|
LoadPackage( "SCO" );
if not IsBound(input) then
input := InputTextUser();
fi;
Print( "@@@@@@@@ SCO @@@@@@@@\n" );
if LoadPackage( "RingsForHomalg" ) = true then
Print( "\nSelect base ring:\n 1) Integers (default)\n 2) Rationals\n 3) Z/nZ\n:" );
base := Int( Filtered( ReadLine( input ), c->c <> '\n' ) );
if base = fail or not base in [ 1, 2, 3 ] then
base := 1;
fi;
if base = 1 then
n := 0;
fi;
if base = 3 then
Print( "\nPlease type in the value of 'n' (default = 2)\n:" );
n := Int( Filtered( ReadLine( input ), c -> c <> '\n' ) );
if n = fail or n <= 0 then
n := 2;
fi;
if not IsPrime( n ) then
base := 4;
fi;
fi;
Names_of_CAS := [ "GAP", "External GAP", "MAGMA", "Maple", "Sage", "Singular" ];
List_of_CAS := [ "", "ExternalGAP", "MAGMA", "Maple", "Sage", "Singular" ];
if base = 1 then #Z
sublist := [ 1, 2, 3, 4, 5 ];
else
if base = 2 then #Q
sublist := [ 3, 4, 5, 6 ];
elif base = 3 then #Z/pZ
sublist := [ 3, 4, 5, 6 ];
elif base = 4 then #Z/nZ
sublist := [ 4 ];
fi;
if LoadPackage( "GaussForHomalg" ) = true then
sublist := Concatenation( [ 1, 2 ], sublist );
else
Print( "\nYou do not have the GaussForHomalg package installed. Try it for extended GAP functionality.\n" );
fi;
fi;
Print( "\nSelect Computer Algebra System:\n" );
for i in [ 1 .. Length( sublist ) ] do
str := Names_of_CAS[sublist[i]];
Print( " ", i, ") ", str );
if i = 1 then
Print( " (default)" );
fi;
Print( "\n" );
od;
Print( ":" );
CAS := Int( Filtered( ReadLine( input ), c -> c <> '\n' ) );
if CAS = fail or not CAS in [ 1 .. Length( sublist ) ] then
CAS := 1;
fi;
CAS := sublist[ CAS ];
if CAS in [ 1, 2 ] then
if base = 1 then
Print( "\nAll computations will be done with GAP dense matrices.\n" );
fi;
if base in [ 2, 3 ] then
Print( "\nYou have the choice to work with sparse or dense matrices:\n" );
Print( " 1) sparse (default)\n 2) dense\n:" );
matrix := Int( Filtered( ReadLine( input ), c -> c <> '\n' ) );
if matrix = 2 then
HOMALG.PreferDenseMatrices := true;
fi;
fi;
if base = 4 then
Print( "\nAll computations will be done with Gauss sparse matrices.\n" );
fi;
fi;
if base = 2 then
HOMALG_RINGS.FieldOfRationalsDefaultCAS := List_of_CAS[ CAS ];
R := HomalgFieldOfRationalsInDefaultCAS( );
else
HOMALG_RINGS.RingOfIntegersDefaultCAS := List_of_CAS[ CAS ];
R := HomalgRingOfIntegersInDefaultCAS( n );
fi;
else
Print( "\nYou do not have the RingsForHomalg package installed, therefore you can only work with GAP.\n" );
if LoadPackage( "GaussForHomalg" ) = true then
Print( "\nSelect base ring:\n 1) Integers (default)\n 2) Rationals\n 3) Z/nZ\n:" );
base := Int( Filtered( ReadLine( input ), c->c <> '\n' ) );
if base = fail or not base in [ 1, 2, 3 ] then
base := 1;
fi;
if base = 3 then
Print( "\nPlease type in the value of 'n' (default = 2)\n:" );
n := Int( Filtered( ReadLine( input ), c -> c <> '\n' ) );
if n = fail or not n in Integers then
n := 2;
elif not IsPrime( n ) then
base := 4;
fi;
fi;
if base = 1 then
Print( "\nAll computations will be done with GAP dense matrices.\n" );
R := HomalgRingOfIntegers( );
fi;
if base in [ 2, 3 ] then
Print( "\nYou have the choice to work with sparse or dense matrices:\n" );
Print( " 1) sparse (default)\n 2) dense\n:" );
matrix := Int( Filtered( ReadLine( input ), c -> c <> '\n' ) );
if matrix = 2 then
HOMALG.PreferDenseMatrices := true;
fi;
fi;
if base = 2 then
R := HomalgFieldOfRationals( );
elif base = 3 then
R := HomalgRingOfIntegers( n );
fi;
if base = 4 then
Print( "\nAll computations will be done with Gauss sparse matrices.\n" );
R := HomalgRingOfIntegers( n );
fi;
else
Print( "\nYou do not have the GaussForHomalg package installed, therefore you can only work over the Integers.\n" );
R := HomalgRingOfIntegers( );
fi;
fi;
HOMALG.PreferDenseMatrices := false;
if IsIntegralDomain( R ) then
Print( "\nSelect Method:\n 1) Full syzygy computation (default)\n 2) matrix creation and rank computation only\n:" );
method := Int( Filtered( ReadLine( input ), c->c <> '\n' ) );
if method = fail or not method in [ 1, 2 ] then
method := 1;
fi;
else
method := 1;
fi;
Print( "\nSelect orbifold (default=\"C2\")\n:" );
orbifold := Filtered( ReadLine( input ), c->c<>'\n' );
if orbifold = "" then
orbifold := "C2.g";
fi;
if orbifold{[Length( orbifold ) - 1, Length( orbifold )]} <> ".g" then
Append( orbifold, ".g" );
fi;
if IsBound( PackageInfo( "SCO" )[1] ) and IsBound( PackageInfo( "SCO" )[1].InstallationPath ) then
directory := PackageInfo( "SCO" )[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;
info := "";
Read( Concatenation( directory, "examples", separator, "orbifolds", separator, orbifold ) );
if info = "" then
info := orbifold{ [ 1 .. Length( orbifold ) - 2 ] };
fi;
Print( "\nSelect mode:\n 1) Cohomology (default)\n 2) Homology\n:" );
mode := Int( Filtered( ReadLine( input ), c->c <> '\n' ) );
if mode = fail or not mode in [ 1, 2 ] then
mode := 1;
fi;
Print( Concatenation( "\nSelect dimension (default = ", String( dim ), ")\n:" ) );
d := Int( Filtered( ReadLine( input ), c -> c<>'\n' ) );
if d <= 0 or d = fail then
d := dim;
fi;
ot := OrbifoldTriangulation( M, iso, mu, info );
ss := SimplicialSet( ot );
if mode = 2 then #homology: ker( M[i] ) / im( M[i+1] )
Print( "Creating the boundary matrices ...\n" );
M := CreateBoundaryMatrices( ss, d, R );
if method = 1 then
Print( "Starting homology computation ...\n" );
H := Homology( M, R );
elif method = 2 then
Print( "Starting rank computation ...\n" );
L := [];
for i in [ 1 .. Length( M ) ] do
L[i] :=[ NumberRows( M[i] ), NumberColumns( M[i] ) ];
Print( "# ", i, ": ", L[i][1], " x ", L[i][2], " matrix " );
t := Runtimes().user_time;
L[i][3] := RowRankOfMatrix( M[i] );
d := Runtimes().user_time - t;
L[i][4] := L[i][2] - L[i][3];
Print( "with rank ", L[i][3], " and kernel dimension ", L[i][4], ". Time: ", TimeToString( d ), "\n" );
od;
H := [ L[1][4] ]; #first image dimension
for i in [ 2 .. Length( L ) ] do
H[i] := L[i][4] - L[i-1][3]; #dim ker - dim im
od;
for i in [ 1 .. Length( H ) ] do
Print( "# Homology dimension at degree ", i - 1, ": ", RingName( R ), "^(1 x ", H[i], ")\n" );
od;
fi;
elif mode = 1 then #cohomology: ker( M[i+1] ) / im( M[i] )
Print( "Creating the coboundary matrices ...\n" );
M := CreateCoboundaryMatrices( ss, d, R );
if method = 1 then
Print( "Starting cohomology computation ...\n" );
H := Cohomology( M, R );
elif method = 2 then
Print( "Starting rank computation ...\n" );
L := [];
for i in [ 1 .. Length( M ) ] do
L[i] :=[ NumberRows( M[i] ), NumberColumns( M[i] ) ];
Print( "# ", i, ": ", L[i][1], " x ", L[i][2], " matrix " );
t := Runtimes().user_time;
L[i][3] := RowRankOfMatrix( M[i] );
d := Runtimes().user_time - t;
L[i][4] := L[i][1] - L[i][3];
Print( "with rank ", L[i][3], " and kernel dimension ", L[i][4], ". Time: ", TimeToString( d ), "\n" );
od;
H := [ L[1][4] ]; #first kernel dimension
for i in [ 2 .. Length( L ) ] do
H[i] := L[i][4] - L[i-1][3]; #dim ker - dim im
od;
for i in [ 1 .. Length( H ) ] do
Print( "# Cohomology dimension at degree ", i - 1, ": ", RingName( R ), "^(1 x ", H[i], ")\n" );
od;
fi;
fi;
[ Dauer der Verarbeitung: 0.8 Sekunden
(vorverarbeitet)
]
|
