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## Examples.g ##
LoadPackage( "RingsForHomalg" );
LoadPackage( "Modules" );
old_RingOfIntegers := HOMALG_RINGS.RingOfIntegersDefaultCAS;
HOMALG_RINGS.RingOfIntegersDefaultCAS := "Maple";
old_FieldOfRationals := HOMALG_RINGS.FieldOfRationalsDefaultCAS;
HOMALG_RINGS.FieldOfRationalsDefaultCAS := "Singular";
input := InputTextUser();
Print( "@@@@@@@@ Examples for Homalg @@@@@@@@\n\n" );
Print( Concatenation( "\nSelect Computer Algebra System:\n",
" 1) Internal GAP\n",
" 2) External GAP\n",
" 3) Sage\n",
" 4) MAGMA\n",
" 5) Macaulay2\n",
" 6) Maple (default for Z-algebras)\n",
" 7) Singular (default for Q-algebras)\n",
":" ) );
CAS := Filtered( ReadLine( input ), c->c <> '\n' );
i := Int( CAS );
if CAS = "" or i = fail then
CAS := "default";
else
CAS := i;
fi;
List_of_CAS := [ "", "ExternalGAP", "Sage", "MAGMA", "Macaulay2", "Maple", "Singular" ];
if CAS <> "default" then
HOMALG_RINGS.RingOfIntegersDefaultCAS := List_of_CAS[ CAS ];
HOMALG_RINGS.FieldOfRationalsDefaultCAS := List_of_CAS[ CAS ];
fi;
if not IsBound( HOMALG_EXAMPLES.OwnRingOrReadFile ) or
not HOMALG_EXAMPLES.OwnRingOrReadFile in [ 1, 2 ] then
HOMALG_EXAMPLES.OwnRingOrReadFile := 1;
fi;
Print( "\nSelect Mode:\n " );
if HOMALG_EXAMPLES.OwnRingOrReadFile = 1 then
Print( "1) Create your own ring (default)\n 2) Read example from file\n:" );
else
Print( "1) Create your own ring\n 2) Read example from file (default)\n:" );
fi;
mode := Int( Filtered( ReadLine( input ), c->c <> '\n' ) );
if mode = fail or not mode in [ 1, 2 ] then
mode := HOMALG_EXAMPLES.OwnRingOrReadFile;
fi;
if mode = 2 then
Print( "\nSelect example file (default=\"ReducedBasisOfModule\")\n:" );
file := Filtered( ReadLine( input ), c->c<>'\n' );
if file = "" then
file := "ReducedBasisOfModule.g";
fi;
if file{[Length( file ) - 1, Length( file )]} <> ".g" then
Append( file, ".g" );
fi;
if IsBound( PackageInfo( "ExamplesForHomalg" )[1] ) and IsBound( PackageInfo( "ExamplesForHomalg" )[1].InstallationPath ) then
directory := PackageInfo( "ExamplesForHomalg" )[1].InstallationPath;
else
directory := "./";
fi;
if IsBound( GAPInfo.UserHome ) then
separator := GAPInfo.UserHome{[1]};
else
separator := "/";
fi;
if Length( directory ) > 0 and directory{[Length( directory )]} <> separator then
directory := Concatenation( directory, separator );
fi;
Read( Concatenation( directory, "examples", separator, file ) );
elif mode = 1 then
Print( "\nSelect base ring:\n(-) Type Q for the field of rationals (default)\n(-) Type 0 for the Ring of Integers Z\n(-) Type n (Integer > 0) for Z / < n >\n:" );
f := Filtered( ReadLine( input ), c->c <> '\n' );
i := Int( f );
Print( "\n" );
if f = "" or i = fail then
if CAS <> "default" then
if List_of_CAS[ CAS ] = "" then
Print( "\033[01mgap> R := HomalgFieldOfRationals( );\033[0m" );
else
Print( "\033[01mgap> R := HomalgFieldOfRationalsIn", List_of_CAS[ CAS ], "( );\033[0m" );
fi;
else
Print( "\033[01mgap> R := HomalgFieldOfRationalsInDefaultCAS( );\033[0m # (Default = Singular)" );
fi;
Print( "\n" );
R := HomalgFieldOfRationalsInDefaultCAS( );
else
if i <> 0 then
str := Concatenation( " ", String( AbsInt( i ) ), " " );
else
str := " ";
fi;
if CAS <> "default" then
if List_of_CAS[ CAS ] = "" then
Print( "\033[01mgap> R := HomalgRingOfIntegers(", str, ");\033[0m" );
else
Print( "\033[01mgap> R := HomalgRingOfIntegersIn", List_of_CAS[ CAS ], "(", str, ");\033[0m" );
fi;
else
Print( "\033[01mgap> R := HomalgRingOfIntegersInDefaultCAS(", str, ");\033[0m # (Default = Maple)" );
fi;
Print( "\n" );
R := HomalgRingOfIntegersInDefaultCAS( AbsInt( i ) );
fi;
HOMALG_RINGS.RingOfIntegersDefaultCAS := old_RingOfIntegers;
HOMALG_RINGS.FieldOfRationalsDefaultCAS := old_FieldOfRationals;
Print( "\033[01mgap> R;\033[m\n" );
Display( StringView( R ) );
HOMALG_RINGS.NamesOfDefinedRings := "R";
Print( "\nSelect polynomial extension:\n(-) Hit Enter for no polynomial extension (default)\n(-) Otherwise, type in the names of your variables, seperated by commas - e.g. x,y,z\n:" );
variables := Filtered( ReadLine( input ), c->c <> '\n' );
if variables <> "" then
Print( "\n\033[01mgap> S := R[\"", variables, "\"];\033[m #alternatively: 'gap> S := PolynomialRing( R, \"", variables, "\" );'\n" );
S := R * variables;
Print( "\033[01mgap> S;\033[m\n" );
Display( StringView( S ) );
Append( HOMALG_RINGS.NamesOfDefinedRings, ", S" );
Print( "\nIt is possible to work over the Weyl Algebra:\n(-) Hit Enter for the commutative case (default)\n(-) Otherwise, type in the names of your differential variables, seperated by commas - e.g. Dx,Dy,Dz (same number as before!)\n:" );
diff_variables := Filtered( ReadLine( input ), c->c <> '\n' );
if diff_variables <> "" then
Print( "\n\033[01mgap> T := RingOfDerivations( S, \"", diff_variables, "\" );\033[m\n" );
T := RingOfDerivations( S, diff_variables );
Print( "\033[01mgap> T;\033[m\n" );
Display( StringView( T ) );;
Append( HOMALG_RINGS.NamesOfDefinedRings, ", T" );
fi;
fi;
if Length( HOMALG_RINGS.NamesOfDefinedRings ) = 1 then
Print( "\nThe ring \033[01m", HOMALG_RINGS.NamesOfDefinedRings, "\033[m has been created..\n" );
else
Print( "\nThe rings \033[01m", HOMALG_RINGS.NamesOfDefinedRings, "\033[m have been created.\n" );
fi;
fi;
[ Dauer der Verarbeitung: 0.15 Sekunden
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