Quelle ZFunctions.gi Sprache: unbekannt

# 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 );

Quelle ZFunctions.gi Sprache: unbekannt

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