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# SPDX-License-Identifier: GPL-2.0-or-later
# ToolsForHomalg: Special methods and knowledge propagation tools
#
# Implementations
#
DeclareRepresentation( "IsZFunctionRep",
IsComponentObjectRep and IsAttributeStoringRep,
[ ] );
DeclareRepresentation( "IsZFunctionWithInductiveSidesRep",
IsComponentObjectRep and IsAttributeStoringRep,
[ ] );
BindGlobal( "FamilyOfZFunctions",
NewFamily( "z functions" ) );
BindGlobal( "FamilyOfZFunctionsWithInductiveSides",
NewFamily( "z functions with inductive sides" ) );
BindGlobal( "TheTypeOfZFunctions",
NewType( FamilyOfZFunctions,
IsZFunction and IsZFunctionRep ) );
BindGlobal( "TheTypeOfZFunctionsWithInductiveSides",
NewType( FamilyOfZFunctionsWithInductiveSides,
IsZFunctionWithInductiveSides and IsZFunctionWithInductiveSidesRep ) );
##
InstallGlobalFunction( VoidZFunction,
function( )
local z_function;
z_function := rec( );
ObjectifyWithAttributes( z_function, TheTypeOfZFunctions );
return z_function;
end );
##
InstallMethod( AsZFunction,
[ IsFunction ],
function( func )
local z_function;
z_function := rec( );
ObjectifyWithAttributes( z_function, TheTypeOfZFunctions,
UnderlyingFunction, func );
return z_function;
end );
##
InstallMethod( ZFunctionWithInductiveSides,
[ IsInt, IsObject, IsFunction, IsFunction, IsFunction ],
function( N, value_N, lower_func, upper_func, compare_func )
local z_function, func;
func :=
function( i )
local prev_value, value;
if i = N then
return value_N;
elif i > N then
if HasStableUpperValue( z_function ) then
return StableUpperValue( z_function );
else
prev_value := z_function[ i - 1 ];
value := upper_func( prev_value );
if compare_func( value, prev_value ) then
SetStableUpperValue( z_function, i - 1, value );
fi;
return value;
fi;
elif i < N then
if HasStableLowerValue( z_function ) then
return StableLowerValue( z_function );
else
prev_value := z_function[ i + 1 ];
value := lower_func( prev_value );
if compare_func( value, prev_value ) then
SetStableLowerValue( z_function, i + 1, value );
fi;
return value;
fi;
fi;
end;
z_function := rec();
ObjectifyWithAttributes( z_function, TheTypeOfZFunctionsWithInductiveSides,
UnderlyingFunction, func,
StartingIndex, N,
StartingValue, value_N,
UpperFunction, upper_func,
LowerFunction, lower_func,
CompareFunction, compare_func );
return z_function;
end );
##
InstallMethod( SetStableLowerValue,
[ IsZFunction, IsInt, IsObject ],
function( z_func, n, val )
SetStableLowerValue( z_func, val );
SetIndexOfStableLowerValue( z_func, n );
end );
##
InstallMethod( SetStableUpperValue,
[ IsZFunction, IsInt, IsObject ],
function( z_func, n, val )
SetStableUpperValue( z_func, val );
SetIndexOfStableUpperValue( z_func, n );
end );
##
InstallMethod( ZFunctionValueOp,
[ IsZFunction, IsInt ],
{ z_function, i } -> UnderlyingFunction( z_function )( i )
);
##
InstallMethod( ZFunctionValueOp,
[ IsZFunction and HasIndexOfStableLowerValue, IsInt ],
function( z_function, i )
if i <= IndexOfStableLowerValue( z_function ) then
return StableLowerValue( z_function );
else
TryNextMethod( );
fi;
end );
##
InstallMethod( ZFunctionValueOp,
[ IsZFunction and HasIndexOfStableUpperValue, IsInt ],
function( z_function, i )
if i >= IndexOfStableUpperValue( z_function ) then
return StableUpperValue( z_function );
else
TryNextMethod( );
fi;
end );
##
InstallMethod( \[\],
[ IsZFunction, IsInt ],
{ z_function, i } -> ZFunctionValue( z_function, i )
);
##
InstallMethod( ApplyMap,
[ IsDenseList, IsFunction ],
function( z_functions, map )
local z_function;
z_function := AsZFunction( i -> CallFuncList( map, List( z_functions, z_function -> z_function[ i ] ) ) );
SetBaseZFunctions( z_function, z_functions );
SetAppliedMap( z_function, map );
return z_function;
end );
##
InstallMethod( ApplyMap,
[ IsZFunction, IsFunction ],
{ z_function, map } -> ApplyMap( [ z_function ], map )
);
##
InstallMethod( CombineZFunctions,
[ IsDenseList ],
L -> ApplyMap( L, function( arg ) return arg; end )
);
##
InstallMethod( Reflection,
[ IsZFunction ],
function( z_function )
local reflection;
reflection := AsZFunction( i -> z_function[ -i ] );
SetReflection( reflection, z_function );
return reflection;
end );
##
InstallMethod( Replace,
[ IsZFunction, IsInt, IsDenseList ],
function( z_function, n, L )
local func;
func :=
function( i )
if i in [ n .. n + Length( L ) - 1 ] then
return L[ i - n + 1 ];
else
return z_function[ i ];
fi;
end;
return AsZFunction( func );
end );
##
InstallMethod( ApplyShiftOp,
[ IsZFunction, IsInt ],
function( z_function, n )
local shift;
shift := AsZFunction( i -> z_function[ i + n ] );
SetApplyShift( shift, -n, z_function );
return shift;
end );
##
InstallMethod( ViewObj,
[ IsZFunction ],
function( z_function )
Print( "<ZFunction>" );
end );
[ Dauer der Verarbeitung: 0.31 Sekunden
(vorverarbeitet)
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