNextMethod( );
fi;
end );
####################################
#
# global functions and variables:
#
####################################
##
InstallGlobalFunction( _MapleHomalg_SetRing,
function( R )
local stream;
stream := homalgStream( R );
## since _MapleHomalg_SetRing might be called from homalgSendBlocking,
## we first set the new active ring to avoid infinite loops:
stream.active_ring := R;
if IsBound( R!.MapleHomalgOptions ) then
homalgSendBlocking( [ R!.MapleHomalgOptions[1], "(\"set\",", R!.MapleHomalgOptions[2], ")" ], "need_command", "initialize" );
fi;
if IsBound( HOMALG_IO_Maple.setring_post ) then
homalgSendBlocking( HOMALG_IO_Maple.setring_post, "need_command", stream, "initialize" );
fi;
end );
##
InstallGlobalFunction( _Maple_multiple_delete,
function( var_list, stream )
local str;
str := [ "for _del in ", String( var_list ), " do unassign(convert(_del,symbol)) od" ];
homalgSendBlocking( str, "need_command", stream, "multiple_delete" );
end );
##
BindGlobal( "MapleMacros",
rec(
Eliminate := "\n\
Eliminate := proc(L,indets::list,var::list)\n\
local IB,elim;\n\
IB := `Involutive/InvolutiveBasis`(L,[indets,remove(member,var,indets)]);\n\
elim := remove(has,IB,indets);\n\
if elim = [] then elim := matrix([[]]); fi;\n\
elim;\n\
end:\n\n",
CoefficientsOfPolynomial := "\n\
CoefficientsOfPolynomial := proc(h,x)\n\
if h = 0 then\n\
[ ]\n\
else\n\
map(i->coeff(h,x,i),[$0..degree(h,x)]);\n\
fi;\n\
end:\n\n",
CoefficientsOfLaurentPolynomial := "\n\
CoefficientsOfLaurentPolynomial := proc(h,x)\n\
local hdeg,ldeg,degs;\n\
if h = 0 then\n\
0\n\
else\n\
hdeg := degree(h,x);\n\
ldeg := ldegree(h,x);\n\
degs := map(i->coeff(h,x,i),[$ldeg ..hdeg]);\n\
op(degs),ldeg;\n\
fi;\n\
end:\n\n",
CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries := "\n\
CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries := proc(mat,var,s,n)\n\
`Involutive/InvolutiveBasis`(mat,var);\n\
CoefficientsOfPolynomial(expand(simplify(`Involutive/PolHilbertSeries`(s)*(1-s)^n)),s);\n\
end:\n\n",
CoefficientsOfUnreducedNumeratorOfWeightedHilbertPoincareSeries := "\n\
CoefficientsOfUnreducedNumeratorOfWeightedHilbertPoincareSeries := proc(mat,var,s,denom)\n\
`Involutive/InvolutiveBasis`(mat,var);\n\
CoefficientsOfLaurentPolynomial(expand(simplify(`Involutive/PolWeightedHilbertSeries`(var,s)*denom)),'homalg_variable_for_HP');\n\
end:\n\n",
BestBasis := "\n\
`InvolutiveQS/homalg`[BestBasis] := proc() `homalg/Involutive/BasisQS`(convert(args[1],listlist),args[2..-1]):\n\
end:\n\n",
MyReverse := "\n\
MyReverse := proc(h)\n\
map(i->h[-i],[$1..nops(h)])\n\
end:\n\n",
)
);
##
InstallGlobalFunction( InitializeMapleMacros,
function( stream )
return InitializeMacros( MapleMacros, stream );
end );
####################################
#
# constructor functions and methods:
#
####################################
##
InstallGlobalFunction( RingForHomalgInMapleUsingPIR,
function( arg )
local nargs, stream, o, display_color, homalg_version, package_version,
ar, ext_obj, R, RP;
nargs := Length( arg );
if nargs > 1 then
if IsRecord( arg[nargs] ) and IsBound( arg[nargs].lines ) and IsBound( arg[nargs].pid ) then
stream := arg[nargs];
elif IshomalgExternalObjectRep( arg[nargs] ) or IsHomalgExternalRingRep( arg[nargs] ) then
stream := homalgStream( arg[nargs] );
fi;
fi;
if not IsBound( stream ) then
stream := LaunchCAS( "HOMALG_IO_Maple" );
if not IsBound( stream.path_to_maple_packages ) then ## each component in HOMALG_IO_Maple is now in the stream
stream.path_to_maple_packages := Concatenation( PackageInfo( "RingsForHomalg" )[1].InstallationPath, "/maple" );
fi;
homalgSendBlocking( [ "libname := \"", stream.path_to_maple_packages, "\",libname" ], "need_command", stream, "initialize" );
o := 0;
else
o := 1;
fi;
InitializeMapleMacros( stream );
homalgSendBlocking( "with(PIR)", "need_command", stream, "initialize" );
if ( not ( IsBound( HOMALG_IO.show_banners ) and HOMALG_IO.show_banners = false )
and not ( IsBound( HOMALG_IO.show_maple_package_banner ) and HOMALG_IO.show_maple_package_banner = false )
and not ( IsBound( stream.show_banner ) and stream.show_banner = false ) )
and not ( IsBound( stream.show_banner_PIR ) and stream.show_banner_PIR = false ) then
if IsBound( stream.color_display ) then
display_color := stream.color_display;
else
display_color := "";
fi;
homalg_version := homalgSendBlocking("\`homalg/version\`", "need_output", stream, "initialize" ){[ 3 .. 8 ]};
package_version := homalgSendBlocking("\`PIR/version\`", "need_output", stream, "initialize" ){[ 3 .. 8 ]};
Print( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
## leave the below indentation untouched!
Print( display_color, "\
PIR - Maple package loaded (version: ", package_version, ")\n\
Copyright (C) (2004-2006)\n\
Lehrstuhl B fuer Mathematik, RWTH Aachen, Germany\n\
(will be used as a ring package via Maple's homalg (ver: ", homalg_version, "))\033[0m\n\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
stream.show_banner_PIR := false;
fi;
ar := [ [ arg[1], ",", "copy(`PIR/homalg`)" ], TheTypeHomalgExternalRingObjectInMapleUsingPIR, IsCommutative, IsPrincipalIdealRing, stream, "CreateHomalgRing" ];
if nargs > 1 then
ar := Concatenation( ar, arg{[ 2 .. nargs - o ]} );
fi;
ext_obj := CallFuncList( homalgSendBlocking, ar );
R := CreateHomalgExternalRing( ext_obj, TheTypeHomalgExternalRingInMaple, IsCommutative, IsPrincipalIdealRing );
homalgSendBlocking( [ "`homalg/homalg_options`(", R, "[-1])" ], "need_command", "initialize" );
_MapleHomalg_SetRing( R );
LetWeakPointerListOnExternalObjectsContainRingCreationNumbers( R );
RP := homalgTable( R );
RP!.Sum :=
function( a, b )
return homalgSendBlocking( [ a, "+(", b, ")" ], "Sum" );
end;
RP!.Product :=
function( a, b )
return homalgSendBlocking( [ "(", a, ")*(", b, ")" ], "Product" );
end;
return R;
end );
##
InstallGlobalFunction( RingForHomalgInMapleUsingInvolutive,
function( arg )
local nargs, stream, o, display_color, homalg_version, package_version,
var, ar, ext_obj, R, RP;
nargs := Length( arg );
if nargs > 1 then
if IsRecord( arg[nargs] ) and IsBound( arg[nargs].lines ) and IsBound( arg[nargs].pid ) then
stream := arg[nargs];
elif IshomalgExternalObjectRep( arg[nargs] ) or IsHomalgExternalRingRep( arg[nargs] ) then
stream := homalgStream( arg[nargs] );
fi;
fi;
if not IsBound( stream ) then
stream := LaunchCAS( "HOMALG_IO_Maple" );
if not IsBound( stream.path_to_maple_packages ) then ## each component in HOMALG_IO_Maple is now in the stream
stream.path_to_maple_packages := Concatenation( PackageInfo( "RingsForHomalg" )[1].InstallationPath, "/maple" );
fi;
homalgSendBlocking( [ "libname := \"", stream.path_to_maple_packages, "\",libname" ], "need_command", stream, "initialize" );
o := 0;
else
o := 1;
fi;
homalgSendBlocking( "with(Involutive)", "need_command", stream, "initialize" );
if ( not ( IsBound( HOMALG_IO.show_banners ) and HOMALG_IO.show_banners = false )
and not ( IsBound( HOMALG_IO.show_maple_package_banner ) and HOMALG_IO.show_maple_package_banner = false )
and not ( IsBound( stream.show_banner ) and stream.show_banner = false ) )
and not ( IsBound( stream.show_banner_Involutive ) and stream.show_banner_Involutive = false ) then
if IsBound( stream.color_display ) then
display_color := stream.color_display;
else
display_color := "";
fi;
homalg_version := homalgSendBlocking("\`homalg/version\`", "need_output", stream, "initialize" ){[ 3 .. 8 ]};
package_version := homalgSendBlocking("\`Involutive/version\`", "need_output", stream, "initialize" );
Print( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
## leave the below indentation untouched!
Print( display_color, "\
Involutive - Maple package loaded (version: ", package_version, ")\n\
Copyright (C) (2000-2009) Carlos F. Cid and Daniel Robertz\n\
Lehrstuhl B fuer Mathematik, RWTH Aachen, Germany\n\
(will be used as a ring package via Maple's homalg (ver: ", homalg_version, "))\033[0m\n\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
stream.show_banner_Involutive := false;
fi;
homalgSendBlocking( "with(QuillenSuslin)", "need_command", stream, "initialize" );
if ( not ( IsBound( HOMALG_IO.show_banners ) and HOMALG_IO.show_banners = false )
and not ( IsBound( HOMALG_IO.show_maple_package_banner ) and HOMALG_IO.show_maple_package_banner = false )
and not ( IsBound( stream.show_banner ) and stream.show_banner = false ) )
and not ( IsBound( stream.show_banner_QuillenSuslin ) and stream.show_banner_QuillenSuslin = false ) then
if IsBound( stream.color_display ) then
display_color := stream.color_display;
else
display_color := "";
fi;
homalg_version := homalgSendBlocking("\`homalg/version\`", "need_output", stream, "initialize" ){[ 3 .. 8 ]};
package_version := homalgSendBlocking("\`QuillenSuslin/version\`", "need_output", stream, "initialize" );
Print( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
Print( display_color, "\
QuillenSuslin - Maple package loaded (version: ", package_version, ")\n\
Copyright (C) (2003-2008) Anna Fabianska\n\
Lehrstuhl B fuer Mathematik, RWTH Aachen, Germany\n\
(will be used as a ring package via Maple's homalg (ver: ", homalg_version, "))\033[0m\n\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
stream.show_banner_QuillenSuslin := false;
fi;
if IsString( arg[1] ) then
var := arg[1];
else
var := Flat( [ "[", JoinStringsWithSeparator( arg[1] ), "]" ] );
fi;
ar := [ [ var, ",", "copy(`Involutive/homalg`)" ], TheTypeHomalgExternalRingObjectInMapleUsingInvolutive, IsCommutative, stream, "CreateHomalgRing" ];
if nargs > 1 then
ar := Concatenation( ar, arg{[ 2 .. nargs - o ]} );
fi;
ext_obj := CallFuncList( homalgSendBlocking, ar );
R := CreateHomalgExternalRing( ext_obj, TheTypeHomalgExternalRingInMaple, IsCommutative );
## we need homalg_options(matrix,...) until `homalg/Involutive/BasisQS` is fixed
homalgSendBlocking( [ "`homalg/homalg_options`(matrix,", R, "[-1])" ], "need_command", "initialize" );
homalgSendBlocking( [ R, "[-1][BestBasis]:=`InvolutiveQS/homalg`[BestBasis]" ], "need_command", "initialize" );
_MapleHomalg_SetRing( R );
LetWeakPointerListOnExternalObjectsContainRingCreationNumbers( R );
R!.MapleHomalgOptions :=
[ "`Involutive/InvolutiveOptions`",
homalgSendBlocking( [ "`Involutive/InvolutiveOptions`(\"get\")" ], R, "initialize" )
];
RP := homalgTable( R );
RP!.Sum :=
function( a, b )
return homalgSendBlocking( [ a, "+(", b, ")" ], "Sum" );
end;
RP!.Product :=
function( a, b )
return homalgSendBlocking( [ "(", a, ")*(", b, ")" ], "Product" );
end;
return R;
end );
##
InstallGlobalFunction( RingForHomalgInMapleUsingJanet,
function( arg )
local nargs, stream, o, display_color, homalg_version, package_version,
var, ar, ext_obj, R, RP_BestBasis, RP;
nargs := Length( arg );
if nargs > 1 then
if IsRecord( arg[nargs] ) and IsBound( arg[nargs].lines ) and IsBound( arg[nargs].pid ) then
stream := arg[nargs];
elif IshomalgExternalObjectRep( arg[nargs] ) or IsHomalgExternalRingRep( arg[nargs] ) then
stream := homalgStream( arg[nargs] );
fi;
fi;
if not IsBound( stream ) then
stream := LaunchCAS( "HOMALG_IO_Maple" );
if not IsBound( stream.path_to_maple_packages ) then ## each component in HOMALG_IO_Maple is now in the stream
stream.path_to_maple_packages := Concatenation( PackageInfo( "RingsForHomalg" )[1].InstallationPath, "/maple" );
fi;
homalgSendBlocking( [ "libname := \"", stream.path_to_maple_packages, "\",libname" ], "need_command", stream, "initialize" );
o := 0;
else
o := 1;
fi;
homalgSendBlocking( "with(Janet)", "need_command", stream, "initialize" );
if ( not ( IsBound( HOMALG_IO.show_banners ) and HOMALG_IO.show_banners = false )
and not ( IsBound( HOMALG_IO.show_maple_package_banner ) and HOMALG_IO.show_maple_package_banner = false )
and not ( IsBound( stream.show_banner ) and stream.show_banner = false ) )
and not ( IsBound( stream.show_banner_Janet ) and stream.show_banner_Janet = false ) then
if IsBound( stream.color_display ) then
display_color := stream.color_display;
else
display_color := "";
fi;
homalg_version := homalgSendBlocking("\`homalg/version\`", "need_output", stream, "initialize" ){[ 3 .. 8 ]};
package_version := homalgSendBlocking("\`Janet/version\`", "need_output", stream, "initialize" );
Print( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
## leave the below indentation untouched!
Print( display_color, "\
Janet - Maple package loaded (version: ", package_version, ")\n\
Copyright (C) (2000-2009) Carlos F. Cid and Daniel Robertz\n\
Lehrstuhl B fuer Mathematik, RWTH Aachen, Germany\n\
(will be used as a ring package via Maple's homalg (ver: ", homalg_version, "))\033[0m\n\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
stream.show_banner_Janet := false;
fi;
if IsString( arg[1] ) then
var := arg[1];
else
var := Flat( [ "[", JoinStringsWithSeparator( arg[1] ), "]" ] );
fi;
ar := [ [ var, ",", "copy(`Janet/homalg`)" ], TheTypeHomalgExternalRingObjectInMapleUsingJanet, stream, "CreateHomalgRing" ];
if nargs > 1 then
ar := Concatenation( ar, arg{[ 2 .. nargs - o ]} );
fi;
ext_obj := CallFuncList( homalgSendBlocking, ar );
R := CreateHomalgExternalRing( ext_obj, TheTypeHomalgExternalRingInMaple );
homalgSendBlocking( [ "`homalg/homalg_options`(", R, "[-1])" ], "need_command", "initialize" );
_MapleHomalg_SetRing( R );
LetWeakPointerListOnExternalObjectsContainRingCreationNumbers( R );
R!.MapleHomalgOptions :=
[ "`Janet/JanetOptions`",
homalgSendBlocking( [ "`Janet/JanetOptions`(\"get\")" ], R, "initialize" )
];
if IsBound( HOMALG_IO_Maple.UseJacobsonNormalForm ) and
HOMALG_IO_Maple.UseJacobsonNormalForm = true and
homalgSendBlocking( [ "nops(", R, "[1])" ], "need_output" ) = "1" then
homalgSendBlocking( [ R, "[-1][BestBasis]:=`Janet1/homalg`[BestBasis]" ], "need_command", "initialize" );
RP := homalgTable( R );
RP_BestBasis := ShallowCopy( CommonHomalgTableForMapleHomalgBestBasis );
Perform( NamesOfComponents( RP_BestBasis ),
function( component ) RP!.(component) := RP_BestBasis.(component); end );
fi;
SetIsLocalizedWeylRing( R, true );
SetRingProperties( R, var );
return R;
end );
##
InstallGlobalFunction( RingForHomalgInMapleUsingJanetOre,
function( arg )
local nargs, stream, o, display_color, homalg_version, package_version,
ar, ext_obj, R, RP;
nargs := Length( arg );
if nargs > 1 then
if IsRecord( arg[nargs] ) and IsBound( arg[nargs].lines ) and IsBound( arg[nargs].pid ) then
stream := arg[nargs];
elif IshomalgExternalObjectRep( arg[nargs] ) or IsHomalgExternalRingRep( arg[nargs] ) then
stream := homalgStream( arg[nargs] );
fi;
fi;
if not IsBound( stream ) then
stream := LaunchCAS( "HOMALG_IO_Maple" );
if not IsBound( stream.path_to_maple_packages ) then ## each component in HOMALG_IO_Maple is now in the stream
stream.path_to_maple_packages := Concatenation( PackageInfo( "RingsForHomalg" )[1].InstallationPath, "/maple" );
fi;
homalgSendBlocking( [ "libname := \"", stream.path_to_maple_packages, "\",libname" ], "need_command", stream, "initialize" );
o := 0;
else
o := 1;
fi;
homalgSendBlocking( "with(JanetOre)", "need_command", stream, "initialize" );
if ( not ( IsBound( HOMALG_IO.show_banners ) and HOMALG_IO.show_banners = false )
and not ( IsBound( HOMALG_IO.show_maple_package_banner ) and HOMALG_IO.show_maple_package_banner = false )
and not ( IsBound( stream.show_banner ) and stream.show_banner = false ) )
and not ( IsBound( stream.show_banner_JanetOre ) and stream.show_banner_JanetOre = false ) then
if IsBound( stream.color_display ) then
display_color := stream.color_display;
else
display_color := "";
fi;
homalg_version := homalgSendBlocking("\`homalg/version\`", "need_output", stream, "initialize" ){[ 3 .. 8 ]};
package_version := homalgSendBlocking("\`JanetOre/version\`", "need_output", stream, "initialize" );
Print( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
## leave the below indentation untouched!
Print( display_color, "\
JanetOre - Maple package loaded (version: ", package_version, ")\n\
Copyright (C) (2003-2009) Daniel Robertz\n\
Lehrstuhl B fuer Mathematik, RWTH Aachen, Germany\n\
(will be used as a ring package via Maple's homalg (ver: ", homalg_version, "))\033[0m\n\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
stream.show_banner_JanetOre := false;
fi;
ar := [ [ arg[1], ",", "copy(`JanetOre/homalg`)" ], TheTypeHomalgExternalRingObjectInMapleUsingJanetOre, stream, "CreateHomalgRing" ];
if nargs > 1 then
ar := Concatenation( ar, arg{[ 2 .. nargs - o ]} );
fi;
ext_obj := CallFuncList( homalgSendBlocking, ar );
R := CreateHomalgExternalRing( ext_obj, TheTypeHomalgExternalRingInMaple );
homalgSendBlocking( [ "`homalg/homalg_options`(", R, "[-1])" ], "need_command", "initialize" );
_MapleHomalg_SetRing( R );
LetWeakPointerListOnExternalObjectsContainRingCreationNumbers( R );
R!.MapleHomalgOptions :=
[ "`JanetOre/JanetOreOptions`",
homalgSendBlocking( [ "`JanetOre/JanetOreOptions`(\"get\")" ], R, "initialize" )
];
RP := homalgTable( R );
RP!.Sum :=
function( a, b )
return homalgSendBlocking( [ a, "+(", b, ")" ], "Sum" );
end;
return R;
end );
##
InstallGlobalFunction( RingForHomalgInMapleUsingOreModules,
function( arg )
local nargs, stream, o, display_color, homalg_version, package_version,
ar, ext_obj, R, RP;
nargs := Length( arg );
if nargs > 1 then
if IsRecord( arg[nargs] ) and IsBound( arg[nargs].lines ) and IsBound( arg[nargs].pid ) then
stream := arg[nargs];
elif IshomalgExternalObjectRep( arg[nargs] ) or IsHomalgExternalRingRep( arg[nargs] ) then
stream := homalgStream( arg[nargs] );
fi;
fi;
if not IsBound( stream ) then
stream := LaunchCAS( "HOMALG_IO_Maple" );
if not IsBound( stream.path_to_maple_packages ) then ## each component in HOMALG_IO_Maple is now in the stream
stream.path_to_maple_packages := Concatenation( PackageInfo( "RingsForHomalg" )[1].InstallationPath, "/maple" );
fi;
homalgSendBlocking( [ "libname := \"", stream.path_to_maple_packages, "\",libname" ], "need_command", stream, "initialize" );
o := 0;
else
o := 1;
fi;
homalgSendBlocking( "with(OreModules)", "need_command", stream, "initialize" );
if ( not ( IsBound( HOMALG_IO.show_banners ) and HOMALG_IO.show_banners = false )
and not ( IsBound( HOMALG_IO.show_maple_package_banner ) and HOMALG_IO.show_maple_package_banner = false )
and not ( IsBound( stream.show_banner ) and stream.show_banner = false ) )
and not ( IsBound( stream.show_banner_OreModules ) and stream.show_banner_OreModules = false ) then
if IsBound( stream.color_display ) then
display_color := stream.color_display;
else
display_color := "";
fi;
homalg_version := homalgSendBlocking("\`homalg/version\`", "need_output", stream, "initialize" ){[ 3 .. 8 ]};
package_version := homalgSendBlocking("\`OreModules/version\`", "need_output", stream, "initialize" );
Print( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
## leave the below indentation untouched!
Print( display_color, "\
OreModules - Maple package loaded (version: ", package_version, ")\n\
F. Chyzak, A. Quadrat, D. Robertz\033[0m\n\
(will be used as a ring package via Maple's homalg (ver: ", homalg_version, "))\033[0m\n\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n" );
stream.show_banner_OreModules := false;
fi;
ar := [ [ arg[1], ",", "copy(`OreModules/homalg`)" ], TheTypeHomalgExternalRingObjectInMapleUsingOreModules, stream, "CreateHomalgRing" ];
if nargs > 1 then
ar := Concatenation( ar, arg{[ 2 .. nargs - o ]} );
fi;
ext_obj := CallFuncList( homalgSendBlocking, ar );
R := CreateHomalgExternalRing( ext_obj, TheTypeHomalgExternalRingInMaple );
homalgSendBlocking( [ "`homalg/homalg_options`(", R, "[-1])" ], "need_command", "initialize" );
_MapleHomalg_SetRing( R );
LetWeakPointerListOnExternalObjectsContainRingCreationNumbers( R );
RP := homalgTable( R );
RP!.Sum :=
function( a, b )
return homalgSendBlocking( [ a, "+(", b, ")" ], "Sum" );
end;
return R;
end );
##
InstallGlobalFunction( HomalgRingOfIntegersInMaple,
function( arg )
local nargs, c, d, param, minimal_polynomial, R, name;
nargs := Length( arg );
if nargs > 0 and IsInt( arg[1] ) and arg[1] <> 0 then
## characteristic:
c := AbsInt( arg[1] );
arg := arg{[ 2 .. nargs ]};
if nargs > 1 and IsPosInt( arg[1] ) then
d := arg[1];
if d > 1 then
param := Concatenation( "Z", String( c ), "_", String( d ) );
minimal_polynomial := UnivariatePolynomial( ConwayPol( c, d ), param );
arg := Concatenation( [ c ], arg{[ 2 .. nargs - 1 ]} );
R := CallFuncList( RingForHomalgInMapleUsingPIR, arg );
SetIsFieldForHomalg( R, true );
SetRingProperties( R, c, d );
R!.NameOfPrimitiveElement := param;
name := homalgSendBlocking( [ "convert(", minimal_polynomial, ",symbol)" ], "need_output", R, "homalgSetName" );
R!.MinimalPolynomialOfPrimitiveElement := name;
SetName( R, Concatenation( "GF(", String( c ), "^", String( d ), ")" ) );
return R;
fi;
arg := arg{[ 2 .. Length( arg ) ]};
fi;
if IsPrime( c ) then
R := [ c ];
else
R := [ [ ], [ c ] ];
fi;
else
## characteristic:
c := 0;
if nargs > 0 and arg[1] = 0 then
arg := arg{[ 2 .. nargs ]};
fi;
R := [ ];
fi;
R := Concatenation( [ R, IsPrincipalIdealRing ], arg );
R := CallFuncList( RingForHomalgInMapleUsingPIR, R );
SetIsResidueClassRingOfTheIntegers( R, true );
SetRingProperties( R, c );
return R;
end );
##
InstallMethod( HomalgRingOfIntegersInUnderlyingCAS,
"for an integer and homalg ring in Maple",
[ IsInt, IsHomalgExternalRingInMapleRep ],
HomalgRingOfIntegersInMaple );
##
InstallGlobalFunction( HomalgFieldOfRationalsInMaple,
function( arg )
local nargs, param, Q, R;
nargs := Length( arg );
if nargs > 0 and IsString( arg[1] ) then
param := ParseListOfIndeterminates( SplitString( arg[1], "," ) );
arg := arg{[ 2 .. nargs ]};
Q := CallFuncList( HomalgFieldOfRationalsInMaple, arg );
SetRingProperties( Q, 0 );
fi;
R := "[0]";
R := Concatenation( [ R ], arg );
if IsBound( Q ) then
## R will be defined in the same instance of Maple as Q
Add( R, Q );
fi;
R := CallFuncList( RingForHomalgInMapleUsingPIR, R );
if IsBound( param ) then
R!.AssociatedPolynomialRing := Q * param;
param := List( param, function( a ) local r; r := HomalgExternalRingElement( a, R ); SetName( r, a ); return r; end );
SetRationalParameters( R, param );
SetIsFieldForHomalg( R, true );
SetCoefficientsRing( R, Q );
else
SetIsRationalsForHomalg( R, true );
fi;
SetRingProperties( R, 0 );
return R;
end );
##
InstallMethod( HomalgFieldOfRationalsInUnderlyingCAS,
"for a homalg ring in Maple",
[ IsHomalgExternalRingInMapleRep ],
HomalgFieldOfRationalsInMaple );
##
InstallMethod( FieldOfFractions,
"for homalg rings in Maple",
[ IsHomalgExternalRingInMapleRep and IsIntegersForHomalg ],
function( zz )
return HomalgFieldOfRationalsInMaple( zz );
end );
##
InstallMethod( PolynomialRing,
"for homalg rings in Maple",
[ IsHomalgExternalRingInMapleRep, IsList ],
function( R, indets )
local ar, r, var, nr_var, properties, param, c, stream, show_banner, S, l, RP;
ar := _PrepareInputForPolynomialRing( R, indets );
r := ar[1];
var := ar[2]; ## all indeterminates, relative and base
nr_var := ar[3]; ## the number of relative indeterminates
properties := ar[4];
param := ar[5];
c := Characteristic( R );
if Length( var ) = 1 and HasIsFieldForHomalg( R ) and IsFieldForHomalg( R ) then
stream := homalgStream( R );
if IsBound( stream.show_banner ) then
show_banner := stream.show_banner;
fi;
stream.show_banner := false;
S := RingForHomalgInMapleUsingPIR( Flat( [ "[", Flat( var ), ",", String( c ), "]" ] ), R );
if IsBound( show_banner ) then
stream.show_banner := show_banner;
else
Unbind( stream.show_banner );
fi;
else
if HasIndeterminatesOfPolynomialRing( R ) then
r := CoefficientsRing( R );
fi;
S := RingForHomalgInMapleUsingInvolutive( var, R );
if c > 0 then
if IsPrime( c ) then
homalgSendBlocking( [ "`Involutive/InvolutiveOptions`(\"char\",", c, ")" ], "need_command", R, "initialize" );
else
Error( "the coefficient ring Z/", c, "Z (", c, " non-prime) is not directly supported by Involutive yet\nYou can use the generic residue class ring constructor '/' provided by homalg after defining the ambient ring over the integers\nfor help type: ?homalg: constructor for residue class rings\n" );
fi;
elif HasIsIntegersForHomalg( r ) and IsIntegersForHomalg( r ) then
homalgSendBlocking( [ "`Involutive/InvolutiveOptions`(\"rational\",false)" ], "need_command", R, "initialize" );
fi;
## we need to save the global options again after setting some of them
S!.MapleHomalgOptions :=
[ "`Involutive/InvolutiveOptions`",
homalgSendBlocking( [ "`Involutive/InvolutiveOptions`(\"get\")" ], R, "initialize" )
];
fi;
var := List( var, a -> HomalgExternalRingElement( a, S ) );
l := Length( var );
Perform( var, Name );
SetIsFreePolynomialRing( S, true );
if HasIndeterminatesOfPolynomialRing( R ) and IndeterminatesOfPolynomialRing( R ) <> [ ] then
SetBaseRing( S, R );
SetRelativeIndeterminatesOfPolynomialRing( S, var{[ l - nr_var + 1 .. l ]} );
fi;
if IsBound( R!.AssociatedPolynomialRing ) then
S!.AssociatedPolynomialRing := R!.AssociatedPolynomialRing * List( var{[ l - nr_var + 1 .. l ]}, Name );
fi;
SetRingProperties( S, r, var );
_MapleHomalg_SetRing( S );
RP := homalgTable( S );
RP!.RingName := CommonHomalgTableForRings!.RingName;
return S;
end );
##
InstallMethod( RingOfDerivations,
"for homalg rings in Maple",
[ IsHomalgExternalRingInMapleRep, IsList ],
function( R, indets )
local var, nr_var, der, nr_der, properties, stream, ar, r, c, S, RP;
#check whether base ring is polynomial and then extract needed data
if HasIndeterminatesOfPolynomialRing( R ) and IsCommutative( R ) then
var := IndeterminatesOfPolynomialRing( R );
nr_var := Length( var );
else
Error( "base ring is not a polynomial ring" );
fi;
##compute the new indeterminates (the derivatives) for the ring and save them in der
if IsString( indets ) and indets <> "" then
der := SplitString( indets, "," );
elif indets <> [ ] and ForAll( indets, i -> IsString( i ) and i <> "" ) then
der := indets;
else
Error( "either a non-empty list of indeterminates or a comma separated string of them must be provided as the second argument\n" );
fi;
nr_der := Length( der );
if not(nr_var=nr_der) then
Error( "number of indeterminates in base ring does not equal the number of given derivations" );
fi;
if Intersection2( der , var ) <> [ ] then
Error( "the following indeterminates are already elements of the base ring: ", Intersection2( der , var ), "\n" );
fi;
properties := [ ];
stream := homalgStream( R );
ar := JoinStringsWithSeparator( Concatenation( der, List( var, Name ) ) );
ar := Concatenation( "[ [ ", ar, " ], [ ], [ " );
ar := Concatenation( ar, JoinStringsWithSeparator( List( [ 1 .. nr_var ], i -> Concatenation( "weyl(", der[i], ",", Name( var[i] ), ")" ) ) ), " ] ]" );
c := Characteristic( R );
r := R;
if HasIndeterminatesOfPolynomialRing( R ) then
r := CoefficientsRing( R );
fi;
S := RingForHomalgInMapleUsingJanetOre( ar, stream );
if c > 0 then
if IsPrime( c ) then
homalgSendBlocking( [ "`JanetOre/JanetOreOptions`(\"char\",", c, ")" ], "need_command", R, "initialize" );
else
Error( "the coefficient ring Z/", c, "Z (", c, " non-prime) is not directly supported by JanetOre yet\nYou can use the generic residue class ring constructor '/' provided by homalg after defining the ambient ring over the integers\nfor help type: ?homalg: constructor for residue class rings\n" );
fi;
elif HasIsIntegersForHomalg( r ) and IsIntegersForHomalg( r ) then
homalgSendBlocking( [ "`JanetOre/JanetOreOptions`(\"rational\",false)" ], "need_command", R, "initialize" );
fi;
## we need to save the global options again after setting some of them
S!.MapleHomalgOptions :=
[ "`JanetOre/JanetOreOptions`",
homalgSendBlocking( [ "`JanetOre/JanetOreOptions`(\"get\")" ], R, "initialize" )
];
der := List( der , a -> HomalgExternalRingElement( a, S ) );
Perform( der, Name );
SetIsWeylRing( S, true );
SetBaseRing( S, R );
SetRingProperties( S, R, der );
_MapleHomalg_SetRing( S );
RP := homalgTable( S );
RP!.RingName := CommonHomalgTableForRings!.RingName;
return S;
end );
##
InstallMethod( ExteriorRing,
"for homalg rings in Maple",
[ IsHomalgExternalRingInMapleRep, IsHomalgExternalRingInMapleRep, IsHomalgExternalRingInMapleRep, IsList ],
function( R, Coeff, Base, indets )
local ar, var, anti, comm, stream, S, RP;
ar := _PrepareInputForExteriorRing( R, Base, indets );
var := ar[3];
anti := ar[4];
comm := ar[5];
stream := homalgStream( R );
ar := JoinStringsWithSeparator( Concatenation( comm, anti ) );
ar := Concatenation( "[ [ ", ar, " ], [ ], [ " );
ar := Concatenation( ar, Concatenation( "exterior(", JoinStringsWithSeparator( anti ), ")" ), " ] ]" );
S := RingForHomalgInMapleUsingJanetOre( ar, stream );
anti := List( anti , a -> HomalgExternalRingElement( a, S ) );
Perform( anti, Name );
comm := List( comm , a -> HomalgExternalRingElement( a, S ) );
Perform( comm, Name );
SetIsExteriorRing( S, true );
SetBaseRing( S, Base );
SetRingProperties( S, R, anti );
_MapleHomalg_SetRing( S );
RP := homalgTable( S );
RP!.RingName := CommonHomalgTableForRings!.RingName;
return S;
end );
##
InstallMethod( RationalShiftAlgebra,
"for homalg rings in Singular",
[ IsHomalgExternalRingInMapleRep, IsList ],
function( R, indets )
local ar, r, var, shift, param, base, stream, display_color, switch, ext_obj,
alg, b, n, steps, d, Y, RP, Ds, S, B, T;
ar := _PrepareInputForShiftAlgebra( R, indets );
r := ar[1];
var := ar[2];
shift := ar[3];
param := ar[4];
base := ar[5];
stream := homalgStream( R );
switch := ValueOption( "switch" );
b := Length( base );
n := Length( shift );
steps := ValueOption( "steps" );
if IsRat( steps ) then
steps := ListWithIdenticalEntries( n, steps );
elif not ( IsList( steps ) and Length( steps ) = n and ForAll( steps, IsRat ) ) then
steps := ListWithIdenticalEntries( n, 1 );
fi;
Ds := shift;
if IsIdenticalObj( switch, true ) then
Error( "not supported in Maple\n" );
else
if HasIsIntegersForHomalg( r ) and IsIntegersForHomalg( r ) then
Error( "not supported in Maple\n" );
else
ext_obj := ListN( Ds, var, {a,c} -> [ a, c ] );
if Set( steps ) = [ 1 ] then
ext_obj := List( ext_obj, a -> Concatenation( "`shift`=[", JoinStringsWithSeparator( a ), "], " ) );
elif Set( steps ) = [ -1 ] then
ext_obj := List( ext_obj, a -> Concatenation( "`dual_shift`=[", JoinStringsWithSeparator( a ), "], " ) );
else
Error( "these steps = ", steps, " are not yet supported\n" );
fi;
ext_obj := Concatenation( ext_obj );
ext_obj := Concatenation( ext_obj, "characteristic=", String( Characteristic( R ) ), ", comm=[", JoinStringsWithSeparator( base ), "]" );
if base <> "" then
else
fi;
fi;
fi;
ext_obj := Concatenation( [ "`OreModules/DefineOreAlgebra`(", ext_obj, ")" ] );
ext_obj := homalgSendBlocking( [ ext_obj ], R, "initialize" );
homalgSendBlocking( [ ext_obj, "[4] := [", JoinStringsWithSeparator( Ds ), "]" ], "need_command", "initialize" );
## as we are not yet done we cannot call CreateHomalgExternalRing
## to create a HomalgRing, and only then would homalgSendBlocking call stream.setring,
## so till then we have to prevent the garbage collector from stepping in
stream.DeletePeriod_save := stream.DeletePeriod;
stream.DeletePeriod := false;
Y := RingForHomalgInMapleUsingOreModules( ext_obj, R );
SetName( Y,
Concatenation(
Concatenation( RingName( r ), "(", JoinStringsWithSeparator( base ), ")(", JoinStringsWithSeparator( var ), ")" ),
"<", JoinStringsWithSeparator( shift ), ">" ) );
## now it is safe to call the garbage collector
stream.DeletePeriod := stream.DeletePeriod_save;
Unbind( stream.DeletePeriod_save );
var := List( var , a -> HomalgExternalRingElement( a, Y ) );
Perform( var, Name );
shift := List( shift , a -> HomalgExternalRingElement( a, Y ) );
Perform( shift, Name );
SetIsRationalShiftAlgebra( Y, true );
SetBaseRing( Y, R );
SetRingProperties( Y, R, shift );
RP := homalgTable( Y );
if not ( HasIsFieldForHomalg( r ) and IsFieldForHomalg( r ) ) then
Unbind( RP!.IsUnit );
Unbind( RP!.GetColumnIndependentUnitPositions );
Unbind( RP!.GetRowIndependentUnitPositions );
Unbind( RP!.GetUnitPosition );
fi;
if HasIsIntegersForHomalg( r ) and IsIntegersForHomalg( r ) then
RP!.IsUnit := RP!.IsUnit_Z;
RP!.GetColumnIndependentUnitPositions := RP!.GetColumnIndependentUnitPositions_Z;
RP!.GetRowIndependentUnitPositions := RP!.GetRowIndependentUnitPositions_Z;
RP!.GetUnitPosition := RP!.GetUnitPosition_Z;
RP!.PrimaryDecomposition := RP!.PrimaryDecomposition_Z;
RP!.RadicalSubobject := RP!.RadicalSubobject_Z;
RP!.RadicalDecomposition := RP!.RadicalDecomposition_Z;
Unbind( RP!.CoefficientsOfUnreducedNumeratorOfWeightedHilbertPoincareSeries );
Unbind( RP!.MaximalDegreePart );
fi;
shift := List( shift, String );
## the "commutative" shift algebra
S := R * shift;
## does not reduce elements instantaneously
## S := HomalgQRingInSingular( AmbientRing( S ), RingRelations( S ) );
Y!.CommutativeShiftAlgebra := S;
## the Laurent algebra
B := BaseRing( R );
T := B * shift;
Y!.LaurentAlgebra := T;
#if not IsIdenticalObj( switch, true ) then
# P!.SwitchedPseudoShiftAlgebra := PseudoShiftAlgebra( R, indets : switch := true );
#fi;
return Y;
end );
##
InstallMethod( RationalPseudoDoubleShiftAlgebra,
"for homalg rings in Singular",
[ IsHomalgExternalRingInMapleRep, IsList ],
function( R, indets )
local ar, r, var, shift, param, base, stream, display_color, switch, ext_obj,
alg, b, n, steps, pairs, d, P, RP, Ds, D_s, S, B, T, Y;
ar := _PrepareInputForPseudoDoubleShiftAlgebra( R, indets );
r := ar[1];
var := ar[2];
shift := ar[3];
param := ar[4];
base := ar[5];
stream := homalgStream( R );
switch := ValueOption( "switch" );
b := Length( base );
n := Length( shift ) / 2;
steps := ValueOption( "steps" );
if IsRat( steps ) then
steps := ListWithIdenticalEntries( n, steps );
elif not ( IsList( steps ) and Length( steps ) = n and ForAll( steps, IsRat ) ) then
steps := ListWithIdenticalEntries( n, 1 );
fi;
pairs := ValueOption( "pairs" );
if IsIdenticalObj( pairs, true ) then
Ds := shift{List( [ 1 .. n ], i -> 2 * i - 1 )};
D_s := shift{List( [ 1 .. n ], i -> 2 * i )};
else
Ds := shift{[ 1 .. n ]};
D_s := shift{[ n + 1 .. 2 * n ]};
fi;
if IsIdenticalObj( switch, true ) then
Error( "not supported in Maple\n" );
else
if HasIsIntegersForHomalg( r ) and IsIntegersForHomalg( r ) then
Error( "not supported in Maple\n" );
else
if Set( steps ) = [ 1 ] then
ext_obj := ListN( Ds, D_s, var, {a,b,c} -> [ a, b, c ] );
elif Set( steps ) = [ -1 ] then
ext_obj := ListN( Ds, D_s, var, {a,b,c} -> [ b, a, c ] );
else
Error( "these steps = ", steps, " are not yet supported\n" );
fi;
ext_obj := List( ext_obj, a -> Concatenation( "`shift+dual_shift`=[", JoinStringsWithSeparator( a ), "], " ) );
ext_obj := Concatenation( ext_obj );
ext_obj := Concatenation( ext_obj, "characteristic=", String( Characteristic( R ) ), ", comm=[", JoinStringsWithSeparator( base ), "]" );
if base <> "" then
else
fi;
fi;
fi;
ext_obj := Concatenation( [ "`OreModules/DefineOreAlgebra`(", ext_obj, ")" ] );
ext_obj := homalgSendBlocking( [ ext_obj ], R, "initialize" );
homalgSendBlocking( [ ext_obj, "[4] := [", JoinStringsWithSeparator( Concatenation( D_s, Ds ) ), "]" ], "need_command", "initialize" );
## as we are not yet done we cannot call CreateHomalgExternalRing
## to create a HomalgRing, and only then would homalgSendBlocking call stream.setring,
## so till then we have to prevent the garbage collector from stepping in
stream.DeletePeriod_save := stream.DeletePeriod;
stream.DeletePeriod := false;
P := RingForHomalgInMapleUsingOreModules( ext_obj, R );
SetName( P,
Concatenation(
Concatenation( RingName( r ), "(", JoinStringsWithSeparator( base ), ")(", JoinStringsWithSeparator( var ), ")" ),
"<", JoinStringsWithSeparator( shift ), ">" ) );
## now it is safe to call the garbage collector
stream.DeletePeriod := stream.DeletePeriod_save;
Unbind( stream.DeletePeriod_save );
var := List( var , a -> HomalgExternalRingElement( a, P ) );
Perform( var, Name );
shift := List( shift , a -> HomalgExternalRingElement( a, P ) );
Perform( shift, Name );
SetIsRationalPseudoDoubleShiftAlgebra( P, true );
SetBaseRing( P, R );
SetRingProperties( P, R, shift );
RP := homalgTable( P );
if not ( HasIsFieldForHomalg( r ) and IsFieldForHomalg( r ) ) then
Unbind( RP!.IsUnit );
Unbind( RP!.GetColumnIndependentUnitPositions );
Unbind( RP!.GetRowIndependentUnitPositions );
Unbind( RP!.GetUnitPosition );
fi;
if HasIsIntegersForHomalg( r ) and IsIntegersForHomalg( r ) then
RP!.IsUnit := RP!.IsUnit_Z;
RP!.GetColumnIndependentUnitPositions := RP!.GetColumnIndependentUnitPositions_Z;
RP!.GetRowIndependentUnitPositions := RP!.GetRowIndependentUnitPositions_Z;
RP!.GetUnitPosition := RP!.GetUnitPosition_Z;
RP!.PrimaryDecomposition := RP!.PrimaryDecomposition_Z;
RP!.RadicalSubobject := RP!.RadicalSubobject_Z;
RP!.RadicalDecomposition := RP!.RadicalDecomposition_Z;
Unbind( RP!.CoefficientsOfUnreducedNumeratorOfWeightedHilbertPoincareSeries );
Unbind( RP!.MaximalDegreePart );
fi;
shift := List( shift, String );
## the "commutative" double-shift algebra
S := R * shift;
## does not reduce elements instantaneously
## S := HomalgQRingInSingular( AmbientRing( S ), RingRelations( S ) );
P!.CommutativeDoubleShiftAlgebra := S / ListN( Ds, D_s, {d, d_} -> ( d / S ) * ( d_ / S ) - 1 );
## the Laurent algebra
B := BaseRing( R );
T := B * shift;
P!.LaurentAlgebra := T / ListN( Ds, D_s, {d, d_} -> ( d / T ) * ( d_ / T ) - 1 );
## the double-shift algebra
Y := P / ListN( Ds, D_s, {d, d_} -> ( d / P ) * ( d_ / P ) - 1 );
Y!.CommutativeDoubleShiftAlgebra := P!.CommutativeDoubleShiftAlgebra;
Y!.LaurentAlgebra := P!.LaurentAlgebra;
SetBaseRing( Y, BaseRing( P ) );
SetParametersOfRationalDoubleShiftAlgebra( Y,
List( ParametersOfRationalPseudoDoubleShiftAlgebra( P ), d -> d / Y ) );
if HasRelativeParametersOfRationalPseudoDoubleShiftAlgebra( P ) then
SetRelativeParametersOfRationalDoubleShiftAlgebra( Y,
List( RelativeParametersOfRationalPseudoDoubleShiftAlgebra( P ), d -> d / Y ) );
fi;
SetIndeterminateShiftsOfRationalDoubleShiftAlgebra( Y,
List( IndeterminateShiftsOfRationalPseudoDoubleShiftAlgebra( P ), d -> d / Y ) );
P!.RationalDoubleShiftAlgebra := Y;
#if not IsIdenticalObj( switch, true ) then
# P!.SwitchedPseudoDoubleShiftAlgebra := PseudoDoubleShiftAlgebra( R, indets : switch := true );
#fi;
return P;
end );
##
InstallMethod( RationalDoubleShiftAlgebra,
"for homalg rings in Maple",
[ IsHomalgExternalRingInMapleRep, IsList ],
function( R, indets )
local P;
P := RationalPseudoDoubleShiftAlgebra( R, indets );
return P!.RationalDoubleShiftAlgebra;
end );
##
InstallGlobalFunction( MapleHomalgOptions,
function( arg )
local nargs, R, s, ar;
nargs := Length( arg );
R := arg[nargs];
if not IsHomalgExternalRingInMapleRep( R ) then
Error( "the last argument must be an external ring residing in Maple\n" );
fi;
s := "";
for ar in arg{[ 1 .. nargs-1 ]} do
if IsString( ar ) then
s := Concatenation( s, ar, "," );
elif IsList( ar ) and Length( ar ) = 2 and ForAll( ar, IsString ) then
s := Concatenation( s, "\"", ar[1], "\"=", ar[2] , "," );
else
Error( "wrong argument: ", ar, "\n" );
fi;
od;
Print( homalgSendBlocking( [ "`homalg/homalg_options`(", s, R, "[-1])" ], "need_display", "initialize" ) );
end );
##
InstallMethod( AddRationalParameters,
"for Maple rings",
[ IsHomalgExternalRingInMapleRep and IsFieldForHomalg, IsList ],
function( R, param )
local c, par;
if IsString( param ) then
param := [ param ];
fi;
param := List( param, String );
c := Characteristic( R );
if HasRationalParameters( R ) then
par := RationalParameters( R );
par := List( par, String );
else
par := [ ];
fi;
par := Concatenation( par, param );
par := JoinStringsWithSeparator( par );
## TODO: take care of the rest
if c = 0 then
return HomalgFieldOfRationalsInMaple( par, R );
fi;
return HomalgRingOfIntegersInMaple( c, par, R );
end );
##
InstallMethod( AddRationalParameters,
"for Maple rings",
[ IsHomalgExternalRingInMapleRep and IsFreePolynomialRing, IsList ],
function( R, param )
local c, par, indets, r;
if IsString( param ) then
param := [ param ];
fi;
param := List( param, String );
c := Characteristic( R );
if HasRationalParameters( R ) then
par := RationalParameters( R );
par := List( par, String );
else
par := [ ];
fi;
par := Concatenation( par, param );
par := JoinStringsWithSeparator( par );
indets := Indeterminates( R );
indets := List( indets, String );
r := CoefficientsRing( R );
if not IsFieldForHomalg( r ) then
Error( "the coefficients ring is not a field\n" );
fi;
## TODO: take care of the rest
if c = 0 then
return HomalgFieldOfRationalsInMaple( par, r ) * indets;
fi;
return HomalgRingOfIntegersInMaple( c, par, r ) * indets;
end );
##
InstallMethod( SetMatElm,
"for homalg external matrices in Maple",
[ IsHomalgExternalMatrixRep and IsMutable, IsPosInt, IsPosInt, IsString, IsHomalgExternalRingInMapleRep ],
function( M, r, c, s, R )
homalgSendBlocking( [ M, "[", r, c, "]:=", s ], "need_command", "SetMatElm" );
end );
##
InstallMethod( AddToMatElm,
"for homalg external matrices in Maple",
[ IsHomalgExternalMatrixRep and IsMutable, IsPosInt, IsPosInt, IsHomalgExternalRingElementRep, IsHomalgExternalRingInMapleRep ],
function( M, r, c, a, R )
homalgSendBlocking( [ M, "[", r, c, "]:=", a, "+", M, "[", r, c, "]" ], "need_command", "AddToMatElm" );
end );
##
InstallMethod( CreateHomalgMatrixFromString,
"constructor for homalg external matrices in Maple",
[ IsString, IsHomalgExternalRingInMapleRep ],
function( S, R )
local ext_obj;
ext_obj := homalgSendBlocking( [ R, "[-1][matrix](", S, ")" ], "HomalgMatrix" );
return HomalgMatrix( ext_obj, R );
end );
##
InstallMethod( CreateHomalgMatrixFromString,
"constructor for homalg external matrices in Maple",
[ IsString, IsInt, IsInt, IsHomalgExternalRingInMapleRep ],
function( S, r, c, R )
local ext_obj;
ext_obj := homalgSendBlocking( [ R, "[-1][matrix](`homalg/ConvertToListList`(", r, c, ",", S, ",", R, "[-1]))" ], "HomalgMatrix" );
return HomalgMatrix( ext_obj, r, c, R );
end );
##
InstallMethod( CreateHomalgMatrixFromSparseString,
"constructor for homalg external matrices in Maple",
[ IsString, IsInt, IsInt, IsHomalgExternalRingInMapleRep ],
function( S, r, c, R )
local M, s;
M := HomalgInitialMatrix( r, c, R );
s := homalgSendBlocking( S, R, "sparse" );
homalgSendBlocking( [ "for i in ", s, " do ", M, "[i[1],i[2]]:=i[3]: od" ] , "need_command", "HomalgMatrix" );
return M;
end );
##
InstallMethod( MatElmAsString,
"for homalg external matrices in Maple",
[ IsHomalgExternalMatrixRep, IsPosInt, IsPosInt, IsHomalgExternalRingInMapleRep ],
function( M, r, c, R )
return homalgSendBlocking( [ "convert(", M, "[", r, c, "],symbol)" ], "need_output", "MatElm" );
end );
##
InstallMethod( MatElm,
"for homalg external matrices in Maple",
[ IsHomalgExternalMatrixRep, IsPosInt, IsPosInt, IsHomalgExternalRingInMapleRep ],
function( M, r, c, R )
local Mrc;
Mrc := homalgSendBlocking( [ M, "[", r, c, "]" ], "MatElm" );
return HomalgExternalRingElement( Mrc, R );
end );
##
InstallMethod( GetListOfHomalgMatrixAsString,
"for homalg external matrices in Maple",
[ IsHomalgExternalMatrixRep, IsHomalgExternalRingInMapleRep ],
function( M, R )
return homalgSendBlocking( [ "convert(map(op,convert(", M, ",listlist)),symbol)" ], "need_output", "GetListOfHomalgMatrixAsString" );
end );
##
InstallMethod( GetListListOfHomalgMatrixAsString,
"for homalg external matrices in Maple",
[ IsHomalgExternalMatrixRep, IsHomalgExternalRingInMapleRep ],
function( M, R )
return homalgSendBlocking( [ "convert(convert(", M, ",listlist),symbol)" ], "need_output", "GetListListOfHomalgMatrixAsString" );
end );
##
InstallMethod( GetSparseListOfHomalgMatrixAsString,
"for homalg external matrices in Maple",
[ IsHomalgExternalMatrixRep, IsHomalgExternalRingInMapleRep ],
function( M, R )
return homalgSendBlocking( [ "map(i->op(map(j->if ", M, "[i,j]<>", Zero( R ), " then [i,j,convert(", M, "[i,j],symbol)] fi, [$1..", NumberColumns( M ),"])), [$1..", NumberRows( M ),"])" ], "need_output", "GetSparseListOfHomalgMatrixAsString" );
end );
####################################
#
# transfer methods:
#
####################################
##
InstallMethod( SaveHomalgMatrixToFile,
"for homalg external matrices in Maple",
[ IsString, IsHomalgMatrix, IsHomalgExternalRingInMapleRep ],
function( filename, M, R )
local mode, command;
if not IsBound( M!.SaveAs ) then
mode := "ListList";
else
mode := M!.SaveAs; #not yet supported
fi;
if mode = "ListList" then
command := [ "_fs := fopen(\"", filename, "\",WRITE): ",
"fprintf( _fs, %s, convert(convert(", M, ",listlist),string)): ",
"fflush( _fs ): ",
"fclose( _fs )" ];
homalgSendBlocking( command, "need_command", "SaveHomalgMatrixToFile" );
fi;
return true;
end );
##
InstallMethod( LoadHomalgMatrixFromFile,
"for external rings in Maple",
[ IsString, IsHomalgExternalRingInMapleRep ],
function( filename, R )
local mode, command, M;
if not IsBound( R!.LoadAs ) then
mode := "ListList";
else
mode := R!.LoadAs; #not yet supported
fi;
M := HomalgVoidMatrix( R );
if mode = "ListList" then
command := [ "_fs := fopen(\"", filename, "\",READ): ",
"_str := readbytes( _fs, infinity, TEXT ): ",
"fclose( _fs ): ",
M, ":=", R, "[-1][matrix](parse( _str ))" ];
homalgSendBlocking( command, "need_command", "LoadHomalgMatrixFromFile" );
fi;
return M;
end );
##
InstallMethod( homalgSetName,
"for homalg ring elements",
[ IsHomalgExternalRingElementRep, IsString, IsHomalgExternalRingInMapleRep ],
function( r, name, R )
SetName( r, homalgSendBlocking( [ "convert( ", r, ", symbol )" ], "need_output", "homalgSetName" ) );
end );
####################################
#
# View, Print, and Display methods:
#
####################################
##
InstallMethod( Display,
"for homalg external matrices in Maple",
[ IsHomalgExternalMatrixRep ], 1,
function( o )
if IsHomalgExternalRingInMapleRep( HomalgRing( o ) ) then
Print( homalgSendBlocking( [ "eval(", HomalgRing( o ), "[-1][matrix](", o, "))" ], "need_display", "Display" ) );
else
TryNextMethod( );
fi;
end );
##
InstallMethod( DisplayRing,
"for homalg rings in Maple",
[ IsHomalgExternalRingInMapleRep ], 1,
function( o )
homalgDisplay( [ o, "[1]" ] );
end );
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